# Calculating Viscous and Pressure Drag On A Sphere

I've been doing some research on sphere aerodynamics, in particular that of soccer balls, and was wondering if there was any way to separately calculate the pressure / form drag, and also the surface / viscous / skin drag.

I know that Stoke's Law of F=6(pi)RnVc, where R is the radius of the sphere, n is the viscosity, and Vc is the velocity through a continuous fluid, can give the viscous drag on a sphere, but was informed that this only applies to very small spheres, so it is no use in my application for the drag on a soccer ball.

I also know of the formula that Force(drag) = 0.5 C.P.A.v^2 where C = coefficient of drag, P = fluid density, A = area of the object, v = velocity of the object, but I didn't know which aspect of the drag force (pressure, viscous or total drag) this formula calculates.

If anyone could help me out here that would be greatly appreciated.

You are correct in assuming Stokes drag cannot be used here.

The equation you wrote will give you the total drag on the sphere. You might be able to find some information about the pressure distribution around a sphere and integrate that to determine the pressure drag.

arildno
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That would be the total drag coefficient.

An engineer might rewrite C=c_v+c_p, defined in obvious manners, and sought to determine experimentally what goes into c_v and what goes into c_p.

Perhaps, they probably use more refined approaches than my dumb brutish ones..

That would be the total drag coefficient.

An engineer might rewrite C=c_v+c_p, defined in obvious manners, and sought to determine experimentally what goes into c_v and what goes into c_p.
..

That actually does sound like quite a good idea, unfortunately I don't know either c_v or c_p. If I knew one I'm sure I could derive the other from the overall formula for C, but without knowing the formula for one of these components of the drag force I'm afraid I'm still stuck... :/

the aerodynamics around the ball are turbulent, and this makes it difficult to treat analytically. what you could do to obtain the drag force on the ball is to perform an experiment on the trajectory through air, and compare that to the ideal case of no air resistance (hyperbola). better yet, search scholar.google.com or arxiv.org for articles on this topic.

...to obtain the drag force on the ball is to perform an experiment on the trajectory through air, and compare that to the ideal case of no air resistance (hyperbola).

Thanks, I like this idea and it sounds pretty useful as a good comparison showing the affects of the drag on the ball's flight.

My issue is that using the formula I stated before I can find the overall drag, its just I was wondering if there was any way I could specifically calculate the pressure / form drag, and then the viscous / surface drag, and try to compare them, so that I can show the vast majority of the drag around a sphere is pressure drag, compared to an aerofoil for example, where the majority is viscous drag.

Thanks for all the responses so far, and for any future input it's all been really helpful!

In regards to the adidas jabulani soccer ball that was used at the recent world cup in south africa, it seems that the ball is not any lighter as some may say (it is actually on the heavier side of the strictly regulated limits for ball weight), but just moving faster through the air. I understand that this is due to all the dimples and ridges on the surface of the ball (tripping a turbulent boundary layer, less pressure drag), but would this not be negated by fewer seams (i.e. less seams, less places to trip turbulent boundary layer, more pressure drag) ?