Zero-lift drag coefficient
Encyclopedia
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, 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
which compares very favorably even with the best modern aircraft.
The zero-lift drag coefficient 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 (0.8110435392 m²), compared to 3.8 sq ft (0.353031552 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:
.
.
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/ft².
Aerodynamics
Aerodynamics is a branch of dynamics concerned with studying the motion of air, particularly when it interacts with a moving object. Aerodynamics is a subfield of fluid dynamics and gas dynamics, with much theory shared between them. Aerodynamics is often used synonymously with gas dynamics, with...
, the zero-lift drag coefficient
is a dimensionless parameter which relates an aircraft's zero-lift dragDrag (physics)
In fluid dynamics, drag refers to forces which act on a solid object in the direction of the relative fluid flow velocity...
force
Force
In physics, a force is any influence that causes an object to undergo a change in speed, a change in direction, or a change in shape. In other words, a force is that which can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a flexible object to deform...
to its size, speed, and flying altitude.
Mathematically, zero-lift drag coefficient
Drag coefficient
In fluid dynamics, the drag coefficient is a dimensionless quantity that is used to quantify the drag or resistance of an object in a fluid environment such as air or water. It is used in the drag equation, where a lower drag coefficient indicates the object will have less aerodynamic or...
is defined as
, where is the total drag coefficient for a given power, speed, and altitude, and is the lift-induced dragLift-induced drag
In aerodynamics, lift-induced drag, induced drag, vortex drag, or sometimes drag due to lift, is a drag force that occurs whenever a moving object redirects the airflow coming at it. This drag force occurs in airplanes due to wings or a lifting body redirecting air to cause lift and also in cars...
coefficient at the same conditions. Thus, zero-lift drag coefficient is reflective of parasitic drag
Parasitic drag
Parasitic drag is drag caused by moving a solid object through a fluid medium . Parasitic drag is made up of many components, the most prominent being form drag...
which makes it very useful in understanding how "clean" or streamlined an aircraft's aerodynamics are. For example, Sopwith Camel
Sopwith Camel
The Sopwith Camel was a British First World War single-seat biplane fighter introduced on the Western Front in 1917. Manufactured by Sopwith Aviation Company, it had a short-coupled fuselage, heavy, powerful rotary engine, and concentrated fire from twin synchronized machine guns. Though difficult...
biplane of World War I
World War I
World War I , which was predominantly called the World War or the Great War from its occurrence until 1939, and the First World War or World War I thereafter, was a major war centred in Europe that began on 28 July 1914 and lasted until 11 November 1918...
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
P-51 Mustang
The North American Aviation P-51 Mustang was an American long-range, single-seat fighter and fighter-bomber used during World War II, the Korean War and in several other conflicts...
of World War II
World War II
World War II, or the Second World War , was a global conflict lasting from 1939 to 1945, involving most of the world's nations—including all of the great powers—eventually forming two opposing military alliances: the Allies and the Axis...
which compares very favorably even with the best modern aircraft.
The zero-lift drag coefficient 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 (0.8110435392 m²), compared to 3.8 sq ft (0.353031552 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 ConstellationLockheed Constellation
The Lockheed Constellation was a propeller-driven airliner powered by four 18-cylinder radial Wright R-3350 engines. It was built by Lockheed between 1943 and 1958 at its Burbank, California, USA, facility. A total of 856 aircraft were produced in numerous models, all distinguished by a...
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:
.Estimating zero-lift drag
As noted earlier,.The total drag coefficient can be estimated as:
,where
is the propulsive efficiencyPropulsive efficiency
In aircraft and rocket design, overall propulsive efficiency \eta is the efficiency, in percent, with which the energy contained in a vehicle's propellant is converted into useful energy, to replace losses due to air drag, gravity, and acceleration. It can also be stated as the proportion of the...
, P is engine power in horsepower
Horsepower
Horsepower is the name of several units of measurement of power. The most common definitions equal between 735.5 and 750 watts.Horsepower was originally defined to compare the output of steam engines with the power of draft horses in continuous operation. The unit was widely adopted to measure the...
,
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 coefficientLift coefficient
The lift coefficient is a dimensionless coefficient that relates the lift generated by a lifting body, the dynamic pressure of the fluid flow around the body, and a reference area associated with the body...
, A is the aspect ratio
Aspect ratio (wing)
In aerodynamics, the aspect ratio of a wing is essentially the ratio of its length to its breadth . A high aspect ratio indicates long, narrow wings, whereas a low aspect ratio indicates short, stubby wings....
, and
is the aircraft's efficiency factor.Substituting for
gives:,where W/S is the wing loading
Wing loading
In aerodynamics, wing loading is the loaded weight of the aircraft divided by the area of the wing. The faster an aircraft flies, the more lift is produced by each unit area of wing, so a smaller wing can carry the same weight in level flight, operating at a higher wing loading. Correspondingly,...
in lb/ft².