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Design of UAV Systems. c 2002 LM Corporation . Air vehicle geometry. Lesson objective - to discuss Air vehicle geometry including … Fundamentals Design drivers Geometry models. Expectations - You will understand how to define an air vehicle without having to draw it. 20-1.

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  1. Design of UAV Systems c 2002 LM Corporation Air vehicle geometry • Lesson objective - to discuss • Air vehicle geometry • including … • Fundamentals • Design drivers • Geometry models Expectations - You will understand how to define an air vehicle without having to draw it 20-1

  2. Design of UAV Systems c 2002 LM Corporation Air vehicle geometry Editorial comment • Not drawing a configuration is generally a bad idea • - Air vehicles are highly integrated machines and good geometry is what makes them work • - Drawings bring multi-discipline teams together • But drawing and analyzing airplanes takes time • - Up front trade studies need to address a wide range of concepts and time is always at a premium • And sometimes design teams (especially designers) fall in love with their concepts • - Alternate concepts don’t get much attention • Therefore we will develop simple analytical geometry models for initial trade studies and concept screening • - Physically capture the important design variables but minimize the time and effort required to assess them • - Use it to develop the “best” configuration concept • - Then we will draw the airplane 20-2

  3. Design of UAV Systems c 2002 LM Corporation Air vehicle geometry Notation and constraints • In this section, some notation could be confusing • - For geometry, L and D represent length and diameter. • In previous sections, they represented lift and drag • The differences should be obvious but be alert • L/D (Length/Diameter) vs. Lift/Drag could also be confusing • - Both are primary parametrics, one for geometry, the other for aerodynamics • D(geom) typically is an equivalent, not a true diameter • It is calculated from cross sectional area (Ac) where • D = Deq = 2sqrt(Ac/) • Acceptable values of Lth/Deq vary with speed range and application • For low subsonic speeds, fuselage Lth/Deq  7, nacelles and pods Lth/Deq  5 • For higher speeds, higher values are required 20-2a

  4. Design of UAV Systems c 2002 LM Corporation Air vehicle geometry Fundamentals • Air vehicle geometry is not just about aerodynamics, structures and signature - it is also about packaging • Efficient arrangement of pieces, parts and systems to maximize performance and minimize penalties (cost, weight, drag, etc.) • Surface (wetted) area - the most powerful design driver • For any given volume nothing has less wetted area (albeit at high drag) than a sphere where • V(sphere) = (4/3)**R^3 and Swet(sphere) = 4**R^2 • Veff(max theoretical)* = V/Swet = R/3 • Cylinders are reasonably efficient but not at high fineness ratios. “Flattened” cylinders are inefficient or *Note - Volumetric efficiency(Veff) increases with size regardless of shape 20-3

  5. Design of UAV Systems End View Side View D L c 2002 LM Corporation Air vehicle geometry Parametric cylinder comparison • For purposes of comparison we assume cylinders with hemispherical end domes so that • Vol = (4/3)(D/2)^3 + [(D/2)^2](L-D) • = (/12)(3L/D-1)D^3 = 100 cuft • Swet = 4(D/2)^2 + D(L-D) = (L/D)D^2 • Sphere (Lth/D = 1) D = 5.76 ft; Swet = 104.2 sqft • Cylinder (Lth/D = 4) D = 3.26 ft; Swet = 133.7 sqft • Cylinder (Lth/D = 8) D = 2.55 ft; Swet = 163.6 sqft • Cylinder (Lth/D = 16) D = 2.01 ft; Swet = 203.2 sqft or • Study this carefully – it is a generalized cylindrical tank geometry model. • The required inputs are Volume or D and Lth/Deq (or fineness ratio) • Later we will develop similar models for fuselages, wings and tails 20-4

  6. Design of UAV Systems c 2002 LM Corporation Air vehicle geometry Overall geometry drivers • Speed and L/D drive what an air vehicle looks like • - Very high speeds require high fineness ratio while low speed vehicles can be significantly “blunter” • - (L/D)max establishes the allowable span (b) and Swet • Aerodynamic “rules” focus on wings and tails • - E.g. maximize span (b) to minimize induced drag • Fuselage rules are subjective with few parametrics • - Minimize Swet, keep forward and aft facing slopes < 5 -15 Provide optimum “moment arm” for control surfaces • Length-to-span ratios range from 0.5 to 2.5 • - Slow vehicles have low Lth/b Raw data sources - Roskam and Janes All the World’s Aircraft 20-5

  7. Design of UAV Systems c 2002 LM Corporation Air vehicle geometry Fuselage and pods • For minimum drag, we want to minimize wetted area and select shapes that match the design speed regime • - Subsonic - ogive or elliptical forebodies with tapered aftbodies (See RayAD 8.2) or shapes based on symmetrical NACA-4 Digit series • - Transonic - Sears-Haack bodies of revolution (See RayAD Fig 8.3) • - Supersonic - Modified Sears-Haack bodies per RayAD Eq. 12.46 • For minimum weight, minimize wetted area and use simple geometry and “load paths” 20-6

  8. Design of UAV Systems Fuselage cross sectional area 2.5 ppcf 5 ppcf 100 70 Nominal internal area (sqft) 40 10 10 40 70 100 Nominal external area (sqft) c 2002 LM Corporation Air vehicle geometry Payload volume • Varies widely with application • - People + baggage ≈ 5 lbm/ft^3 (ppcf) • - Typical cargo ≈ 10 ppcf • - Typical cargo area / fuselage cross section ≈ 0.67 • UAV payloads vary with type • - Density typically  25 ppcf (as is almost everything else!) 10 ppcf Raw data sources - Janes All the World’s Aircraft 20-7

  9. Design of UAV Systems c 2002 LM Corporation Air vehicle geometry Wings and tails • During pre-concept design, the most critical design issues are area and span • - Sweep, thickness and taper are important but are less critical • - See RayAD 4.3 (Wing Geometry) • Wing design drivers • - Wing area establishes wing loading (W0/Sref) • - Slow flight or high flight (subsonic) means low W0/Sref • - The other parameters drive weight and drag • - Thin wings have lower profile drag, but higher weight • - Induced drag is driven by span, not aspect ratio • Di = (Cl^2)*q*S/(*e*AR) = (Cl^2)*q/(*e*b^2) • Horizontal and vertical tail geometry is another consideration • - For pre-concept design, we only need to know tail type (conventional, “V”or tailless) and area Parametrics provide inputs for initial sizing 20-8

  10. Design of UAV Systems c 2002 LM Corporation Air vehicle geometry Wing parametrics Reasonable tip t/c upper limit = 13% (RosAD.2,pp 156) (a) (b) (d) (c) Raw data sources - Roskam, Janes All the World’s Aircraft and unbublished sources 20-9

  11. Design of UAV Systems Sht/Sref Svt/Sref Single engine - prop 0.20 0.14 Multi engine -prop 0.26 0.14 0.24 0.16 Business Jet Regional Turbprop 0.25 0.19 Jet Transport 0.29 0.17 Military Trainer 0.23 0.13 Fighter 0.25 0.13 Average 0.246 0.151 c 2002 LM Corporation Air vehicle geometry Wing and tail parametrics See RayAD Fig’s 4.20 for Le vs. Mmax and 4.24 for wing taper ratio () vs. .25c Le (degrees) (a) (b) Raw data sources - Roskam, Janes All the World’s Aircraft and unbublished sources 20-10

  12. Design of UAV Systems c 2002 LM Corporation Air vehicle geometry Geometry models – why? From Chart 20-2 • Drawing and analyzing airplanes takes time • - Up front trade studies need to address a wide range of concepts and time is always at a premium • And sometimes design teams (especially designers) fall in love with their concepts • - Alternate concepts don’t get much attention • Therefore we will develop simple analytical geometry models for initial trade studies and concept screening • - Physically capture the important design variables but minimize the time and effort required to assess them • - Use them to develop the “best” configuration concept • - Then draw the airplane and analyze it to confirm the geometry model estimates 20-11

  13. Design of UAV Systems c 2002 LM Corporation Air vehicle geometry Analytical geometry model • Objective - to capture key pre-concept design variables (See RayAD 7.8-7.10) • 1. Independent variables • - Wing reference area (Sref) • - Wing span (b) or aspect ratio (AR) • - Wing taper ratio () • - Wing thickness ratio (t/c) • - Fuselage length (L,Lf or Lth) and diameter (D,Df or Deq) • - Horizontal tail exposed area ratio (Kht) • - Vertical tail exposed area ratio (Kvt) • - Engine length (Leng) and diameter (Deng) • 2. Dependent variables • - Total and component and wetted areas (Swet-wing, fuse, ht, vt) • - Component volumes (V-wing,fuse) We will do this without making a configuration drawing 20-12

  14. Design of UAV Systems L L1 L2 D c 2002 LM Corporation Air vehicle geometry Fuselage model • Geometry model – Similar to cylindrical tank models except we use elliptical fore and aft bodies • V-fuse = (π/4)*[(L/D)*D^3]*[1-(k1+k2)/3] (20.1) • Swet-fuse = [(π/2)*D^2]*{1+(L/D)*[k1*(fe1-2)+ k2*(fe2-2)+2]} • Where (20.2) • k1 = L1/L, fe1 = arcsin(1)/ 1, 1 = sqrt(1-(D/L)/(2*K1))^2) • k2 = L2/L, fe2 = arcsin(2)/ 2, 2 = sqrt(1-(D/L)/(2*K2))^2) • Note - arcsin() is expressed in radians 20-13

  15. Design of UAV Systems 2.29 ft 2.29  4.58 9.16 c 2002 LM Corporation Air vehicle geometry Example - TBProp • Calculate Vfuse and Swet for example TBProp UAV • - We assume payload goes in a constant area payload section and previously caluclated required volume = 26.55 cuft (720 lbm at 27.1 lbm/cuft). We assume a cargo section packing efficiency (Pf) of 70% (30% not useable) • - Center section volume required, therefore, is 37.7 cuft • - We assume a minimum center section Lth/Diam = 4 and calculate diameter (Dcyl) of the cylindrical section • Vcyl = (/4)*(Lcyl/Dcyl)*Dcyl^3 or Dcyl = 2.29 ft • - We assume the fuselage forebody transitions to maximum diameter over a length of one diameter and that the aftbody transitions in 2 fuselage diameters or Lth = 16.1 ft 20-14

  16. Design of UAV Systems 2.36 ft 2.36  4.72 9.43 c 2002 LM Corporation Air vehicle geometry Example – cont’d • From the resulting dimensions, we calculate: • k1 = 1/7 = 0.143, k2 = 2/7 = 0.286 • 1 = sqrt(1-(0.143/(2*0.143))^2) = 0.866 • fe1 = arcsin(0.866)/0.866 = 1.209 • 2 = sqrt(1-(0.143/(2*0.286))^2) = 0.968 • fe2 = arcsin(0.968)/0.968 = 1.361 • Swet = ((π/2)*2.29^2)*(1+(0.143)*(0.143*(1.209-2) + • 0.286*(1.361-2)+2) = 106.3 ft^2 • Vol = (π/4)*[(7)*D^3]*[1-(.143+.286)/3] = 56.5 cuft • Of the total fuselage volume available of 39.7 cuft • - 26. 6 cuft is allocated to payload, leaving 13.1 cuft available for fuel and systems 20-15

  17. Design of UAV Systems Dnac Multi-engine prop Lnac D Top L Front • Combined Swet  fuselage Swet + nengKswetnacelle Swet • Note - 0.0 < Kswet < 1.0 • - Dnac  1.25Deng • - neng = Number of engines (20.3) Single engine prop Lnac Dnac D Side Front L c 2002 LM Corporation Air vehicle geometry Fuselage/nacelle model Combined Swet fuselage Swet+Kswet nacelle Swet (20.4) 20-16

  18. Design of UAV Systems c 2002 LM Corporation Air vehicle geometry Example – nacelle (prop) • We estimate TBProp nacelle diameter from engine size required using uninstalled parametric engine weight = 100.7 lbm (chart 19-27) and density = 22 pcf • - Engine volume = Wprop/density = 100.7/22 = 4.58 cuft and nominal Leng/Deng = 2.5. Therefore, • Deng = [4*Vol/(*Lth/Deng)]^1/3 ≈ 1.33 • - Dnac, therefore, ≈ 1.33*1.25 = 1.66 ft • We assume a minimum Lth/Dia = 5 for the pod mounted nacelle (Lth = 8.29 ft), K1 = .2 and K2 = .4 • - L1 and L2 are estimated at 1.66 and 3.32 ft and … • Swet-nac = 38.6 sqft • We also assume that nacelle volume is allocated entirely to the propulsion subsystem • - No other systems or fuel will be accommodated within 20-17

  19. Design of UAV Systems Lnac Dnac D D Top Front L Lnac Dnac Side Front c 2002 LM Corporation Air vehicle geometry Fuselage/nacelle model Multi-engine jet • Combined Swet fuselage Swet+nengKswetDnacLnac • Note - 0.0 < Kswet < 1.0 • - Dnac  1.25Deng • - neng = Number of engines (20.5) Single engine jet Kswet0.5 L Combined Swet fuselage Swet+nengKswetDnacLnac (20.6) 20-18

  20. Design of UAV Systems Top Front Deng D Dnac L Front L1 L2 w Top h L c 2002 LM Corporation Air vehicle geometry Fuselage/nacelle - cont’d Integrated jet Combined area fuselage area + 5*Aeng Note - Aeng = Engine area at front face (20.7) Non-circular cross section Swet-fuse = [(π/2)*De^2]*{1+(L/De)*[k1*(fe1-2)+k2*(fe2-2)+2]} *sqrt[h/w+w/h]/sqrt(2) (20.8) De = sqrt(wh) where 20-19

  21. Design of UAV Systems c 2002 LM Corporation Air vehicle geometry Example – nacelle (jet) • Jet engine nacelle diameters are also estimated from engine size required but use engine airflow (WdotA) to calculate diameter using Raymer’s engine size parametric (chart 18-18) • Deng(ft) = WdotA/26 • Nacelle Lnac/Dnac is assumed to equal engine Leng/Deng • Leng/Deng is determined parametrically from BPR • See the lower right hand plot in chart 18-17 • Jet engine nacelle volume is also assumed to be allocated entirely to the propulsion subsystem 20-19a

  22. Design of UAV Systems Front L1 w L2 Top h L c 2002 LM Corporation Air vehicle geometry Pods, stores and multi-fuselages Model as multiple ellipse-cylinders per Eqs. 20.1 and 20.2 ……with non-circular cross sections Apply Eq. 20.8 as correction factors 20-20

  23. Design of UAV Systems c 2002 LM Corporation Air vehicle geometry Data correlation • Fuselage volume and area data not widely published • - RosA&P Table 5.1 has Swet-fuse data for some general aviation (GA) aircraft and jet transports • - Data correlates reasonably well with Eq’n 20.2 (+/- 10%) • - Eq 20.1 predicts Raymer Fig 7.3 fuselage volume (+/- 10%) Fuselage wetted area Total wetted area 6000 10000 5000 8000 4000 6000 Swet-fuse from Eq 20.2 3000 Swet-fuse from Eq 20.2 4000 2000 2000 1000 0 0 0 2000 4000 6000 8000 10000 0 1000 2000 3000 4000 5000 6000 Swet – Raymer Fig 7.3 Swet - Roskam (RosAP) Table 5.1 20-21

  24. Design of UAV Systems c 2002 LM Corporation Air vehicle geometry WIngs and tails • During pre-concept design, the most critical design issues are area and span • - Sweep, thickness and taper are important but are less critical • - See RayAD 4.3 (Wing Geometry) • Wing design drivers • - Wing area establishes wing loading (W0/Sref) • - Slow flight or high flight (subsonic) means low W0/Sref • - Other parameters drive weight and drag • - Thin wings have lower profile drag, higher weight • - Induced drag is driven by span, not aspect ratio • Di = (Cl^2)*q*S/(*e*AR) = (Cl^2)*q/(*e*b^2) • Horizontal and vertical tail geometry is another consideration • - For pre-concept design, we need to know tail type and area Parametrics provide inputs for initial sizing 20-22

  25. Design of UAV Systems b/2 Kc*Cr Y1 Cr Y2 D/2 Ct c 2002 LM Corporation Air vehicle geometry Wing model Geometry model - Truncated pyramid for fuel volume - Wing exposed area for Swet Vpyrmd = A(base)hgt/3 Cr = 2*Sref/b*(1+ ) V-fuel = (4/3)*{[(Kc*Pf*(t/c)*Sref^2]/[b*(1-)*(1+ )^2]}* [(1-1*(1- ))^3 - ((1-2*(1- ))^3] (20.9) Where Kc = Tank chord ratio Pf = packing factor (≈ 0.8) 1 = 2*Y1/b  = taper ratio (Ct/Cr) 2 = 2*Y2/b SrefExp = Sref*(1-(D/b)*(2-(D/b)*(1- ))/(1+ )) (20.10) 20-23

  26. Design of UAV Systems c 2002 LM Corporation Air vehicle geometry Example • 1. Calculate SwetExp for the example TBProp UAV • - We select a nominal taper ratio ( = 0.5) and use starting values of t/c = 0.13, AR = 20 and Sref = 82.1 sqft • - Fuselage diameter is 2.29 ft (chart 20-14) • - We calculate wing basic wing geometry • - b = sqrt (Sref*AR) = 40.5 ft • - Cr = 2*Sref/[b*(1+ )] = 2*(82.1)/[40.5*(1.5)] = 2.7 ft • - Ct = *Cr = 1.35 ft • - From equation 20.10, we calculate SrefExp = 76 sqft • 2. Calculate wing fuel volume • - Assume the tank extends from centerline to 80% span (1 = Df/b = 0, 2 =0.8) and nominal packing factor (Pf = 0.8) and tank chord ratios (Kc = 0.5) • - From equation 20.10, Vwing-fuel = (2/3)*{[Kc*Pf*(t/c)*Sref^2]/[b*(1-)*(1+ )^2]}* • [(1-1*(1- ))^3 - ((1-2*(1- ))^3] = 4.5 cuft 20-24

  27. Design of UAV Systems c 2002 LM Corporation Air vehicle geometry Tails • Tails - Horizontal and vertical tail areas can be expressed as nominal fractions of Sref • Sht = Kht*Sref (20.11) • Svt = Kvt*Sref (20.12) • Where for an average air vehicle (chart 20-10) • Kht ≈ .25 • Kvt ≈ .15 • Tail wetted area ≈ 2*planform area • For V-tails - Use projected areas or • KV-tail = 2*sqrt(Kht/2^2+Kvt^2) (20.13) 20-25

  28. Design of UAV Systems c 2002 LM Corporation Air vehicle geometry Final example – areas & aero • Using typical air vehicle horizontal and vertical tail area ratios (Kht = 0.25 and Kvt = 0.15) we can estimate tail areas for the example UAV: • - Sht = 0.25(82.1) =20.5 sqft, Svt = 0.15(82.1) =12.3 sqft • We can also calculate total wetted area (fuselage and nacelle plus 2 times the exposed wing and tail areas) • Swet = 106.3+38.6+2*(75.8+20.5+15.6) = 362.6 sqft • With these areas and assuming nominal values of Cfe = 0.0035 (RayAD Table 12.3) and e = 0.8 (chart 16-6) we can make basic aero performance estimates: • b^2/Swet = 4.53, Swet/Sref = 4.42 and … • (L/D)max = 28.5 (Eq 16.8) • We can also use calculated component areas and wing-body-tail unit weights to estimate airframe weight 20-26

  29. Design of UAV Systems c 2002 LM Corporation Air vehicle geometry Example – airframe weights • Unfortunately, we have no data on UAV unit weights: • All we have are RayAD Table 15.2 unit weights for fighters, transports/bombers and general aviation where from chart 19-31, for an aircraft at our estimated wing loading (W0/Sref = 30), Waf/Sref should be  30% greater than typical general aviation aircraft • From this we can extrapolate from RayAD Table 15.2 unit weights: • Wing: UWW  1.3*2.5 = 3.25 psf • Tails: Uwht = Uwvt  1.3*2.0 = 2.6 psf • Fuselage (+nacelle)  1.3*1.4 = 1.8 psf • Using these values we can estimate from geometry: • Waf = (106.3+38.6)*1.8+75.8*3.25+32.8*2.6 = 593 lbm or Waf/Sref = 7.23 psf • This value is 80% of the previous estimate (chart 19-27) but it should be more accurate since it captures geometry features not previously included 20-27

  30. Design of UAV Systems c 2002 LM Corporation Air vehicle geometry New weights and volume • Using on the area based Waf/Sref, the bottoms up weight spreadsheet will converge to a new set of weights • Using typical densities for fuel (50 pcf) and payload and remaining systems (25 pcf), fuselage volume required for payload, fuel (less 4 cuft in the wing) and systems is: • Vr pfs = [26.55+(360/40)+350/25-4.5]/0.7 = 64.4 cuft • Which compares to total fuselage volume available of 56.5 cuft (chart 20-15) Converged TBP weights (lbm) Waf 496 Wpay 720 Weng (instl) 109 WF 360 Wlg 103Wmisc 22 Wspa 247 W0 2056 We 954 EWF = 0.46 20-28

  31. Design of UAV Systems c 2002 LM Corporation Air vehicle geometry New size and airframe weights • Since the volume available exceeds volume required, we need to resize the fuselage (and the rest of the air vehicle) to eliminate the excess • Since fuselage volume scales with the cube root of diameter (Eq 20.1), new fuselage geometry would be • Df = 2.29*cube(64.4/56.5) = 2.4 ft • At Lf/Df = 7, Lf = 2.4*7 = 16.8 • Engine size would also change • Bhp0 = 0.092*2056 lbm = 189.1 Bhp • Weng = 189.1/2.25 = 84.1 lbm, Vol eng = 84.1/22 = 3.8 cuft, Deng = [4*Vol/(*Lth/Deng)]^1/3 = 1.25 ft and Dnac = 1.25*1.25 = 1.56 ft • Which then changes the geometry model, the calculated areas and weight and aero calculations ….. And the cycle continues until weight, aero, propulsion and geometry converge 20-29

  32. Design of UAV Systems c 2002 LM Corporation Air vehicle geometry Converged weight/volume/size • After a number of iterations, the weight, volume and size calculations will converge to a consistent set of values • Volume available = Volume required/0.7 = 67.4 cuft • Df = 2.44 ft, Lf = 2.43*7 = 17 ft • Engine size = 201 Bhp, Weng(uninstalled) = 89.3 lbm • Vol eng = 4.0s cuft, Dnac = 1.6 ft • Sref = 72.9 sqft, Swet = 348 sqft, b = 38.2 ft, Swet/Sref = 4.78, b^2/Swet = 4.19; LoDmax = 27.4, Waf/Sref = 7.88 Converged TBP weights (lbm) Waf 572 Wpay 720 Weng (instl) 116 WF 382 Wlg 109Wmisc 22 Wspa 262 W0 2184 We 1160 EWF = 0.49 20-30

  33. Design of UAV Systems c 2002 LM Corporation Air vehicle geometry Parametric comparison Comparison shows the airframe weights are consistent with the parametric data but that fuel fraction continues to be low for a TBProp Global Hawk 20-31

  34. Design of UAV Systems c 2002 LM Corporation Air vehicle geometry Reference • For more information on geometry model methodology see my paper • - Preliminary Sizing Methodology for Hypersonic Vehicles, AIAA Journal of Aircraft, March 1992 20-32

  35. Design of UAV Systems c 2002 LM Corporation Air vehicle geometry Homework • Work your way through the example problems in this lesson and check/document the area, volume available, volume required, LoDmax and weight calculations. Compare your results using ASE261.Geometry.xls and identify any differences (team grade) • 2. Use spreadsheet ASE261.Geometry.xls to calculate first and second pass values for your proposed air vehicle using the example problem inputs for Cfe, e and component unit weights (individual grade) • 3. Discuss ABET issues #3 and #4 and document your conclusions (one paragraph each – team grade) 2nd week 20-33

  36. Design of UAV Systems c 2002 LM Corporation Air vehicle geometry Intermission 20-34

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