How Do You Calculate Accurate Muzzle Velocity in an Air Cannon Project?

[bulldogbaseba]

ok I am doing a project where i shoot a baseball from an air cannon. i am trying to solve for the muzzle velocity of what i should get at certain pressures. also i used the cross sectional area of the baseball, is that what i should use? when i solved for the force i used the force acting on the baseball from (10 psi of pressure+air pressure)-(air pressure) and once i found the force, i divided by the mass of the baseball and got the acceleration. anyways after using si units and everything i got the final velocity to be 60.79 m/s or 136.7 mph. i know for a fact that is not right. how can i get close to the actual velocity i measured? could i try and figure out the force of friction between leather and pvc and subtract that from my force earlier?

 

[dacruick]

Yes the force of friction will definitely affect your answer. Another thing is that your calculating is for an air tight tube. Baseballs have seems that no doubt allow air through, decreasing your overall pressure. Also, the pressure will not be constant. You will start off at 0 and then it will take some amount of time to get to 10. The volume also increases as the baseball gets closer to moving out of the "muzzle". So you are dealing with pressure gradients the whole way through.

 

[bulldogbaseba]

well my professor never told me to just assume that it is air tight but he also never brought that up when discussing why there was a difference in the measured and expected velocities. i also have a cloth that goes over the baseball to make it fit snug in the barrel. I am not looking for an exact answer because i already know the measured velocity and for this i will assume that it is air tight. i guess what I am trying to ask then is how do i find the friction between pvc pipe and the baseball wrapped in cloth to find the total of the forces acting on the ball?

 

[dacruick]

wrap the cloth around the PVC tube and pierce a little hole into it. Put one of these spring scales through the hole (http://en.wikipedia.org/wiki/File:Weeghaak.JPG) and pull. This will give you the value of force that you have to pull with to maintain a constant velocity. If you measure the time that it takes to travel the distance of the PVC pipe(once again at a constant velocity), you will have enough info to calculate friction.

well my professor never told me to just assume that it is air tight but he also never brought that up when discussing why there was a difference in the measured and expected velocities.

who cares if your professor discussed it? You know that it's a factor that adds the discrepency between experimental and theoretical results.

 

[Delphi51]

Very interesting! It seems to me there would be a kind of tradeoff between the friction and pressure drop due to leakage. The tighter you make it, the higher the friction and the lower the pressure drop. Wouldn't there be a pressure drop in the pipe delivering air to the cannon, too? Very complicated. I wonder if you could come up with a model to compare with actual muzzle velocities and work back to find the parameters (friction, pressure drop) in the model? With data for a few different shots you could potentially find more than one parameter.

 

[dacruick]

The tighter you make it, the higher the friction and the lower the pressure drop. Wouldn't there be a pressure drop in the pipe delivering air to the cannon, too?

Very nice, I like.