Mass vs Launch Velocity

James Rivas & Stuart Legg

Background Information:

The term potato cannon refers to a device intended to use combustion to propel potatoes at high velocities. There have been various names for this invention over the years including potato gun, potato cannon, spud gun, and similar names. The earliest reference to a potato cannon is the “Colorado Goose Gun”. The “Colorado Goose Gun” has been around since the 60s. This version of the potato cannon was made from beverage cans with the end removed taped together. A single can with one end left on and hole in it was used as the end piece. Potato cannons have gone on to be made out of various materials; popular materials being steel and plastic. They have also been modified to use a variety of propellants for combustion as well as air compression. Potato guns grew in popularity because of how easy to build and use they are and how common the materials necessary to build them are. Potato cannons are mostly used for recreational use; so the average joe can have the experience of using artillery.

Statement of the Problem:

The purpose of this experiment is to find the relationship between mass and initial launch velocity of a projectile when launched from a combustion powered potato cannon.

Review of Literature:

A previous study done by William Eric Marsh determined that a longer barrel would result in an increased launch velocity of the potato. This was due to the fact that the forces from the combustion have longer to act on the potato in the longer barrel while a shorter barrel will not be able to use the full force of the combustion. A generally accepted fact mentioned on multiple websites is that there is an ideal barrel length that, depending on the size of the combustion chamber, will be able to harness the largest amount of the combustion energy possible. If the barrel is too short then combustion will not be finished an the remaining energy will be wasted. If the barrel is too long then combustion will finish and the potato will lose energy to friction. The optimum barrel length would be one that allows the potato to exit the barrel right after combustion has finished. Objects with more mass have more inertia and objects with less mass have less inertia.

Hypothesis:

We believe that there will be an optimum mass that is neither too heavy or too light that will be launched with the highest velocity. Projectiles that are too small will not have enough inertia to remain in the barrel long enough to use all of the energy from combustion. Projectiles that are too large will have too much inertia and will remain in the barrel after combustion is complete losing energy to friction. We will try to find the mass of the projectile with the right amount of inertia to remain in the barrel long enough to harness the energy from combustion.

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To study how launch velocity relates to mass we decided to use a preexisting potato cannon. The potato cannon followed the design in the picture at the left, plus a few additions for safety. The basic method for firing the aforementioned cannon is to load the cannon from the front of the barrel(as opposed to through the combustion chamber). A ramrod is used to ensure that the round is the at the same position in the barrel for every shot. The propellant, 10 ml of methyl alcohol, is then loaded into the combustion chamber. The end cap is placed on and the cannon is ready to be fired. The methyl alcohol is ignited by an electric spark, created using a barbecue lighter.

The method we planned to use to determine launch velocity was to fire the potato cannon straight up into the air and record the time before it hit the ground. We would then, using SUVAT, calculate how fast the projectile was traveling when it left the barrel. We used the apparatus pictured at right to hold the cannon so that it could be repeatedly fired as straight up as possible. Using multiple trials we could find the average launch velocities for various masses and use these to find a relationship between initial launch velocity and mass.

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We took five data points for each mass of projectile(except the 150g and 200g for which we took only 3 data points). We then used Excel to calculate the initial launch velocity from the time spent in the air. We took this data and averaged it; the averages are shown in this table. The data follows a downward trend with the heavier projectiles having a lesser initial launch velocity. The relationship between initial launch velocity and mass can be seen in the following graph. This graph shows that the relationship is nearly linear.

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Looking at the data we see that the results found in the experiment do not match what we predicted would happen in the hypothesis. There are a variety of reasons for this happening. One possibility is that there is an ideal mass, however it was lower than the range of masses that we experimented with. Another possibility is that there is no ideal mass; the more inertia an object has the lower velocity it will propelled at. This would mean that the idea that more inertia allows more energy to be transferred is flawed or that the extra energy transferred is not enough to make up for the energy lost moving the heavier object. We cannot tell without further study and experimentation which of these possibilities it might be, or if it might be another cause altogether. The data that we collected supports the idea that lighter objects will have a higher velocity because they are easier to move. They therefore gain a higher velocity with the same amount of energy.

There were several sources which could possibly have caused errors in our data. The first source that we must consider is temperature. As we cannot control temperature we are left with what nature provides. This can be problematic as the effectiveness of the combustion may vary with the temperature. Any experiments in the future should be conducted in more regulated weather, preferably in the summer where the cold will not hinder the combustion. Another possible source of error was the amount of fuel. It is near impossible to keep the amount of fuel the same for every firing. More fuel could equate to higher velocity throwing off the data. A limitation of our experiment was that it did not include masses lower than 25 grams. Testing of these masses could possibly provide the “ideal mass” that was the subject of our hypothesis. A future experiment could try our procedure with smaller masses and see if the pattern that emerged in our data holds true. Another experiment that could be conducted related to ours would be to compare the initial velocity the the coefficient of friction of the outside of a projectile. It would be interesting to see if the data from that experiment reflected ours or the experiment on barrel length.

In putting our experiment together there were a number of challenges we had to overcome. The first challenge we experienced was in the operation of our equipment. We found that it was difficult to fire a combustion powered potato cannon in cold environments. In colder environments the fuel would not ignite. This caused us to schedule our data gathering around the weather and limited the time we could use. This was especially problematic because of the time of year; the cold weather and shortened periods of sunlight cut down the possible opportunities in which our apparatus could operate. We also encountered a problem when trying to calculate our data. We were not including the starting height of the barrel in our velocity calculations. After a brief period of research to find the correct formula this problem was solved.

In conclusion, our hypothesis was flawed and new experiments should be conducted to see how it was flawed. It would be interesting to find out if the relationship we identified holds true in other conditions or with smaller masses. Experiments conducted in the future could clarify and expound on the results found by this experiment.

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NMP Products. Ed Haas. Jan.10 2008 <http://www.nmpproducts.com/faqspud.htm >

Spud Tech. Joel Suprise. Jan. 10 2008 <http://www.spudtech.com/default.asp>

Spud Speed Test. William Eric Marsh. 2005. Farm Devil. Jan. 10 2008 <http://www.farmdevil.net/wp-content/uploads/old/spud.pdf >

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Spud Gun Technology Center Contains general info about potato cannons

How Stuff Works Describes how potato cannons operate.

Spud Files A collection of files relating to potato cannons.

Advanced Spuds Collection of 'spud gun' information.

Instructables Instructional video on how to build a potato cannon.

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