Trajectory Calculations

Admiral Griffith · Post by **Admiral Griffith** » 2003-04-23 03:24pm

I'm trying to figure out what angle is going to allow a pneumatic cannon to fire a ping pong ball as far as possible. If somebody could just give me an equation for this or point me to a site, I'd be extremely thankful.

Post by **Dalton** » 2003-04-23 03:26pm

I'm no math/physics whiz, but isn't 45 degrees the best angle for what you require?

Admiral Griffith · Post by **Admiral Griffith** » 2003-04-23 03:33pm

Dalton wrote:I'm no math/physics whiz, but isn't 45 degrees the best angle for what you require?

That sounds reasonable. Thanks.

Durandal · Post by **Durandal** » 2003-04-23 03:46pm

Yes, a 45 degree firing angle will give you the maximum possible distance.

Post by **Sea Skimmer** » 2003-04-23 03:49pm

Dalton wrote:I'm no math/physics whiz, but isn't 45 degrees the best angle for what you require?

45 degrees is the ideal for maximum range with a ballistic weapon.

Zoink · Post by **Zoink** » 2003-04-23 03:55pm

45 is good. But it would also depend on wind (if you are outside), because a ping-pong ball is really light, it will be carried easily in the air currents. A shallower trajectory might be warranted in that case and might produce longer distances more consistently.

Pu-239 · Post by **Pu-239** » 2003-04-23 04:20pm

I thought it was 36 degrees.

Post by **Sea Skimmer** » 2003-04-23 04:32pm

Pu-239 wrote:I thought it was 36 degrees.

I've never heard that one. Some people think its 30 degrees, but thats a myh that seems to have been spawned by many battleships only having 30 degrees of elevation for there main battery. That however was a limit of the mountings.

Simply taking a look at warships1s naval weapons pages will show that guns got there longest ranges at 45 degrees.

Post by **Colonel Olrik** » 2003-04-23 04:41pm

Pu-239 wrote:I thought it was 36 degrees.

It's 45º period. Elementary physics.

A launch at angle a from the origin at velocity vo is given by

x=Vo*cos(a)*t

y=Vo*sin(a)*t-1/2*g*t^2

do y = 0 (when the projectile is at ground level), take t as function of the angle

replace in x, and differenciate in order to the angle a.

Then find the minimum by equalizing it to 0, and you'll get a = 45º

Post by **Sea Skimmer** » 2003-04-23 04:44pm

Colonel Olrik wrote:
It's 45º period. Elementary physics.

And if you want to find out what happens after you have fire, http://www.warships1.com/index_tech/tech-073.htm

Post by **Colonel Olrik** » 2003-04-23 04:48pm

Sea Skimmer wrote:
Colonel Olrik wrote:
It's 45º period. Elementary physics.

And if you want to find out what happens after you have fire, http://www.warships1.com/index_tech/tech-073.htm

That's one of the best parts of the mechanical engineer degree. You get to learn all these wonderfully fantastic things (together with a bunch of crap, of course). all my life I've been fascinated by physics and mechanic.

Today I went to a job interview. If I'm in, I'll spend my next two years designing a new robotic welding system for aircraft turbines. Life doesn't get much cooler than that

Nathan F · Post by **Nathan F** » 2003-04-23 06:29pm

Colonel Olrik wrote: That's one of the best parts of the mechanical engineer degree. You get to learn all these wonderfully fantastic things (together with a bunch of crap, of course). all my life I've been fascinated by physics and mechanic.

Today I went to a job interview. If I'm in, I'll spend my next two years designing a new robotic welding system for aircraft turbines. Life doesn't get much cooler than that

Wow, that sounds great!

The more I learn about Engineering, the more I like it...

Post by **Colonel Olrik** » 2003-04-23 06:54pm

Nathan F wrote: Wow, that sounds great!

The more I learn about Engineering, the more I like it...

It is great. I'll make a big party here if they accept me. There's a problem, though. I have a contract that only ends in June and they'd prefer if I had immediate availability. Well, I just have to wait and see if they can't find someone free as good as me and so cheap to them (I'm almost fresh out of college, big wages are still to come

).

namdoolb · Post by **namdoolb** » 2003-04-24 11:48am

If we didn't have to deal with air resistance then 45 degrees would always be the optimum firing angle.

As it is, you have to pay attention to the density of your projectile.

If your projectile has a high density (a ball bearing or a marble for example) then you can safely fire at 45 degrees and get the optimum distance.

However, if your projectile has a low density (ping-pong ball for example) then air resistsance will cause it to lose horizontal velocity quickly after launch. In these cases you can sometimes gain further distance by firing at a slightly lower angle. (finding the optimum angle in this case may require trial and error).

**Edit** You could get round the air resistance problem (and probably gain a considerable amount of distance) by filling the ping-pong ball with a heavier substance (water maybe, or sand), but you'd have to check to see if that was allowable **Edit**