# Air resistance, how to calculate it?

#### shizzznit

Im taking AP Physics as well as Calculas but haven't covered the topic of Air Resistance yet. Im trying to figure out what the air resistance would be on a baseball. Could someone help me out?
Much thanks

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#### jamesrc

Gold Member
Roughly:

$F_D = \frac{C_D\rho A v^2}{2}$

where FD is the drag force, CD is the drag coefficient, &rho; is the density of air, A is the cross-sectional area of the ball (a regulation baseball has a circumference between 9 and 9.25 inches), and v is the velocity of the ball. The drag coefficient is a function of things like surface roughness, ball speed, and spin, varying between 0.2 and 0.5 for speeds commonly occuring during game play, but if you'd like to ballpark it (pardon the pun), 0.3 is a good number to use.

#### ahrkron

Staff Emeritus
Gold Member
What level is AP Physics?

Air resistance is usually taken into account via a differential equation; in simple situations, it grows linearly with the speed of the object.

#### shizzznit

AP Physics is equivalent to first year college physics study.

Thanks very much Jamesrc
having some trouble figuring out the velocity (after the bat) but thanks for the help!

#### enigma

Staff Emeritus
Gold Member
There is no closed form solution for it.

You need to multiply the force times a small step size and add it to the velocity and repeat. Works best on a computer.

#### heckticz

hey im doing an assignment for senoir school physics could you tell me how to calculate the air resistance on say the bonnet of a car?? nothing advanced just the basic formulae using the surface area of the bonnet and the force exerted by the air?? i know it has something to do with splitting it up into components??

#### Bob S

Look at

http://en.wikipedia.org/wiki/Drag_coefficient

The drag force depends on whether the air flow around the object is linear or turbulent, which then determines whether the drag force is proportional to the velocity, or the velocity squared. Also, the drag depends not only on the object size (frontal area) and shape but also on the surface roughness.

Bob S

#### rcgldr

Homework Helper
Roughly:
$F_D = \frac{C_D\rho A v^2}{2}$
It turns out that in the real world it's more complicated, but instead of modifying the equation to one more realistic, Cd is redefined as a function (often implemented as an interpolated table) that varies with speed for a given medium, such as air, and a specific object (such as a bullet, http://en.wikipedia.org/wiki/External_ballistics).

#### xxChrisxx

I was going to say this earlier, but I don't know the level of detail the OP needs.

Jamesrc suggests taking an average value of Cd, in reality you cannot do this. As Cd depends heavily on Reynolds number. Above a critical number for a ball (and it depends on the ball) the Cd will be a steady 0.2sh. Below the critical Re number the Cd will raise until it nears the critical Re number and will then drop sharply.

I did not mention it beucase if this is a generic textbook case for a baseball, his assumption of taking a middle Cd value is probably valid.

#### devildweep

hey guys i am yr 9 and doing a subject for my science fair this year: how much friction is redueced when a normal wheeled vechicle is changed into a maglev vechicle?
how can i measure friction in this case
and how can a measure air resistence

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