Basic aerodynamics relationships Design of UAV Systems Aerodynamics c 2002 LM Corporation Lesson objective - to review Basic aerodynamics relationships ….the minimum level of fidelity required for pre-concept and conceptual design assessments of subsonic UAVs Expectations - You will understand how to apply the basics and to avoid unnecessary detail 16-1

Design of UAV Systems Importance Aerodynamics c 2002 LM Corporation Importance These are the fundamental aerodynamic relationships needed to define a subsonic air vehicle for a UAV system 16-2

Design of UAV Systems Forces and geometry   V horizon L = lift Aerodynamics c 2002 LM Corporation Forces and geometry V   horizon L = lift W = weight T = Thrust  = Flight path angle Side view D = Drag cg = center of gravity le = LE sweep Cr = Root chord Ct Cmac = Mean aerodynamic chord Svt = Exposed VT area Sht = Exposed HT area Sref = Wing reference area (both sides to CL) Swexp = Exposed wing area (both sides) Swet = Total wetted area excluding inlet and nozzle area Swet-x = Wetted area of x Ai = Inlet area Anoz = Nozzle area Cr Ct 16-3

Lift (L) = ClqSref = ClqSref (16.1) Design of UAV Systems Aerodynamics c 2002 LM Corporation Aerodynamic lift Lift (L) = ClqSref = ClqSref (16.1) Cl = lift curve slope (theoretrical = 2/rad; see RayAD Eq 12.6 for more exact formulation)  = angle of attack Sref = aerodynamic reference area Dynamic pressure (q) = (/2)V^2 (16.2)  = air density (lb-sec^2/ft^4) V = airspeed (ft/sec) where… and… where… For uncambered airfoils Cl = 0 at  = 0  V 16-4

= Cdmin+Cdi = Cdmin+k[Cl-Clmin]^2 (16.4) k = 1/[Ae] Design of UAV Systems Aerodynamics c 2002 LM Corporation Aerodynamic drag Drag (D) = CdqSref (16.3) Cd = drag coefficient = Cdmin+Cdi = Cdmin+k[Cl-Clmin]^2 (16.4) k = 1/[Ae] A = Aspect ratio = b^2/Sref e = Oswold wing efficiency = f(,A)  = sweep Cdmin = CfKd(Swet/Sref) = Cfe(Swet/Sref) (16.5) Cf = flat plate skin friction coefficient (See RayAD Fig 12.21) Kd  1.2 = Factor to account for non-friction drag items such as pressure and interference) Cfe = Equivalent skin friction coefficient (RayAD12.3) where… and … For uncambered airfoil Cdmin = Cd0 where… These relationships are for “untrimmed” drag polars, good aerodynamic design will minimize trim drag impact (which we will ignore for now) 16-5

Oswold efficiency factor Design of UAV Systems Aerodynamics c 2002 LM Corporation Oswold efficiency factor Source - Lee Nicolai, Conceptual Design Process, LM Aero 16-6

Design of UAV Systems Lift and drag - cont’d Aerodynamics c 2002 LM Corporation Lift and drag - cont’d Notional Lift Characteristics 0.2 0.4 0.6 0.8 1 1.2 1.4 5 10 15 20 Alpha (deg) High AR, low sweep Lower AR and/or higher sweep slope = Cl Clmax Nominal Drag Characteristics (uncambered airfoil) 0.2 0.4 0.6 0.8 1 1.2 0.02 0.04 0.06 CD Cdmin Max slope = L/Dmax CL@ L/Dmax CL and Cdmin are approximately constant for low-to-medium subsonic speed range (below drag rise) This simplifying assumption makes our aero analysis task really easy (and reasonably correct) 16-7

L/D max - another perspective Design of UAV Systems Aerodynamics c 2002 LM Corporation L/D max - another perspective Theoretical (L/D)max If Cd = Cd0 + KCl^2 then D/L = Cd0/Cl + KCl) and (L/D) max will occur when d(D/L)/dCl = 0 - Cd0/Cl^2 + K = 0 or Cd0 = KCl^2 = Cdi or…. Cdmin = Cdi (L/D)max @ Minimum drag 16-8

Since (L/D)max occurs when Cd = 2Cd0 ≈ 2Cfe(Swet/Sref) (16.6) Design of UAV Systems Aerodynamics c 2002 LM Corporation L/D cont’d Since (L/D)max occurs when Cd = 2Cd0 ≈ 2Cfe(Swet/Sref) (16.6) Cl = sqrt (AReCdo) (16.7) (L/D)max = sqrt((e/Cfe)(b^2/Swet))/2 (16.8) For typical aircraft Cfe = .003 - .005 (Table 12.3), e ≈ 0.8, Kd = 1.2 (L/D)max ≈ 11.2-14.5sqrt (b^2/Swet) (16.9) Airspeed at (L/D)max (aka LoDmax ) is calculated using equations 16.1 and 16.7 At other conditions (where speed is given) q is calculated using Equation 16.2, Cl from16.1, Cd from 16.4 and 16.5 and L/D (aka LoD) from L/D = Cl/Cd (16.10) then….. and….  Compare this to RayAD Figure 3.6 16-9

A subsonic UAV has the following characteristics W0/Sref = 40 psf Design of UAV Systems Aerodynamics c 2002 LM Corporation Example A subsonic UAV has the following characteristics W0/Sref = 40 psf AR = 20  = 0 deg Swet/Sref = 5 or b^2/Swet = 20/5 = 4 Cfe = .0035 From chart 16.6 at AR = 20 and  = 0 deg, e ≈ 0.8 and Cd @ LoDmax ≈ 2Cfe(Swet/Sref) = .035 Cd0 = .0175 Cl @ LoDmax = sqrt (AReCdo) = 0.938 LoDmax = sqrt{[e/Cfe][AR/(Swet/Sref)]}/2 = 26.8 q @ LoDmax = (W0/Sref)/Cl = 42.6 psf EAS @ LoDmax = 112.2 KEAS 16-10

If not we could correct the estimate by putting a multiplier on Cdmin Design of UAV Systems Aerodynamics c 2002 LM Corporation Correction factors For pre-concept studies, equations 16.1 - 16.5 will yield reasonable estimates of lift and drag Nonetheless it is good practice to always compare estimates to data from similar aircraft and to apply appropriate correction factors Our previous calculation of LoDmax = 26.8 for AR = 20, Swet/Sref = 5, for example, when compared to parametric data from other aircraft shows that our estimate is consistent with the parametric data If not we could correct the estimate by putting a multiplier on Cdmin LoDmax comparisons 35 30 25 (L/D)max 20 Chart 16-10 estimate 15 10 5 Manned aircraft Global Hawk (est) 2 4 6 8 Wetted AR = b^2/Swet Manned aircraft data : LM Aero data handbook 16-11

More refined estimates Design of UAV Systems Aerodynamics c 2002 LM Corporation More refined estimates For conceptual design studies, a component build-up method (see RayAD 13.5) will yield higher fidelity drag estimates and capture: Reynolds number effects Overall and for individual components Form factor effects Such as wing thickness Interference drag effects Miscellaneous drag contributions As we will see later, our pre-concept design spread sheet methods could also incorporate these higher fidelity methods with little additional work They will be included at a later date A better approach for conceptual design, however, would be a combination of component build up for trade studies and Euler CFD for baseline analysis 16-12

Compressibility effects Design of UAV Systems Aerodynamics c 2002 LM Corporation Compressibility effects On subsonic UAVs we can ignore compressibility effects for lift and drag, but not for jet engine performance - The effects are estimated assuming a perfect gas, where specific heat ratio ( = 1.4) Pressure effect P/Pa = {1+[(-1)/2]M^2}^[/(-1)] = [1+0.2M^2]^3.5 (16.11) Temperature effect T/Ta = {1+[(-1)/2]M^2} = [1+0.2M^2] (16.12) P and T = Total (isentropic stagnation) pressure and temperature Pa and Ta = Static atmospheric pressure and temperature Example : M = 0.8; 36Kft (Pa = 472.6 psf; Ta = 390R) P/Pa = 1.52 or P = 720 psf (≈ 27Kft @ M=0) T/Ta = 1.13 or T = 440R = -19.8F (≈ 22Kft @ M=0) where… 16-8

Design of UAV Systems Intermission Aerodynamics c 2002 LM Corporation 16-8