Researched by Joey Punzel and Zack Ham
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Table of Contents
Background | Top
An air cannon is set up with a barrel that has a hole in one end that is connected to something that will release an amount of pressurized air capable of propelling a projectile some distance. With too short of a barrel, a projectile will not reach its maximum velocity because it will leave the barrel before the release of pressurized air has finished accelerating it, which will cause it to cover less distance that it could otherwise. With too long of a barrel, the projectile will reach its maximum velocity and the friction and other forces of traveling through the barrel will be greater than that of air friction alone, which will cause the projectile to exit the barrel with a velocity that is less than optimal.
Review of literature | Top
According to Zeb (2001), firing a 1.5lb object at 50 PSI can reach a potential distance of 300 yards under optimal conditions.
According to Mr. Thames (Master Blaster 1998), creating an air cannon with a 10ft barrel length and an air tank consisting of 100 PSI or less, has the potential to launch a 2lb projectile 440 yards.
Hypothesis | Top
We believe that the optimal barrel length for maximal exit velocity of a golf ball will be approximately four feet when launched at 40 PSI.
Procedure | Top
Obtain all materials
Set up air cannon based off of Construction Procedure with a 72” barrel length.
Pump 40 PSI into the air tank making sure the air valve is closed.
Aim the cannon straight up and load a golf ball into the barrel.
Fire the air cannon by rapidly opening the ball valve and record the time in seconds from release to impact on the ground.
If the golf ball does not land within 15 feet of the launch site, return to step three because due to bad aiming or a crosswind, data will not be accurate enough.
Repeat steps three through siz and compute the average time.
Cut six inches from the current barrel length with a handsaw or PVC cutters.
Perform steps three through eight until there are six different barrel sizes with three trials each.
Perform steps three through seven twice more with barrels cut to be the two even numbered lengths in inches in between the two optimal barrel lengths. (EX. If 72” and 66” were the two optimal barrel lengths, 70” and 68” would be tested.)
Determine the final optimal barrel length by use of data table or graph.
Materials | Top
12’ 200 PSI rated 1.5” PVC
3’ schedule 40 2” PVC
One 2” PVC end cap
One 2” to ¾” PVC female threaded reducer bushing
Two 1.5” to ¾” PVC female threaded reducer bushings
Two 1.5” PVC couplings
One 2” PVC coupling
Two ¾” male threaded PVC straight joints
One ¾” female threaded PVC ball valve
Teflon tape
PVC glue
One tire valve stem
One saw or set of PVC cutters
A drill
Diagram | Top
Construction | Top
Cut the 12’ piece of 1.5” PVC into two 6’ sections. These will be the two barrels you will be working with. Attach a 1.5” to ¾” threaded reducer bushing to one end of each barrel with a 1.5 coupling. Now that the barrels are complete, carefully drill a hole in the 2” end cap that will allow the tire valve stem to be pulled through properly and not create any leaks, then insert the tire valve stem. Attach the 2” end cap to one end of the 3’ of 2” PVC to begin making the air chamber. Attach the 2” to ¾” threaded reducer bushing to the other end of the air chamber with the 2” coupling. Apply a layer of Teflon tape to each side of the two ¾” threaded straight joints, and screw them into each side of the ball valve. Now you can screw the air chamber and barrel into each side of the ball valve, connecting the straight joints to the reducer bushings.
Notes: Make sure to use schedule 40 PVC for the air chamber as it is very strong. If something too weak is used, it is liable to explode when pressurized. When attaching threaded items, always use Teflon tape to create a secure connection that will not leak. When attaching non-threaded items, use PVC glue liberally and allow at least 24 hours to completely dry.
Data collected | Top
Analysis | Top
The velocity calculations in our second data table were calculated using the formula v=u+at. Since our launches were done with the cannon aiming straight up, horizontal displacement was negligible (less than 15 feet). We used the formula v=u+at by setting a to 9.8m/s/s (the acceleration constant of gravity), to the respective time cut in half, and u to 0. The reason u, or initial velocity, was set to zero was because we were doing a calculation of the final velocity, starting from when the projectile has an initial velocity of 0 (during its instantaneous rest at the peak of its flight). We know that the time it takes to go up is equal to the time it takes to go down, and this why we assumed that from the peak of its flight to its destination was half of the recorded time. We also know that when we ignore air resistance, on a level surface the final velocity is equal to the initial velocity. We were on a level surface, and since we were launching a golf ball (which has a minimal surface area) on a calm, near-windless day, we decided that the effects of air resistance were small enough to be neglected.
To visually analyze the significance of our data, below is the graph comparing average exit velocities for each barrel length.
Our data shows that
from the barrel lengths we tested, a 60” barrel is the optimal
length for maximal exit velocity. Between the 60: barrel length and
the longest barrel we tested (72”) there is a 9 m/s difference
in exit velocity. Between the 60” barrel and the shortest
barrel length we tested (42”) there is a 5.1 m/s difference in
exit velocity. Shown by our graph and confirmed by our raw data,
there indeed was too short or too long of a barrel, and the optimal
barrel length was able to make significant improvements on exit
velocity. Our 60” barrel projected a golf ball at a rate that
was 34% faster than our 72” barrel, and 17% faster than our 42” barrel.
Conclusion | Top
Our hypothesis turned out to be wrong under the conditions we tested it (3’ long, 2” diameter air chamber pressurized to 40 PSI). Our experiment, however, was successful, and we were able to gather meaningful data that shows that barrel length has a significant effect on exit velocity. We gather that the explanation for this is rather simple. A burst of air enters the barrel as the ball valve releases pressure from the air chamber, and depending on the size of the air chamber and how pressurized the air was, this sudden force canb e expected to last until the pressurized air spreads into an area large enough that it can once again expand to normal atmospheric pressure. As the pressurized air moves out into the barrel, it is expanding along the length of the barrel, and as a result the pressure is being relieved and the force that expanding air is creating will diminish along the length of the barrel,. Hence, a longer barrel has a more diminished force a the end, whereas a shorter barrel has a stronger force at the end. There must be a threshold where the negative forces of the barrel (friction, for example) combined with the positive force of the expanding air result in a level of restrictiveness equal to the negative forces the projectile experiences while moving freely though air. Around this threshold we find the optimal barrel length, because the forces created by the rapidly expanding air have done as much work on the projectile as will be helpful. A shorter barrel while result in the projectile exiting before the expanding air can finish its work, and a longer barrel will slow down the projectile after the expanding air has done all it can. We believe that this threshold, or optimal barrel length, would be affected by the size of the air chamber, the pressure in the air chamber, the angle of launch, the diameter of the barrel, and the weight of the projectile. Since all of these factors may affect the optimal barrel, length, we conclude that for a pneumatic cannon equipped with a 3’ long, 2” diameter air chamber pressurized to 40 PSI, shooting a golf ball tightly fitting a 1.5” barrel, the optimal barrel length is approximately 60”.
There are four important problems that I will note of our data collection. First, the effect of air resistance and that it has been ignored. We consider this a minor problem, because although it does give an undetermined error to our velocity calculations, we believe this error to be consistent throughout our data. If it is consistent, it equally affects all data and our determination that the optimal barrel length is approximately 60” stands firm. To improve upon this and get more accurate velocity calculations, we could determine the air resistance present on our day of testing and factor this into our calculations. The second problem is that we used a manual ball valve. We originally tried to use an electronically opening irrigation valve, but after much testing and two different valves we failed to get the air to flow at a rapid enough rate once the valve was opened. The problem with a manual valve is that there is no way to control the rate that air is release from the chamber. We did our best to release it as quickly as possible each time but it would be careless to pretend there was no error. The obvious solution to this problem would be to consult others who have gotten an electronic valve to function well and get it working properly. The third error to note is simple an expected inaccuracy with out method of timing. Joey manually started and stopped his stopwatch to time the duration of each trail, and he is not perfect in his timing abilities. A way to improve this would be to have used that electronic valve I just discussed. It is much easier to press two buttons at the same time, the valve opening button and the stopwatch’s start button than it is to time up a manual launch and the stopwatch start time. The final error worth noting is in the reliability of our data. For a more accurate experiment, it would be wise to test numerous more barrel lengths, perhaps taking data for every inch or two differences in length. Also, you can always get more accurate results by taking more trials. If I was using this data for anything important, I would probably take 10 trials and average those for each barrel length.
Bibliography | Top
http://blizzard.rwic.und.edu/~nordlie/cannon - John C. Nordlie’s Air Cannon Website: This was the first site we visited, and it provided some motivation to go forth with the project and seek out more details. Some good tips can be found here, but not entire instructions.
http://www.xinventions.com/main/spud/home.htm - X Inventions Pneumatic Cannons: During our project we felt the desire to exceed the basic requirements and branch out a little. If you are interested in automatic pneumatic guns, this site has plenty of information.
http://www.geocities.com/z_e_b_deming/current.html - Zeb’s Air Cannons: Zeb is the man. Here you can find some clear and simple plans for making your own air cannon. We used this site partially on our design.
http://www.valuelinx.net/~dthames/spudguns.htm - Master Blaster Pneumatic Cannons: Plenty of information here is available to make your air gun with ease. Be sure to check out the videos, this guy is nuts!
