Design of UAV Systems
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
c 2002 LM Corporation
Aerodynamics
16-1
Design of UAV Systems
Importance
These are the fundamental aerodynamic
relationships needed to define a
subsonic air vehicle for a UAV system
c 2002 LM Corporation
Aerodynamics
16-2
Forces and geometry
Design of UAV Systems
Side view

Ai = Inlet area
Svt = Exposed VT area

V
Swet = Total wetted area
excluding inlet
and nozzle area
Swet-x = Wetted area of x
L = lift
horizon
D = Drag
 = Flight path angle
W = weight
T = Thrust
Sref = Wing reference area
(both sides to CL)
cg = center of
gravity
Anoz = Nozzle
area
Ct
Cr = Root chord
Swexp = Exposed wing area
(both sides)
Cmac = Mean aerodynamic chord
c 2002 LM Corporation
Aerodynamics
Sht = Exposed HT area
Cr
Cr
16-3
Design of UAV Systems
Aerodynamic lift
Lift (L) = ClqSref = ClqSref
(16.1)
where…
Cl = lift curve slope (theoretrical = 2/rad; see
RayAD Eq 12.6 for more exact formulation)
 = angle of attack
Sref = aerodynamic reference area
and…
Dynamic pressure (q) = (/2)V^2
(16.2)
where…
 = air density (lb-sec^2/ft^4)
V = airspeed (ft/sec)
For uncambered airfoils
Cl = 0 at  = 0

V
c 2002 LM Corporation
Aerodynamics
16-4
Design of UAV Systems
Aerodynamic drag
Drag (D) = CdqSref
(16.3)
where…
Cd = drag coefficient
= Cdmin+Cdi = Cdmin+k[Cl-Clmin]^2 (16.4)
and …
For uncambered
k = 1/[Ae]
airfoil Cdmin = Cd0
A = Aspect ratio = b^2/Sref
e = Oswold wing efficiency = f(,A)
 = sweep
Cdmin = CfKd(Swet/Sref) = Cfe(Swet/Sref)
(16.5)
where…
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)
•These relationships are for “untrimmed” drag polars, good aerodynamic
design will minimize trim drag impact (which we will ignore for now)
c 2002 LM Corporation
Aerodynamics
16-5
Design of UAV Systems
Oswold efficiency factor
Source - Lee Nicolai, Conceptual Design Process, LM Aero
c 2002 LM Corporation
Aerodynamics
16-6
Lift and drag - cont’d
Design of UAV Systems
Notional Lift Characteristics
1.4
Nominal Drag Characteristics
(uncambered airfoil)
Clmax
1.2
1.2
slope = Cl
1
Max slope = L/Dmax
1
0.8
0.8
Cdmin
0.6
0.6
High AR, low sweep
0.4
Lower AR and/or
higher sweep
0.2
CL@ L/Dmax
0.4
0.2
0
0
0
5
10
15
20
0
0.02
0.04
0.06
CD
Alpha (deg)
• CL and Cdmin are approximately constant for lowto-medium subsonic speed range (below drag rise)
• This simplifying assumption makes our aero analysis
task really easy (and reasonably correct)
c 2002 LM Corporation
Aerodynamics
16-7
Design of UAV Systems
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
or…. - Cd0/Cl^2 + K = 0 or Cd0 = KCl^2 = Cdi
(L/D)max @
Minimum drag
Cdmin
= Cdi
c 2002 LM Corporation
Aerodynamics
16-8
Design of UAV Systems
L/D cont’d
Since (L/D)max occurs when
Cd = 2Cd0 ≈ 2Cfe(Swet/Sref)
(16.6)
then…..
Cl = sqrt (AReCdo)
(16.7)
and….
(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)
Compare this to
RayAD Figure 3.6
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)
c 2002 LM Corporation
Aerodynamics
16-9
Design of UAV Systems
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
c 2002 LM Corporation
Aerodynamics
16-10
Correction factors
Design of UAV Systems
(L/D)max
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
LoDmax comparisons
of LoDmax = 26.8 for AR
35
= 20, Swet/Sref = 5, for
example, when compared 30
25
to parametric data from
20
other aircraft shows that
Chart 16-10
15
estimate
our estimate is consistent
10
with the parametric data
5
Manned aircraft
Global Hawk (est)
• If not we could correct the
0
estimate by putting a
multiplier on Cdmin
0
2
4
Wetted AR = b^2/Swet
6
8
Manned aircraft data
: LM Aero data handbook
c 2002 LM Corporation
Aerodynamics
16-11
Design of UAV Systems
More refined estimates
For conceptual design studies, a component buildup 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
c 2002 LM Corporation
Aerodynamics
16-12
Design of UAV Systems
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)
where…
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)
c 2002 LM Corporation
Aerodynamics
16-8
Design of UAV Systems
c 2002 LM Corporation
Aerodynamics
Intermission
16-8