Zero-lift drag coefficient
# 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 sq ft (0.811 $m^2),$ compared to 3.80 sq ft (0.353 $m^2)$ 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 $ft^2$ vs. 8.73 $ft^2).$

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:

    $C_{D}=1.456\times 10^{5}({\frac {\eta P}{\sigma SV^{3}}})$.

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 $lb/ft^2.$

