In aerodynamics, the zero-lift drag coefficient
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
, where
C
D
is the total drag coefficient for a given power, speed, and altitude, and
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
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
) which is simply the product of zero-lift drag coefficient and aircraft's wing area (
C
D
,
0
×
S
where
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. 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
.
As noted earlier,
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
]
,
where
η
is the propulsive efficiency, P is engine power in horsepower,
ρ
0
sea-level air density in slugs/cubic foot,
σ
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
, the equation is simplified to:
C
D
=
1.456
×
10
5
(
η
P
σ
S
V
3
)
.
The induced drag coefficient can be estimated as:
C
D
,
i
=
C
L
2
π
A
ϵ
,
where
C
L
is the lift coefficient, A is the aspect ratio, and
ϵ
is the aircraft's efficiency factor.
Substituting for
C
L
gives:
C
D
,
i
=
4.822
×
10
4
A
ϵ
σ
2
V
4
(
W
/
S
)
2
,
where W/S is the wing loading in lb/ft².
