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, 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 ($$C_{D,0} \times S$$ 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 sqft, compared to 3.80 sqft 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:


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

Estimating zero-lift drag
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 $$\eta$$ is the propulsive efficiency, P is engine power in horsepower, $$\rho_0$$ sea-level air density in slugs/cubic foot, $$\sigma$$ 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 $$\rho_0$$, 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:


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

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

Substituting for $$C_L$$ gives:


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

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