16-1

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

16-2

Design of UAV Systems

Aerodynamics c 2002 LM Corporation

Importance

These are the fundamental aerodynamic relationships needed to define a subsonic air vehicle for a UAV system

Forces

16-3

Design of UAV Systems

Aerodynamics c 2002 LM Corporation

Ct

V

horizon

L = lift

W = weight T = Thrust

= Flight path angle

Side view

D = Drag

cg = center of gravity

le

= LE

sw

eep

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 xAi = Inlet area

Anoz = Nozzle area

Cr Cr

and geometry

Aerodynamic lift

16-4

Design of UAV Systems

Aerodynamics c 2002 LM Corporation

V

Lift (L) = ClqSref = ClqSref (16.1)

Cl = lift curve slope (theoretrical = 2/rad; see RayAD Eq 12.6 for more exact formulation)

= angle of attackSref = aerodynamic reference area

Dynamic pressure (q) = (/2)V^2 (16.2)

= air density (lb-sec^2/ft^4)V = airspeed (ft/sec)

and…

where…

where…

For uncambered airfoilsCl = 0 at = 0

Aerodynamic drag

16-5

Design of UAV Systems

Aerodynamics c 2002 LM Corporation

Drag (D) = CdqSref (16.3)

Cd = drag coefficient = Cdmin+Cdi = Cdmin+k[Cl-Clmin]^2 (16.4)

k = 1/[Ae]A = Aspect ratio = b^2/Srefe = Oswold wing efficiency = f(,A) = sweep

Cdmin = CfKd(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)

For uncambered airfoil Cdmin = Cd0

where…

and …

where…

•These relationships are for “untrimmed” drag polars, good aerodynamic design will minimize trim drag impact (which we will ignore for now)

16-6

Design of UAV Systems

Aerodynamics c 2002 LM Corporation

Oswold efficiency factor

Source - Lee Nicolai, Conceptual Design Process, LM Aero

16-7

Design of UAV Systems

Aerodynamics c 2002 LM Corporation

Lift and drag - cont’d

Notional Lift Characteristics

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 5 10 15 20

Alpha (deg)

High AR, low sweep

Lower AR and/orhigher sweep

slope = Cl

Clmax

Nominal Drag Characteristics(uncambered airfoil)

0

0.2

0.4

0.6

0.8

1

1.2

0 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)

16-8

Design of UAV Systems

Aerodynamics c 2002 LM Corporation

L/D max - another perspective

Minimum vs. Induced Drag

0

2

4

6

100 125 150 175 200

Speed (KEAS)

Min DragInduced DragTotal Drag

Cdmin = Cdi

(L/D)max @ Minimum drag

Theoretical (L/D)max• If Cd = Cd0 + KCl^2 then D/L = Cd0/Cl + KCl) and

(L/D) max will occur when d(D/L)/dCl = 0 - Cd0/Cl^2 + K = 0 or Cd0 = KCl^2 =

Cdior….

16-9

Design of UAV Systems

Aerodynamics c 2002 LM Corporation

L/D cont’d

Since (L/D)max occurs whenCd = 2Cd0 ≈ 2Cfe(Swet/Sref) (16.6)

Cl = sqrt (AReCdo) (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 ≈ 11.2-14.5sqrt (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

16-10

Design of UAV Systems

Aerodynamics c 2002 LM Corporation

Example

A subsonic UAV has the following characteristicsW0/Sref = 40 psfAR = 20 = 0 deg Swet/Sref = 5 or b^2/Swet = 20/5 = 4Cfe = .0035

From chart 16.6 at AR = 20 and = 0 deg, e ≈ 0.8 and Cd @ LoDmax ≈ 2Cfe(Swet/Sref) = .035Cd0 = .0175 Cl @ LoDmax = sqrt (AReCdo) = 0.938LoDmax = sqrt{[e/Cfe][AR/(Swet/Sref)]}/2 = 26.8q @ LoDmax = (W0/Sref)/Cl = 42.6 psfEAS @ LoDmax = 112.2 KEAS

16-11

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

0

5

10

15

20

25

30

35

0 2 4 6 8

(L/D

)ma

x

Wetted AR = b^2/Swet

Manned aircraftGlobal Hawk (est)

Manned aircraft data: LM Aero data handbook

Chart 16-10 estimate

16-12

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 dateA better approach for conceptual design, however, would be a combination of component build up for trade studies and Euler CFD for baseline analysis

Compressibility effects

16-8

Design of UAV Systems

Aerodynamics c 2002 LM Corporation

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 effectP/Pa = {1+[(-1)/2]M^2}^[/(-1)] = [1+0.2M^2]^3.5 (16.11)

Temperature effectT/Ta = {1+[(-1)/2]M^2} = [1+0.2M^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…

Intermission

16-8

Design of UAV Systems

Aerodynamics c 2002 LM Corporation