16-1 design of uav systems aerodynamicsc 2002 lm corporation lesson objective - to review basic...
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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…