Drag coefficient

[Flofloflo]

Hello,

I am trying to determine the Cd of a basketball, and I 'm having a bit of trouble with it.
Wikipedia says the Cd of a sphere is 0,47. But I 'm sure the surface, and maybe also the material have influence on a Cd value. So I 'm trying to determine it (unless somebody has acces to the actual data?). But I think thats pretty much impossible; how am I supposed to see/calculate the speed with which the basketball comes falling down?! (I'm talking about Fw = Rho * 0,5 * Cd * V^2 * A, FYI).

Now, in the best case the Drag can be neglected because it's to small anyways, but I am not sure about that yet.

So basically the three possibilities I have right now are:
a - There's some way of establishing it by experiment.
b - The number can be estimated using known values
c - The value is already known, but hidden away carefully

So yeah, does anybody know a way of finding the value?

[GloryMXE7]

air resistance is a tricky equation thats hard to do
id ask your physics techer about that or look up the solution

[simplethinker]

It has to be determined experimentally (or by the use of a really, really expensive computer program). The way it's calculated uses the drag force, but unless you measure the force in an experiment you need the coefficient to calculate the force. Thus, you have to do it by experiment. Tables can be found online or in fluid mechanics texts.

The drag coefficient is a vast simplification used to approximate the effects of shape, material, velocity, stresses, viscosity, and direction of motion. The same object will have different drag coefficients depending on its velocity and a few other parameters, so it really isn't a constant at all. There's no straight-up analytical way to calculate it since it's a made-up quantity to make the otherwise ugly drag force equation (it's actually a fourth-rank tensor equation) manageable. (This is also the case for springs, and Hook's law in full generality is far uglier than the drag equation)

[DigiTan]

Heh heh. With this question, you could change you name to flowflowflow. Heh...'cause of the. Nevermind...

Well, the easiest experiment that comes to mind to hang the ball from a thread and push it with a jet of air. If you're fairly confident of the airspeed and it's uniform you could assume Fw = mass*gravity*tan(θ) once you know the deflection angle. The rho you can look up in a good reference and the other factors could be measured on the spot. And maybe compare it to other stuff. Kind of cheap, but what works works.

[Flofloflo]

Uuhm, what does the Rho mean?? ( the TAN( thing)??

[GloryMXE7]

how much phisics do you know anyway

[Bronco]

Lol. Silly kids. Tan( is Tangent. Look it up on MathWorld or in your math book.

[GloryMXE7]

I know that i dont understand how someone could know something about drag but not know abaut tan
simp

[simplethinker]

[DigiTan]

[GloryMXE7]

yes i knew it was tangent

[DigiTan]

Heh heh. Just checkin'.

---------
But yeah. Hang that basketball up like a pinata with some fishing line or something. Then blast it with a leaf blower or one of those industrial fans. As long as you have something to measure the wind speed with, you've already fought half the battle. Anemometers For The Wind!

[Flofloflo]

Well, I don't hope this is rude, but I kinda don't get how taking the tangent of the density of air makes any sense whatsoever... So basically right now where gonna use some other constants ( I am not exactly sure which, a friend of mine did some research on it), but use that to find the value in some other way...

Btw, yeah, some dude didnt read the question correct:P Like Digitan answered, I didn;t know what Rho meant

[DigiTan]

Don't worry, don't worry. This one's in the bag.

1. Hang the basketball from a string.

2. Use some kind of high-output fan to blow air sideways at the ball. This part is kind of tough because you need to know the exact wind speed of that air. So I don't know if you have access to something like that or need a loaner. Anyway, measure the windspeed.

3. Make it blow air at the ball so that you ball-string setup gets pushed by some angle. You also want to make sure the ball is directly in front of the fan. If the ball won't stay steady at any particular angle, just try to get an average. That angle is θ. The ball hanging straight down to the ground with no wind at all would represent a 0° angle. Basically, your angle is going to fall somewhere between 0° and 90° with the fan on.

4. Calculate the force of the wind. Which is F_wind = mass*gravity*tan(θ)
mass - mass of the ball (kg)
gravity - 9.8m/sec²
tan(θ) - the tangent of the string's angle.

5. Now you know F_wind

6. Put this F_wing in your drag coefficient. Fill in all the known variables and then solve for Cd.

6.a - F_wind = Rho * 0.5 * Cd * V² * A
6.b - Cd = F_wind / (0.5 * Rho * V² * A)

Rho - Density of air (1.2 kg/m³)
A - Effective cross-section of a sphere. (This might not be as simple as pi*r². Textbooks will have it)
V - Windspeed (m/s)
Cd - ♫ Duhn dunn dunnnnnnnnnn!....♫

Nothing but net!

[GloryMXE7]

the cross section of a spher is pi r^2 the r varies throughout the sphere

[simplethinker]

[DigiTan]

On second thought, an air compressor like the kind you have in a highschool auto shop would be better than a fan. You'll get a more uniform air stream and hopefully less rotation on the ball. And from what I hear about the drag equation--it looses some of its meaning as the object starts to spin anyway.