- Source: Zero-lift drag coefficient
In aerodynamics, the zero-lift drag coefficient
C
D
,
0
{\displaystyle C_{D,0}}
is a dimensionless parameter which relates an aircraft's zero-lift drag force to its size, speed, and flying altitude.
Mathematically, zero-lift drag coefficient is defined as
C
D
,
0
=
C
D
−
C
D
,
i
{\displaystyle C_{D,0}=C_{D}-C_{D,i}}
, where
C
D
{\displaystyle C_{D}}
is the total drag coefficient for a given power, speed, and altitude, and
C
D
,
i
{\displaystyle C_{D,i}}
is the lift-induced drag coefficient at the same conditions. Thus, zero-lift drag coefficient is reflective of parasitic drag which makes it very useful in understanding how "clean" or streamlined an aircraft's aerodynamics are. For example, a Sopwith Camel biplane of World War I which had many wires and bracing struts as well as fixed landing gear, had a zero-lift drag coefficient of approximately 0.0378. Compare a
C
D
,
0
{\displaystyle C_{D,0}}
value of 0.0161 for the streamlined P-51 Mustang of World War II which compares very favorably even with the best modern aircraft.
The drag at zero-lift can be more easily conceptualized as the drag area (
f
{\displaystyle f}
) which is simply the product of zero-lift drag coefficient and aircraft's wing area (
C
D
,
0
×
S
{\displaystyle C_{D,0}\times S}
where
S
{\displaystyle S}
is the wing area). Parasitic drag experienced by an aircraft with a given drag area is approximately equal to the drag of a flat square disk with the same area which is held perpendicular to the direction of flight. The Sopwith Camel has a drag area of 8.73 sq ft (0.811 m2), compared to 3.80 sq ft (0.353 m2) for the P-51 Mustang. Both aircraft have a similar wing area, again reflecting the Mustang's superior aerodynamics in spite of much larger size. In another comparison with the Camel, a very large but streamlined aircraft such as the Lockheed Constellation has a considerably smaller zero-lift drag coefficient (0.0211 vs. 0.0378) in spite of having a much larger drag area (34.82 ft2 vs. 8.73 ft2).
Furthermore, an aircraft's maximum speed is proportional to the cube root of the ratio of power to drag area, that is:
V
m
a
x
∝
p
o
w
e
r
/
f
3
{\displaystyle V_{max}\ \propto \ {\sqrt[{3}]{power/f}}}
.
Estimating zero-lift drag
As noted earlier,
C
D
,
0
=
C
D
−
C
D
,
i
{\displaystyle C_{D,0}=C_{D}-C_{D,i}}
.
The total drag coefficient can be estimated as:
C
D
=
550
η
P
1
2
ρ
0
[
σ
S
(
1.47
V
)
3
]
{\displaystyle C_{D}={\frac {550\eta P}{{\frac {1}{2}}\rho _{0}[\sigma S(1.47V)^{3}]}}}
,
where
η
{\displaystyle \eta }
is the propulsive efficiency, P is engine power in horsepower,
ρ
0
{\displaystyle \rho _{0}}
sea-level air density in slugs/cubic foot,
σ
{\displaystyle \sigma }
is the atmospheric density ratio for an altitude other than sea level, S is the aircraft's wing area in square feet, and V is the aircraft's speed in miles per hour. Substituting 0.002378 for
ρ
0
{\displaystyle \rho _{0}}
, the equation is simplified to:
C
D
=
1.456
×
10
5
(
η
P
σ
S
V
3
)
{\displaystyle C_{D}=1.456\times 10^{5}({\frac {\eta P}{\sigma SV^{3}}})}
.
The induced drag coefficient can be estimated as:
C
D
,
i
=
C
L
2
π
A
R
ϵ
{\displaystyle C_{D,i}={\frac {C_{L}^{2}}{\pi A\!\!{\text{R}}\epsilon }}}
,
where
C
L
{\displaystyle C_{L}}
is the lift coefficient, AR is the aspect ratio, and
ϵ
{\displaystyle \epsilon }
is the aircraft's efficiency factor.
Substituting for
C
L
{\displaystyle C_{L}}
gives:
C
D
,
i
=
4.822
×
10
4
A
R
ϵ
σ
2
V
4
(
W
/
S
)
2
{\displaystyle C_{D,i}={\frac {4.822\times 10^{4}}{A\!\!{\text{R}}\epsilon \sigma ^{2}V^{4}}}(W/S)^{2}}
,
where W/S is the wing loading in lb/ft2.
References
Kata Kunci Pencarian:
- Grumman F6F Hellcat
- F-104 Starfighter
- Pesawat terbang
- Northrop F-5
- F-4 Phantom II
- Consolidated B-24 Liberator
- Boeing B-52 Stratofortress
- Zero-lift drag coefficient
- Drag coefficient
- Lift-to-drag ratio
- 0L
- Lift coefficient
- Automobile drag coefficient
- Oswald efficiency number
- Drag (physics)
- Aspect ratio (aeronautics)
- Drag count
