Learning Air Resistance: Questions & Answers

[Storm Butler]

I don't know much about air resistance but i would like to learn. Basically all i know is that you assume a basic Taylor expansion and then (for some reason unknown to me) you drop out all terms other then the linear and quadratic ones. Both terms in the equation are velocity dependent (intuitively so) with some coefficient with the linear forms of Beta*D or Y*D (this is only for spheres) where Beta and Y are some terms dependent on the medium and D is the diameter of the sphere. Where my questions come in are what happens to the other terms? also what is the difference (like what causes the different drags?) is the linear shape dependent while the quadratic is more abstract and deals with pressure differences caused by the rushing fluid? and do the other terms get used, for example would a cubic air resistance get used when traveling near the speed of sound? (also what causes the cubic air resistance to arise?). plus how are B and C decided for shapes that aren't spheres, like if i wanted to work out a problem dealing with a rocket ship (a cone with a cylinder) how would the equation get adjusted? Finally are the values of Beta and Y shape dependent? or strictly medium dependent and are there such values for something like higher order terms such as a cubic one?

any info would be greatly appreciated.

 

[rcgldr]

Real world ballistics, especially when you consider near sonic or super sonic speeds are so complicated that tables of coefficients to differential equations are required just to accurates approximate the results. The values are typically determined by physical experiement as opposed to mathematical modeling.

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

 

[Storm Butler]

Thanks that page was actually fairly informative. However i still have a lot of questions, like why are there different levels (if that is what you call them) of air resistance and what causes some to arise at higher speeds? also where would you find a table of the different air resistance terms? Finally, while looking at the problem of air resistance (linear) i keep trying to solve the differential but i keep getting V=e^((b/m)*t) but my book tells me that the answer is v(t)=V*e^-((b/m)*t) (i think it is negative but i can't remember). Why does my answer keep coming up incorrect (I used both separation of variables as well as putting it in the form of a linear equation and solving using the integration factor e^int(b/m)dt.