20-1 Design of UAV Systems Air vehicle geometryc 2002 LM Corporation 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

20-2 Design of UAV Systems Air vehicle geometryc 2002 LM Corporation 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

20-2a Design of UAV Systems Air vehicle geometryc 2002 LM Corporation 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

20-3 Design of UAV Systems Air vehicle geometryc 2002 LM Corporation 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

20-4 Design of UAV Systems Air vehicle geometryc 2002 LM Corporation 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 = sqft Cylinder (Lth/D = 4)D = 3.26 ft; Swet = sqft Cylinder (Lth/D = 8)D = 2.55 ft; Swet = sqft Cylinder (Lth/D = 16)D = 2.01 ft; Swet = sqft or Side View L End View D 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

- Minimize Swet, keep forward and aft facing slopes <  Provide optimum “moment arm” for control surfaces Length-to-span ratios range from 0.5 to Slow vehicles have low Lth/b 20-5 Design of UAV Systems Air vehicle geometryc 2002 LM Corporation 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 Raw data sources - Roskam and Janes All the World’s Aircraft

20-6 Design of UAV Systems Air vehicle geometryc 2002 LM Corporation 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 For minimum weight, minimize wetted area and use simple geometry and “load paths”

20-7 Design of UAV Systems Air vehicle geometryc 2002 LM Corporation 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!) 2.5 ppcf5 ppcf 10 ppcf Fuselage cross sectional area Nominal external area (sqft) Nominal internal area (sqft) Raw data sources - Janes All the World’s Aircraft

20-8 Design of UAV Systems Air vehicle geometryc 2002 LM Corporation 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

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

20-10 Design of UAV Systems Air vehicle geometryc 2002 LM Corporation Wing and tail parametrics Sht/SrefSvt/Sref Single engine - prop Multi engine -prop Business Jet Regional Turbprop Jet Transport Military Trainer Fighter Average (b) See RayAD Fig’s 4.20 for  Le vs. Mmax and 4.24 for wing taper ratio ( ) vs. .25c (a)  Le (degrees) Raw data sources - Roskam, Janes All the World’s Aircraft and unbublished sources

20-11 Design of UAV Systems Air vehicle geometryc 2002 LM Corporation Geometry models – why? 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 From Chart 20-2

20-12 Design of UAV Systems Air vehicle geometryc 2002 LM Corporation Analytical geometry model Objective - to capture key pre-concept design variables (See RayAD ) 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

20-13 Design of UAV Systems Air vehicle geometryc 2002 LM Corporation Fuselage model Geometry model – Similar to cylindrical tank models except we use elliptical fore and aft bodies L L1L2 D 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

20-14 Design of UAV Systems Air vehicle geometryc 2002 LM Corporation 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 = 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 2.29 ft

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

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

20-17 Design of UAV Systems Air vehicle geometryc 2002 LM Corporation Example – nacelle (prop) We estimate TBProp nacelle diameter from engine size required using uninstalled parametric engine weight = 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 ≈ 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

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

20-19 Design of UAV Systems Air vehicle geometryc 2002 LM Corporation Fuselage/nacelle - cont’d Combined area  fuselage area + 5*Aeng Note - Aeng = Engine area at front face (20.7) Integrated jet L D Dnac Top Front Deng 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) Non-circular cross section h Front Top w L L1 L2 where

20-19a Design of UAV Systems Air vehicle geometryc 2002 LM Corporation 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 Jet engine nacelle volume is also assumed to be allocated entirely to the propulsion subsystem

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

20-21 Design of UAV Systems Air vehicle geometryc 2002 LM Corporation 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%) Data correlation Fuselage wetted area Swet - Roskam (RosAP) Table 5.1 Total wetted area Swet – Raymer Fig 7.3 Swet-fuse from Eq 20.2

20-22 Design of UAV Systems Air vehicle geometryc 2002 LM Corporation 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

20-23 Design of UAV Systems Air vehicle geometryc 2002 LM Corporation Wing model Geometry model - Truncated pyramid for fuel volume - Wing exposed area for Swet V-fuel = (4/3)*{[(Kc*Pf*(t/c)*Sref^2]/[b*(1- )*(1+ )^2]}* [(1-  1*(1- ))^3 - ((1-  2*(1- ))^3] (20.9) WhereKc = 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) Cr Ct Y1 D/2 Y2 b/2 Kc*Cr Cr = 2*Sref/b*(1+ ) Vpyrmd = A(base)hgt/3

20-24 Design of UAV Systems Air vehicle geometryc 2002 LM Corporation 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

20-25 Design of UAV Systems Air vehicle geometryc 2002 LM Corporation 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) Tails

20-26 Design of UAV Systems Air vehicle geometryc 2002 LM Corporation 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 = *( ) = sqft With these areas and assuming nominal values of Cfe = (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

20-27 Design of UAV Systems Air vehicle geometryc 2002 LM Corporation 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 = ( )* * *2.6 = 593 lbm or Waf/Sref = 7.23 psf This value is 80% of the previous estimate (chart ) but it should be more accurate since it captures geometry features not previously included

20-28 Design of UAV Systems Air vehicle geometryc 2002 LM Corporation 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 103 Wmisc 22 Wspa 247 W We 954 EWF = 0.46

20-29 Design of UAV Systems Air vehicle geometryc 2002 LM Corporation 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 = Engine size would also change Bhp0 = 0.092*2056 lbm = 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 New size and airframe weights

20-30 Design of UAV Systems Air vehicle geometryc 2002 LM Corporation 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 weight/volume/size Converged TBP weights (lbm) Waf 572 Wpay 720 Weng (instl) 116 WF 382 Wlg 109 Wmisc 22 Wspa 262 W We 1160 EWF = 0.49

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

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

20-33 Design of UAV Systems Air vehicle geometryc 2002 LM Corporation Homework 1.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) 2 nd week

20-34 Design of UAV Systems Air vehicle geometryc 2002 LM Corporation Intermission