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# Air resistance and drag coefficient - calculating them watch

1. OK, so I'm trying to write a computer program to simulate the motion of a model railway carriage, and I need to work out the air resistance... Is there anyone who could help me figure out how to do it? I've spoken to physics and technology teachers at my school, and the answer I've had from them is generally either "It's ridiculously complicated to work out, don't bother" or "It's ridiculously complicated to work out, you'd do best to do a set of experiments to see what results you'd get." In terms of the Reynolds number, the carriage is roughly cuboid, about 30cm long, 3cm wide and 5cm tall, with blunt ends, and the speeds involved would be anything up to maybe 0.5m/s.

The main problem is there are so many different equations for calculating the drag, and I'm not sure which one to go for... And then of course there's the Drag Coefficient to work out, which has got me stumped. Any hints?

I think I may be in this wayyyyy over my head...

Any help would be very gratefully received.

James
2. I'm not too sure whether the air resistance is proportional to v or v^2 for that Reynolds number, but taking the v^2 case:

Drag Coefficients - http://en.wikipedia.org/wiki/Drag_coefficient

You could just model your train as a long cylinder or a long cubiod for simplicity (and a fairly good approximation) and once you have this you then know the drag force by the formula on that page, so you can set up the differential equation:

where F is the force being created by the trains engine. For this you could try and solve it analytically for a few simple cases of F or you could solve it numerically using something like the Runge-Kutta method.
3. Thanks - I swear when I looked at that page yesterday it didn't have the drag coefficients set at the bottom!

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