# Zero-lift drag coefficient

In aerodynamics, the **zero-lift drag coefficient** 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 , where is the total drag coefficient for a given power, speed, and altitude, and 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 value of 0.0161 for the streamlined P-51 Mustang of World War II[1] which compares very favorably even with the best modern aircraft.

The drag at zero-lift can be more easily conceptualized as the **drag area** (**) which is simply the product of zero-lift drag coefficient and aircraft's wing area ( where 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.[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 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:

- .[1]

## Estimating zero-lift drag[1]

As noted earlier, .

The total drag coefficient can be estimated as:

- ,

where is the propulsive efficiency, P is engine power in horsepower, sea-level air density in slugs/cubic foot, 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 , the equation is simplified to:

- .

The induced drag coefficient can be estimated as:

- ,

where is the lift coefficient, *A* is the aspect ratio, and is the aircraft's efficiency factor.

Substituting for gives:

- ,

where W/S is the wing loading in lb/ft^{2}.

## References

- Loftin, LK Jr. "Quest for performance: The evolution of modern aircraft. NASA SP-468". Retrieved 2006-04-22.