Understanding Terminal Velocity

[davenn]

hi gang,

from wikipedia...
Mathematically, terminal velocity — without considering the buoyancy effects — is given by

where

Vt = terminal velocity,
m = mass of the falling object,
g = acceleration due to gravity,
Cd = drag coefficient,
ρ = density of the fluid through which the object is falling, and
A = projected area of the object.

how do I know what the drag coefficient is ?
I realize air density depends on temperature and pressure and it changes throughout a column on atmosphere.
when a given Vt is quoted for an object ... are they just averaging the air density over the
"drop path" ?

cheers
Dave

 

[Rap]

hi gang,

from wikipedia...
Mathematically, terminal velocity — without considering the buoyancy effects — is given by

where

Vt = terminal velocity,
m = mass of the falling object,
g = acceleration due to gravity,
Cd = drag coefficient,
ρ = density of the fluid through which the object is falling, and
A = projected area of the object.

how do I know what the drag coefficient is ?
I realize air density depends on temperature and pressure and it changes throughout a column on atmosphere.
when a given Vt is quoted for an object ... are they just averaging the air density over the
"drop path" ?

cheers
Dave

The drag coefficient is mostly dependent on the geometry of the object and which direction on the object is "down". To a small extent, on the nature of the surface of the object. When an object falls, the force of the atmosphere will orient it so that it does not spin, and that orientation will determine the drag coefficient. You can find the drag coefficients for simple objects, but for more complicated objects, probably the best way is to measure it.

The formula is for constant density. If the density changes, the terminal velocity will change. For example, if the density is low, the terminal velocity will be high, but if the density increases, the object will slow down to a lower terminal velocity. You also have to take into account the time it takes to achieve terminal velocity. If, during the time it takes to change, the density changes appreciably, then there is no "terminal velocity", the object will be responding to density changes in a complicated way.

 

[AlephZero]

If depends on the shape of the object, and it is dimensionless (i.e. it is just a number. it doesn't have "units" like length, etc).

Typical values are less than 0.1 for a streamlined shape like an aircraft wing, 0.3 to 0.35 for a typical small car, about 1.0 for a sphere, and 1.3 for a flat plate perpendicular to the flow direction.

If the air density changes (for example with altitude), the terminal velocity will also change.