I am currently working on an artillery simulation but I came across a problem: I require an equation that will give me the required initial angle when given a velocity the range and elevation, gravitational acceleration and all bullet properties but with airdrag, so far I have found this:


It works well, but the bullets dont hit the target at the predicted time so I am assuming it's airdrag that is slowing them down (it is programmed in an already existing game so i can't access the source code).

Could anyone post me an equation that would give me the required angle with airdrag?

  • $\begingroup$ physics.stackexchange.com/q/57801 this may help $\endgroup$ – Ed Yablecki Jan 13 '16 at 22:01
  • $\begingroup$ i saw that post but didnt understand half of it :/ could you be so kind to extract what i need from there in terms of the angle ? $\endgroup$ – Max Mozolewski Jan 13 '16 at 22:13
  • $\begingroup$ farside.ph.utexas.edu/teaching/336k/Newtonhtml/node29.html Try this link, $\endgroup$ – Ed Yablecki Jan 13 '16 at 22:19
  • $\begingroup$ this i also looked through but the equations dont take into account the X and Y, is there a way to incorprate air drag into the equation in my post ? $\endgroup$ – Max Mozolewski Jan 13 '16 at 22:36
  • $\begingroup$ The ballistic motion obeys differential equations. Requiring an equation for $\theta$ implies to write an analytic solution for the equation and then solve a relation on it in terms of $\theta$. However, not all differential equations can have their solution written as an analytical formula (and even if it is the case, not all equations can be solved for a quantity such as $\theta$). In the present case, I don't think you can write the analytical solution of the full problem, and the extreme cases of very low or very high drag in the link given by @EdYablecki are probably the best you can get. $\endgroup$ – Joce Jan 14 '16 at 13:08