Air Resistance & Wind Resistance Equations

In summary: in summary, drag is proportional to the velocity squared times the air density, wind resistance is proportional to the velocity squared times the wind speed, and drag and wind resistance are proportional to the velocity squared times the area of the object.
  • #1
bomba923
763
0
What equation represents the force of air resistance? Is it simply [itex] \vec F_{air} = c \vec v [/itex], 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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  • #2
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.
 
  • #3
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,

[tex]\vec{F} \propto \vec{v}^2[/tex]

[tex]\vec{v} = \vec{v}_{object}-\vec{v}_{wind}[/tex]
 
  • #4
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,

[tex]\vec{F} \propto \vec{v}^2[/tex]

[tex]\vec{v} = \vec{v}_{object}-\vec{v}_{wind}[/tex]

Ahh..velocity squared! Thanks SpaceTiger :smile:
 
  • #5
I think you are missing a crucial piece of information here. Drag is proportional to the velocity squared times the air density.

[tex]\vec{F} \propto \rho \vec{v}^2 [/tex]

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

[tex]\vec{F} = C_d \frac{1}{2} \rho \vec{v}^2 {S}[/tex]

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

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

edit:Fixed a dumb mistake
 
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  • #6
Jouke said:
I think you are missing a crucial piece of information here. Drag is proportional to the velocity squared times the air density.

[tex]\vec{F} \propto \rho \vec{v}^2 [/tex]

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

[tex]\vec{F} = C_d \frac{1}{2} \rho \vec{v}^2 [/tex]

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

-----
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.
[tex]\vec{F} = C_d \frac{1}{2} \rho S\vec{v}^2 [/tex]
Also, [tex]C_d[/tex] is a hyghly nonlinear coefficient, which depends on the Rayleigh number, the Mach number and on the angle of incidence. For constant Rayleigh and Mach numbers and small incidence angles, [tex]C_d[/tex] can be linearized as [tex]C_d= C_{d0} + C_{di}i[/tex], where [tex]i[/tex] is the angle of incidence: the angle the relative wind velocity makes with the symmetry axis of the body.
 
  • #7
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.
 

1. What is air resistance?

Air resistance, also known as drag, is the force that opposes the motion of an object through the air. It is caused by the collision of air molecules with the surface of the object.

2. How is air resistance calculated?

Air resistance is calculated using the equation Fd = 1/2 * ρ * v2 * A * Cd, where Fd is the drag force, ρ is the density of air, v is the velocity of the object, A is the surface area of the object, and Cd is the drag coefficient which depends on the shape and orientation of the object.

3. What is the difference between air resistance and wind resistance?

Air resistance is the force that acts on an object moving through still air, while wind resistance is the force that acts on an object moving through moving air, or wind. Wind resistance is a combination of air resistance and the force of the wind pushing against the object.

4. How does air resistance affect the motion of an object?

Air resistance causes a decrease in the speed of an object and can also change its direction of motion. As the velocity of the object increases, so does the force of air resistance, eventually reaching a point of equilibrium where the drag force equals the force of gravity. This is known as terminal velocity.

5. How does air resistance vary for different objects?

The amount of air resistance experienced by an object depends on its shape, size, and speed. Objects with a larger surface area or higher velocity will experience more air resistance. The shape of the object also plays a role, as objects with a more streamlined shape will experience less air resistance compared to objects with a more irregular shape.

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