# Air Resistance

What equation represents the force of air resistance? Is it simply $\vec F_{air} = c \vec v$, or must the velocity be raised to a higher power?

*Also, which equation represents wind resistance to an object, in the case where a wind is blowing relative to the ground ?

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Danger
Gold Member
Sorry that I can't do anything about the formula. I can tell you, however, that at least for the purposes of an aircraft the ground is totally irrelevant to your reaction with the air. Ignore it, because there should be no difference between 'static' and 'dynamic' air; everything is relative to the vehicle or whatever that you're dealing with. There is a 'ground effect' involving boundary layers and such, but I get the impression that it doesn't apply to what you're asking about.

SpaceTiger
Staff Emeritus
Gold Member
Air resistance goes as the velocity squared. Wind is just moving air, so you can use the same formula, but you have shift into a frame in which the air is stationary. That is,

$$\vec{F} \propto \vec{v}^2$$

$$\vec{v} = \vec{v}_{object}-\vec{v}_{wind}$$

SpaceTiger said:
Air resistance goes as the velocity squared. Wind is just moving air, so you can use the same formula, but you have shift into a frame in which the air is stationary. That is,

$$\vec{F} \propto \vec{v}^2$$

$$\vec{v} = \vec{v}_{object}-\vec{v}_{wind}$$
Ahh..velocity squared! Thanks SpaceTiger I think you are missing a crucial piece of information here. Drag is proportional to the velocity squared times the air density.

$$\vec{F} \propto \rho \vec{v}^2$$

The formula for "wind" resistance usually written in the following form:

$$\vec{F} = C_d \frac{1}{2} \rho \vec{v}^2 {S}$$

Where "Cd" is the coefficient of drag. For engineering purposes the drag coefficient is usually split between a pressure and a skin friction coefficient.

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Can someone explain to me why my second image says "vecF" and not just F ?

edit:Fixed a dumb mistake

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SGT
Jouke said:
I think you are missing a crucial piece of information here. Drag is proportional to the velocity squared times the air density.

$$\vec{F} \propto \rho \vec{v}^2$$

The formula for "wind" resistance usually written in the following form:

$$\vec{F} = C_d \frac{1}{2} \rho \vec{v}^2$$

Where "Cd" is the coefficient of drag. For engineering purposes the drag coefficient is usually split between a pressure and a skin friction coefficient.

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Can someone explain to me why my second image says "vecF" and not just F ?
If you want to include air density, you should also include the area of the cross section of the flying body.
$$\vec{F} = C_d \frac{1}{2} \rho S\vec{v}^2$$
Also, $$C_d$$ is a hyghly nonlinear coefficient, wich depends on the Rayleigh number, the Mach number and on the angle of incidence. For constant Rayleigh and Mach numbers and small incidence angles, $$C_d$$ can be linearized as $$C_d= C_{d0} + C_{di}i$$, where $$i$$ is the angle of incidence: the angle the relative wind velocity makes with the symmetry axis of the body.

Oops my mistake I've always had a nasty tendency to forget about the (wing) area a major mistake, especially if you're studying aerospace engineering.

It is true that Cd is highly nonlinear coefficient. But for things like bullets, cars, trains, cyclists and people the Value for Cd is pretty much a constant. Things start geting complicated when you're looking at aeroplanes, rockets and other thingy's which go faster then 100m/s.