1. Basic aerodynamics relationships
Design of UAV Systems
Aerodynamics
c 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
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2. Design of UAV Systems Importance
Aerodynamics
c LM Corporation
Importance
These are the fundamental aerodynamic relationships needed to define a subsonic air vehicle for a UAV system
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3. Design of UAV Systems Forces and geometry   V horizon L = lift
Aerodynamics
c 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
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4. Lift (L) = ClqSref = ClqSref (16.1)
Design of UAV Systems
Aerodynamics
c 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^ (16.2)
 = air density (lb-sec^2/ft^4)
V = airspeed (ft/sec)
where…
and…
where…
For uncambered airfoils
Cl = 0 at  = 0  V
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5. = Cdmin+Cdi = Cdmin+k[Cl-Clmin]^2 (16.4) k = 1/[Ae]
Design of UAV Systems
Aerodynamics
c 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)
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6. Oswold efficiency factor
Design of UAV Systems
Aerodynamics
c LM Corporation
Oswold efficiency factor
Source - Lee Nicolai, Conceptual Design Process, LM Aero
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7. Design of UAV Systems Lift and drag - cont’d
Aerodynamics
c 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
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)
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8. L/D max - another perspective
Design of UAV Systems
Aerodynamics
c 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
Minimum drag
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9. Since (L/D)max occurs when Cd = 2Cd0 ≈ 2Cfe(Swet/Sref) (16.6)
Design of UAV Systems
Aerodynamics
c 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))/ (16.8)
For typical aircraft
Cfe = (Table 12.3), e ≈ 0.8, Kd = 1.2
(L/D)max ≈ 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
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10. A subsonic UAV has the following characteristics W0/Sref = 40 psf
Design of UAV Systems
Aerodynamics
c 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
LoDmax ≈ 2Cfe(Swet/Sref) = .035
Cd0 = .0175
LoDmax = sqrt (AReCdo) = 0.938
LoDmax = sqrt{[e/Cfe][AR/(Swet/Sref)]}/2 = 26.8
LoDmax = (W0/Sref)/Cl = 42.6 psf
LoDmax = KEAS
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11. If not we could correct the estimate by putting a multiplier on Cdmin
Design of UAV Systems
Aerodynamics
c LM Corporation
Correction factors
For pre-concept studies, equations 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 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
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12. More refined estimates
Design of UAV Systems
Aerodynamics
c 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
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13. Compressibility effects
Design of UAV Systems
Aerodynamics
c 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 = psf; Ta = 390R)
P/Pa = 1.52 or P = 720 psf (≈ M=0)
T/Ta = 1.13 or T = 440R = -19.8F (≈ M=0)
where…
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14. Design of UAV Systems Intermission Aerodynamics c 2002 LM Corporation
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