Drag (physics) - Drag at High Velocity

Drag At High Velocity

The drag equation calculates the force experienced by an object moving through a fluid at relatively large velocity (i.e. high Reynolds number, R_e > ~1000), also called quadratic drag. The equation is attributed to Lord Rayleigh, who originally used L2 in place of A (L being some length). The force on a moving object due to a fluid is:

see derivation

where

is the force of drag,

is the density of the fluid,

is the velocity of the object relative to the fluid,

is the drag coefficient (a dimensionless parameter, e.g. 0.25 to 0.45 for a car)

is the reference area,

The reference area A is often defined as the area of the orthographic projection of the object—on a plane perpendicular to the direction of motion—e.g. for objects with a simple shape, such as a sphere, this is the cross sectional area. Sometimes different reference areas are given for the same object in which case a drag coefficient corresponding to each of these different areas must be given.

In case of a wing, comparison of the drag to the lift force is easiest when the reference areas are the same, since then the ratio of drag to lift force is just the ratio of drag to lift coefficient. Therefore, the reference for a wing often is the planform (or wing) area rather than the frontal area.

For an object with a smooth surface, and non-fixed separation points—like a sphere or circular cylinder—the drag coefficient may vary with Reynolds number R_e, even up to very high values (R_e of the order 107). For an object with well-defined fixed separation points, like a circular disk with its plane normal to the flow direction, the drag coefficient is constant for R_e > 3,500. Further the drag coefficient C_d is, in general, a function of the orientation of the flow with respect to the object (apart from symmetrical objects like a sphere).