Drag coefficient
The drag coefficient, drag coefficient / drag or Cd value (according to the usual formulas ) is a dimensionless measure (coefficient ) for the flow resistance of a fluid flow around the body.
Colloquially speaking, the value is a measure of the " aerodynamics " of a body. It is, however, only with the additional knowledge of speed, the end face and density of the fluid (eg air) to the actual flow resistance.
Definition
The flow resistance coefficient by:
Defined. Here, the resistance is normalized to the dynamic pressure of the flow and a reference surface. Further, the density and the velocity of the undisturbed oncoming flow form. The reference surface is by definition dependent. Usually it is equal to the face of the body is flocked. In the aircraft aerodynamic wing, however, the surface is used as a reference.
Other names for the drag coefficient are ( air ) resistance coefficient, coefficient of resistance or forehead. The symbol ( with w for resistance) is common only in the German language; in English the drag coefficient is recorded as or.
The product is often referred to as a resistance surface. The consideration of resistance surfaces is useful for example for comparing vehicles in the original scale because received both the body shape and the dimensions in the total resistance of a body being streamed.
Dependence of the drag coefficient
In general, in incompressible flow [A 1], the drag coefficient Cd of the Reynolds number Re depends on:
This statement is obtained if one assumes that the drag force FW of a body in a certain position depending on the flow velocity v, the density ρ and the viscosity ( resistance) η of the fluid and a characteristic length L of the body. The characteristic length L is a certain geometrical dimension, the square of L2 is in a fixed ratio to the reference area A.
By means of a dimensional analysis after Buckinghamschen Π theorem can be deduced that the two similarity metrics drag coefficient Cd and Reynolds number Re are sufficient to describe the flow resistance of a particular body, which allows a more straightforward general representation of the resistance of a particular body shape.
Dull, angular body have a large range of Reynolds number a substantially constant drag coefficient. That is, for example, the air resistance of vehicles at the relevant speed the case.
In compressible flows, ie when currents with variable density, there is also a dependence of the flow resistance coefficient of the Mach number. In the transonic range and in the supersonic range, the flow resistance coefficient changes greatly. Near the speed of sound, it increases to several times and decreases at very high Mach numbers to about twice the subsonic drag coefficient. The graph illustrates the relationship schematically. Above the critical Mach number Teilumströmungen exceed the speed of sound. Above the resistance divergence Mach number of the flow resistance increases sharply. The behavior in the supersonic range is determined by the geometry of the body. In the drawing, the green curve is a streamlined body.
The resistance coefficient determined for Satellite her life in orbit. At an altitude above 150 km the atmosphere is so thin that the flow is approximated no more than laminar continuum flow, but as a free molecular flow. In this area, the Cd value is typically between 2 and 4, often is expected with a value of 2.2. With increasing altitude reduces the influence of the atmosphere and is negligible above about 1000 km.
Determination
The drag coefficient is typically determined in the wind tunnel. The body stands on a plate, which is equipped with force sensors. The force in the direction of the incoming flow is measured. Out of this resistance and the known quantities such as air density and face the flow resistance coefficient is calculated for a given flow velocity. In addition to the experimental determination of resistance can also be calculated numerically integrating the distribution of friction and pressure coefficient on the model surface, depending on the complexity of the model shape and available computer capacity.
Application
The resistance force is calculated as follows from the flow resistance coefficient:
The flow resistance is thus dependent on
- The density of the flowing fluid (compare air density! )
- The reference surface,
- The flow rate and
- The drag coefficient.
The air resistance is therefore proportional, respectively, to the flow resistance coefficient, to the projected frontal area and the square of the speed. The required drive power is actually proportional to the cube of the speed of motion. Therefore, the choice of the speed of motor vehicles in addition to the other two factors has particular effect on the fuel consumption.
The air resistance is crucial for the deviation of the actual ballistic curve of the idealized parabolic trajectory.
Examples
Drag coefficients of typical body shapes
Herein, the Reynolds number
Drag coefficient of some series and experimental cars
The drag coefficient quantifies the aerodynamic quality of a body. By multiplication with the reference surface (in vehicles usually the face ) is obtained, the resistance surface of a vehicle: resistance surface. The air resistance, which determines the consumption of a motor vehicle at high speeds is proportional to the resistance surface. From the producers face is rarely indicated.