__
The Effects of Barrel Length on the Range of a
Projectile Fired From A Pneumatic Cannon__

Table Of Contents

Humans have always known that which goes up must come down. Sir Isaac Newton converted this knowledge into mathematical law. However, this fact has largely disappointed our species, and thus we devise new ways to counteract gravitational force. From the creation of the catapult to the invention of the airplane, man has constantly fought against nature. The latest step in our struggle is the Pneumatic Cannon. We, being the inquisitive people we are, search for ways to improve the efficiency of the aforementioned cannon. Thus, the question arises: “What barrel length will maximize the range of a juggling ball fired from the cannon?”

While mulling around on the internet, we ran across some information on air cannons, and also found that another group of people, labeled #3 in our bibliography, has previously done research in our subject of study. While researching their experiment, we found that they did not find any correlation between barrel length and range. We decided that they did not make their barrel lengths extreme enough to form any correlation, so we improved on their experiment by making our barrels either longer or shorter than theirs. We can use linear kinematics to find the distance the projectile travels.

Using the equation s = ut + ½ at^{2} we can find the vertical range of
the projectile. Finally, we reach the dependent variable of our experiment. We
plan to compare the distances that the projectile reaches and the length of the
barrel of the cannon. Hence, we arrive at our hypothesis-

The length of a cannon’s barrel affects the projectile’s range.

The Method Log is not of great importance to the experiment itself, but if you feel inclined to read it, go right ahead.

1. Gather materials

2. Set up cannon- see diagram.

3. Fire the cannon to record data about the distance, acceleration, time, etc.

4. Repeat steps 1 – 3 using several different barrel lengths.

5. Graph the data to determine the line of best fit.

6. Using the equation of line of best fit, find the maximum range for the cannon at the constant pressure used.

7. Find the optimum barrel length for the range.

1. An electrical button or similar device (not crossing two wires).

2. A sprinkler solenoid

3. An old pressure valve (AKA nipple, like the one on your bike)

4. 3" diameter ABS piping

5. 3" end cap (ABS)

6. 3" male threaded adapter (ABS)

7. 3" to 2" female adapter (ABS)

8. 2" diameter PVC pipe

9. 2" female coupler (1 plus the number of barrels you make)

10. 1" threaded coupler (x2)

11. 2" to 1" male to female adapter (x2)

12. Electrical power source (i.e. batteries - 9V x 3)

13. Teflon tape

14. ABS glue

15. PVC primer

16. PVC glue

17. 2" diameter projectiles

18. Duct tape

19. Electrical tape

20. Pressure pump (air compressor, bike pump, etc.)

21. Pressure gauge

Construction

1. Drill hole in 3" ABS End cap

2. Glue tire valve in to that hole. Make sure to have a tight seal.

3. Glue together the adapters until the 3" air chamber can be attached to the 1" sprinkler solenoid 'entrance.'

4. Glue the dry end cap from step one onto the other end of the air chamber.

5. Cut the 2" PVC tube to the desired length for the barrel.

6. Glue the 2" female adapter to the end to be able to attach it to the 'exit' side of the solenoid.

7. Wire the batteries to the solenoid and the button. Make sure it works. Blackrain and Cow's website will help if you need it.

8. Attach the air chamber

9. Attach the barrel.

10.
Allow all the glue to dry overnight (it ** will** explode if it
doesn't!). Enjoy!

We took different lengths of pipe and turned them into barrels for our cannon. More specifically, we cut lengths of pipe that were 1’, 2’, 3’, and 7’ in length. The reason for this was funding, and we wanted to get the two extremes in length, extremely short and extremely long. We designed the cannon as a modular piece of equipment, which made repairs extremely easy, except that more pieces could break because of it. We also shot two different objects, both juggling balls, out of our cannon in an effort to avoid damage to the projectile and also to make sure there was nothing special about the particular object we shot that would make it go higher or otherwise skew our data. We labeled them balls #1 and #2. When we collected enough data, we took the average hang times of the two objects, and found the average final velocities of the balls in different barrels. Oh yeah, we always shot our balls at 80 psi.

Because time is
directly proportional to range, we found that by graphing the times of the
balls, we could see which ball was in the air the longest, which must have gone
the highest. By analyzing the graph of the times, we found that the ideal
barrel length will be within half a foot of two feet, that is between 1.5’ and
2.5’. We predict that there will be a plateau effect, and after 2.5’, the range
of the projectile will drop suddenly. While it would be nice to test this
theory, the availability of funding was rather limited, which made it such that
we could not afford the amount of materials that such an undertaking would
incur. We realized that because we recorded the times that the objects were in
the air, we could simply use linear kinematics to discern the ranges that they
reached. By using the equation v=u+at, where v=0, we could figure out the
initial velocity. Because half the time in the air is spent coming down, we
simply found the initial velocity by setting the final velocity at zero, using
the accepted acceleration due to gravity, 9.8m/s^{2}, as a, then using
half the time we recorded. Then, using the final velocities we found, we
calculated the range using the equation v^{2}=u^{2}+2as, where
u, v and a are the same as in the other equation, and s is the vertical
displacement. We noticed that there is a peak in the data at a 2 foot barrel
length, and by making a graph of best fit , and then looking at that graph, we
decided that the graph will peak around approximately .5 feet within either side
of the 2 foot barrel length.

Our hypothesis, that barrel length affects the range of the projectile, was correct, insofar as we were able to test it. We came up with many theories to explain the phenomenon. Our first theory is that the friction between the ball and the sides of the barrel causes the ball to slow down, and thus, not go as high. This cannot be the entire explanation however, because it does not explain the peak in the data at the 2-foot barrel length. Another theory lies in Pascal’s research. Because the pressure in the compression chamber is constant, then the amount of pressure at the end of the barrel is variable depending on the length of it. When the barrel is longer, there is more volume, and because PV=PV, the amount of pressure behind the ball at the end of the barrel is lessened. However, we still have the problem of the smaller ranges with smaller tubes. Our hypothesis for that is that the pressure is higher behind the ball, yes, but because there is less time for acceleration, the ball does not go as high. An analogy for this would be punching the accelerator in your car for one second rather than holding it at 75% acceleration for 3 seconds. Yes, the acceleration is higher at maximum acceleration, but the increased time at a smaller acceleration still results in a higher velocity. Also, the more time there is a force being applied behind an object, gravity gets less of a chance to take over. There are problems inherent in our experiment, just as there are in any. Specifically, we ran into problems timing, and also with getting the correct pressure in the compression chamber. We solved these problems by using a pressure gauge, and also by having multiple timers. Our other major problem was a lack of funding, coupled with time constraints. We were unable to solve these problems, but we did the best we could given the situation presented to us. In the future, if we were ever to redo this experiment, we decided that having a computer time the flight of the ball, and having a computer fill the compression chamber with a perfectly constant pressure, we would be able to gather more accurate data. Also, we decided that we would use more barrels, take more data, and then try changing the pressure in the chamber to see what affects the range of the projectiles launched from our cannon. After all, launching spark plugs a quarter mile is all in the interests of science, right?

http://www.glenbrook.k12.il.us/gbssci/phys/Class/newtlaws/newtltoc.html <This site is a good review of Newton's laws of motion.>

tuhsphysics.ttsd.k12.or.us/Research/ib02/LelaWint/page1.html <This site has good ideas and is quite humorous as well>

www.stinggroup.addr.com/cannon/cannon.html <This site has detailed instructions on how to build a cannon>

__International Baccalaureate Organization Physics
Data Booklet. __ 2001. Geneva, Switzerland. <This booklet
helped us find the formulas used for our analysis>

www.mla.org <This website is important in explaining how to write bibliographies>

Giancoli, Douglas. “Pressure in Fluids”. __Physics:
Principles with Applications__. Ed. Corey, Paul F. 1998. New Jersey:
Prentice Hall Press. <This book was our class text, and we used it to find
things about pressure and fluids and stuff>

http://www.bosik.com/impact.htm <Take a look at what happens when you make an EXTREME pneumatic cannon! Also the practical side to having a air powered howitzer...>

http://84paintball.tripod.com/davidspaintballpics/id13.html <Possible military applications?>

Guten Spielen Haben Fühlen!!!

That's Jerman.