Notes on CQ #1
1
p∞V12
2
1
q∞ 2 = p∞V22 = 4q∞1
2
V1C
Re 1 =
V∞
V2 C
Re 2 =
V∞
q∞1 =
D1′ = q∞1 cCd ( Re1 )
D2′ = q∞2 cCd ( Re 2 )
⇒ Drag scales withV∞2 × Cd (V∞ )
D′ = q∞ c Cd (Re)
From data, Cd ∝ Re
−
1
2
⇒ Laminar flow behavior
1
−
2
D′ ∝ qN∞ c Re
N
1
∝ V∞2
−
∝ V∞ 2
3
−
1
13
D′ ∝ V∞2 , c. f . Turbulent Cd ∝ Re 7 , D′ ∝V∞7
⇒ D′ ↑ withV∞ ↑
1
6
Note dependence on chord D′ ∝ c 2 , c.f. Turbulent D′ ∝ c 7
Drag Polar
CL ≡
L
L′
or Cl ≡
q∞ S ref
q∞ A ref
N
N
usually
wing
planform
usually
chord
CL
stall
increasing α
CL
min
0
CD
min
CD
0
CD
Notes on CQ
For many aircraft,
(
CD ≅ CDmin + k min CL − CLmin
)
2
Also, since CDmin ≈ CDo & CLmin ≈ 0
CD ≅ CDO + kCL2
The first option will be slightly more accurate, but both are reasonable
approximations.
Notes on CQ #2
(1) First, we note that CDO & k will almost certainly depend on the Reynolds
number. But, this dependence is probably weak since the b.l. flow will be
turbulent. So, we assume CDO & k remain constant to good approximation.
Also important is that for a general aviation aircraft, we expect no wave drag
since the flight is subsonic.
(2)
D=
=
1
ρV 2 S CDO + kCL2
2
(
1
ρV 2 SCDO
2
)


W 
1
2 
+ k  ρV S  

2
  1 ρV 2 S 
2

2



 1
1
k


D =  ρ SCDO V 2 + 
W2 2
2 
  1 ρS
V
2 D0


DL
So we see that D0 ∝ V 2 & DL ∝
1
V2
(3) Often at cruise, D0C ≈ DLC for prop-aircraft.
DC = D0C + DLC = 2 D0C
At approach:
1
1
DA = 4 D0C + D0C = 4 D0C
4
4
Note: DA > DC
16.100
2