Zero-lift drag coefficient

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, Sopwith Camel biplane of World War I festooned with wires, bracing struts, and fixed landing gear, had a zero-lift drag coefficient of approximately 0.0378, compared to 0.0161 for the streamlined P-51 Mustang of World War II^[1] which compares very favorably even with the best modern aircraft.

The zero-lift drag coefficient 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 ($C_{D,0} \times S$ 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^[1]. 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:

$V_{max}\ \propto\ \sqrt[3]{power/f}$^[1].

Estimating zero-lift drag^[1]

As noted earlier, C_D,0 = C_D − C_D,i.

The total drag coefficient can be estimated as:

$C_D = \frac{550 \eta P}{\frac{1}{2} \rho_0 [\sigma S (1.47V)^3]}$,

where η is the propulsive efficiency, P is engine power in horsepower, ρ₀ 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 ρ₀, the equation is simplified to:

$C_D = 1.456 \times 10^5 (\frac{\eta P}{\sigma S V^3})$.

The induced drag coefficient can be estimated as:

$C_{D,i} = \frac{C_L^2}{\pi A \epsilon}$,

where C_L is the lift coefficient, A is the aspect ratio, and $\epsilon$ is the aircraft's efficiency factor.

Substituting for C_L gives:

$C_{D,i}=\frac{4.822 \times 10^4}{A \epsilon \sigma^2 V^4} (W/S)^2$,

where W/S is the wing loading in lb/ft².

References

1. ^ ^{a b c d} Loftin, LK, Jr.. "Quest for performance: The evolution of modern aircraft. NASA SP-468". http://www.hq.nasa.gov/pao/History/SP-468/cover.htm. Retrieved 2006-04-22.