Pressurized Dart Gun!
The effects of pressure on displacement
By: Adam Gage Kevin Oliver Shanon Turner
Background.:.Question.:.Hypothesis.:.Method.:.Set-up.:.Data.:.Conclusion/Error Analysis.:.Related Pages
The dart gun is a “weapon” with many different purposes. Its potential uses range from a child’s toy to a tool that is used to capture animals by wildlife researchers. In general, dart guns are instruments like regular guns that are specially designed to fire suction-tipped darts rather than bullets, and they are powered by pressurized carbon dioxide cartridges (Smith 2003). Many of them, such as toys, like the gun used in our experiment, are virtually harmless. Others have to be able to knock out animals so that wildlife researchers can do things like fit them with radio tracking collars, take blood samples, or relocate the animals (Predator Conservation Trust 2003).
Modern dart guns are made with plastic, which was first man-made in 1862 (American Chemistry Council 2007). The first creation of the plastic dart gun occurred in the 1950s (Sweeney 1998). However, similar weapons were used way back into ancient history. For example, the blow dart was used by Native American tribes such as the Cherokee, and is so old that its exact origins are unknown, though it is suspected that they were used BCE (Cherokee Nation Cultural Research Center 2008).
Dart guns are relatively easy items to use; all that has to occur is pressure entering the tube to force the projectile out. Because of this, balloons can be used as a tool instead of CO2 pumps. A balloon blown up to a large size should be able to shoot a dart a relatively far distance out of a plastic tube, as more air inside of a balloon tends to mean more pressure (Vernier 2003).
What is the effect of changing the size of a balloon serving as a pressurized launcher on the displacement of a dart out of a blow gun? Size will be defined as the diameter of a balloon in centimeters (cm), and displacement will be defined as the flight of a dart in meters (m).
If the diameter of a balloon placed on the end of a tube is increased, then upon release of the balloon, a more heavily-inflated balloon will force a dart in the tube to fly farther than a less-inflated balloon will because the added air in the balloon will create more air pressure, which causes a greater force (which is suggested by the formula F=PA, where F=force, P=pressure, and A=area). Pressure will be defined in terms of pascals (Pa).
The first step in the process of carrying out the experiment was gathering all necessary materials, which included balloons that are capable of inflating up to a 19-inch (48.26 cm), a tube measuring 75.5 cm, darts that fit the tube, and a landing area that is at least seven meters long. Additionally, in order to measure pressure, the method of observing the displacement of x inches of water was used, so a curved glass tube is necessary for that (see Diagram 1 next page). After viewing how many inches the water in the tube rose in inches, we converted this unit of pressure to pascals.
To test the effect of the balloon’s size on dart displacement, the balloon was inflated to the desired diameter (ranging from 7.62 cm to 48.26 cm), and attached to the back end of the tube (which was the main part of a disassembled dart gun). The dart was placed in the back of the tube. Then the tube was placed on a surface 18 inches (45.72 cm) off of the ground. Finally, the balloon was released, and the dart was fired out of the tube. Diagram 2 below illustrates this set-up.
After the firing of each dart, we observed where the darts landed, and measured how far (in meters) they had traveled. Darts were fired from balloon diameters of 7.62 cm, 10.16 cm, 12.7 cm, 15.24 cm, 17.78 cm, 20.32 cm, 22.86 cm, 36.83 cm, and 48.26 cm. Five trials were taken at each balloon diameter, and then the distances were averaged. After we observed which balloon diameters and pressures led to the greatest distance traveled by the darts, we were able to make our conclusions.
The set-up of the experiment is described in the method. Here are the diagrams.
Diagram 1:
Diagram 2:
The tables and graphs below show the relationship between balloon diameter and pressure, followed by the relationship between balloon diameter and average dart displacement.
|
Balloon Diameter (cm) |
Pressure (Pa) |
|
7.62 |
797 |
|
10.16 |
1145 |
|
12.7 |
846 |
|
15.24 |
822 |
|
17.78 |
996 |
|
20.32 |
1121 |
|
22.86 |
1220 |
|
36.83 |
1294 |
|
48.26 |
1569 |
|
Balloon Diameter (cm) |
Dart Displacement (m) |
|
7.62 |
0.1016 |
|
10.16 |
4.445 |
|
12.7 |
2.9464 |
|
15.24 |
2.7686 |
|
17.78 |
3.6322 |
|
20.32 |
4.2418 |
|
22.86 |
4.9784 |
|
36.83 |
5.5372 |
|
48.26 |
6.731 |
Surprisingly (to us, at least), the balloon that was inflated to just a four-inch (10.16 cm) diameter had more pressure than all of the other levels of inflation up to nine inches (22.86 cm). As predicted, the higher the pressure levels in the balloons were, the farther the dart was shot.
Our hypothesis was incorrect, but for the most part our reasoning was sound. Higher pressure leads to greater force, as discussed in the hypothesis. A simple fact about balloons, however, was overlooked. As most people know, it is somewhat difficult to start the process of blowing up a balloon, and then it gets easier before the balloon gets to large and resists more pressure. This high pressure point occurred at around a 10 cm diameter, which caused the darts launched from that balloon to travel farther than previously expected. The 7.62 cm diameter balloon actually had a pressure comparable to some of the larger balloons, but the tube was too long for that amount of air to push the dart out with much force.
There were several sources of error in the experiment. Our measurements were not particularly precise. Many of the trials were carried out at night, in the dark, and it wasn’t easy to see where the darts were landing exactly. Because of this, there is about a 0.1 m uncertainty on either side from where we stated the darts landed. Additionally, the measurements of each balloon may not have been exact (about a .2 cm uncertainty), which would also have thrown off the pressure readings. However, regardless of the uncertainty, the pattern of the data relative to the pressure we determined for each balloon supports the idea that greater pressure in the launcher leads to a greater distance traveled by the dart.
If we were to repeat the experiment, I would try to perform more trials, and perhaps use different objects and see what kind of effects air resistance would have. Obviously, if the inaccuracies in measurement could be resolved, that would also be beneficial. Despite this, the experiment taught me about balloon pressure, and how it can be used in concordance with a potential minor weapon.
“Cherokee Weapons.” Cherokee Nation Cultural
Has some information on early usage of dart guns.
“Darting.” Predator Conservation Trust. 2003. http://www.predatorconservation.com/darting.htm.
Usages and capabilities of different dart guns.
“Fun With Balloon Pressure.” Vernier. 2002. http://www.vernier.com/caliper/spring02/balloon.html.
Basic facts about balloon pressure.
Smith, S.E. “What is a Dart Gun?” 2003. http://www.wisegeek.com/
Uh, read the title. Basic description of what a dart gun is.
Sweeney, Brian. “Inventors.”
Contains history of the invention of the dart gun.
“The History of Plastic.” American Chemistry Council. 2007. http://www.americanchemistry.com/.
Again... read the title. Dart guns are made of plastic; this site talks about history and uses of plastic.