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SURFACES – Vortex-Lattice Module

1. En 75 9 4 Induced Drag Coefficient inp Mr 84 9 5 Peta Drag ae 85 9 6 Compressibilty Modeling siae du petu lanier anu LER MPa d fme Ed 86 9 8 How SURFACES Calculates Do Df Di and 87 9 9 Limitations of Drag Estimation Methodologies ecce eere elei rese 67 9 10 Setting up Drag Modeling on Example 88 9 11 Summary of SURFACES Drag Analysis Methodology ecce 101 10 Validation Sanipl6S orsus vnd MEC VEV qe RENS GRE MEE 102 Validation 1 2 Flat Plate Airfoil e 103 VT AEE PE AAA E P AN EA EXER EpL ORATOR RAPID V RR FIERI OE AT 103 LAE HESS EENE EAS EAE S SEHEN CREE BAET E A A neces 103 Resuls SURFACES FN MEM MM 104 Validation 2 3 0 Properties Of Two Wings sss 106 Lp Eoo LTEM nc erm p 106 eorr ec nn mene 106 V2 3 Results trom SURFACES sena ic oni M VUE ernst 107 Validation 3 Warren 12 searceancestewceeuctisvecavetevccesetsceusc
2. Fom SURFACES 120 Validation 7 F 104 Starfighter 122 LT ee ae AS en ee an ae er Mere remy ee MEM EA 122 re om SURFACE S eee 122 Validation 8 Ryan Navion denuded desienss 124 Vn NMOUBLA ne eee eee ree MEE Ei M EE M ae ee 124 D EE TE AMEDEO 125 TOM SURT ACE 127 Validation 9 Comparison to 1208 130 LC TATOO GOI Pat 130 V9 2 EPEC RESU emc T M 131 V9 9 Mesults Fom SURFACES Lesssessuz naindbi RE EEREESEPuRAM PERRA sa RE DONI Ea 131 Validation 10 Comparison NACA TN 1422 133 OI cases vase np EP 133 VIO 2 FROST tom a p EDS Hi aed RE RS Rida a Leld 133 Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 4 of 136 Great OWL Publishing INTRODUCTION Thank you for purchasing SURFACES We are certain you will find SURFACES priceless for your aircraft design projects
3. _ Cn at a I Carr CREF Ci Ci da Document Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 125 of 136 Great OWL Publishing Engineering Software Where note that numerical values are obtained from the document Crer Reference wing chord 5 7 ft Clow Slope of wing lift coefficient 4 3 per rad Croat Slope of HT lift coefficient 3 91 per rad Slope of fuselage moment coefficient 0 12 per rad dz da Variation of downwash with angle of attack 0 45 Vpr Horizontal tail volume 0 66 Xac Aerodynamic center of wing body combination 1 425 ft 1 Tail efficiency 1 X vey _ 1 425 0 12 1 0 66 1 0 45 0 552 C REF 5 7 4 3 4 3 Note that the reference document which is a First Edition states the Xneu is at 0 37 but in conversation with the author R C Nelson it was confirmed this was an error that had been corrected for later editions of the book Note that the planform properties of the VL model were determined using SURFACES built in tool which printed out the following analysis report MEAN AERODYNAMIC CHORD ANALYSIS Surface chord Cr 7 200 ft Surface LE Xr 0 000 ft P 0 000 ft Surface chord tip Ct 4 022 ft SUPT aCe LE CIP eae dial Xr 0 806 ft EE E ee eee Yr 16 446 ft
4. 1 46162 1 45543 gt Distance from Point 1 of vector AtoXP YP ZP o lt Rx Ry Rz Components of the vector R from Point 1 of vector A Ri The length of vector R Qx Qy Qz Components of the vector Q from XP YP ZP to XF YF ZF JQ The length of vector Panel force body system in global coordinate system i i 1 gridCntrl Col i gridCntrl Text Fbx i i 1 gridCntrl Col i gridCntrl Text i i 1 gridCntrl Col i gridCntrl Text Foz i i 1 gridCntrl Col i gridCntrl Text IFb Panel force airspeed system in global coordinate system i i 1 gridCntrl Col i gridCntrl Text Fx i i 1 gridCntrl Col i gridCntrl Text Fy i i 1 gridCntrl Col i gridCntrl Text Fz i i 1 gridCntrl Col i gridCntrl Text F Panel moment in global coordinate system i i 1 gridCntrl Col i gridCntrl Text i i 1 gridCntrl Col i gridCntrl Text i i 1 gridCntrl Col i gridCntrl Text Mz i i 1 gridCntrl Col i gridCntrl Text M Panel force in global coordinate system Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 62 of 136 Great OWL Publishing Engineering Software i 1 1 gridCntrl Col i gridCntrl Text Ftx i i 1 gridCntrl Col i gridCntrl Text Fty i i 1 gridCntrl Col i gridCntrl Te
5. Product of inertia about Z axis Lift coefficient for o 0 03757 12 Slope of lift coefficient Lift coefficient Parasitic drag coefficient 0 0390 0 039 a p 0 04952 from Total drag coefficient CD 0 05 quadratic drag 0 051 polar NY 0 258 quantic fit 0830 Span efficiency Oswald s e o8 08 1 CXA 02 0 ove T cv BEEN 4850 495 To 1 1 SSS cma o0 1 1 oe cB t dB oomo 0 cm oono 00739 cxi NWepredeed __Notpredicted M 1700 Noetpedeed Son Ras GOLA Nepedceed T cma 436 Notpedced Netpedeed M cxu 20100000 Notpredited D Notprdited EN HN Not predicted CDL GU F Not predicted Notpredicted ONU T Not predicted cp BRENNEN asp on om D i cNP oos 005 Mme nk co amu Q DERIVATIVES co RENE ere From analysis on page 54 of Reference document Document Page Numbers VLM docx Surfaces User Manual Vor
6. Surface half span Bhalf 16 446 ft Sete 18 OUr BEDS duobus ie os ore ue ere ora oes BS 2208903 ape Surface half area Shalf 92 28 ft Surface total area Stot 184 56 ft Surface LE sweep angle GLE 2 805 Surface aspect ratio AR 5 8621 Surface taper ratio TR 0 5586 Surface Mean Aerodynamic Chord Cmac 5 761 ft Surface MAC location Xmac 0 365 ft P Ymac 7 447 ft This information can be used when calculating the CG and neutral point locations as percentages of the Mean Aerodynamic Chord MAC For instance the CG located at Xcg 2 0465 ft becomes 100 2 0465 0 365 5 7 29 5 MAC Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 126 of 136 Great OWL Publishing Engineering Software Estimate Neutral Point First CG Location Second Cl Location cg 1 85 Aog 2 0465 ADAT 0 0 ADAT 0 0 Chri 7 603072E 03 1 894557E 02 ADA2 P00 ADA2 1 CMY2 2 5734459E 03 CMY2 2 8 61551E 03 Report 4ngle af Attack l Coefficient of moment o 61L551E 03 Pass 4 of 4 complete Elapsed time Oh 00m 17s Aneu 7214351091289 Compute Close Figure 8 4 Computing the neutral point The neutral point was estimated by computing the slope of the CMY curve for two different values of X
7. mE P P INIT NL A Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 42 of 136 Great OWL Publishing Engineering Software STAB Console SIMPLE DEMO SRF File Edit View UR Simulation ER Lateral d cillation Dutch Roll 4 LE DEMO SRF A cos w t q Exp n t E 10 12 Time seconds Figure 4 24 Stability analysis module Step 29 You can get a report detailing the properties of the response by selecting View gt Show Comparison Table The resulting table is shown below This is but one of many ways to extract information from the STAB module Also try Analysis gt Create Analysis Report to get a more detailed dynamic stability report Description Symbol Unit SIMPLE DEMO SRF Airspeed Vtas KTAS 100 Altitude Href ft 0 Period of oscillation i sec cycle 2 450 Damping coefficient n 1 sec 0 0612 Natural frequency Wn cycles sec 2 5648 Damped frequency Wd cycles sec 2 5641 Damping Ratio Zeta 0 0238 Time to 0 5 Amplitude tV Sec 11 3324 Cycles to 0 5 Amplitude cycles 4 6246 Time to 0 1 Amplitude tO 1 Sec 3 6454 Cycles to 0 1 Amplitude NO 1 cycles 15 3626 This concludes the introductory example This model is also used for a skin friction drag demo in Section 9 so it will be convenient to save it Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 43 of 136 Gr
8. nam Acte objecks wath formats c ET ects wih oma ofall Press to Select Objects for Legend D xv xz YL o X Y E Status 8 35 PM 3 16 2009 Snap Grid Grid Off Version 2 73 Figure 4 11 We can see the CG location black white circle is too far aft When completed your model should look like the one in Figure 4 11 It is immediately evident that the CG is too far aft To fix this and to allow us to control the location of the CG let s create a ballast point OB LJ Lu VLM docx Surfaces User Manual Vortex Lattice Module Page 29 of 136 Great OWL Publishing Surfaces Pro Untitled File Edit Insert Modify Tools View Window Help amp Oo OR GAL RIZ ROSS O Ee This point will mum be converted to Ymacw 4 201 ft 27 HORIZONTAL TAIL GEOMETRY a Node Sht 9 00 f Cht 1 500 ft TRht 0 5000 Xcht 11 26 ft cor it iht 0 000 TE 15 676 E Lht 1077 ft Vht 0 8496 Fht 4 2503 2 TICAL TAI METRY 39 VERTICAL TAIL GEOMETRY Wit Bvt 3 00 ft Svt 7 50 ft Cvt 2 500 ft TRvt 0 6667 Xcvt 9 67 ft Zcvt 1 40 ft HH 8 42 PM 3 16 2009 Snap Grid Grid Off Version 2 79 Figure 4 12 Drop the point to be converted to a node in a location similar as shown Step 11 Edit Node Point 33 Edit Node Point 35 General Inertia Forces and Moments Spatial Constraints
9. Cla 0 06011 3 442 rad SURFACES yields a difference of 0 26 Another VLM code called Tornado considers the same problem In his Master Thesis A Vortex Lattice MATLAB Implementation for Linear Aerodynamic Wing Applications the author of Tornado Mr Tomas Melin reports a lift curve slope of 3 450 rad using Tornado The difference using that code is 0 5 It can be seen that both codes are very close to the theoretical calculations in the source but SURFACES yields less difference than Tornado It should also be noted that the calculations in the source only carries 4 significant digits through the calculations SURFACES uses a double floating point accuracy Summary Symbol TORNADO SURFACES Lift curve slope Cu 3433 3 450 0 50 3 442 0 26 Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 112 of 136 Great OWL Publishing Validation 5 Cessna 172 Comparison of Several Codes V5 1 Model A model of the Cessna 172 was constructed to compare stability derivatives from SURFACES to other VLM codes AVL VIRGIT TORNADO and the panel code CMARC as well as published Cessna data The model has the camber line of the NACA 2412 airfoil of the Cessna 172 Additionally it has a 1 30 angle of incidence at the root of the wing and 1 30 at the tip and a 1 44 dihedral like the original airplane A sweep of parameters was performed at an airspeed of
10. Finally noticing the the centroid of the force V is at x 1 ft we find that M V Ax 20 16 1 ft 20 ft Ib 6 5 Presentation of Data in SURFACES The user selects Results gt Force Integrator from the VLM Console in SURFACES as shown in Figure 11 below m SurfacesPro Ryan Navion SRF ooo zr E a Console Ryan Navion SRF x i Helr XIRI RO File Edit Tasks Analyze Virtual WT 72710 Help D ERR a ou Ganan Groups Information Files Objects Panel Results Body Results Stip Aes Determine Vx Vy Vz at Point X Y Z ERR BEI Ei Panel IDs Surface IDs Plot Flow Solution POINTS EE Plot Streamline through Point 2 vi 2 VECTORS Trapezcidu creas EGund uerrex amt eant Dons Plot Streamlines 71 3 L WING 250 0 bf m ete iM 4 ROWING 250 0 Ib Wieignt af surfaces Vortex srengtns wi 5 FUSELAGE 600 0 Ibf BC Velocities Vx HVY VIE v HT 100 0 Ibf iv 7 NODES 1580 0 lbf View Solution Files olution velocity vectors Force vector FX by pre a Ae y 56 Total force Co pressure coefficient smades cn pressure coefficient contours Cn pressure coeficient values voe ic ifr enetpcsenz Center of zressurae Panes wiih potential flow separation MAC Anar zs lony in XY plone xv K Z YL Sta
11. VLM docx Surfaces User Manual Vortex Lattice Module Page 93 of 136 Great OWL Publishing File Edit Insert Modify Tools View Window Help De Ox BE SAL ES Sa Groups Information Files Objects 4 SNOW Active objects w tn Formats mM Press to Select Objects for Legend Dh xv X z Y YY Version 2 8 1 3 43 AM 7 22 2008 Snap Grid Grid On azed Status Figure 9 10 9 Image shows the laminar flow region green the and VT Note that when you select to enter the skin friction coefficient directly see Cf i in Figure 9 10 5 rather than using the A1 A2 curves won t know the extent of laminar flow and thus will not plot the green areas as shown here Note that at computation time will compare the actual AOA to the ones filled in Figure 9 10 7 and estimate the transitions at that angle of attack If the AOA is less than the value AOA1 it will use the transition values entered for the low angle of attack condition If the AOA is larger than AOA2 then it will use the values entered for the high angle of attack condition Now let s set up the mixed boundary layer conditions on the wing VLM docx Surfaces User Manual Vortex Lattice Module Page 94 of 136 Great OWL Publishing Surfaces Pro SIMPLE DEMO SRF File Edit Insert Modify Tools View Window Help Deel BAX KRIG ROB c Groups Information Files O
12. 2 354 2 096 N o N N gt d Is o Ph LS ce 4 N 4 tn gt e J on J i on to e n 205080810818 o e ex Uu Uu m t N m o A A m S s Figure 2 1 The two 3 D wing models V2 2 Expected Result The following parameters are given Airspeed V 168 8 ft s M 168 8 1116 0 151 Wing area 10x 1 10 ft Aspect Ratio AR b S 102 10 10 Assume 2 0 lift curve slope of C 0 1063 deg for NACA0009 from Theory of Wing Sections by Abbott and Doenhoff Start by computing a 3 D lift curve slope from Method 1 of USAF DATCOM Section 1 page 1 7 2m AR Where AR Wing Aspect Ratio 10 Mach number parameter Prandtl Glauert 1 2 0 989 Ratio of 2D lift curve slope to 2x 0 1063 x 180 2 0 96934 Age Sweepback of mid chord 0 and 35 Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 106 of 136 Great OW r d L Publishi nfb are woTtware 2T AR 202 2 K 27 10 oer 0 Dae z Is 0 96934 0 989 5 068 per rad 0 08846 per deg The lift coefficient at 10 is thus C 10 xC 0 8846 The total lift of the wing is L 1pV SC Induced drag is found from the standard relation C 0 8846
13. General Inertia Forces and Moments Spatial Constraints Mame Ballast Node Inertia Properties Note This point will be used to allow the CG to be moved Weight 30d around Mate that itis necessary to specify weight with it as well inertia tab D Point Location lsz E ae 4 22 ke z 0 NOTE 1 Moments and Products of Inertia entered here are added to the lex lyz of the point about the paint cg T cg co Size and Color NOTE 2 Inertia properties are WOT treated as applied forces 0 25 Color moments They solely used for inertia analysis and automatic determination of the CG IF so desired by the user OF Cancel Figure 4 13 Information entered with Step 12 Return to the 3 D view by pressing the X Y Z tab see the bottom of Figure 4 12 When completed your model should look like the one in Figure 4 14 To see what the true location of the CG is at this point locate the math objects Pmac and in the object list on the left hand side Pmac is highlighted in Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 30 of 136 Great OWL Publishing Figure 4 14 The variable Pmac stores the CG location as a percentage of the Mean Aerodynamic Chord Cref found under the REFERENCE PARAMETERS block in the Math Object list We see the CG is located at 13 967 MAC or at 0 47 ft Often it is necessary to specify dir
14. Great OWL Publishing SURFACES VORTEX LATTICE MODULE id nad ar jn en aus a Ji fn MS ea ite entre User Manual August 2009 G t OWL Publishing Engineering Software SURFACES Vortex Lattice Module ee zn t n ur V Er m P zd Xu s A ee ee s PF file a E m p put ui x i a P d j if a Document Title Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 2 of 136 Great OWL Publishing Engineering Software SURFACES Vortex Lattice Module INTRODUCTION Pee 5 Vortex Lattice Methods Why Should You Care 6 UOTE SUAS m 7 1 Orientation of Forces and Moments 9 2 Force and Moment 10 SM arte 11 4 Creating a Simple Model with 14 5 Accomplishing Special Projects with SURFACES 44 5 1 Tailoring Wings to Improve Stall Characteristics 44 5 2 Determine Shear Moment a
15. 12 6 becomes 0 656 Document Title Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 122 of 136 a a g E xe oS Be Be 73 5 nct bar T nTT Bm EB ESSERE Ee Wek EEE Se wwe ee OS Figure 7 2 A Starfighter in flight Image from http www starfighters net gallery 1999gallery 1999gallery htrr VLM docx Surfaces User Manual Vortex Lattice Module Page 123 of 136 Great OWL Publishing Validation 8 Ryan Navion V8 1 Model A model of the Ryan Navion was constructed compare to the analysis of Example Problem 2 1 found in Robert C Nelsons Flight Stability and Automatic Control on pages 53 58 The VL model was based on the three view in Figure 8 1 Figure 8 1 A three view drawing of the Ryan Navion The reference document determines several parameters for the Navion in Problem 2 1 The calculation of selected parameters is repeated in Section V8 1 for convenience Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 124 of 136 Great OWL Publishing Engineering Software Figure 8 2 A Ryan Navion in flight Photographer unknown Figure 8 3 The SURFACES Vortex Lattice model of the Ryan Navion V8 2 Expected Result The stick fixed neutral point is estimated from Equation 2 37 in the reference document here written using variables more consistent with this document
16. Generally you should pick the neutral point with the lower value of Xneu here this implies Method 2 Let s transfer the resulting value to the variable Xneu in the model which currently has the initial value O turtur SimplePlane 03162009 SRF DAE Se pe 03 16 2009 e NU Mee 21e 10 ANALYSIS VALUES LD AOA CL CMY 1 7 5022e 01 2 00007 3 980596 01 1T7T761e 01 2 1 7503e 00 29000 9 9059e 01 3 2670e9 02 3 1 50326 01 3 00007 4 6946e 01 1 5413 01 4 1 7503e 00 3 0000 4 6946e 01 3 1248e 02 METHOD 1 Calculates Xneu from the expression Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 33 of 136 Great OWL Publishing Engineering Software Xneu Xog Cre 0 75032 2 534505 0 036512 0 088875 12791557 660 002477 MAC Calculates Xneu by evaluating changes of CG and AOA on Cm Function 1 degrees 0 036512 AOA 0 044590 Funct vom b radmans s 2091999908 0 044590 Function 2 degrees 0 001422 AOA 0 154126 Wu ncetagonoz radians 0 08142749A0A 0 154126 Xneu 1 790844 66 05433 MAC Total time 0h 00ms05s STEP 18 Press the Transfer button and select the option Neutral point using Method 2 This displays a notification Press the OK button to close it Press the Close button on the form to close it as well Note the Copy Report button in the form in Figure 4 17 It allows you to copy the
17. Set a acurr Aa and 8 0 to determine C and Cro STEP 4 Compute Ca and C from Ci Cro Cj M and 0 LO L2 La 2 Document Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 65 of 136 Great OWL Publishing Engineering Software C Cao C om m gt om and C 9 Cm2 B C mo t C na 0 Ol TA C C STEP 5 Compute Ol arget L a STEP 6 Set a and Se Se curr Ade to determine and Cms STEP 7 Set a and Se cunn to determine and Cm4 STEP 8 Compute C 5 Cmse from Cis Ce ccu Cus Cno LO I m3 and C ms 5 STEP 9 Compute the required C to support the desired lift and knowing that C 0 for a balanced condition we populate the matrix of Equation 2 as follows Cre a _ C C 3 om C s Cao And solve for the a and 8 which define the trimmed condition SURFACES solves this using an iterative algorithm and can do so about each of the airplane s three axes This is necessary because the deflection of a control surface modifies the geometry which in turn requires a new flow solution The program comes with an easy to use Trim Wizard that makes this a breeze Additionally you can trim for multiple airspeeds creating an individual flow solution for each trimmed condition This is handy when you want multiple solutions
18. TORNADO all have at least one worst score The most frequent low score 1 was received by CMARC 7 times The most frequent high score 5 was received by SURFACES 4 times In fact SURFACES was the only code to correctly compute a restoring dihedral effect for the Cessna 172 Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 118 of 136 Great OWL Publishing Engineering Software Validation 6 2 0 CL Cp Cm for NACA 23012 V6 1 Model A high aspect ratio AR 20 wing model was constructed to perform a 3 D similarity evaluation to a standard 3 D aerodynamic analysis The model has a wing span of 20 ft and a chord of 1 ft An angle sweep of attack from 8 through 8 at an airspeed of 100 ft sec and density of 0 002378 slugs f was performed The model has 16 chordwise and 60 spanwise panels The panels form the camber line of the NACA 23012 airfoil The purpose of this validation is to demonstrate how SURFACES simulates airfoil properties Figure 6 1 3 D wing model with a 23012 airfoil V6 2 Expected Result The following parameters are given Airspeed V 100 ft s Wing area S 20 x 1 20 ft Aspect Ratio AR b S 202 10 20 The 2 D lift curve slope of C 0 1051 perdeg C 0 1233 C 0 000200 0 01198 is obtained from interpolation for NACA 23012 from Theory of Wing Sections by Abbott and Doenhoff Compute a 3 D lift curve slope from Method 1 of USAF DATC
19. Upon completion you will see the results as shown in Figure 4 22 Without going into too many details we can see from values for Cma 2 119 Clb 0 105 and Cnb 0 172 that our airplane is statically stable about all three axes What we don t know at this time are its dynamic stability properties And this is what we intend to investigate next First however we must transfer these results to the airplane model STEP 24 Select the Transfer tab Follow the remaining steps closely STEP 25 Press the Select All button to select all the derivatives in the list STEP 26 Press the Deselect Nonrequested button to deselect the derivatives that were not calculated STEP 27 In addition uncheck the following variables CL CDi CD CDa hcg and hn see Figure 4 23 This will prevent them from being overwritten but they already contain algebraic expressions that we don t want to be deleted STEP 28 Press the Transfer button Press Yes in this example if prompted to overwrite formulas Press the OK button on the form that appears to notify you of a successful transfer Then press the Close button to close the Stability Derivatives form Now let s proceed to the dynamic stability analysis Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 40 of 136 t OWL Publishing Engineering Software VLM Stability Derivatives SIMPLE DEMO SRF Parameters Result Matri
20. along trailing edge of wings fuselage wing juncture etc increasing its drag Such flow adds a considerable complexity to analysis work In fact it is so complex in nature that even state of the art Navier Stokes solvers have a hard time predicting it accurately Extracting drag from wind tunnel testing presents challenges as well and requires great expertise especially for scaled wind tunnel models This is so because the angle of attack at which flow separation begins differs from that of the full scale airplane These difficulties must always kept in mind when predicting drag using any computer code The calculation of drag is estimation only and as such must be taken with a grain of salt It is the purpose of this section to explain how SURFACES computes drag and that way help you make drag predictions that are as useful as possible As is revealed in the famous Navier Stokes equations drag really has only two causes pressure and friction although the multitude of specialty drags that abound in aerospace engineering literature imply otherwise The SURFACES development team uses these two drag sources to simplify drag estimation in the program Drag estimation involves several parameters the geometry of the exposed area known as the wetted area aircraft orientation e g angle of attack and angle of yaw and flow physics density A Li IMPORTANT SURFACES is a symbolic vortex lattice solver It allows the user to crea
21. is 3 ft and tip chord Curve A2 is 2 ft see Figure 4 1a Also the reference area is 45 ft as you will know if you created the model per the instructions in Section 4 Assume that at the given condition the airfoil of curve A1 is a true laminar airfoil which is capable of sustaining 55 laminar flow on upper surface and 35 on the lower The airfoil of curve A2 is a turbulent flow airfoil but still sustains laminar flow to 15 on the upper surface and 15 on the lower This airplane is cruising at 100 KTAS 168 8 ft s near sea level where the air density is 0 002378 slugs ft Determine the skin friction drag coefficient and force acting on the wing due to the mixed laminar and turbulent regions Figure 9 3 2 Example aircraft from Section 4 One way to tackle this problem is to assume a linear change in laminar transition from A1 to A2 We ll calculate the skin friction using the mixed boundary layer formulation as follows STEP 1 Start by using Equation 5 to compute the viscosity assuming an atmospheric temperature of 518 67 R 15 Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 81 of 136 Great OWL L Publishing ineel Softy 734 7 u 3 170 x 107 518 67 518 67 216 3 745 10 lbrs ft STEP 2 Using Equation 7 we compute the Reynolds Number for airfoil 1 using a standard day air density of 0 002378 slugs ft pVL 0 002378 16
22. 0 02491 Coi TAR x 10 D tpV SC Lift to drag ratio V2 3 Results from SURFACES Document VLM docx Title 27 AR 202 2 K 21 10 100 0 989 _ tan 35 7 4 0 96934 0 989 4 286 per rad 0 07480 per deg The lift coefficient at 10 is thus C 10 0 7480 The total lift of the wing is L 1pV SC 1 0 002378 168 8 100 7480 253 4 lb Induced drag is found from the standard relation C 0 7480 0 01781 Coi TAR 10 L 0 7480 Lift to drag ratio D 0 01781 Page Numbers Surfaces User Manual Vortex Lattice Module Page 107 of 136 Great OWL Publishing Summary for wing with 0 leading edge sweep Symbol Classic Method SURFACES Lift curve slope 0 0885 0 0860 Lift coefficient 0 885 0 845 Induced drag force D 77l Lift to drag ratio Span efficiency for both cases is unrealistically assumed to be 1 Summary for wing with 35 leading edge sweep Induced drag force D 60b 56l Span efficiency for both cases is unrealistically assumed to be 1 Printout from SURFACES Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 108 of 136 Great OWL Publishing Validation 3 Warren 12 Wing V3 1 Model The Warren 12 wing is a standard Vortex Lattice model used to check the accuracy of vortex lattice
23. 178 9 ft s at an altitude of 4921 ft p 0 002054 slugs ft and at a weight of 2207 Ibs Figure 5 1 A Model of the C 172 V5 2 Expected Result Range for Ca The following parameters are given Wing area o 174 ft Aspect Ratio AR b S 36 082 174 7 48 Assume a 2 D lift curve slope of C 0 107 deg for NACA 2412 from Theory of Wing Sections by Abbott and Doenhoff page 478 Compute a 3 D lift curve slope from Method 1 of USAF DATCOM Section 1 page 1 7 Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 113 of 136 Great OWL Publishing Engineering Software 27 AR ARB tan A 2 SUR o pen 4 K Where AR Wing Aspect Ratio 7 48 Mach number parameter Prandtl Glauert 1 M 9 1 Ratio of 2 D lift curve slope to 2x 0 107 x 180 n 2x 0 97572 Age Sweepback of mid chord 0 B 2T AR D ter ENCORE NN 2 e i as Joa K verdes 7 48 1 0 97572 Range for Cng Consider the following check for Crs The height root and tip chord of the fin is 5 50 ft 4 25 ft and 2 30 ft respectively The leading edge sweep is 40 The airfoil is a NACA 0009 airfoil whose properties are discussed in Validation Sample 2 Using this data we compute the following lift curve slope for the fin Fin area Siin Ve 4 25 2 30 5 50 18 01 ft Aspect Ratio biin Sg 5 502 18 01 1 679 Assume a 2 D lift
24. 4 point Bezier curve a list of points or a B spline In order to do this effectively the user must keep the some rules in mind when manipulating or managing curves The following example in which a parametric curve is created gives an insight into how this is done STEP 1 Start a new project Select File New STEP 2 Go into sketch mode by pressing the LOOM Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 45 of 136 Great OWL Publishing P JEIR ESL SIN Pro l Ttt 2d File Edit Insert Modify Tools View Window Help i Dale dS BEX Om OB c vil git e fs ina cas LI 7 Groups Information Files Objects pec Es win mats mM Press to Select Objects for Legend acne PM 421622009 Status Figure 5 3 Defining start end points for a vector in the X Y plane If you select the X Y Z view you can see that has created a third point see Figure 5 5 This point is called an alignment point If you select the vector you ll see that highlights the vector but also a line extending from the start point to this third point see Figure 5 6 The purpose of this point is to allow you to orient the parametric curve in 3D space Let us create a simple parametric curve to demonstrate this better VLM docx Surfaces User Manual Vortex Lattice Module Page 46 of 136 Great OWL Publishing 4
25. AD Y 0 00000 0 00020 ihedral Effect CMB 0 00183 0 10486 itching Moment wrt ADY CMYB Cmb 0 00000 0 00015 Directional Stability CMZB 0 00284 0 16289 Copy Table Copy Sel Compare to Existing Project aw rate asic lift coefficient ift coefficient ift curve slope nduced drag coefficient rag coefficient rag coefficient slope FX variation with AOA FY variation with FZ variation with ADA olling Moment wrt ADA CMA itching Moment wrt ADA CMY A awing Moment wrt ADA CMz G location hca Xcg xref Cref eutral point hn heg Cma CLa FX variation with AO Y ide force derivative E HOOD e x 5 Figure 4 22 Stability derivatives for the model Step 23 Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 41 of 136 t OWL Publishing Engineering Software VLM Stability Derivatives SIMPLE DEMO SRF Parameters Result Matrix Stability Derivatives Transfer Options Use this utility to transfer the computed stability derivatives to your current project Be aware of how the transfer takes place by reading the Caution statement NOTE 1 Only selected stability derivatives will be transferred NOTE 2 Only values dependent on radians will be transferred as stability and control analyses use these Basic lift coefficient CLo Select All Lift coefficient CL a J Lift curve slope CLa Deselect Al In
26. Great OWL Publishing Engineering Software Modelling from the VLM Console This step tells SURFACES how to compute our three crucial drag coefficients We will now set up the skin friction modeling for the surfaces and tell SURFACES how exactly to compute the skin friction drag Reference Drag Modeling Drag modelling assumes the total drag coefficient CD is calculated from see VLM PDF for more details CD CDi CDo Basic drag coefficient CDT Skin friction drag coefficient CDi Induced drag coefficient Drag Properties Properties Basic drag coefficient CDa 0 001 0 s sn API SO 2 0 02740 0 00262 Skin fiction drag coefficient CDE 0 01509 Induced drag coefficient CD CDi 0 00212 Induced Drag Methodology t Surface integration Standard CDi2 CL CL CBimin EA FAR reF E ref methodology Reference Aspect Ratio SAret ARw 7 20 span efficiency Eref fa 0 923 CL of minimum drag CL CO min 10 2 0 20000 t Prandtl Betz using plane Compressibility Modelling None incompressible Flow t Prandtl Glauert t Karman Tsien f Laitane C User defined compressibility model stored in variable model SS Allows the user to define own models shoukd the others fail to represent the true compressibility effect on the model Recalculate Standard Drag Formulation Cancel Figure 9 10 3 Step 3 call
27. Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 72 of 136 G t OWL Publishing Engineering Software Example Drag Buildup C o C f C o C H CDi 2 E e a Angle of Attack Figure 9 1 4 Basic drag coefficient plotted for AOA and AOY Now let s look at the three constituent drag coefficients in greater detail 9 2 Basic Drag Coefficient Cp Basic drag is caused by pressure differences integrated over the entire external surface of the aircraft and always results in a force 1 that impedes its motion It includes the effects of interference of IMPORTANT ae gia such as E e lt ibd Entry is accomplished through the math Increase In flow separation and therefore generally not be considered constant although many do so in interest of 15 convenience especially during early concept studies of new aircraft SURFACES assumes this coefficient is supplied by the 120 and therefore the default value for every new project is 0 EEUU I A E user w an i Pro to account for changes with respect to any The coefficient is stored in the math object CDo Table 9 2 1 other variable in the program shows some examples of possible user entries for Cpo If compressibility modeling has been selected the returned value is the compressible basic drag coefficient Table 9 2 1 Examples of User Entr
28. OWL Publishing 5 2 Determine Shear Moment and Torsion ca Navn Del em 2 B x ALA L7 BOOS Ble tX EE Groups Object Info Files Force Integrator 1 POIs General Results Analysis Surfaces to Include 8 FUSE W005 10 FUSE Yoo 11 FUSE YOO 12 FUSE YOO 13 FUSE HOO 14 FUSE HOO M 4 wo cC E FUSE HOD pM edi 10542 B ft lbf 6 FUSE HOO p 45271 3 Detining Yectors for Plane Vector to represent X axis Vector ID 72 Fick gt gt Vector to represent Y axis Vector ID 3 Pick gt gt Column to plat Ts Toptloat me 10 13 AM 2 28 2006 Snap 4 point Grd Off Figure 5 2 Obtaining shear and moment distribution for a lifting surface SURFACES comes equipped with a tool that allows you to analyze cantilevered shear and moment acting on any surface Figure 5 2 shows the Force Integrator tool as applied to the right wing on the Ryan Navion model The bending moments along the right wing are plotted Note the wing curvature represents the camber line of the aircraft s airfoils 5 3 How to Manage Airfoils in SURFACES SURFACES allows the user to study the influence of airfoils on flight characteristics This is done by specifying the camber line of the airfoil The program comes with a tool that helps the user to do this more easily see Figure 4 1d The user can define camber lines using four different curves a parametric a
29. Sret SUM Cf i Siy Swet pue 10 005119 mm Skin Friction Drag Use entered skin friction coefficient Use Curve and 42 skin friction drag cr i 0 005115 This option will use skin friction stored with Curves A1 Use Curve and 42 skin Friction drag Cancel Apply OF Cancel Figure 9 3 2 Method 1 Figure 9 3 3 Method 2 Skin Friction Drag 9 4 Induced Drag Coefficient Cp The induced drag is caused when the airflow perturbs the flow field as it makes its way around the wingtip generating the wi ngtip vortices of a 3D wing see Figure 9 4 1 compared to what would happen to an infinitely long wing An 65 of the pressure field over the wing yields a higher drag than would be obtained if this tip flow did not occur In other words the generation of the wingtip vortices induces the extra drag and the higher the lift the higher is this additional drag The coefficient is stored in the math object CDi If compressibility modeling has be selected the returned value is the compressible induced drag coefficient SURFACES allows the user to determine the induced drag using three different methods METHOD 1 Surface integration sums the pressure forces acting on each panel and resolves it into a three orthogonal components and rotates this to the wind axis coordinate system Using the wing axis coordinate system the force in the X direction is by definition the drag the force in the Y dire
30. Surfaces Pro Untit 2n F4 File Edit Insert Modify Tools view Window Help ie D 86 X K OE m ff Ps iS X us i Ben i Groups Information Files Objects Press to Select Objects for Legend DN vil Parametric curve Status Insert parametric curves by clicking on two points Right click mouse button to quit 8 54 4 15 2003 snap Figure 5 4 Creating a parametric curve Pay attention to the data in the form in Figure 5 7 You can see that the start point ID is 1 point A the end point ID is 2 point B and the alignment point ID is 3 point C Press the Preview button to see what the curve looks like in 2 dimensions see Figure 5 7 Note that the curve should consist of 30 points If you did everything correctly you should see a curve identical to the one of Figure 5 8 Note how the curve has been drawn aligned to a plane formed by two vectors one extending from point A to B and the other from point A to C VLM docx Surfaces User Manual Vortex Lattice Module Page 47 of 136 Great OWL Publishing P d surfaces Pro Untitled File Edit Insert Modify Tools View Window Help Leek amp X KAGE Rk Of 6 n rum iS oe MAC Groups Information Files Objects x Es Vil i now Active objects With Formats EM Press to Select Objects for Legend Point This point was created by SURFACES when the parametric curve was c
31. TN 1208 Experimental and WLM Experiment NACA R 1208 ML 32 spanwise panels Pitching Moment Coefficient CM 0 2 0 4 0 6 0 8 Lift Coefficient CL Figure 9 5 Comparing moment curve from SURFACES to experimental data from NACA R 1208 The experimental data shows the well known early tip stall phenomena of swept back wings caused by spanwise flow near the tips This is reproduced here to remind the user that all inviscid codes vortex lattice doublet lattice panel codes etc do not model this viscous phenomena accurately because the mathematical solution forces the flow to stay attached Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 132 of 136 Great OWL Publishing Eng ing Softw Validation 10 Comparison to NACA TN 1422 V10 1 Introduction This validation compares SURFACES analysis to two of the three tapered and twisted wings featured in the NACA report TN 1422 This report compares several aerodynamic properties of three wings obtained in wind tunnel tests In this validation sample the section lift coefficients lift curves and moment curves for two of these wings from hereon referred to as WING 2 and WING 3 from SURFACES will be compared to the wind tunnel test results The general planform shape is shown in Figure 10 1 and is reproduced from the original document NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS Figure 1 General dimensio
32. as follows 2D 2D 2 edge su amem e 16 pV S uy pV Dei pV S ur For internal consistency we could thus write Document Title Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 85 of 136 Great OWL Publishing 2D 2D S 2D i C SS e S ef 2 S ur DVS D D ref D wet Which is how SURFACES returns the total drag coefficient Table 9 5 1 Example user entries for CD Here the math objects CDo CDf and CDi have CDo CDf CDi already been defined as it is in the standard template This could be a way to account for changes in skin friction with Reynolds Number Here a user is adding contribution of the wetted 0 004570 000023 1 05 T5Wet 5 9 area of surfaces 5 and 6 multiplying the result by a 1 05 to account for curvature 9 6 Compressibility Modeling SURFACES allows the user several options in compressibility modeling Figure 9 6 1 shows the form used to select compressibility modeling If no modeling is selected SURFACES will return the incompressible coefficients C Cp Cpr and Otherwise the values returned will include the compressibility corrections The following corrections are included Table 9 6 1 Compressibility formulation in SURFACES Reference E Typically under predicts experimental Ref 6 Prandtl Glauert C _ values Simple enough to be applicable Equation
33. codes to display a value here V5 4 Comparison of Codes Table 5 1 prompts some interesting questions for instance how do the codes compare Table 5 2 displays one such comparison Here a grade from 1 worst to 5 best is assigned to those stability parameters that can be compared to the source The parameters are compared by computing difference using ig CODE P SOURCE Adifference P ource Then the code with the largest difference scores 1 and the code with the smallest one 5 A total of 30 derivatives are considered in Table 5 1 of which 12 have a value from the source document Airplane Flight Dynamics and Automatic Flight Controls by Jan Roskam The highest total score a code can receive is 5 x 12 60 The lowest total score is 12 The scores for the 5 codes are compared in Table 5 2 Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 117 of 136 Great OWL Publishing Table 5 2 Comparison of Several VLM Codes and the Panel Code CMARC a 5 Gy OMe G P e P C P CNE P 4 3 Number of 1s Number of 2s Number of 3s Number of 4s Number of 5s NO 0j NO Oy N 0 o gt Table 5 2 shows that SURFACES scores highest 44 points CMARC scored worst 25 points Two codes never scored worse than 2 VIRGIT and SURFACES On the other hand AVL CMARC and
34. curve slope of C 0 1063 deg for NACA0009 from Theory of Wing Sections by Abbott and Doenhoff Compute a 3 D lift curve slope from Method 1 of USAF DATCOM Section 1 page 1 7 2 AR 202 2 24 B Ly 2 2 K Where Mach number parameter Prandtl Glauert 1 M 1 Ratio of 2D lift curve slope to 2x 0 1063 x 180 2 0 96934 Age Sweepback of mid chord 28 Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 114 of 136 Great OWL Publishi Engineering Software 2 C _ C __2_ P 202 2 2 ER nien K 21 1 679 2 2 gt 1 679 tan on 0 96934 1 10 54947 2 197 per rad 0 03835 per deg 24 43 00019 x 1 28271 4 If one considers the fin at a 1 the fin lift coefficient is given by C 1 xC 0 03835 The total lift of the fin at V 178 9 ft s and p 0 002054 slugs ft is found to be Lim 1pV SC 1 0 002054J 178 9 18 01 0 03835 22 7 fin Assuming a tail arm from reference point of 16 0 ft the total moment is found to be 363 2 ft lb which yields a C of N 363 2 C gt A 0 00176 LpV Sb 1x0 002054 x178 9 x 174 x 36 17 Since N equals 0 ft lb at 0 Cng can be found to be _ 0C 0 00176 1 0 00176 per 0 1006 per rad From this a reasonable Cng for this plane should be of the order of 0 03 0 17 d
35. entire text in the form to the clipboard We consider it a good practice to copy and paste it as a comment under Edit gt Remark in the main worksheet for future reference Now let s trim the aircraft for a level flight First we must define which surfaces serve as the elevators To do that return back to the worksheet where the model is STEP 19 Double click on one of the two surfaces that serve as the horizontal tail This opens the dialog box shown in Figure 4 18 Select the Edge Deflections tab Set number of chordwise panels on the aft edge to deflect CO 2 STEP 20 In the same dialog select the Reference tab Check the Surface is used for Pitch Control Press the OK button If a warning appears stating there s already a VLM solution in memory just press the Yes button STEP 21 Repeat Steps 19 and 20 for the other horizontal surface Also by now it would be a good idea to save the work Here we select File gt Save As and call it SIMPLE DEMO SRF You should do the same Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 34 of 136 Great OWL Publishing Engineering Software Edit Surface 4 General Edge Deflections Reference Tuning Edge Along Curve B1 Number of Forward panels Fwd rotation angle deg al Bi Leading edge up right Leading edge down left Fix coordinate Edge Along Curve BZ Number of aft pane
36. in Step 13 Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 96 of 136 Great OWL Publishing Engineering Software Now only one thing remains The wetted area for all the surfaces involved must be accounted for or SURFACES won t be able to compute the skin friction drag coefficient Let s do this STEP 14 In the math objects list under the Objects tab tab on the pane in left hand side of the worksheet find the variable Swet It should be in a block of variables under the title REFERENCE PARAMETERS Double click on it to open the variable editor see Figure 9 10 1 and enter the function Swet 1 2 3 4 5 the order of the arguments doesn t matter here This will calculate the wetted area of the selected surfaces Press OK when done Edit Variable Swet Formula Swet 2 1 5 3 4 Edit Geometic Relations for Formula Use this tool to help construct Formulas that involve the geometry itself For instance Inserting Fes 21 at the cursor will retrieve the coordinate of point 21 when the object i calculated This allows dependent properties to be automatically updated if point 21 1s moved to a new location Note that same functions don t have any arguments Available functions CD Total drag coefficient CDo CBEEDI Insert Function Skin friction drag coefficient Vortex induced drag coefficient per selected method L Da Basic drag coefficient o
37. of images Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 36 of 136 t OWL Publishing Engineering Software VEM Trimmed Level Flight SIMPLE DEMO SRF General Progress Table Progress Plot Summary Trim Wizard This tool will help you trim your aircraft such that Lift equals its Weight and Moments about the three axes are all zero Y our model must have movable controls surfaces for trimming to be possible STEP 22a Press the Next gt gt button Start Over VEM Trimmed Level Flight SIMPLE DEMO SRF General Progress Table Progress Plot Summary Airspeed Specify the airspeed or airspeeds the model is flying at prefer airspeed in terms of Calibrated airspeed Vcas v STEP 22b EN Arspeedis to I rm a Ensure th selection shown oco Press the Next gt gt button Multiple airspeeds We will just trim to a single airspeed but multiple airspeeds can also be analyzed Specific airspeeds separate with commas as 100 150 175 250 Start Over lt lt Previou e Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 37 of 136 Great OWL Publishing Engineering Software VEM Trimmed Level Flight SIMPLE DEMO SRF General Progress Table Progress Plot Summary Flight Condition Specify weight and yaw attitude of the model angle of attac
38. of the point Xr yg ze on to the vector A see Figure 6 It is denoted by the point Xp yp Zp Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 55 of 136 Great OWL Publishing Engineering Software Figure 6 Determination of moment vector M The location of this point is obtained using standard vector algebra The reader is referred to the one presented on page 31 in ntroduction to Vector Analysis by Davis and Snyder The method can be explained using Figure 7 which defines the arbitrary vectors V and W W Wi V Figure 7 Projection of vector W onto vector V Then the parallel projection of W onto V is given by W YN 4 The perpendicular projection is simply found from W W W S Using this we first determine the vector R from the start point of the vector A to the force point i e Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 56 of 136 Great OWL Publishi a ra C bung mm ng oortware EngineerIi T 54 6 ZF i The location is then found by referencing Figure 7 and Equation 4 and by writing Xp X A R Yp Ji 7 2a i The length of the parallel projection the rightmost term of Equation 7 is denoted by the letter r It will be used in Section 4 to sort the discrete loads and moments along the vector A Now one must determine the vector from the
39. on VLM docx Surfaces User Manual Vortex Lattice Module Page 92 of 136 Great OWL Publishing Vector Skin Friction Parameters This tool will help you to properhy setup skin friction characteristics of vectors that represent the A1 or 2 curves of a lifting surface SURFACES will then use this data to estimate the skin friction drag coefficient of the surface Low Angle of Attack Condition 1 deg 15 hr Ipwer L 1 05 tr upper L 1 05 Xtr upper High amp nale af Attack Condition 2 deg 15 hr Ipwer L 2 05 lt 2 05 Surface for cutoff Revnold s Number C Camouflage paint on aluminum Smooth paint C Production sheet metal C Polished sheet metal C User defined Re cutoff Xtr lower 0 Tez meso ok Figure 9 10 7 Entering laminar to turbulent transition information for the selected vectors VLM Console SIMPLE DEMO SRF File Edit Tasks Analyze Virtual WT Results Help eH SPA COSE Panel Results Forces Moments Strip Resulte Report Controllers Solutions Panel IDs Surface IDs iN Trapezoidal areas Bound vortex Vortex strengths EDU E lution velocity vectors p 6 m v vector skin friction drag coefficient skin friction drag force Figure 9 10 8 Display laminar turbulent regions Document Title Page Numbers
40. related tools Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 10 of 136 Great OWL Publishing 3 Project Task List A typical project in SURFACES is conducted per the following list Model Creation Task Description Remar Ponie us as required to represent the extremes of the Draw vectors parametric curves or Bezier curves as 2 Define Vectors needed using the points Use parametric or Bezier curves to represent cambered airfoils Define surfaces by selecting the opposite curves A1 and 3 Create Surfaces A2 and B1 and B2 Only use curves A1 and A2 for curved surfaces Model Preparation Task Description 1 Remak Select Tools gt Trapezoidal Mean Aerodynamic Chord from the VLM Console This tool will determine several important geometric reference parameters to use with your model including D the MAC its location the wing area and wing span It 4 etermine the Trapezoida Mean also allows you to specify the CG location in terms of Aerodynamic Chord y A MAC You must use the Transfer tab on the form to transfer the calculated values to your model While not necessary its recommended you copy the analysis report and paste as a Remark with your model Do this by selecting Edit gt Remark from the Surfaces Worksheet window Select Tools gt Horizontal Vertical Tail Volume fr
41. surfaces are always sized such that this is achievable The primary advantage is that drag is minimum at such conditions and therefore the airplane is the most efficient Under these circumstances forces and moments change linearly with these angles However when the airplane slows down before it lands or for some other extreme maneuvering it begins to operate at larger AOAs and AOYs causing the flow to separate This will introduce a nonlinearity into forces and moments Linear codes including SURFACES do not account for this phenomena At this point you may be asking yourself why then resort to linear analysis if it has this shortcoming The answer is as simple as it is resounding Speed Accuracy is an additional benefit if your model is well created But the primary reason is speed Linear analysis is extremely fast when compared to nonlinear analysis At the time of this writing using SURFACES one can create and analyze an aircraft in the linear range with an incredible accuracy in a matter of minutes The same model may take 4 6 weeks to prepare for a nonlinear Navier Stokes solver and would give one yes one AOA say every 24 hours if one s computer network holds up And you should ask the question But isn t the Navier Stokes N S method more accurate The answer is yes and no In fact in the linear range it will give a similar answer as the Vortex Lattice Method VLM it will just take much much longer to get those answers T
42. suspect this template file is corrupt or accidentally delete it you can download a new one from assigned to any of the surfaces www greatowlpublishing com Note 7 As said earlier actual change in AOA or AOY will change Cp but this change is not to be confused with the change in induced drag whose magnitude depends on the lift coefficient C The change in Cp is solely due to a change in pressure over the airplane which is not used directly for lift generation although those lines are blurred at times It depends on the attitude of the airplane i e angular orientation in the air but this affects the shape and size of flow separation regions The Cpi on the other hand depends on the C Induced drag can be defined as the drag created by a wing in excess of what it would create in an inviscid flow at the same C One way the aerodynamicist can estimate a variation in Cpo with AOA and AOY is to wind tunnel test an aircraft with the lifting surfaces removed See Note 9 for additional information For instance see page 186 of Reference 5 Title Surfaces User Manual Vortex Lattice Module Document Page Numbers Page 70 of 136 VLM docx Great OWL Publishing Note 8 Figure 9 1 2 shows a schematic of how SURFACES handles drag calculations First incompressible drag coefficients are computed Second if compressibility correction is to be included the coefficients are modified Third the coeffic
43. the interest of time and simplicity the user can create trapezoidal surfaces more easily using this tool Note that you can hide points vectors and surfaces While this is not necessary it may clean up the view Here let s hide the points Do this by clicking somewhere on the black background This ensures the workspace image has the focus Then simultaneously press Shift and P for Points This selects all the points Then simultaneously press Ctrl and H for Hide The resulting image appears in Figure 4 7 VLM docx Surfaces User Manual Vortex Lattice Module Page 26 of 136 Great OWL Publishing Surfaces Pro Untitled File Edit Insert Modify Tools View Window Help DaeeH oo RK DIE AG Groups Information Files Objects Show Active objects with formats Press to Select Objects for Legend Ymacw 4 201 ft 27 HORIZONTAL TAIL GEOMETRY Bht 6 00 ft Sht 9 00 ft Cht 1 500 ft TRht 0 5000 Xcht 11 26 ft iht 0 000 G_C4ht 15 676 i ht AN 77 A 39 VERTICAL TAIL GEOMETRY Bvt 3 00 ft Svt 7 50 ft Cvt 2 500 ft TRvt 0 6667 Xcvt 9 67 ft Zcvt 1 40 ft G_C4vt 42 510 IR EE 93 BE KP 0 9919 52 FUSELAGE GEOMETRY Lfuse 0 00 ft xv X Z YZ 2 cmm Status 8 27 PM 3 16 2009 Snap Grid Grid Off Version 2 73 Figure 4 7 The basic model after the points have been hidden As you can see identified by th
44. theory Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 104 of 136 Great OWL Publishing Engineering Software Data from Figure 3 17 X CP 0 02 4 88 5 0 0 03 4 47 1 0 03 4 22 0 03 4 01 N 0 04 3 45 4 0 02 0 04 3 23 x 5 0 05 2 93 Cp o 10 0 07 2 52 15 0 10 2 06 0 13 1 77 0 17 1 54 0 21 1 35 0 26 1 16 Exact theory 0 34 0 96 2 0 0 39 0 85 0 46 0 75 0 54 0 64 0 60 0 55 1 0 0 68 0 47 0 74 0 41 0 79 0 33 0 86 0 27 oL 0 92 0 18 0 0 2 0 4 0 6 0 8 1 0 0 97 0 08 i Figure 1 2 2 D from Figure 3 17 of reference document Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 105 of 136 Great OWL Publishing Engineering Software Validation 2 3 D Properties of Two Wings V2 1 Models Two moderately high aspect ratio wing models were constructed to compare results from the VLM to a standard 3 D aerodynamic analysis The models have a wing span of 10 ft and a chord of 1 ft One model has a 0 leading edge sweep and the other 35 The angle of attack is 10 at an airspeed of 100 KCAS 168 8 ft s and density of 0 002378 slugs ft Each of the two surfaces has 32 spanwise and 8 chord wise panels W Pressure Coefficient F 3 404 tot 287 amp Liff 283 Ibf et Ftot 246 pi Pressure Coefficien 3 194 Liftz242 Ibf 2 05 2 442 9 t 2 564 2 269
45. vV1 M to most of the coefficients 9 36 C Is applied directly to panel pressure C coefficients inside SURFACES and is thus not applied Approaches 1 J1 M 2 Prandtl Glauert for low Mach Numbers Ref 6 Equation 9 40 Karman Tsien C oo Is applied directly to panel pressure Ref 6 Laitone 1 M Exe 0 2M coefficients inside SURFACES and is Equation Po thus not applied to 9 39 Is applied directly to panel pressure User defined coefficient inside SURFACES and also to 000162M 0 00383 Based on Frankl Voishel The Ref 3 Frankl Voishel gos 0 118M polynomial is obtained by interpolating Br e the data in the graph on that page 0 0204 0 996 Table 9 6 2 Compressibility Modeling SURFACES Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 86 of 136 Great OWL Publishing amp F z mit r e cl a NFTA arc Enc lIneerinq ortware When user selects these compressibility models are applied Prandtl Prandtl Prandtl E Karman Tsien Karman Tsien Karman Tsien ee Frankl Voishel Karman Tsien Prandtl Laitone aitone aitone Frankl Voishel L aitone Glauert User defined defined User defined defined User defined defined User defined Frankl Voishel Voishel User defined As can be seen from Table 9 6 2 the compressible Cpo alwa
46. versus turbulent boundary layer and therefore changes the skin friction drag This is the second factor to be considered The third factor is compressibility effects This is a high speed phenomenon but a simple explanation is that compressibility causes streamlines to align closer together and farther into the flow field than they do in an incompressible flow This results in a higher speed over the airfoil than indicated by incompressibility which increases the low pressure on the airfoil and thus the rate at which both lift and i Reproduced from NACA R 824 Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 68 of 136 compressibility effects and if selected bi Engineering Software eventually if the airspeed increases further a shockwave will form SURFACES does not predict shockwave formation so results in which shock would have formed in real flow are unreliable Typically shockwaves begin to form when airplanes fly at airspeeds faster than Mach 0 85 but may happen at a far lower airspeed for instance if the airplane has thick wings The theory of compressible flow is beyond the scope of this discussion but the interested reader can refer to engineering texts such as References 2 3 and 6 for further information The user must be cognizant of such high speed effects SURFACES has been designed to automatically include compressibility corrections if the user chooses to apply
47. wing side the second one has 32 spanwise panels and the third has 64 spanwise panels per side The comparison takes place at 4 7 angle of attack per the NACA report Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 130 of 136 Great OWL Publishing Engineering Software V9 2 Expected Result o Experimental data a 4 7 Weissinger 7x Multhopp 23x Figure 9 2 Original graph of spanwise loading from NACA R 1208 V9 3 Results from SURFACES The comparison of the numerical to the experimental data shows a close agreement but also that the accuracy improves with number of panels Section Lift Coefficients from NACA R 1208 R 1208 DATA at 4 77 VLM at 4 77 16 spanwise panels LM at 4 7 32 spanwise panels CI CICL Cmean WLM at 4 7 64 spanwise panels 0 4 0 5 0 6 Spanwise station Figure 9 3 Comparing spanwise loading from SURFACES to experimental data from NACA R 1208 Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 131 of 136 Great OWL Publishing Shs M7 Engineering Software Lift Coefficient versus AOA per NACA TN 1206 Experimental and LM Lift Coefficient CL Experiment NACA 1208 32 spanwise panels 4 8 6 10 12 14 16 18 20 22 24 Angle of Attack degrees CM versus CL per NACA
48. y axis at y 0 5 ft assuming the span to be partitioned into 10 1 ft wide strips Note that each strip will carry 2 Ib of load Z 37 i Figure 9 Lifting surface with a uniform pressure distribution Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 59 of 136 Great OWL Publishing Engineering Software 2 lb 2 lb 2 Ib 2 Ib 6 5 ft m Vz 7 5 ft 8 5 ft m 9 5 ft a Figure 10 Discrete forces replace the uniform distribution Reaction forces are shown in green Solution N Shear is determined from Equation 11 V 2 2 2 20 lb i l Moment is determined from Equation 12 F Fy y F yo y Fo 0 x 2 1 42 7 2 8 2 9 90 ft lb Torsion is determined from Equation 13 Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 60 of 136 Great OWL Publishing En gin eerin 0 F x x x F x xX HF xio Xy 2 1 2 1 2 1 2 1 20 ft lb The exact value for the shear is determined from V w A 1 Ibjft 10 ft x 2 ft 20 1 Similarly noticing that the centroid of the force V is at y 5 ft the moment about a point y 0 5 ft necessitated by the discreteness of the strip solution is M V Ay 20 Ib 5 ft 0 5 ft 90 ft Ib
49. 012 t Upper line curvetit Midline curvefit t Lower line curvefit Curvefit 3 720758 03 1 847312 01 T 2 38453e O1 T 2 1 13466e 017T 34 3034 22 01 Preview Create Cancel Figure 4 1d Creating the wing Picking airfoil Here select NACA 4416 for the root airfoil and NACA 4410 for the tip Step 3 Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 17 of 136 Great OWL Publishing Surfaces Pro Untitled File Edit Insert Modify Tools View Window Help D mE e m Xo KRAE Sm DIE dh c Groups Information Files Objects Show Active objects with Formats idera Press to Select Objects for Legend zDouble Click to change valuez 1 FILE INFORMATION DATE 16 03 2008 TIME 18 43 57 4 WING GEOMETRY Crw 3 00 ft Xrw 0 00 ft rw 0 00 ft Ctw 2 00 ft Xtw 0 25 ft tw 9 00 ft Bw 18 00 ft Sw 45 02 fF Xcw 0 75 ft Wow 420 f TRw 0 666 ARw 7 196 DHw 5 166 F iw 0 000 This list contains the Math decalage 0 000 LEw 15917 Objects which are algebraic G 0 000 expressions used for G C2w 1 591 Cmacw 2 535 ft everything in SURFACES Kmacw 0 117 ft Ymacw 4 201 ft 27 HORIZONTAL TAIL GEOMETRY _ oo Status 7 44 PM 3 15 2009 Snap Grid Grid Of Version 2 735 Figure 4 2 If you followed Steps 1 through 3 correctly the wing will appear as shown contain
50. 10 User can investigate panel orientation in addition to surface A1 B1 curve orientation by pressing Ctrl T Ee 7 31 09 2 8 10 A bug that allowed any number of categories in the Project Properties form was fixed EN 7 31 09 2 8 10 Function Swet surf1 surf2 added to extract wetted area E 7 31 09 2840 E geometry recognition when user selects a math object referring to the User can turn AutoCalc on or off by double clicking a panel on the status bar This is handy for slower computers as it will prevent math objects from being solved after 24 8 15 09 2 8 10 each change which is what happens when AutoCalc is on It is intended to allow the user to temporarily turn the feature off but user must know that while off the math objects will not update correctly Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 8 of 136 Great OWL Publishing Engineering Software 1 Orientation of Forces and Moments Positive Fz Positive My a Positive Mx STABLE Mx STABLE My NEUTRAL Mz My Positive Mz Positive Fy B B Y Positive Mx X STABLE Mx NEUTRAL My STABLE Mz Mx My B B B My Mz Document Title VLM docx Surfaces User Manual Vortex Lattice Module Page Numbers Page 9 of 136 Great OWL Publishing 2 Force and Moment Nomenclature KK Axial force m X EL lt lt Side force along Y axis Y Y Norma
51. 8 8 3 Re 3215539 u 3 745 x10 STEP 3 Then compute the Reynolds Number for airfoil 2 Re _ 0 002378 168 82 _ ere u 3 745 x10 STEP 4 Using Equation 12 we compute the location of the fictitious turbulent boundary layer on the upper and lower surfaces of airfoil 1 noting the different locations of the Xy on each surface X X 0 625 1 0 375 1 0 375 Lower 36 9 x e 36 9x o3 0 06948 C C Re 3215539 X 1 0 375 Upper 29 36 9x 0 55 0 09216 C 3215539 STEP 5 Repeat for airfoil 2 noting an equal value for each surface X 0 625 1 di Lower 291236 9x 0 15 _ 0 04763 C 2143692 X Upper 0 04763 STEP 6 The skin friction coefficient for upper and lower surface of airfoil 1 is determined using Equation 13 as follows 0 8 0 074 X X 0 074 Lower Re I 391553902 1 0 35 0 06948 0 002841 0 074 upperl 3215539 E 0 55 0 09216 0 002265 Upper Call the average of the two the representative skin friction coefficient for airfoil 1 i e 0 002841 0 002265 0 002553 STEP 7 Repeat for airfoil 2 noting an equal value for each side Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 82 of 136 Great OWL Publishing 10 EZ al f m T 0 8 0 074 0 074 0 8 Lower C
52. BIA GAR zz JE Groups Information Fies Objects Press to Select Objects for Legend Oh xv XE VY 7 Status 3 35 4 15 2003 inap Figure 5 10 The parametric curve t t shown parallel to the X Z plane Note how the curve is always drawn as if on an imaginary 2D plane that is oriented in 3D space VLM docx Surfaces User Manual Vortex Lattice Module Page 51 of 136 Great OWL Publishing Engineering Software 6 Transformation of Load Vectors from a Global to a Local Coordinate System The following derives mathematical formulation to determine shear forces and moments about an arbitrary axis The goal is to provide SURFACES with a tool that helps the structural analyst retrieve aerodynamic loads However the formulation is in fact applicable to any load analysis involving a discrete distribution of elemental loads Consider a lifting surface in a 3D coordinate system from now on referred to as the global coordinate system For structural purposes it is desired to determine the shear and moments about an axis called the guarter chord SURFACES allows this to be done quickly and effectively The analysis requires a coordinate system to be constructed which from now on referred to as the local coordinate system A more descriptive example of this is shown with the typical Vortex Lattice model in Figure 1 A vector on the leading edge and along the fuselage have been highlight
53. E I 0 15 0 04763 0 003677 Upper 0 00367 The average of the two is of course C 0 003677 STEP 8 The representative skin friction coefficient for the total wetted surface is simply the average of the coefficient for both airfoils i e _ 0 002553 0 003677 j 0 003115 2 STEP 9 Determine wetted area of the wing 5 2x 3 2 x18 90 0 fr STEP 10 Estimate skin friction drag due to the laminar flow D tan EPV XS yo XC 1 0 002378J168 8 x 90x 0 003115 9 5 Ibf Note that an equivalent skin friction drag coefficient which is based on Syer would be found from Equation 15 S EID 2 0 003115 0 006230 Df f S 45 Also note that the value 0 003115 and not 0 006230 is what one could enter as Cf i for the wing surface when using the internal generation of Cp in SURFACES see the red box for each method below in Figures 9 3 2 and 3 This can be done by one of the two following methods Method 1 Surface by surface basis Method 2 Multiple surface entry Double click on a surface to open its properties form The user can select any number of surfaces by Click on the Tuning tab Enter the skin friction holding Shift while clicking on surfaces and then coefficient for the surface in the textbox in the red select Modify gt Surface Properties Enter the frame desired value which will be applied to all selected surfaces Document Title Page Numbers V
54. LM docx Surfaces User Manual Vortex Lattice Module Page 83 of 136 Great OWL Publishing Engineering Software Edit Surface 2 6 4 Change Surface Properties General Edge Deflections Reference Tuning Change Surface Mesh Leave text box blank to not change a conesponding segment Tuning Forces Model tuning i a common way of helping the Chordwise panels and 42 aenxhynamicist to adjust the effectiveness of selected aiee a ea Spanwise panels B1 and B2 tunnel or flight testing The vortex strengths of the panels on this surface will be multiplied by the tuning Change Surface Edge Deflection factor giving the user a great control over effectiveness of panels on overall forces and moments generated by 3 E 2 it A tuning factor of 1 is the default value Leading edge up right Leading edge down left Tuning factor 11 Trailing edge upright Tailing edge down left Reference Values Value at curve AT Use entered skin friction coefficient Value at curve 42 Allows the user to account for skin friction drag on surfaces Enter the surfaces skin friction coefficient F 2 eference eight here and SURFACES will sum up the coefficients of all surfaces and return the result in the Math Object CDF NOTE The below value is used to compute Tuning CDf using the following expression Delete Tuning Factor I Suet
55. OM Section 1 page 1 7 Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 119 of 136 Great OWL L Publishing ineeri ng SoTrtw lt AR C 7 202 2 2 BD en 2 2 Where AR Wing Aspect Ratio 20 Mach number parameter Prandtl Glauert 1 M 9 1 Ratio of 2D lift curve slope to 2x 0 1051 x 180 2 0 95840 Age Sweepback of mid chord 0 2T AR oe 7 202 2 T idi pee pea K ee 5 472 per rad 0 09551 per deg 400 0 0 95840 1 12 Compute zero lift angle for the 2D airfoil using C 0 a d ES 1 i C 0 1051 Compute lift at zero angle for the 3D wing using 0 1 173 0 095512 0 1121 Compute pitching moment for 3D wing Av a a C C Ax c Ma 3 E La La C 0 09551 0 01158 0 1051 0 01089 V6 3 Results from SURFACES Summary Parameter Symbol Experiment Classical Method Surfaces Moment coefficient 0 00020 a 0 01198 0 00016 a 0 01888 me Theory of Wing Sections by Abbott amp Doenhoff graph on page 498 Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 120 of 136 Great OWL Publishing Engineering Software CL versus AOA for 23012 CL 2D Experiment CL 30 Experiment CL 3D S
56. STEP 15 Press the Adjust button Respond to the warning that appears by pressing Yes Then press Close button to exit the form When completed your node will appear closer to the wing than before or but SURFACES has automatically changed its X location from 4 to 3 347556 ft moving the CG in the process i e to the 25 MAC Now let s learn some more details about the model Let s determine the neutral point per the following steps Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 31 of 136 Great OWL Publishing STEP 16 Press the VLM Console icon This will open the mA Vortex Lattice Method Console shown in Figure 4 16 LN RE KENT Specify a CG Location EJ Use this tool to mowe the to desired location All the nodes vau have selected will be moved the same distance from their current locations Specific Variables to Move Wearable scg Variable cg Wearable cq f cog in terms of Pmac Desired location 2 Adjust Close Figure 4 15 Specifying a CG location Step 14 VLM Console Untitled File Edit Tasks Analyze Virtual WT Results Help eh CORP A Ace BE Panel Flesults Forces Moments Strip Results Report Controllers Solutions Panel 105 Surface IDs Normal vectors No i My j Nz k ee areas Bound vortex and control points E Weight of Surfaces Vortex strengths SC velocities BC velocity ve
57. SURFACES was developed in real aircraft design environment and is loaded with highly developed tools that give you answers quickly We consider the program analogous to an extremely sophisticated airplane calculator Create a model of your aircraft and then use SURFACES to extract hard to get information about it Stability derivatives loads performance parameters are just the beginning of your discoveries You can extract in a matter of seconds some super complicated parameters that would take a trained aerospace engineer weeks to calculate using classical methods Use the extra time to study variations of your design to make it even better for its intended mission Whatever the design task SURFACES will save you weeks if not months of work SURFACES is the ultimate tool for anyone designing subsonic aircraft whether it be a professional aerospace engineer or the designer of homebuilt aircraft SURFACES is not just user friendly it provides you with very powerful features to help design your aircraft SURFACES uses a Three Dimensional Vortex Lattice Method VLM to solve the airflow around an aircraft and extract an incredible amount of information from the solution Plot the flow solution to better understand how the flow behaves around the airplane SURFACES is the perfect solution in any preliminary design environment or to reverse engineer existing airplanes It allows you to quickly extract loads and stability and control data SURFACES al
58. Two vectors A and B are given as the basis for our local coordinate system as follows A i jt k B 0 5i 7 0 5k Determine the components of F in the local coordinate system created by the vectors A and B Solution Step 1 Determine the vector C from C AxB i j C AxB 1 1 1 0 5i j 1 5k 0 5 1 0 5 Step 2 Determine the vector By from B AxC i j k B AxC 1 1 1 05 1 15 2 51 2 0 5 Step 3 Determine force component per Equation 5 Start by determining the unit vectors and assemble into the transformation matrix Hu U y Uy 0 57735 0 57735 0 57735 Uy 0 77152 0 61721 0 15430 te Ue Ve 0 26726 0 53452 0 80178 This yields the following force components using Equation 3 i 0 57735 0 57735 0 57735 10 2 8868 Fy 0 77152 0 61721 0 15430 5p 5 12 3443 It 0 26726 0 53452 0 80178 10 5 0178 6 3 Determination of Moment Vector in Coordinate System A By C As stated in the introduction ultimately the goal of the analysis presented herein is the determination of shear forces and moments about an axis due to the cumulative effects of multiple discrete forces It was demonstrated in Section 2 how shear forces are transformed to a local coordinate system The same methodology can be applied to the generation of moments but it involves a tranformation about a point P through which the vector A goes This point will be called the projection point from now on It is the projection
59. Z value from 0 to 6 Press the Apply button The resulting orientation can be seen in Figure 5 8 Re orient the image CTRL mouse center button to see how the airfoil is still being drawn in the plane formed by the three points Now let us align the curve so it is parallel to the X Z plane This is done in Step 9 Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 49 of 136 Great OWL Publishing P urfaces Pro Unttlec eal File Edit Insert Modify Tools View Window Help de OES EN Groups Information Files Objects Vil Press to Select Objects for Legend Ea 1 xx X Z Wee xx Status 0 panels were created 9 23 PM 4 15 2003 inap Figure 5 8 The parametric curve t t shown as originally created in the X Y plane F Surfaces Pro Untitlec 3 File Edit Insert Modify Tools View Window Help EFE Balm X co meum D BP BRS Groups Information Files Objects Shaw Active objects wita Formats ms Press to Select Objects for Legend x X Z xx 3 42 PM 4 15 2003 nap Figure 5 9 The parametric curve 1 1 shown at an angle VLM docx Surfaces User Manual Vortex Lattice Module Page 50 of 136 Great OWL Publishing _ Surfaces Pro Untit zi File Edit Modify Tools View Window Help D eS Bex oo Dm S
60. ariable CDo Description Basic drag coefficient Symbol 10 001 O0 ae AD A PILAT80 240 O27 Cr P121 80 2 Format 10 0000 Typical values 0 01 8 0 030 for jets 0 025 0 050 for pistons Drag estimation i art Be careful not to underestimate it Advanced OK Cancel Figure 9 2 1 Entering the formula for Example 3 in Table 9 2 1 for the math object CDo Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 74 of 136 G t OWL Publishing Engineering Software Basic Drag Coefficient as a Function of AOA and AOY C WARN LAS Basic Drag Coefficient CDo gt 0 0050 m 0 0045 0 0050 MO 0040 0 0045 O0 0035 0 0040 m 0 0030 0 0035 m 0 0025 0 0030 m 0 0020 0 0025 O0 0015 0 0020 L1 0 001 0 0 0015 m 1 0 005 0 001 C BO 0000 0 0005 Figure 9 2 2 Basic drag coefficient of Example 3 plotted for AOA and AOY 9 3 Skin Friction Drag Coefficient Cp Skin friction is caused by the fluid viscosity as it flows over a surface Its magnitude depends on the viscosity of air and the wetted or total surface area in contact with it The coefficient is stored in the math object cpf If compressibility modeling has been selected the returned value is the compressible skin friction drag coefficient G The analysis of skin friction drag is complicated by a process called transition when laminar boundary layer becomes turbulent see Figure 9 3 1 This
61. bjects CLa_ht 0 00000 per radian CLa vt 0 00000 per radian deda 0 44986 155 DRAG ANALYSIS Cf_turb 0 00373 Piam 0 Df_lam Error Df turb Error 176 AOA DERIVATIVES Cxa 0 42985 Cya 0 00488 Cza 5 08902 Cla 0 00013 Status 9 52 4M 7 22 2008 Snap Grid Grid On Version 2 8 1 Figure 9 10 10 Selecting the wing tip vector in Step 10 Vector Skin Friction Parameters This teal will help you to properhy setup skin friction characteristics of vectors that represent the Al or AZ curves of a lifting surface SURFACES will then use this data to estimate the skin friction drag coefficient of the surface Low Angle af Attack Condition ADA 1 deg 15 trlower C 1 10 15 tr upper L 1 10 15 High Angle of Attack Condition 2 deg 15 pitir 2 10 15 patr upper L 2 015 Surface Type far cutoff Heunold s Number Xir upper xir upper Xr lower Chord f Camouflage paint on aluminum f Smooth paint Production sheet metal uper f Polished sheet metal ie User defined cutoff Al lower Typ 0 Typ 25x Typ 50x OF Cancel Figure 9 10 11 Entering transition information for the wing tip in Step 11 Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 95 of 136 Great OWL Publishing show Active objects with formats detailed Press to Select Objects
62. btained directly fram user Pick Paint ID gt gt CL Lift coefficient From VL analysis ixi 0 Total drag force Do DrDi DATE Current date Pick Vector ID DF Skin friction drag force Di Induced drag force s Pick Surface ID Simple zz OK Cancel Figure 9 10 14 Editing variable Swet That s it The model is ready to be used for drag estimation The model with the entered laminar flow regions is shown in Figure 9 10 15 The reported skin friction drag coefficient for the entire aircraft is 0 00907 but this yields a skin friction drag of a 38 Ibf But there is more SURFACES allows us to take a closer look at some other details about the skin friction drag From the VLM Console s Panel Results tab you can select to have the program display the resulting skin friction drag coefficients or forces on each surface For instance Figure 9 10 16 shows that each half of the HT is generating 2 6 Ibf of skin friction drag while the VT produces some 3 9 Ibf remember that the airplane modeled is small perhaps UAV sized Additionally it is of interest in noting that by setting the transition of all airfoils to 0 turbulent airfoils Cp jumps to 0 01179 and skin friction drag to 49 4 Ibf i e by almost 30 Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 97 of 136 Great OWL Publishing Surfaces Pro SIMPLE DEMO SRF File Edit Insert Modify Tools View Window He
63. but also due to possible power effects For instance SURFACES and VIRGIT use 29 5 of MAC Tornado uses 31 9 MAC AVL and CMARC reference points are unknown SURFACES has the reference point located 2 ft below the wing plane and does not account for power effects it is unknown where the other codes place the vertical location of the reference point or if propeller normal force is accounted for 4 Note that for SURFACES the standard coordinate system is used with the Angle of Yaw positive beta coming from the left rather than the right Consequently a sign change is added to compare to Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 116 of 136 Great OWL Publishing Engineering Software the other codes 5 SURFACES evaluated a restoring dihedral effect for the C 172 the only one of the above codes 6 Deleted 7 The rate of roll and yaw derivatives are obtained with respect to P Bref 2 Vinf For that reason derivatives with respect P or R are multiplied by the factor 2 Vinf Bref 8 The rate of pitch derivative is obtained with respect to P Cref 2 Vinf For that reason derivatives with respect to are multiplied by the factor 2 Vinf Cref 9 Differences are most likely due to modeling differences and differences in location of reference point 10 A change in lift should be associated with a change in drag It is not known why Tornado and SURFACES are the only
64. cg 1 85 ft and 2 0465 ft The corresponding values of CMY for two angles of attack AOA1 and AOA2 was evaluated SURFACES provides a tool to make this simple shown in Figure 8 4 The resulting Xneu is 2 21 ft This corresponds to X 721 0 sa gg 2721 0365 _ 41 REF V8 3 Results from SURFACES Summary note that values from Nelson and Schmidt appear to be from the same source Flight Stability Introduction to Source and Automatic VLM using poe Aircraft Flight Symbol Control R C SURFACES 1DWT Dynamics Louis Nelson V Schmidt p t 0 002378 3105 ao AS AOA 088 076 065 Air density Outside Air Temperature Speed of sound Altitude Far field speed Mach Number Baseline AOA Reference span Source http www aerologic com stab corr html Document is cited in footnote 1 Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 127 of 136 Great OWL Publishing Reference wing chord Reference wing area Reference aspec ratio Reference weight 0 295 Center of gravity along X axis 0 295 Cref 2 0465 ft 0 25 Cref LO Neutral point along X axis 0 552 Cref Ce m 0 38 Cref BENE Moment of inertia about X axis 1048 slugs ft Moment of inertia about Y axis 3000 slugs ft Moment of inertia about Z axis 3530 slugs ft Product of inertia about X axis Product of inertia about Y axis
65. codes It provides a ready check case for the evaluation of any new or modified code as well as a check on the panel scheme layout This wing is known as the Warren 12 planform and is defined together with the official characteristics from previous calculations in Fig 3 1 below For the results cited the reference chord used in the moment calculation is the average chord slightly nonstandard normally the reference chord used is the mean aerodynamic chord and the moment reference point is located at the wing apex which is also nonstandard Published Data 1 81 ft 0 50 ft AR 2 83 7 Ate 93 94 EFE Cret 1 00 1 50 ft Xcc 0 00 gy 7574 wing 2 83 Aina Cio 2 743 rad 53 54 ae ae TaN LIN ee 2831 Figure 3 1 Warren 12 planform Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 109 of 136 Great OWL Publishing Engineering Software Htift 1 Figure 3 2 Warren 12 planform VL results V3 2 Expected Result The following results are expected Cla 2 743 rad CMa 3 10 rad V3 3 Results from SURFACES The following results where obtained from SURFACES for 6 chordwise by 16 spanwise panels on each wing total of 192 panels Cia 2 790 rad Cua 3 174 rad The following results where obtained from SURFACES for 8 chordwise by 24 spa
66. construction phase At any rate it is a good practice to check for errors in the assignment of geometric references before solving STEP 1 Open the demo airplane project from Section 4 Select File gt Open and navigate to find the file SIMPLE DEMO SRF Double click to open STEP 2 Select the X Y Z view and orient the airplane similar to what is shown in Figure S109 Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 88 of 136 Great OWL Publishing a j File Edit Insert Modify Tools View Window Help a Dabo 36 X RK B SOE AMS Groups Information Files Objects Press to Select Objects for Legend x Ei ay xv X Z YZ XYZ Status 8 37 7 22 2008 Snap Grid Grid On Version 2 8 1 Figure 9 10 1 The model if Step 2 was followed Let s define the basic drag coefficient as follows CDG 0 05 AOATP17 100 270602 0 AOY PI I180 2 Lets define the skin friction drag coefficient as f oll OWS File Tasks Analyze Virtual WT Results Help 2 _ Par Reference Geometry Report Controllers Solutions CDI CDI Reference Inertia And lets define the induced drag coefficient as follows pi usc ances CDi LCD aleve ameters Now let s enter these Transparent background Figure 9 10 2 Select Reference Drag VLM docx Surfaces User Manual Vortex Lattice Module Page 89 of 136
67. create the VERTICAL TAIL VT by filling the form using the numbers in the dialog in Figures 5a through 5c Trapezoidal Surface Preview Geometry Wing span b b Wing area 5 15 Inboard chord Bo Aspect ratio 2 4 Outboard chord MAD 22522113 MAC 1 4 f LE Sweep C 4 Sweep An oar dihedral T waist wash out Create Surface in Plane ey fe Location EN a Figure 4 5a Creating the VT Entering geometry Note the option selected in the Create Surface in Plane frame is now the X Z plane rather than the X Y plane used for the wing and HT Step 5 Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 23 of 136 Great OWL Publishing Engineering Software Trapezoidal Surface This tab will automaticalhy create formulas that are Wing span dependent on the geometry These formulas will Wing area 5 15 calculate many different parameters such as wing span area taper ratio aspect ratio and so Aspect ratio 2 Taper ratio TA 0 666666 Details MA pm 533333 Y MAC 1 4 Symmetrical about plane Create a 14 chord vector Create a 1 chord vector Create formulation t For wing Bw Sw etc t For HT Sht etc For VT Byt Swt Figure 4 5b Creating the VT This tab will help you create geometrically dependent formulas Note the selected c
68. ction drag Induced drag User entry only User entry PON User entry or internal formulation formulation internal function name CDn CDi CDf returns the skin friction coefficient by summing up skin friction CDi returns the induced coefficients assigned to drag using one of three selected surfaces The modeling techniques function calculates the surface integration k CL area of the surface and method or Trefftz plane multiplies with the user integration entered skin friction coefficient EX e e es CORIBISSSIDIT Canusariank voine n 0 ___ How does it work Depends on user entry References 1 Aircraft Performance and Design Anderson John D McGraw Hill 1999 2 Convair Performance Methods 3 USAF DATCOM Hoak D E et al Flight Control Division Air Force Flight Dynamics Laboratory 1970 4 Aircraft Design A Conceptual Approach Raymer Daniel P AIAA Education Series1989 5 Aerodynamics Aeronautics and Flight Mechanics McCormick Barnes W John Wiley amp Sons 1979 Modern Compressible Flow Anderson John D McGraw Hill XXXX Airplane Aerodynamics and Performance Roskam Jan DARcorporation 1997 Boundary Layers Young A D AIAA Education Series 1989 po Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 101 of 136 Great OWL Publishing Engineering Software 10 Validation Samples Document Ti
69. ction is the side force and the force in the Z direction is the lift The astute student will recognize that D Alembert s 2D paradox that a body in inviscid flow produces no drag does not apply in 3D flow due to the downwash created by the trailing wake Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 84 of 136 Great OWL Publishing Engineering Software METHOD 2 C C cpmin 2 x ARref Eref method computes the induced drag based on the current lift coefficient the CL where minimum drag occurs C reference Aspect Ratio ARref and reference span efficiency Eref METHOD 3 Trefftz plane integration uses flow perturbations in an imaginary plane infinitely far behind the model to determine the induced drag The location of the plane is a mathematical simplification that allows one to neglect the x perturbation from the flow field formulation as it is theoretically zero that far from the model This way a 3D relationship volume can be considered as 2D plane Figure 9 4 1 A 3D wing in airflow 9 5 Total Drag Coefficient Cp Once SURFACES has determined the basic skin friction and induced drag coefficients it computes the total drag coefficient using Equation 3 repeated here for convenience The coefficient is stored in the math object CD C Cp Cor Cp 3 It should be noted that the coefficients are based on Sre forces Equation 3 can be rewritten
70. ctors lll Solution velocity vectors Force vector duri Total force Cp pressure coefficient shades Cp pressure coefficient contours Cp pressure coefficient values Pressure values Panel lift coefficients CL MAC Analysis only in XY plane Figure 4 16 The VLM Console Step 16 Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 32 of 136 Great OWL Publishing Engineering Software Note that when you create a new project SURFACES has preset values for a multitude of variables Among those are the airspeed variables Vcas Vtas Vinf altitude Href and angle of attack AOA Naturally you can change these with ease but currently Vcas 100 knots Href 0 ft and AOA 2 In interest of saving time for this demo let s assume these will suffice for our analysis STEP 17 begin and after a few seconds Select Tasks Determine Neutral Point Press the Analyze button to once done review the results in Figure 4 17 Determine Neutral Point Untitled NEUTRAL POINT ANALYSIS Untitled 03 16 2009 21 07 17 1 1B9Be 01 3 3050e 02 1_5592e 01 8502 01 3 8502e 01 4_7492e 01 7 5032e 01 1 7503er 00 7 5032e 01 1 7503er 00 METHOD 1 Copy Stop Transfer 1 Figure 4 17 Determining neutral point Step 17 The full report is displayed below Note that SURFACES uses two methods to compute the neutral point
71. cussion in Aircraft Performance and Design John D Anderson pages 115 116 3 Great OWL Publishing Engineering Software Cp C t Cy 3 Where Cp Total drag coefficient dimensionless Stored in the variable CD Cp Basic drag coefficient dimensionless Stored the variable Cp Skin friction drag coefficient dimensionless Stored in the variable CDf Cp Induced drag coefficient dimensionless Stored in the variable CDi Note 1 The form of Equation 3 preserves the idea expressed in most texts on aircraft design Note 2 Since SURFACES is symbolic code the user can enter complicated expressions for each component However SURFACES also provides the user with several tools to help and these will be discussed in greater detail in this section Note 3 Although many aerodynamic texts treat Cp and Cp as if they were constant with respect to a and B there is no guarantee this is true in reality For instance a change in a will move the laminar to turbulent flow transition point and reshape flow separation regions Additionally compressible skin friction coefficient reduces slightly with Mach Number whereas the basic drag coefficient increases Note 4 Sometimes the basic drag coefficient is lumped together with the skin friction coefficient and called profile drag This will not be done here for the simple reason that it adds complexity to keep track of yet another drag coefficient and hides the contrib
72. derivation details the requirements for a trimmed flight condition A trimmed flight is defined as a flight in which the moment about all three axes is zero For instance when determining longitudinal trim assuming a solution can be found the following must hold C Cio Cry A Cys 1 C A Cu 9 M Where C lift coefficient Cio lift coefficient for zero angle of attack and zero elevator deflection Close lift coefficient for zero angle of attack Crtarget lift coefficient obtained from the lift equation CL lift coefficient change with angle of attack Cise lift coefficient change with elevator deflection Cm pitching moment coefficient Cmo pitching moment coefficient for zero angle of attack and zero elevator deflection Cmose pitching coefficient for zero angle of attack Cima pitching moment change with angle of attack Cmse pitching moment change with elevator deflection a angle of attack OcurR current angle of attack Aa deviation from current angle of attack de elevator deflection Ade deviation elevator deflection If the coefficient are known we can write Equation 1 as follows a C Ci Cr lla C C PN E Cae Qr Cs m C mo oan Cus The solution protocol is a follows W Ltarget pV s STEP 1 Compute C STEP 2 Establish a value for Aa and A Set a a and 8 0 to determine C Cri STEP 3
73. duced drag coefficient CDi Deselect Nonrequested Drag coefficient CD Drag coefficient slope CDa Deselect Formula FX variation with AOA Cxa FY variation with AOA Cya FZ variation with AOA Cza Rolling Moment wrt 404 Cla Pitching Moment wrt ADA CMYA Yawing Moment wrt AOA CMzA CG location heg lt cg lt ref Cref heg Neutral point hn heg Cma CLa hn FX variation with Cxb Side force derivative Cyb FZ variation with Czb Dihedral Effect CMB Clb Pitching Moment wrt CMB Cmb Directional Stability CM2ZB Cnb v When transferring warn if variable contains a formula before replacing Tee CAUTION Transferring variables will overwrite existing formulas or values For instance placing a checkmark next to the variable CL would replace a formula such as CLo CLa amp O Pi 180 with a numeric value If you want to prevent the formula from being overwritten make sure its corresponding variable is not checked qe eed lt Figure 4 23 Stability derivatives for the model Steps 24 28 STEP 28 Press the STAB Console icon This will open the L Ee Stability Analysis Console shown in Figure 4 29 It is left as an exercise for the user to press the various icons to experience functionality The simulation icons will display the motion of the aircraft in real time STAB Console SIMPLE DEMO SRF
74. e model Document Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 35 of 136 Great OWL Publishing OSBUS SLAK oou RAQH KOASAS Groups Information Files Objects show Active objects with formats Press to Select Objects for Legend 0 Double Click to change values gt VLM Console SIMPLE DEMO SRF File Edit Tasks Analyze Virtual WT Results Help DATE 16 03 2009 TIME 21 26 54 eet APA FE o oe Panel Results Forces Moments Strip Results Report Controllers Solutions 1 FILE INFORMATION 4 WING GEOMETRY Control Surfaces Crw 3 00 LXrw 0 00 ft Yrw 0 00 ft Cha 2 00 ft Xtw 0 25 f Bv 9 00 ft Bw 18 00 ft Notice Sw 45 02 fF net TT deflected Lift control 0 TRw 0 668 elevators ML control 0 ARw 7 196 oH DHw 5 166 in 64 Reset fiw 0 000 7 1 decalage 0 000 G LEw 1 591 G 4 0 000 G Cow 1 591 Cmacw 2 535 ft Xmacw 0 117 ft Ymacw 4 201 ft Note Activating controls will force all associated surfaces to have the same deflection 2f HORIONTAL TAIL GEOMETRY Bht 6 00 ft xz vz eE Status 396 panels were created 9 26 PM 3 16 2009 Snap Orr Grid Off Version 2 7100 Figure 4 19 Demonstrating elevator functionality STEP 22 Select Tasks gt Trimmed Level Flight to display the Trim wizard Follow the steps shown in the subsequent list
75. e red box in Figure 4 6 the wing span Bw is 18 ft and wing area Sw is 45 2 Similarly you can see identified by red boxes in Figure 4 7 the horizontal and vertical tail volumes should be 0 8496 and 0 0826 respectively Now let s add weight to the model using the specialized tools in SURFACES STEP 6 Select Edit gt Select Surfaces Press the Select All button and then the OK button see Figure 4 8 Select Surfaces Select Surfaces v 1 Trapezoid vw 2 Trapezoid v 3 Trapezoid v 1 Trapezoid Mayo Trapezoid ij Deselect All Ok Figure 4 8 Selecting all surfaces simultaneously Step 6 Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 27 of 136 Great OWL Publishing Engineering Software STEP 7 Select Tools Distribute Weight on Selected Surfaces and Nodes Enter 400 in the entry box and press the OK button see Figure 4 9 Distribute Weight Total weight of selected surfaces Figure 4 9 Enter weight of the selected surfaces here as 400 Ibs Step 7 This will distribute a total weight of 400 Ibs onto the model based on the area That is SURFACES calculates the total area of the selected surfaces and then computes weight per total area The weight property of each surface will then be assigned a number which is calculated as weight per total area of the selected surfaces x the area of the su
76. e that the CL method is only a representation that works over a range of C s It becomes increasingly inaccurate if C is too low or too high Analysis done using that drag model will only be reliable within that range For instance predictions based on the red curve in Figure 9 9 1 would indicate less performance at higher AOA than the airplane would display in reality However there might also be a scenario in which the simulated curve indicated less drag and therefore better performance than the real airplane would be capable The point is that the user must understand the limitations of any prediction made 9 10 Setting up Drag Modeling on Example Aircraft One of the advantages in using SURFACES is the geometric information can be utilized directly when determining aerodynamic parameters For instance consider the balance a designer must find between lift and drag A large wing area results in a lower stalling speed but greater drag and structural weight Being able to evaluate such parameters on the fly as one modifies the wing and thus its area is priceless to the aircraft designer This section will show how to use geometric relations in drag modeling The model created in Section 4 will be used in a Step by Step procedure Generally the user should prepare models for geometric relations after they have been constructed in order to prevent relations to become corrupt as a consequence of adding and deleting geometric entities during the
77. eat OWL Publishing 5 Accomplishing Special Projects with SURFACES 5 1 Tailoring Wings to Improve Stall Characteristics Surfaces Curtaces AtlanticaMUDU1 SKF X File Edit Insert Modify Tools View Window Help E Xx D E amp amp A A S c E ww OE Groups Object Info Files amp amp BE Ftot 2921 4 Ibf EE 5 Center of Gravity heviral Point m x nz Wem NEU Status Completed in Oh 00m 01 sec 9 02 2 29 2005 Snap Of Grd Off Figure 5 1 A model whose section lift coefficients near the tip are very high tip loaded Figure 5 1 shows how can be used to help optimize stall characteristics The yellow line represents section lift coefficients at stall These are entered as reference values for curves A1 and A2 for each surface The red lines represent section lift coefficients at the flight condition The image shows the wing tip stalls long before the inboard part of the wing Not only would this cause the airplane to a roll at stall as one wing tip is prone to stalling before the other one but more seriously would result in an uncontrollable nose pitch up moment This situation can be remedied by modifying the wing geometry for instance by adding wing washout increase tip chord reduce sweep or using airfoils with a higher max lift coefficient VLM docx Surfaces User Manual Vortex Lattice Module Page 44 of 136 Great
78. eate geometrically dependent formulas Note the selected checkboxes and options Step 4 Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 20 of 136 Great OWL Publishing Engineering Software Trapezoidal Surface pas Humber of Panels Wing span Wing area 5 9 Chordiwise IB Spanwize Aspect ratio 4 Taper ratio TR 0 5 Select Airfoil Fick Root Airfoil Fick Tip Airfoil Figure 4 3c Creating the HT Setting panel density Note that no airfoils are picked here so the resulting airfoil is a flat plate symmetrical airfoil Step 4 Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 21 of 136 Great OWL Publishing Surfaces Pro ESI File Edit Insert Modify Tools View Window Help BE X Teeth Bm Xx RRQ KR f Ax Groups Information Files Objects SHOW Active objects wath Formats c EE Press to Select Objects for Legend se xv xz Y o X Y E Status 7 58 PM 316 2009 Snap Grid Grid Off Version 2 73 Figure 4 4 If you followed Step 4 correctly the wing and HT will appear as shown Step 4 VLM docx Surfaces User Manual Vortex Lattice Module Page 22 of 136 Great OWL Publishing Engineering Software STEP 5 Select Insert Trapezoidal Surface one more time and
79. ectly the location of the CG SURFACES comes with a tool to help you accomplish that The following steps show how to move the CG to 25 MAC Surfaces Pro Untitled KB File Edit Insert Modify Tools View Window Help Em x DSFS KBE TARAS QS dh IE Groups Information Files Objects Show Active objects with formats detailing Fress to Select Objects for Legend Xref 0 12 ft Bref 18 00 ft Sref 45 02 fF Swet 123 05 fF ARref 7 20 p Wref 700 bf Mref 21 76 slugs Wref variable 68 INERTIA PARAMETERS 9 i Wag pm 29 Xeg 0 47 ft Pmac variable Yeg 0 00 ft cog 0 54 fi Kneu 0 00 ft Yneu 0 ft 0 lxx 242 45 slug fF hry 555 45 slug A7 765 03 slug fF bey 0 00 slug fF 62 62 slug z 0 00 slug TF 0 000 fi s 0 000 fi s Gz 32 174 Ws xv Maz Y XY Status 8 55 PM 3 15 2009 Snap Grid Grid Off Version 2 735 89 PLOT AND SIMULATION Figure 4 14 The model with ballast point defined STEP 13 Click once on the Ballast node to select it We will move it with a special tool Note that SURFACES will only move the selected node or nodes when adjusting the CG location If none are selected a warning message appears STEP 14 Select Tools gt Specify a CG Location Select the option and enter the value shown in Figure 4 15
80. ed in red Additionally the right wing has been highlighted With this information it is now possible to determine the 3D shear and moment distribution along either vector due to the discrete elemental forces generated by the right wing The two vectors are necessary to create the local coordinate system about which the shear and moments are resolved Consequently they are referred to as the basis of the local coordinate system This way one can analyze loads along vectors of arbitrary orientation Figure 1 A typical Vortex Lattice model 6 1 Establishment of a Local Coordinate System Consider the force F generated by an arbitrary panel in the global coordinate system X Y Z as shown in Figure 2 Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 52 of 136 Great OWL Publishing Engineering Software Fx Figure 2 A force in the global coordinate system Consider a local coordinate system identified by the selection of two vectors A and B such that A is not parallel to B see Figure 3 These vectors uniquely define a plane and are thus the basis of the coordinate system whose normal is given by the vector C such that C AxB 1 Z Figure 3 Defining the local coordinate system We can now create a local coordinate system denoted by the vectors A By and C where By is given by B AxC 2 Document Title Page Numbers VLM docx Surfaces User Manual Vo
81. el Results tab on the VLM Console Here you can extract various information pertaining to Panel Results panels such as areas normals vortex strengths velocity over a panel force generated by a panel pressure coefficients panel lift coefficients as well as the center of pressure Select the Body Hesults tab on the VLM Console Body Results Here you can extract information about forces and moments acting on your model Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 12 of 136 Great OWL Publishing Select the Panel Results tab on the VLM Console Here you can extract a number of information about strips of panels chordwise for instance forces moments and coefficients Display strip CL section lift coefficients to help you design for delayed tip stall 11 Stip Results You can conduct even more sophisticated analysis per the following task list Advanced Investigations Task Description Remark Select Tools gt Determine Stability Derivatives from Determine Stability Derivatives the VLM Console Select Tools gt Determine Control Response from Determine Control Response the VLM Console Select Results gt Force Integrator from the VLM Console Select Tools gt Goal Seek from the VLM Console With this tool you can calculate AOA AOY or Vinf 15 Determine Specific Conditions required to generate a spec
82. ent Note that the pitching moment coefficients are not important in this discussion The shape of the drag polar depends on several factors The first is lift which depends on the angle of attack and yaw of the geometry It is also evident that the Cp is always larger than zero achieving a certain minimum value at relatively low values of C It follows it makes sense to consider the drag as the sum of some minimum drag call it Comin and additional drag caused in part by the change in C This additional drag is caused by an increase in flow separation which increases the pressure drag The dip in the drag polar around a C of 0 2 to 0 5 is referred to as a drag bucket and is typically associated with laminar flow airfoils For instance note how all but two of the airfoils in Figure 9 1 1 64 415 and 23012 display this phenomenon Exceeding this band of lift coefficients on either side will result in a notable change in airflow behavior First the location where laminar boundary layer transitions into a turbulent one on the upper surface moves closer to the leading edge of the airfoil Second as the angle of attack increases more flow begins to separate near the trailing edges of the wing This change affects the distribution of pressure around the airfoil and therefore causes a rise in the pressure drag By the same token the transition point on the lower surface will move closer to the trailing edge This changes the extent of laminar
83. epending on the contribution of other components of the airplane V5 3 Results from SURFACES The following results where obtained from SURFACES and compared to that of other VLM codes The data is obtained from the Tornado manual pages 34 38 All the stability derivatives presented below are evaluated at a 0 TABLE 5 1 Stability Derivatives at a 0 TEST VIRGIT CMARC TORNADO SURFACES NOTE Comparison data is obtained from Airplane Flight Dynamics and Automatic Flight Controls by Jan Roskam Appendix page 592 Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 115 of 136 Great OWL Publishing o 08 0 104 0 370 0 341 4 0 089 0 007 0 063 0 025 0 0479 0 045 D 9 o o o o Lo pce 94 os 9 008 018 78949111 89 EEE 0428 04320256 80 O poe pe _ Coa lo o o o o e ow aos oos sn on orson All derivatives are per radian NOTES 1 There is a known difference in input geometry which will likely cause numerical discrepancies It is not known if the other VLM codes included washout dihedral and wing camber like the SURFACES model 2 A value of zero is expected at C 0 only if the airfoil of the wing is symmetrical flat plate 3 The different values are primarily due to the different reference locations
84. eteusieeetecarcectsearecets 109 DL AIA O E EAE E AIE MM DM d DEUM ME rr MN 109 Ve PL m E E 110 V33 Hess Tom SUBMPACEOSLImaidd pU PERDU MUNERE POUR 110 Validation 4 Bertin Smith 2 D Wing ee 111 Rc A 111 Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 3 of 136 G t OWL Publishing Engineering Software Vha 111 V4 9 Mesuls Tom SUHFACES orla ca wd C GRE RH aie 112 Validation 5 Cessna 172 113 do Bey Nino 0 NR CC c M M 113 iet E 113 V5 3 Results irom SURFACES 115 V34 OI 11 OG S i idanpodKi iK RR EAEEREN 117 Validation 6 2 0 CL Cp for 23012 119 foe X V ee 119 My M I II Em M 119 V5 3
85. f attack of most wing tips to be reduced This is one form of aerodynamic wash out A vortex lattice program allows a designer to quantify these effects before the plane is built and without the need for a wind tunnel The use of this tool does not guarantee a good wing Like any tool it still takes wisdom and proper application to get good results This particular tool is usually reserved for graduate degreed aerospace engineers with specialization in computational fluid dynamics Some of the things a glider designer can do with this program are to 1 Minimize induced drag drag do to tip vortices 2 Manage which part of the wing will stall first 3 Given a planform refine its twist distribution and 4 Calculate the local flow direction on the stab including downwash from the wing In general the refined wings have nearly elliptical chord distributions with finite tip chords no big surprise here Aerospace Engineers will assert that elliptical lift distributions DO result in the minimum possible induced drag for low speed wings At our low Reynold s numbers a truly elliptical chord distribution does NOT result in an elliptical lift distribution At low speeds on a truly elliptical winged model the air flow will separate near the wing tip leading to too little lift in that region and tip stall This is why the refined sailplanes tend to have finite tip chords The nearly elliptical wing has another beneficial quality The downwash angle is relati
86. for Legend CLa ht 0 00000 per radian CLa vt 0 00000 per radian deda 0 44886 Dstyle 1 CDo 0 00117 0 00000 CDi 0 00212 CD 0 00329 CDa 0 00000 Do 1 79 Ibf Df 0 00 16 Di 3 24 lbf D 5 02 lbf LD 0 00 1 0 833 2 0 716 0 833 0 00081 Cfturb 0 00373 Flam 0 Df lam Error Df turb Error 176 AOA DERIVATIVES There are 2 vectors here Cxa 0 42985 Cya 0 00488 Cza 5 08902 Cla 0 00013 BY XZ Y Z xw z Status 9 57 AM ff2ef 2003 Snap Grid Grid On Version 2 8 1 Figure 9 10 12 Selecting the wing root vector in Step 12 Vector Skin Friction Parameters This tool will help you to property setup skin friction characteristics of wectors that represent the AT or AZ curves of a lifting surface SURFACES will then use this data to estimate the skin friction drag coefficient of the surface Low Angle af Attack Condition ADA 1 deg 15 tr lpwer L 1 10 35 tr upper L 1 10 55 High amp nale af amp ttack Condition 2 deg 15 trlower C 2 10 35 tr upper L 2 10 55 Surface far cutoff Heunold s Number Xir upper f Camouflage paint on aluminum t Smooth paint f Production sheet metal f Polished sheet metal fe D User defined Re At lower Typ 0 Typ 254 Typ 50 OF Cancel Figure 9 10 13 Entering transition information for the wing root
87. for the same CG location You can leave your computer overnight running the trim solutions and study the solution files the next day Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 66 of 136 Great OWL Publishing 9 Determination of Drag in SURFACES 9 1 Introduction One of the primary advantages of using the Vortex Lattice Method is speed and accuracy in the estimation of aerodynamic forces and moments A prominent of those is drag Since so many other factors rely on drag performance engine requirements etc any tool that allows for a quick and reliable estimation is priceless Unfortunately drag estimation is wrought with challenges There are several things that make drag remarkable as an aerodynamic force Among those is how hard it is to accurately estimate its magnitude Drag is a rapidly changing variable making its estimation harder and harder as the angle of attack increases and air begins to separate and form separation bubbles Another challenge is the fact that when airspeed increases compressibility effects contribute more and more to the total drag The shape of a properly designed airplane flying at a low angle of attack high speed is such that air flows over it smoothly and its drag is relatively low when compared to other flight conditions Reducing the airspeed requires an increase in angle of attack which eventually causes airflow to separate in various areas e g
88. h the ones obtained herein You will be taken to the Progress Plot when you press Trim Trim STEP 22f Press the Trim button Start Over lt lt Previous Once SURFACES begins to trim you can follow the progress on the Progress Table or Progress Plot tabs see Figure 4 20 The time to trim largely depends on the number of panels in the model and accuracy desired The model presented here took 16 iterations and 31 seconds to trim Press Summary tab to read the results for each completed trim speed In this case the model will fly level at an AOA of 3 3449 and will require an elevator deflection of 4 3966 trailing edge up to balance The lift generated is 699 587 lbf and moment about the y axis located at the CG is 0 287698 ft lbf The model is automatically set to the resulting AOA and elevator deflection Press the Close button to exit the form Next let s determine stability derivatives for the model in this particular configuration STEP 23 Select Tasks gt Determine Stability Derivatives to display the Stability Derivatives form Check and uncheck the boxes shown in Figure 4 21 and press the Analyze button Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 39 of 136 Great OWL Publishing Engineering Software VLM Trimmed Level Flight SIMPLE DEMO SRF Mz 2 197219 Figure 4 20 Trim progress is displayed on the Progress Plot tab
89. he person writing these words has experienced many times that the VLM has been closer to actual wind tunnel data than N S The strength of N S solvers is separated flow but at this time such tools are better at giving the aerodynamicist an idea of what the flow field looks like than trustworthy coefficients Naturally it must be emphasized that SURFACES is performing a mathematical simulation when you use its wind tunnel test tool The same rule applied to all computer codes that emulate wind tunnels a real wind tunnel test always overrides any such calculations assuming the data was obtained by reliable means However assuming you are using SURFACES to create a mathematical model of your design the VWT is a great tool to help you understand the following issues 1 The AOA and AOY the airspeeds and the rotation rates P Q R where your math model breaks down You will want to know at which AOA the linear assumption breaks down 2 Features of your model that well still need to be improved before an accurate comparison can be made of existing wind tunnel The concept of tuning is well known in the world of finite elements flutter and linear modeling and the like Tuning is done by making minor changes to the model un Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 64 of 136 Great OWL Publishi Engineering Software 8 Determination of a Trimmed Flight Condition The following
90. heckboxes and options Step 5 Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 24 of 136 Great OWL Publishing Engineering Software Trapezoidal Surface Humber of Panels Wing span b 6 Wing area 5 15 D hardwi 5 Aspect ratio 2 ee Taper ratio 0 666666 7 Gee eee Select MAC 1 4 Fick Root Airfoil Fick Tip Airfoil Figure 4 5c Creating the VT Setting panel density Note that no airfoils are picked here so the resulting airfoil is a flat plate symmetrical airfoil Step 5 Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 25 of 136 Great OWL Publishing Surfaces Pro File Edit Insert Modify Tools View Window Help BA D eS 55 x oo RRQ KR OB Groups Information Files Objects pe to dee for Legend D xv XZ Y XYZ Status 396 panels were created 817 PM 3 16 2009 Snap Grid Grid Off Version 2 73 Figure 4 6 If you followed Step 5 correctly the wing HT and VT will appear as shown in the completed basic model Step 5 When complete your model should look like the one in Figure 4 6 a T tail design with a straight tapered wing You should be aware of that you can also create the surfaces directly by dropping points stretching vectors and inserting surfaces However in
91. iable Plam means the Plam Swet Sref percentage of laminar flow Plam 50 for laminar flow of up to 50 of wing wetted area Note that Swet here is not the same as Swet See the discussion to follow for more information This formula returns the result of an internal 5 CDE calculation in which all surfaces to which a skin friction coefficient has been defined are summed up using Equation 15 Note that these are just examples of how one might set such formulation up Your formulation is likely to be different Other handy formulations are cited below for the convenience of the user Sutherland s Formula for Viscosity When using the UK system the temperature is in R In that case the viscosity can be found from Ibe s ft2 5 u 3 170 x10 TP T 4 216 When using the SI system the temperature is in K In that case the viscosity can be found from 1 458x10 T N s m 6 T 110 4 Where T Outside Air Temperature in R or K Air viscosity in lb s ft or N s m Reynolds Number fig PME 7 U See Equation 2 90 of Reference 7 See Equation 2 91 of Reference 7 Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 78 of 136 Great OWL Publishing Where L Reference length for instance mean aerodynamic chord in ft or m V Reference airspeed in ft s or m s p Air density in slugs ft or kg m Air viscosity
92. ients are added to return the total drag coefficient Incompressible Cbo CDO COE CEI Basic drag coefficient Skin friction drag coefficient Induced drag coefficient Compressibility Compressibility Compressibility Cor CDE CDi Compressible Compressible skin friction drag induced drag coefficient coefficient Cpo CDO Compressible basic drag coefficient METHOD METHODS Frankl Voishel 1 Prandtl Glauert 2 Karman Tsien 3 Laitone 4 User defined METHODS 1 Prandtl Glauert 2 User defined Total drag coefficient Figure 9 1 2 A schematic showing how SURFACES determines drag coefficients Page Numbers Document Title VLM docx Surfaces User Manual Vortex Lattice Module Page 71 of 136 Great OWL Publishing Note 9 Consider Figure 9 1 3 which shows a simplified example of how Cpo Cpr and Cp might vary with angle of attack only constant airspeed and altitude In reality Cp might show a larger increase with AOA than displayed especially at very low and very high AOA and Cy will likely change as well as the laminar and turbulent flow regions change but one should be careful in assuming Cp and Cp remain constant Figure 9 1 4 show how the same coefficients build up to form Cp Note 10 Aerospace engineering literature introduces the casual reader to an assortment of drag types There is transonic drag nacelle drag external store drag protuberance drag interference drag parasi
93. ies for CDo Example Formula entered in the Formula box of Figure 2 A constant value which might be the result of a 0 001 prior drag breakdown analysis for an single engine piston aircraft An example of how one could account for 0 0014 0 05 AOA P1 180 2 changes in the pressure drag with angle of attack Document Title Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 73 of 136 Great OWL Publishing Engineering Software AOASPSJTO0 240 02 eri 180 2 ODT ACK P 17160 7240 02 AOTP 190 240 0009 I SDarti 3 CDwingtCDruseTCDldgtfCDcoool4 CDbtailtCdna celle Cdprotruberance CDmisc An example of how one could account for changes in the pressure drag with angle of attack and angle of yaw This is the formula of a surface and is plotted in Figure 9 2 2 for AOA ranging from 2 to 12 and AOY ranging from 15 to 15 Also see Figure 9 2 1 An example of how to account for changes in angle of attack and angle of yaw as well as the deflection of a flap here assumed to be surface number When SDaft 3 is 35 a value of 0 0315 is added to the CDo Here the user has independently defined the extra math objects describing the drag buildup and is summing them up to return the basic drag coefficient Note that these are just examples of how one might set such formulation up Your formulation is likely to be different Edit V
94. ific load lift or even lift coefficient Note the result don t necessarily result in an aerodynamically balanced model i e MX MY or MZ Determine Loads will be non zero Select Tools gt Geometric Goal Seek from the VLM Console This tool can be used to move points so that specific conditions are satisfied The best example of its use is to move the leading points on a stabilator in the Z directions at a specific flight condition so the MY is zero In other word determine an ideal angle of incidence of a stabilator Modify Geometry to Satisfy Specific Conditions Select Virtual WT gt Setup and Execute WT Run Virtual Wind Tunnel from the VLM Console Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 13 of 136 Great OWL Publishing Engineering Software 4 Creating a Simple Model with SURFACES The following model is designed to allow the novice user to quickly become familiar with SURFACES Pay close attention to which options and checks are made in each form below before proceeding to the next step STEP 1 Start a new project by selecting File gt New Project This will open a small form on which you need to specify the type of project to create Press the button labeled Surfaces Worksheet to open a blank worksheet Maximize the window for added convenience The move on to create surfaces to represent the wing STEP 2 Select Insert Trapezoida
95. in lb s ft or N s m2 A simple expression valid for UK system at sea level conditions only is V and L are in ft s and ft respectively Re 6400VL 8a A simple expression valid for Sl system at sea level conditions only is V and L are in m s and m respectively 68500VL 8b Laminar Flow Skin Friction Coefficient This is the classical Blasius solution for a laminar boundary layer on a solid surface 1 328 C J Re Turbulent Flow Skin Friction Coefficient This is the so called Schlichting relation which is found to be in good agreement with experiment _ 0 455 10 fturb log Re y Turbulent Flow Skin Friction Coefficient Compressible 20455 11 tog Re 0 144M J Where M Mach Number Equation 10 and not 11 is the preferred form in SURFACES as the program will apply correction for compressibility effect using the Frankl Voishel scheme Using Equation 11 could result in the correction applied twice Mixed Laminar Turbulent Flow Skin Friction Coefficient The method below is taken from Reference 8 Also refer to Figure 9 3 1 for the location of the points Xo and Xy Of these the user must specify the location of the transition point which is used to calculate the start point of the fictitious turbulent laminar flow This is required to ensure the boundary layer thickness is a continuous function The user is referred to Reference 8 about methods on how t
96. ing the selected airfoils twist and dihedral Step 3 Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 18 of 136 Great OWL Publishing Engineering Software STEP 4 Select Insert gt Trapezoidal Surface to create the HORIZONTAL TAIL HT Fill in the form using the numbers in the dialog in Figures 3a through Dia Trapezoidal Surface Geometry diia Geometry Wing span b 6 Wing area 5 9 Inboard chord Aspect ratio 4 Taper ratio 0 5 Outboard chord Halfspan f LE Sweep C4 Sweep An or dihedral T waist wash out m Location 10 T In z E Pick gt gt Figure 4 3a Creating the HT Entering geometry Step 4 Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 19 of 136 Great OWL Publishing Engineering Software Trapezoidal Surface This tab will automatically create formulas that are wing span B dependent on the geometry These formulas will Wing area 5 calculate nanny different parameters such as wing Aspect ratio 4 span area taper ratio aspect ratio and Taper ratio TR 0 5 Details Symmetrical about plane Create a 14 chord vector Create 1 chord vector Create formulation t For wing Bw Sw etc For HT Sht etc t Far VT Bvt Swt Figure 4 3b Creating the HT This tab will help you cr
97. is used 4 6 29 09 2 8 7 when the user presses the Set buttons The modification in ID2 now allows the user to Fixed enter a elevator rudder deflection for V tails New functions added SDfwd i and SDaft i which retrieve forward and aft 9 2309 deflection angles of the selected surface i Added 712109 288 Bug in subroutine VLM_PlotStreamlines which would cause a crash if number of Fixed streamlines was 1 ES 7 2 09 E d ii user information for usage of control deflections in form FormVLM17 stab Added 7 3 09 Overflow message generated when zoom in too far Fixed 9 7 3 09 Recent projects list added Added Data Analyzer multi variable regression states the following in the text output Analysis Fixed assumes X is in Col 7 and it should say ast column to match equation template EN 7 4 09 288 VLM Solution Seeker tool repaired and made visible to user Fixed Math object list is now synchronized with the list that appears when the user presses 909 the Press to Select Objects for Legend button i EN 7 5 09 EJ Vend about vector operations use a left hand coordinate system should be right Fixed EN 7 5 09 Math object list does not recalculate upon opening file Fixed Pressing Browse in VWT form and navigating the directory form could crash the maine program if the selected drive was inop is Drag calculations have been completely scrubbed Now the user can associated skin friction drag with both surfaces and vec
98. k EC velocity vectors Solution velocity vectors Force vector Fx amp Fy j Fzk Total force Cop pressure coefficient shades Cp pressure coefficient contours Cp pressure coefficient values Pressure values Panel lift coefficients CL of selected surfaces see status bar Center of Pressure Panels with potential flow separation WAC Anshrcic in YY ranch Lower surface laminar region Upper surface laminar region 5 skin friction drag coefficient SS Ce Transparent background 2 09466 0 00187 xv Xx YZ xy Status 10 46 7 22 2009 Snap Grid Grd n Version 2 8 12 7 Figure 9 10 16 Displaying the skin friction drag on component basis Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 99 of 136 Great OWL Publishing Engineering Software Drag Polar for SIMPLE DEMO SRF Drag Coefficient CD Lift Coefficient CL Figure 9 10 17 Drag polar generated by the Virtual Wind Tunnel for the example aircraft Lift to Drag Ratio for SIMPLE DEMO SRF Lift to Drag Ratio Angle of Attack Figure 9 10 18 Variation of L D with AOA as generated by the Virtual Wind Tunnel Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 100 of 136 Great OWL Publishing 9 11 Summary of SURFACES Drag Analysis Methodology Skin fri
99. k will be determined and axes to trim about The initial weight is always the current weight of the model but you can change it Take advantage of the fact that 2 2 2 you can enter an arithmatic expression the weight box For instance if you model weighs 3000 Ibs and you want to STEP C s determine loads at 3 8gs simply type 3 8 3000 and hit Enter Ensure the selection shown Analysis Targets Press the Next gt gt button Weight 699 3333 Angle of Y aw 0 n ce CO m p ete y t h e ift g e n e rated WI be Select which axes the model will be trimmed about Y our model must have ailerons to trim about the X axis roll elevator 7 0 0 b S at t h e a Ir S p e e d S p e C fi e d In St e p to trim about the Y axis pitch and rudder to trim about the Z axis 22b scl Trim about Z axis Start Over z Previou Trim Close VEM Trimmed Level Flight SIMPLE DEMO SRF General Progress Table Progress Plot Summary Analysis Specifics STEP 2 2 d Here specify details for the trim algorithm Lift and moment tolerances are used to determine how close to weight the lift is and how close the moment is to zero before trimming is considered complete The smaller the tolerance the closer the final values will be to Ensure the selection shown target values but more time will be required Press the Next gt gt button Analysis Specifics Maximum number of iterations Here we al lo
100. l Surface STEP 3 Create the WING using the numbers in the dialog in Figure 4 la through 4 1d Trapezoidal Surface Geometry Geometry Wing span b 1i Wing area 5 45 Inboard chord Aspect ratio 7 2 Outboard chard MAD 2 525333 Halfspan 42 t LE Sweep C 4 Sweep An or dihedral Teist wash out Location zc RN vio OF Cancel Figure 4 1a Creating the wing Entering geometry Step 3 Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 14 of 136 Great OWL Publishing Engineering Software Trapezoidal Surface This tab will automatically create formulas that are Wing span b 18 dependent on the geometry These formulas will Wing area 5 45 calculate many different parameters such as wing Aspect ratio 7 2 Taper ratio TA 0 6666667 JAC 2533333 Details M Y MAC 4 2 Symmetrical about plane Create a 14 chord vector Create 1 chord vector Create Farmulatian For wing Bw Sw etc t For HT Bht Sht etc C For VT Bvt Svt ete Figure 4 1b Creating the wing This tab will help you create geometrically dependent formulas Note the selected checkboxes and options Step 3 The purpose of the options in Figure 4 1b is to automatically create formulation that calculates wing span aspect ratio wing area taper ratio and other for your convenience There a
101. l force along Z axis o FZ 3 3 2Z Rolling moment about X axis O o MX J L Pitching moment about Y axis J MY M ss Yawing moment about Z axis Jo MZ CN ss lt UU Coefficient of axial force along X axis Coefficient of side force along Y axis Cy 2 O O Coefficient of normal along Z sap o o Coefficient of rolling moment about X axis Cl Q0 Coefficient of yawing moment Z ony i J 42 Standard right handed Aerodynamic Typical right handed Stability Coordinate System ACS Coordinate System SCS Note 1 Positive rotation about an axis is always in the direction of the thumb of the right hand as can be seen in the above figure Note 2 SURFACES uses a standard right handed Aerodynamic Coordinate System ACS which is conventionally used for other aspects of aircraft aerodynamic analyses In this coordinate system the sign of the lift is positive when pointing upwards i e towards positive Z and the sign of the drag is positive when pointing backwards i e towards positive X The user must be cognizant of the orientation of the axes when interpreting results Note 3 SURFACES comes with a routine that will convert stability derivatives to a standard body axes Stability Coordinate System SCS This is typically the default for stability and control
102. lows you to swiftly model any aircraft Do you have a three view drawing of your favorite aircraft Simply import it in to the environment and scale it up No pencils rulers or calculators are needed for scaling up the model You do it all from within SURFACES It s as easy as clicking a mouse button SURFACES determines most stability derivatives and when used with the built in Aircraft Datasheet feature allows you to perform very sophisticated dynamic stability analyses Import stability derivatives directly from your Vortex Lattice analyses into an Aircraft Datasheet and plot the aircraft s Short Period Phugoid Spiral Stability Rolling Convergence and Dutch Roll modes You can even simulate the dynamic response of the aircraft in real time SURFACES allows you to incorporate all the details of your design such as airfoil properties wing twist dihedral multiple lifting surfaces asymmetric geometries winglets deflection of control surfaces and high lift devices SURFACES even allows you to account for engine forces as functions of angle of attack airspeed and altitude whose properties are taken into account when determining trim or stability derivatives SURFACES allows you to extract surface pressures forces and moments force and moment coefficients distributed loads section lift coefficients and create shear moment and torsion diagrams on the model SURFACES comes with video tutorials You will be working on your own airpla
103. lp RA amp ARAK KBE SAL YEA NUE Groups Information Files Objects Active objects w th formats mM Press to Select Objects for Legend Dh xv K Y A XY Status 10 27 7 22 2009 Snap Grid GridOn Version 28 1 azed Figure 9 10 15 The model displaying the extent of laminar flow regions after Step 15 has been completed green panels Note the magnitude of the Cp for the entire aircraft is 0 00907 This generates a skin friction drag of 38 02 Ibf Furthermore now that we have defined the drag for the airplane we can learn a number of performance related things about it This is done by creating the drag polar for the full airplane but this is shown in Figure 9 10 17 It was obtained by running the Virtual Wind Tunnel note that elevator deflection was set to 05 Another interesting performance parameter obtained from the same VWT run is the L D curve in Figure 9 10 18 From it we learn that the expected maximum L D is 16 4 at an AOA of 6 We have just taken the first steps into a world of information about our design VLM docx Surfaces User Manual Vortex Lattice Module Page 98 of 136 Great OWL Publishing DEBS oc Xem OEE SX Pane IDs Surface IDs Trapezoidal areas Sound vortex and control points Weight of Surfaces Surface Tuning factor Vortex strengths EC velocities Vici Vy jr
104. ls ES Aft rotation angle deg r al E Trailing edge upright Tailing edge down left Fix Y coordinate with leading edge slats and B2 as ailerons flaps rudder etc Specify Delete the number of panels along the leading or trailing edges to dedicate for this function Reverse Revese Hie Hide Cancel Edit Surface 4 General Edge Deflections Reference Tuning Reference Values Reference for curve 41 0 Reference for curve AZ r Surface Grouping For VL Analysis Surface is used for Roll Control Surface is used for raw Control C C Surface is an aft edge High Lift Control DE Surface is a leading edge High Lift Control Reverse Surfaces Inertia Enter weight af surface 23 08425 Hide Entering weight here will allow SURFACES ta estimate inertia properties such as Is etc for your model Figure 4 18 Setting up elevator functionality Steps 19 21 You have now given SURFACES information it can use to automatically deflect the elevators to trim the model for level flight You can try the functionality out by displaying the VLM Console and select the Controllers tab For instance enter 20 in the Pitch control textbox and press the Set button to see the model regenerate with that deflection as shown in Figure 4 19 Once done press the Reset button to return the elevators to a neutral deflection 0 and get ready to trim th
105. n roughness value The roughness value is based on the values in the following table which is taken from Reference 4 If these are not acceptable the user can also enter own Rej Value Surface Type k Camouflage paint on aluminum 0 00040 omooth paint 0 00025 Production sheet metal 0 00016 Polished sheet metal 0 00006 omooth molded composite 0 00002 When using the built in function CDf SURFACES uses Equation 15 to calculate the coefficient using all surfaces for which has been defined C 5 S See Equation 12 28 in Reference 4 Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 80 of 136 Great OWL Publishing Engineering Software Where Cj Skin friction coefficient of surface i N Number of surfaces S wetted area of surface i in ft or m Swet Wetted area in ft or m Of these the skin friction coefficient of each surface Cj needs further explanation The user must estimate this value for each surface to be included in the analysis This brings up an additional question How does one handle laminar flow over a surface consisting of two distinct defining airfoils In order to shed light on this the demo aircraft model built in Section 4 will be used Consider the wing of the demo aircraft shown in Figure 9 3 2 which consists of two dissimilar airfoils on a tapered wing planform The wing span is 18 ft the root chord Curve A1
106. nd Torsion ARR ERR REA RR 45 5 3 How to Manage Alois in SUHMPADES unsaiiun MOM Ett x FRI 45 6 Transformation of Load Vectors from a Global to a Local Coordinate System 52 6 1 Establishment of a Local Coordinate System 52 6 2 Transformation of Force Vector in Coordinate System A By C 54 6 3 Determination of Moment Vector in Coordinate System A By C 2 eeeee rennen 55 6 4 Determination of Shear and Moment Distribution 21 eee ee eere e erre esee ean nena 57 6 5 Presentation of Data in SURFACES Fk V cR EN KE 61 7 Using the Virtual Wind eere eere eene nennen nnns 64 8 Determination of a Trimmed Flight Condition 65 9 Determination of Drag in 67 LE etc ee dna T 67 92 Basie Drag COCON Gs RU RAI EDEN ERN UEM NUMINE NU RENE NIMM 73 9 3 Skin Friction Drag Coefficient
107. ne in 30 minutes or less Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 5 of 136 Great OWL Publishing Vortex Lattice Methods Why Should You Care By Mike Garton Some of the latest glider designs are advertised as having computer optimized wings For instance ads for the Saphire Psyko Laser and Edge all list it as a design feature NSP s ad mentions the LinAir program which uses a form of computational fluid dynamics that we aerospace engineers call vortex lattice methods or simple panel codes There is not space here to discuss how these codes work and perhaps not interest either but will briefly describe what can be done with these programs and what it means for the pilot If lose you in technical jargon just skip to the last two paragraphs A vortex lattice program takes a wing planform wing twist and angle of attack as inputs Using this information it calculates the induced velocity field surrounding the wing including the effect of tip vortices It is somewhat non intuitive but the angle of attack of a wing is not simply the angle between your root chord and your tailboom The wing induces some vertical components of velocity that change the effective angle of attack Generally the induced angle is smaller at the root of the wing and larger at the wing tips A tip vortex will add a downward component to the air above the wing tip This causes the effective angle o
108. ned for the surfaces to be used Either method or a combination thereof is very handy if you modify the geometry as they will instantly update the skin friction drag coefficient However the CDf method is handier when you are estimating the skin friction drag of a new design If you choose to use the built in function CD you should follow these steps to properly prepare the formulation see Section 9 11 for an example setup STEP 1 Specify wetted area Use the math object Swet for this purpose The formula for Swet can be as simple as a number if you know the value to an algebraic representation using functions such as SA surfl surf2 or Swet surfl surf2 which computes the total and wetted area of the selected surfaces surfl1 surf2 and so on respectively At computation time the value of Swet is used internally with Equation 4 STEP 2 Specify skin friction coefficients for each surface You can do this in two ways You can estimate a skin friction drag coefficient using your preferred method and enter for each surface Or you can use SURFACES own internal estimation based on a laminar to turbulent boundary layer transition points that you provide The latter method is probably far easier but a numerical example of how SURFACES estimates this is presented later in this section to help clarify the method Since SURFACES models are made from infinitely thin surface panels the program estimates
109. ng the Y axis Vector Approximating shear forces is simple just apply Equation 11 N V 11 i j 6 4 2 Approximation for Moment about X axis Along the Y axis Vector The approximation for the moments is implemented as follows The moment at N 1 is due to the force Fzy acting at a distance yy yn 1 Similarly the moment at 2 is due to the force acting at a distance yy Yn 2 and the force acting at a distance Yn 2 Writing this in a general form leads to Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 58 of 136 Great OWL Publishing Engineering Software M 4 TIC Pao Ena na 7 xi Fac 7 EXON j itl 12 6 4 3 Approximation for Torsion About the Y axis Vector The approximation for the torsion is implemented as follows The torsion at N 1 is due to the force Fy acting at an offset distance of xy Xpn where x denotes the x value of the projection point Similarly the moment at point N 1 is due to the force Fz acting at a distance xy Xpn and the force Fz 4 acting at a distance Xn 1 Xpn 1 Writing this in a general form leads to ei F A b X i E Xn Foy xy X pN 13 Example A lifting surface is 10 ft long span and 2 ft wide chord It carries a uniform pressure load of 1 16 2 Determine the shear in the z direction moment about the x axis and torsion about the
110. ns of 10 percent thick wings tested in Langley 19 foot pressure tunnel Aspect ratio 9 ratio of root chord to tip chord 2 5 dimensions are in inches Figure 10 1 The general shape of the wind tunnel model tested per NACA TN 1422 V10 2 Results from SURFACES The comparison of the numerical to the experimental data shows a close agreement Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 133 of 136 Great OWL Publishing Engineering Software Lift Coefficient versus AOA per NACA 1422 Experimental and WLM NACA 65 210 airfoil WING 2 Dihedral 3 Washout 2 WING 3 Dihedral 3 Washout 0 Experimental WING 2 Experimental WING 3 3D Lift Coefficient CL 2 2 B Angle of Attack degrees Figure 10 2 Match for the lift curve for the twisted and untwisted wings Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 134 of 136 Great OWL Publishing Engineering Software Cm versus CL per NACA TN 1422 Experimental and WLM 65 210 airfoils 0 07 VLM WING 2 Dihedral 3 Washout 2 0 08 Experimental WING 2 0 09 Pitching Moment Coefficient 5 5 0 10 0 50 0 30 0 10 010 030 050 070 090 110 Lift Coefficient CL Figure 10 3 Match for the pitching moment for the twisted wing Note the deviation at higher values of the lift coefficient which is ca
111. nwise panels on each wing total of 384 panels Ci 2 776 rad 3 152 rad The following results where obtained from SURFACES for 16 chordwise by 36 spanwise panels each wing total of 1296 panels Cig 2 767 rad 3 139 Document Title Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 110 of 136 Great OWL Publishing Engineering Software Validation 4 Bertin Smith 2 D Wing V4 1 Model Calculations for a highly swept back high aspect ratio wing is provided in the text Aerodynamics for Engineers by Bertin and Smith This wing has detailed calculations shown in Example 6 2 page 198 in the text The model in the text was recreated using SURFACES Additionally a comparison to another VLM code Tornado is made A LY NA NON NON 10 ftis at 0 00 Figure 4 1 The Bertin Smith swept back wing V4 2 Expected Result Is obtained from the book Aerodynamics for Engineers by Bertin and Smith The data is obtained from the calculations on page 202 but the resulting lift curve slope is Cla 0 05992 3 433 rad Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 111 of 136 Great OWL Publishing Engineering Software V4 3 Results from SURFACES The following results where obtained from SURFACES for 1 chordwise by 4 spanwise panels on each wing total of 8 panels
112. o estimate transition location however often drag analysis in SURFACES involves estimating the impact of 2596 or 5096 See Equation 3 11 in Reference 8 See Equation 6 53 in Reference 8 See Equation 12 28 in Reference 4 12 See Section 6 8 pages 162 164 in Reference 8 Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 79 of 136 Great OWL Publishi Engineering Software transition on the total airplane drag In other words the designer is attempting to answer a question like What is the benefit of achieving a partial laminar boundary layer on my design The answer may help direct the designer towards an appropriate airfoil 0 625 0 375 COE Fa 12 C C Re Then the skin friction coefficient is determined as follows 0 8 0 074 X X ec ez 13 Where C Reference length e g wing chord Xo Location of the fictitious turbulent boundary layer X Location of where laminar boundary layer becomes turbulent Turbulent Flow Skin Friction Coefficient Compressible Note that surface roughness affects Ciuro but this is typically accounted for through the use of a so called cutoff Reynolds Number If the actual Reynolds Number exceed the cutoff Reynolds Number it is used instead For more information on the topic the reader is directed towards texts such as Reference 4 C 1 053 sa E 14 Where C Reference length k Ski
113. om the VLM Console Determine the Horizontal and Vertical Tail Volumes Although not necessary for analysis it is a good idea to tail volume and compare to other airplanes Copy and paste the analysis report into the remark Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 11 of 136 Great OWL Publishing Select Edit 5Model Properties from the VLM Console properties Try to fill in as many properties as possible All entries marked with an asterisk are required for any Vortex Lattice analyses Once your model runs you can initiate a large number of specific investigations Basic Investigations Task Description Remark J e 9 Select Tools gt Determine Neutral Point from the VLM Console Determine Neutral Point This is a necessary step as it will determine your aft CG limit Always consult the CG location of your design with a qualified Aerospace Engineer The CG is typically at least 8 10 MAC forward of the neutral point Select Tools gt Determine Neutral Point from the VLM Console This tool is helpful to determine required surface Trim Analysis deflections for given weights airspeed and yaw angles Note that before you can use this tool you must define control surfaces using edge deflections and proper references under the Edit Surface dialogbox Edge Deflections and Reference tabs Select the Pan
114. ons complicate skin friction drag analysis This image is discussed in greater detail later Atr_ upper Xtr lower aminar boundary layer bulent upper Atr lower Chod Xtr upper lower Figure 9 3 2 The laminar to turbulent transition points move around depending on angle of attack airfoil shape and surface roughness SURFACES employs a standard presentation of skin friction for instance as presented in Reference 1 The skin friction drag coefficient is defined as follows Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 76 of 136 Great OWL Publishing 2D 2 5 ref S uy Where D Skin friction drag force in Ib UK system or N SI system Air density typically in slugs ft or kg m V Far field airspeed typically in ft s or m s Swet Wetted area typically in ft or m Cp Skin friction drag coefficient dimensionless C Skin friction coefficient dimensionless See Equation 15 for more details If known the user can enter an expression for the skin friction drag coefficient or use a combination of built in functions in the two following ways 1 Use any of the built in functions that extract surface areas or wetted area of surfaces in your own formulation 2 Use the built in function directly but this requires skin friction coefficients to be defi
115. projection point to the force point denoted by Q This vector is given by Equation 8 Xp X Q iyk y 8 Zp Zp Then calculate the disrete moment about the projection point from i j k M FxQ F F 9 Q The moment vector M represented as My My Mz is still in the global coordinate system It can now be treated as the force in the local one i e as M M M using the same transformation as for the force vector Uy My 10 Uaz M 6 4 Determination of Shear and Moment Distribution Figure 7 shows several loads whose components have been transformed to the local coordinate system specified by A By and C Each has associated force and moment components and the parameter r which is simply the distance of the projection point from the starting point of vector A point 1 The purpose of the parameter r is to allow sorting to take place say from start towards the end of the vector A The sorted components are then used to construct shear and moment diagrams in a standard fashion Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 57 of 136 Great OWL Publishing EZ La FEE rs Cates gt Engineering o0TtW al A Y Figure 8 Creation of shear and moment diagrams from discrete forces 6 4 1 Approximation for Shear in the Z direction Alo
116. re flying If anyone wants to play with a vortex lattice program contact me and can email you directions on how to obtain a public domain program Reprinted from hitp eiss cnde iastate edu articles VortexLattice htm NOTE This article available online from the above link and is therefore assumed public in the public domain It was not written with SURFACES specifically in mind but is reprinted here as the editor of this manual considered it well written and pertinent to anyone using CFD methods Great OWL Publishing reprints it here for your convenience but assumes no responsibilities for it Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 6 of 136 Great OWL Publishing Current Status Currently the latest version of SURFACES is 2 8 10 The following changes have been made to the program since Version 2 86 or 2 8 6 REPAIR LOG m we Version 6 29 09 Selected surfaces deselected when VLM console icon on MDIForm clicked Fixed Pitch Yaw coupled surfaces e g V tail reset elevator deflection in the VWT 2 6 29 09 2 8 7 Subroutine DOC Surface ModifyDeflection not originally designed to handle Fixed coupled surfaces Revised it to handle such surfaces correctly Controllers tab on VLM console Pressing the Reset button would not change numbers 6 29 09 in the textboxes This has been changed FRED Controllers tab on VLM console Subroutine DOC_Surface_ModifyDeflection
117. re other ways to create such formulas but you will learn these at later time Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 15 of 136 Great OWL Publishing Engineering Software Trapezoidal Surface Properties Frevien Number of Panels wing span b 9 Wing area 5 45 Chordwise 8 Spanwise 18 Aspect ratio 7 2 i Taper ratio TRAST ESRERIED MAC 2 533333 Select Aurfoils Pick Tip Airfoil Figure 4 1c Creating the wing Setting panel density and picking airfoils for root and tip Note that pressing the Pick Root Airfoil or Pick Tip Airfoil buttons will open the Camber Creator form in Figure 4 1d Step 3 You must press each of the buttons in Figure 4 1c to create your airfoils If an airfoil is not recognized a flat plat is assumed You can also create your own airfoils but these are stored as text files that are called shape files They have the extension SHP You can navigate to the Surfaces Shape Files folder and double click on one such file to open it in Windows Notepad and investigate how simple they are Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 16 of 136 Great OWL Publishing Engineering Software Camber Creator Shape Files Arfols Shape Data NACA 4 Digit Series Example 4412 441 b t 5 Digit Series Example 23
118. reated 1 Point xv X Z xx H 9 02 4 16 2003 Figure 5 5 Points define the parametric curve Surfaces Pro Untitled File Edit Insert Modify Tools View Window Help amp x oo Kaan Groups Information Files Objects Oy vil a ae IY Press to Select Objects for Legend x X Z xx Status 9 05 4 15 2003 inap Figure 5 6 Selecting the parametric curve displays how uses points to define a plane VLM docx Surfaces User Manual Vortex Lattice Module Page 48 of 136 Great OWL Publishing Engineering Software Edit Parametric Curve 1 Curve Title 0 Curve Vector Parametric Point List B spline End Points Curve Generation Start point 1 Fl art pair He Number of points 20 End paint 2 Fick Must be selected for parametric and point list Appearance curves for proper alignment in space MEN Alignment paint 3 Pick gt gt au Parametic Curve Parametric Functions Start E In Endt Use Existing Shape File Pit ttt f Streteh in Stretchin Stretch r x y at 0 is D 0 x y at t 1 is 1 0 Delete Preview ok Cancel Figure 5 7 Creating a parametric curve STEP 8 Double click on point C and change its
119. results in a mixed boundary layer each with own skin friction coefficient The nature of this behavior on airfoils is shown in Figure 9 3 2 Airfoils have two transition points one on the upper and one on the lower surface Each transition point moves forward or aft as shown in the figure when the angle of attack of the airfoil changes Naturally IMPORTANT Note that in this text the skin friction coefficient is denoted by C and skin friction drag coefficient by Cp These are interchangeable is determined for laminar or turbulent boundary layer and is related to the wetted area Swe The coefficient Cp is the equivalent skin friction drag coefficient for the entire airplane and is related to the reference area Se For this reason the distinction of the two terms must be kept in mind The two are related as shown in Equation 4 the travel is entirely dependent on the geometry and surface roughness of the airfoil Note that it would be more correct to talk about a transition region The line indicates a location beyond which transition has been completed Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 75 of 136 Great OWL Publishing Engineering Software Xo Xe Start of fictitious turbulent BL Transition 4 Laminar Turbulent lt Chod Figure 9 3 1 Mixed Boundary Layer conditi
120. rface As a consequence the total weight of the wings turns out to be 293 3 Ibs the HT weighs 58 2 lbs and the VT weighs 48 5 Ibs Clearly this adds up to 400 Ibs You can check weight by selecting surfaces and pressing the F6 button or by selecting Tools gt Properties of Selected Surfaces The results will be displayed on the Status bar on the bottom of the main window STEP 8 Make sure the CG is visible Select Tools Options Check the Show CG Neutral Point Aerodynamic Center checkbox and press the OK button see Figure 4 10 Options General Colors Entities Numerical Formats Report windows Calculations Visibility Switches Show point IDs Show vector IDs Iv Show coordinate axes How Hou Show legend W Show CG Neutral Paint Aerodynamic Center Dynamic oom t Only show box indicating extremes of model Rotation speed 2 f Show model as wireframe t Show rendered model Panel Visibility Methodology f Comer point sorting C Back panel removal Fath to the Adobe Reader Browse Cancel Figure 4 10 Confirm the CG checkbox is marked so you can see the CG in the workspace Step 8 Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 28 of 136 Great OWL Publishing _ Surfaces Pro Untitled File Edit Insert Modify Tools View Window Help DERAS BAX 410 Groups Information Files Objects
121. right edge down left Reference values Value at cume Value at curve 2 Reference Weight Tuning Tuning factor Skin Friction Drag f Use entered skin friction coethicient Apply Cancel Figure 9 10 5 A quick selection of all surfaces Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 91 of 136 Great OWL Publishing File Edit Insert Modify Tools View Window Help Decs BAK ona E D RRS 8 m Groups Information Files Objects E Chye objects wath tormata del Fress Select Objects for Legend There are 9 pu 3 irr vectors here 8 28 AM 7 22 2008 Snap Grid Version 2 8 1 Status Figure 9 10 6 1 2 curves have been selected for all surfaces be included This opens the form shown in Figure 9 10 7 As said earlier we are assuming here that the airfoils can sustain 50 laminar flow on the upper and lower surfaces This case is often checked by aircraft designers and is especially prepared here for quick entry You can simply press the buttons labeled 0 25 and 50 to set up these special cases This assumes a constant transition i e independent of AOA throughout the operational range which is not necessarily true but handy for quick studies is equipped with a handy tool to help you visualize your work Let s turn it
122. rtex Lattice Module Page 53 of 136 Great OWL Publishing Engineering Software Note that the three vectors form a mutually perpendicular coordinate system The determination of By is necessary as B may or may not be perpendicular to the vector A Also note that according to convention the vector A represents the X axis of the local coordinate system here denoted by the lower case letters x y z The vectors By and C correspond to the Y and Z axes respectively Finally note that the unit vectors for the local coordinate system are denoted as follows Unit vector for A lus Unit vector for hus Unit vector for lucy Ucy Ucz 6 2 Transformation of Force Vector in Coordinate System A By C The force vector F represented as Fx Fy Fz or E j E k in the global coordinate system can now be represented as a force in the local one as F F2 see Figure 4 This is accomplished with a simple transformation of the vector F onto the three vectors A By and C using the matrix notation of Equation 3 F Py F i Upy 4 Fy 3 F Ucy Fz Figure 4 Transformation of vector F Example Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 54 of 136 na Engineeri The force vector F F i F y F k 10 1 5 j 10 amp is given in a global coordinate system
123. s for this form to be filled out as shown Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 90 of 136 Great OWL Publishing Engineering Software and The the the Now Go back to the worksheet select Edit Select Surfaces press the Select All button in form that opens up and then press OK button see Figure 9 10 4 all the surfaces are selected STEP 4 STEP 5 Then select Modify Surface Properties Select the option Use Curve Al and A2 skin friction drag as shown in Figure 9 10 5 Press OK This step tells SURFACES to calculate the skin friction drag using information we have yet to enter for the A1 and A2 curves of the surfaces First lets assume the HT and VT are to be designed using laminar flow airfoils capable of sustaining 50 laminar flow Let s also assume the wing will sustain laminar flow as discussed in the example of Section 9 3 Document Select Surfaces Edit Select Surfaces Trapezoid Trapezoid Trapezoid Trapezoid 3 Trapezoid i Deselect All Ok Figure 9 10 4 A quick selection of all surfaces Change Surface Properties Change Surface Mesh Leave text blank to nat change a corresponding segment Lhardwise panels and 42 Spanwise panels B1 and Change Surface Edge Deflection EHI 2 Leading edge upinght Leading edge downileft s 2 Trailing edge up
124. t tend to neglect the contribution of the angle of yaw p this is not done here for two reasons First the user must be made aware of the impact asymmetric flight has on aircraft performance especially when designing multi engine aircraft for engine out situations Second by using SURFACES this is simply no more complicated than accounting for angle of attack So let s begin by writing a standard definition of the total drag force D LOVI S yep Cp 2 Where Cp Total drag coefficient dimensionless Stored in the variable CD D Drag force in Ib UK system or N SI system 5 Reference area typically in ft or m V Far field airspeed typically in ft s or m s p Air density typically in slugs ft or kg m Stored in the variable rho Equation 2 explicitly contains three of the variables mentioned for Equation 1 namely geometry V Dependency on a p M and Re is usually handled in the expression for drag coefficient Cp In aircraft design aerodynamicists typically regard the drag coefficient as a function of the lift coefficient C and plot the two on a graph called the drag polar A typical representation of airfoil data is shown in Figure 9 1 1 This shows a lift curve drag polar and pitching moment curves for several 2D airfoils and shows two graphs The left graph shows how the lift coefficient varies with angle of attack The right one shows how the drag coefficient varies with the lift coeffici
125. te mathematical expressions called Math Objects or Variables which are used inter changeably that allow the designer to define own parameters that may be of importance to the airplane involved This adds an incredible power to the analysis work The math objects can use information directly from the geometry of your model For instance to calculate wing area you could enter a constant or you could use a function like Saxy surf1 surf2 So if you modify your wing area for some reason the program will automatically update this value airspeed Reynolds Number and Mach Number Mathematically this is represented in the formula D f geometry D p V Re M 1 Where geometry refers to reference and wetted area M Mach Number Stored in the variable MN Re Reynolds Number Stored in the variable Re V Far field airspeed Stored in the variable vinf a Angle of attack Stored in the variable AOA In SURFACES geometry terms are stored in variables such as ARref Eref Sref and Swet Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 67 of 136 Great OWL Publishing Angle of yaw Stored in the variable Aoy o Air density Stored in the variable rho The word geometry is somewhat nebulous here but it is so on purpose the user may use geometry in own drag estimation beyond the variables cited Also while most texts on the subjec
126. tex Lattice Module Page 128 of 136 Great OWL Publishing ao eO 0 d o jd 0 7 cvR S S pensent CH NEN o cQ 0 1070 osa cH EEE 9 0 1250 DUM ee Additional comparison based on a table from the source http www aerologic com stab corr html Cian Etkin Seckel Datcom SURFACES 4 Flight Test Hage Tunnel 0 732 Angle of attack a iH Elevator deflection de 8 28 0 271 Seckel E Stability and Control of Airplane and Helicopters Academic Press 1964 Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 129 of 136 Great OWL Publishing Ennimaarinmg lt Validation 9 Comparison R 1208 V9 1 Introduction This validation compares SURFACES analysis to the swept back wing featured in the NACA report R 1208 In the report a highly swept back high aspect ratio wing compares three numerical methods to wind tunnel test results In this validation sample a similar approach will be taken and the section lift coefficients from SURFACES will be compared to the wind tunnel test results The wing planform is shown in Figure 9 1 Figure 9 1 The swept back wing wind tunnel tested per NACA R 1208 Inserted image shows the SURFACES VL model Three VL models were generated one has 16 spanwise panel per
127. them In SURFACES you should apply compressibility corrections for cases when the airspeed exceeds Mach drag change with angle of attack Compressibility drag is exclusively a pressure drag effect and numbers of the order of 0 3 to 0 5 automatically computes their effects for the user This will be talked about in greater detail shortly SURFACES provides four different methods to model Great OWL Pu E Page Numbers Page 69 of 136 50001139 Section lift coeffrcie 5 4 16 NACA 64 4 5 nm 1 LLEEZELLELITTILTIT A m 3 8 E 3 3 juaw 24 AD gt 5 E x gt 2 c o D o G 2 2 Figure 9 1 1 Drag polar for several 2D airfoils 8 0 Sectian angle of attoch eq deg 17 Comparison of the serodynamic characteriaties of some NACA alrfoils from tests In the Langley two llmensional low torbulonee pressoro Lift Curve C versus 6 gute FH Document VLM docx PSE SRERCRTASR TERR TEER EE ERE RE SE Ee N 9 a E x S N 9 Y amp Q N N N ld M T 3 JBOD ky UOKLIAS N M X 1 Lg r o jus24902 From this discussion it makes sense to define the drag coefficient as follows For instance see dis
128. tic drag leakage drag just to name a few At times it s not clear whether one is reading about aerospace or medical science With that in mind there are two points that must be emphasized A Textbook authors are prolific inventors of terms for things that either increase pressure drag or skin friction drag or a combination thereof This leaves the impression that there exist imaginary drag types that only affect certain airplane features Only airplanes with nacelles get nacelle drag only airplanes with protuberances suffer from protuberance drag and so on when in fact these features are simply changing the pressure field or modifying the boundary layer While there are probably many who consider this advantageous this can also confuse the issue The confusion does not stem from the names these specialty drags receive but a difference in definition between authors when one author creates a name for a specialty drag another author doesn t even mention B SURFACES handles this assortment of drag types in a simple manner it ignores them It only uses the three terms in Equation 3 and leaves it to the user s to define as many drag terms as desired naturally limited by computer resources only Example Variation in CDo CDf and CDi with AOA a c e z Angle of Attack Figure 9 1 3 Basic drag coefficient plotted for AOA and AOY NOTE THAT THIS APPLIES TO QUADRATIC DRAG MODEL ONLY Document Title Page
129. tle Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 102 of 136 bi Engineering Software Great OWL Pu 2 D Flat Plate Airfoil Validation 1 V1 1 Model 20 wing model was constructed to obtain 2 D pressure coefficients for A high aspect ratio AR The Cp at the center of 3 comparison to theoretical data The model has a wing span of 20 units and a chord of 1 unit The Angle of Attack is 10 at an airspeed of 10 unit sec and density of 1 mass unit length the model was obtained for 2 5 10 and 15 chord wise panel density Each of the two surfaces has 34 span wise panels Figure 1 1 High aspect ratio wing used to evaluate the 2 D Cp V1 2 Expected Result Is obtained from the book Aerodynamics Aeronautics and Flight Mechanics by Barnes W McCormick The data is obtained from Figure 3 17 on page 87 Numbers Document Page 103 of 136 2 gt x gt 2 c G XI o D o G 2 2 VLM docx Great OWL Publishing Engineering Software V1 3 Results from SURFACES CP versus Chord Station for a Flat Plate Exact Theory Cp from Surfaces N 2 B Cp from Surfaces l Cp fram Surfaces Cp fram Surfaces o 2 m m a m 0 40 0 60 Chordwise Station Figure 1 2 2 D Cp for various panel densities from SURFACES compared to exact
130. tors airfoils Usage of drag has been improved simplified and made far more user friendly but yet more powerful Function CDf CDi CD and CL were added to allow user to directly extract drag and lift 16 7 20 09 2 8 9 coefficients from the model and VL solution User can specify CDf directly for surfaces Added or specify transition location on airfoils for mixed laminar turbulent boundary layers Four new features have been added to the VLM Console These help the user to view the extent of the prescribed laminar flow on surfaces and the magnitude of skin friction drag on each surface 7 20 09 A large section on Drag Analysis has been added to VLM PDF This is Section 9 Added Document Title Page Numbers 10 7 4 09 2 8 8 VLM docx Surfaces User Manual Vortex Lattice Module Page 7 of 136 Great OWL Publishing Engineering Software Panel orientation has been made independent of orientation as the program will now reassign panel corner IDs based on a special algorithm This means that the user can 18 7 27 09 2810 use Curves 1 2 for surfaces that are no longer parallel the X axis The panels d stil have to be aligned to the X axis as this is a requirement of the VL method However the user can model circular shapes like an engine nacelle or round fuselage more easily 19 7 31 09 2810 User can press F2 to copy viewport info such as state of zoom and paste into another viewport using F3 20 7 31 09 28
131. tus Selected surfaces CL 0 2171035 CDi 1 070691E 02 Figure 11 Selecting the Force Integrator tool Once the pertinent surfaces and vectors corresponding to vectors A and B have been selected the user can press the ntegrate button as shown in Figure 12 Selecting the Results tab will display a table with analysis results Table 2 details the heading names Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 61 of 136 Great OWL Publishing Engineering Software Force al Right Wing Cuff Region Left wing Cuff Region 3 Right ing Right Wing Fuse Left wing Fuse Right ing Defining Vectors Far Plane Vector to represent 24 Vector ID 1 Vector to represent axis Vector ID 2 Column to plot Vx Help Integrate Close 2 569541 1 278572 2 096049 1 549064 1 522557 3 107112 0 762695 2 046621 2 56613 1 023186 2 325639 1 283676 2 065149 1 54416 1 504658 0 965024 Figure 12 Force Integrator tool Table 2 Heading Names Force Integrate 15 305065 16 90606 16 390606 16 90606 16 90606 17 7202 17 2202 17 2202 17 7202 17 2202 17 2202 17 7202 17 2202 17 2202 17 2202 18 53436 18 53436 ax Copy T able Copy Sel Help Integrate Close 135903 1 36127 1 35539 1 36643 1 35799 1 39788 1 40216 1 40495 1 41271 1 41476 1 42042 1 42243 1 42518 1 42712 1 42954
132. urfaces 6 0 12 0 y 0 00020x 0 01188 y 0 00016x 0 01888 Cm 2D Experiment Chi 3D Surfaces AOA degrees Figure 6 3 3 D wing model with a 23012 airfoil camber line Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 121 of 136 Great OWL Publishing Engineering Software Validation 7 F 104 Starfighter V7 1 Model A model of the Lockheed F 104 Starfighter was constructed to compare selected stability derivatives from SURFACES to that presented in the text Flight Stability and Automatic Control by Robert C Nelson The data can be found in Appendix B of the text on page 253 W 16300 lbs o 196 1 ft 9 5 ft M 0 257 at S L CG at 7 MAC Figure 7 1 3 D Vortex Lattice model of the F 104 Starfighter V7 2 Results from SURFACES Summary Parameter Symbol Source SURFACES Difference Dragcuveslpe n Cw _ 045 0667 45856 Moment slope CMya Side force slope CFyf All derivatives are per radian At M 0 257 1 Flight Stability and Automatic Control by Robert C Nelson 18 Note that V 0 257 x 1116 ft s 286 8 ft s Therefore Lift is 1 0 002378 286 82 196 1 0 735 14097 Ibf This is the same lift SURFACES generated to get the given lift coefficient 9 Using the surface integration method This is highly dependent on drag model Cp 0 0009474 a 0 0004737 180 x which at a
133. used by viscous effects Section Lift Coefficient per NACA TN 1422 VLM WING 2 Dihedral 3 Washout 2 Section Lift Coefficient Cl Experiment NACA TN 1422 65 210 with 2 washout 0 4 0 5 0 6 Halfspan Station 2y b Figure 10 4 Lift distribution at stall for the twisted wing Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 135 of 136 Great OWL Publishing Engineering Software Section Lift Coefficient per NACA TN 1422 VLM WING 3 Dihedral 3 Washout 0 Section Lift Coefficient Cl Experiment NACA TN 1422 65 210 with 0 washout 0 4 0 5 0 6 Halfspan Station 2y b Figure 10 5 Lift distribution at stall for the untwisted wing Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 136 of 136
134. ution of wetted area on the overall airplane drag Note 5 The effect of compressibility is accounted for by modifying Cpo and Cp using corrections that pertain to pressure drag only and using a correction only applicable to skin friction for Note 6 SURFACES has internal functions that calculate most of these coefficients for the user The user must supply Cp only but the other coefficients can be calculated internally if the user so wishes All can be displayed as math objects using the i IMPORTANT When you start a new project in functions for skin friction CDi for induced drag CD for total drag calculated per Equation 3 and CL for lift coefficient This is already set up in this fashion in the standard Math Object template amp So when a new project is created the formulation is already correctly set up by default Note that if these built in functions are used a Cp and C of O will be reported when there is no Vortex Lattice solution in memory or if the user resets the solution clears it out of memory Also a CDf of O will be reported until skin friction coefficient has been SURFACES by selecting File gt New and then Surfaces Worksheet the program will load a standard list of math objects so that you won t have to create commonly used variables each time The program loads this from template file called OBJECTTEMPLATE INI which is stored in the SURFACES TEMP folder If you
135. vely constant along the span This means the whole wing is flying at the same effective angle of attack A constant angle of attack is good because no part of the wing will stall early and the wing can achieve a high average lift coefficient When any section of the wing stalls it will usually propagate sideways and stall the entire wing As an example a straight taper wing with its uneven effective angle of attack will stall at an average lift coefficient roughly 2096 lower than the computer refined four taper wing am assuming that the designer of the four taper wing used the vortex lattice code properly So what might a pilot notice in flight when flying one of these planes refined with a vortex lattice code Most pilots won t notice the differences After trimming the plane an expert pilot should notice that the launch is steeper because the wing can pull a higher lift coefficient before stalling The sink rate and glide ratio should be a tweak better as well We are only talking a couple percent decrease in drag over the eye balled planforms but every little bit helps The plane should be able to fly slower than other planes with the same airfoil and wing loading again because of the higher available lift coefficient Will the computer refined planes always win In general no In most weather conditions a thermal duration contest is still 9096 pilot 1096 airplane The contest placings usually sort the pilots by skill regardless of what they a
136. w 30 ite rations before a Lift tolerance 1 solution will be declared as unachievable If solution is found the resulting lift will be 700 1 Ib and the moment 0 1 ft lb As a rule of thumb acceptable accuracy is provided by specifying 1 of the weight Here the accuracy is closer to 0 14 Start Over Document Title Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 38 of 136 Great OWL Publishing Engineering Software A VLM Trimmed Level Flight SIMPLE DEMO SRF General Progress Table Progress Plot Summary Store Solution Y ou can store the final trimmed solution for further analysis If you have multiple airspeeds multiple solution files will be generated STEP 22e Ensure the selection shown Press the Next gt gt button Note that solution files can be created and saved using the file name entered as a seed Start Over lt lt Previou VEM Trimmed Level Flight SIMPLE DEMO SRF General Progress Table Progress Plot Summary Finish Now we are ready to trim Press the Finish button to begin the operation Depending on your inputs the operation can take some time to complete You can follow the progress of individual airspeed trim on the Progress T able tab and graphically on the Progress Plot tab The Summary tab shows the progress of multiple airspeeds Pressing Finish will replace old values of AO4 ADY da de dr Vcas wref wit
137. wetted area by determining the surface area and then doubles the value to get wetted area Table 9 3 1 shows some examples of possible user entries for If a function such as Swet surfl surf2 iS used to estimate the wetted area the user can multiply it by a factor to account for surface curvature for instance as shown Example 3 in Table 9 3 1 Table 9 3 1 Example user entries for CDf A constant value which might be the result of a 0 05 prior drag breakdown analysis for an single engine piston aircraft itis possible to enter this for multiple surfaces at a time Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 77 of 136 Great OWL Publishi Engineering Software This user accounted for changes in skin friction with Reynolds Number using this formula It returns 0 0208 for Re 3 000 000 and 0 01968 for Re 8 000 000 2 U Ua25 0 DU0L RG Q Z22 This user is adding the contribution of the additional wetted area of winglets surfaces 5 3 0 025 0 000018 1 05 Swet 5 6 and 6 multiplying the result by a 1 05 to correct for their curvature For winglets with 50 ft additional area this formula returns 0 0260 Here the user is accounting for partial laminar flow in this estimation The expression assumes the Sref will be divided out leaving Swet remaining when incorporated in standard drag 0 01 C _lam Plam Cf_turb 100 calculations The var
138. x Stability Derivatives Transfer Options Target Parameters Change under Project Properties Angle of Attack AOA 3 344516 in degrees Angle of Yaw AD Y 0 in degrees Airspeed Vinf 68 8 length sec Mach Number MN 0 1512153285137 714 Altitude Href Compressibility Model None ti J Roll rate in sec Pitch rate Q D in sec Yaw rate fo in sec Stability Derivatives to Determine Angle Of Y aw related derivatives OY Roll related derivatives Iv Pitch related derivatives 0 Yaw related derivatives Roll control derivatives da Pitch control derivatives de Yaw control derivatives dr High lift derivatives df Speed related derivatives U NOTE Results are in the BODY Coordinate System Analyze Figure 4 21 Preparing to determine stability derivatives Step 23 VLM Stability Derivatives SIMPLE DEMO SRF Parameters Result Matrix Stability Derivatives Transfer Options Stability Derivatives Perdegree 3 3445 0 0583728 0 0000 0 0000000 168 8 168 8 0 002378 0 002378 0 oll rate 0 0 0 0 16175 0 16175 0 45857 0 45857 0 08875 5 08503 0 01105 0 01105 0 01105 0 01105 0 00424 0 24270 0 00750 0 42985 0 00009 0 00488 0 08882 5 08902 Cla 0 00000 0 00013 ma 0 03656 2 09466 na 0 00003 0 00187 cg 0 24999 0 24999 0 66192 0 66192 0 00000 0 00012 0 00668 0 38264 FZ variation with
139. xt Ftz i i 1 gridCntrl Col i gridCntrl Text Ft Panel moment in global coordinate system i i 1 gridCntrl Col i gridCntrl Text i i 1 gridCntrl Col i gridCntrl Text Mty i i 1 gridCntrl Col i gridCntrl Text Mtz i i 1 gridCntrl Col i gridCntrl Text Panel force in local coordinate system i i 1 gridCntrl Col i gridCntrl Text Vx i i 1 gridCntrl Col i gridCntrl Text Vy i i 1 gridCntrl Col i gridCntrl Text Vz Panel moment in local coordinate system i i 1 gridCntrl Col i gridCntrl Text Tx i i 1 gridCntrl Col i gridCntrl Text Ty i i 1 gridCntrl Col i gridCntrl Text Tz Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 63 of 136 Great OWL Publishing 7 Using the Virtual Wind Tunnel The Virtual Wind Tunnel VWT allows you to analyze you model exactly as if you were to run it in a real wind tunnel You can vary several parameters from an initial value to a final value in prescribed steps For instance you can perform an alpha or a beta sweep exactly as you would do it in a real tunnel but without the hassle Before you use the tunnel you must understand its limitations Any good airplane design operates most of its lifetime at airsoeeds at which the airflow is relatively smooth and at a low angles of attack AOA and yaw AOY The lifting
140. ys uses the Prandtl Glauert correction when Karman Tsien or Laitone are selected for Cpi Frankl Voishel is always used to correct 9 8 How SURFACES Calculates Do Df Di and D Once SURFACES has determined the constituent drag coefficients is computes the basic drag skin friction drag induced drag and total drag forces using the following formulation Basic Drag Force D ipV S Cp 18 Skin Friction Drag Force D lpV 19 Induced Drag Force D 2ipV S s Cp 20 Total Drag Force D lpV S us 21 9 9 Limitations of Drag Estimation Methodologies Figure 9 9 1 shows what a true drag polar might look like for a real airplane This data might have been collected in flight or wind tunnel testing The figure also shows a simulated drag polar using a standard second order polynomial representation also known CL squared method This is represented by an equation such as Cp Coo CL Document Title Page Numbers VLM docx Surfaces User Manual Vortex Lattice Module Page 87 of 136 Great OWL Publishing Cp Cp Coo Cor C C CDmin c AR e an N F True drag polar from flight testing or wind tunnel testing l l Simulated drag polar e g from k C Ci comin methodology Pd N N ta CL C CDmin Range of reasonable Cp predictions Figure 9 9 1 Typical drag polar The user should realiz

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