How to calculate trajectory of an object with air drag

[ferret_guy]

I am trying to predict the flight of an object with a parabolic trajectory including drag due to air resistance how do I do this? the wiki page was not clear its my understanding its relative to the square of the speed.

 

[Bob S]

I have used numerical integration with this energy loss rate (see http://en.wikipedia.org/wiki/Drag_(physics ))

$$\frac{dE}{dt}=\frac{1}{2}\rho \cdot C_{drag} \cdot A \cdot v^{3} \text { Newton meters per second}$$

The force is $$F=\frac{1}{2}\rho \cdot C_{drag} \cdot A \cdot v^{2} \text { Newtons}$$

 

[D H]

I have used numerical integration

The reason Bob S used numerical integration is because that is pretty much the only choice. There is no closed form solution in the elementary functions. There was a buzz a month ago or so about some kid in Germany who claimed to have found such a closed form solution. He didn't. He found a slowly converging series solution (that's not "closed form"), and what he found is well known and is also well known as pretty much useless. There is no simple closed form solution to this problem.

As a historical note, the problem of a ballistic object with drag was one of the driving forces (if not the driving force) that motivated the development of digital computers back in the 1940s and 1950s.

The force is $$F=\frac{1}{2}\rho \cdot C_{drag} \cdot A \cdot v^{2} \text { Newtons}$$

ferret_guy: Note that this is the magnitude of the drag force. The direction is always against the velocity vector.

 

[ferret_guy]

So I could get a reasonable result by calculating the force of drag and assuming that for a very small period for time (eg 1 second) and do that over and over until the object lands?

 

[Bob S]

I usually do it once per millisecond until the object lands.