# Optimal angle for cannon?

by TheLaughingMan
Tags: angle, cannon, optimal
 P: 9 I was trying to figure out the best angle to shoot a cannon, with air resistance in the differential equation. I came up with ~36.5 degrees, is that right?
 P: 4 I would bend a little more towards 30 degrees...
 P: 9 wanna explain how u got that one. It shouldnt depend on anything except gravity mabye and the air resistance possibly. (assuming we are talking about only 1 type of cannon ball)
P: 4

## Optimal angle for cannon?

 Quote by TheLaughingMan wanna explain how u got that one. It shouldnt depend on anything except gravity mabye and the air resistance possibly. (assuming we are talking about only 1 type of cannon ball)
Well of course you would have to consider the amount of air resistance, but then of course there's the weight of the cannon ball (those are pretty heavy). Most cannons can fire cannon balls pretty far, but to get it to fly the farthest at 45 degrees would take a pretty strong shot. At 36.5 it still would take a little more power than a regular cannon to shoot it farther than 30. I also aimed for 30 because that's the angle that most cannons are aimed at anyway.
 P: 9 Im talking about an idealized situation where the cannon balls are the same and the air is exactly the same. Anyone else have an opinion?
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 Quote by TheLaughingMan I was trying to figure out the best angle to shoot a cannon, with air resistance in the differential equation. I came up with ~36.5 degrees, is that right?
What differential equation? And what value are you using for the air resistance? Don't you think we would need to know that?
 P: 2,162 For realtively low muzzle velocity, it matters whether the distance is measured at the same elevation as the muzzle. For relatively high muzzle velocity, the radius of the planet you are on becomes an issue. With a high enough muzzle velocity, you could put a projectile in orbit using an angle of zero degrees.
 PF Patron HW Helper Sci Advisor P: 2,796 The angle is dependant on a number of variables including initial ball velocity, mass of ball and size of ball (cross sectional area for drag calculation). If you wanted to get more accurate, the variation of air density with altitude and variation of coefficient of drag as a function of velocity would need to be added. There is no single value for the angle which is optimal.
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