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# Paintball Ballistics

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 Areas of Science Sports Science Difficulty Time Required Average (6-10 days) Prerequisites You should have access to a paintball gun, be familiar with how to shoot it safely, and have access to an open area where you can shoot it. This project has a fairly involved procedure, since you are measuring several parameters (velocity, time of flight, distance) and also comparing these measurements to what you would expect based on calculations. Feel free to customize the procedure based on your interests. Material Availability Specialty items: You will need access to a paintball gun and accessories, including safety gear for you and for three helpers, as well as an instrument to measure velocity of the paintballs. See the Materials and Equipment list for details. Cost Average (\$50 - \$100) Safety Minor injury is possible, so wear eye protection. Adult supervision is required.

## Abstract

Have you ever played paintball with your friends? Wonder how you can improve your game? Paintball guns use compressed gas to shoot paint-filled pellets at high speed, and with good accuracy. The flight path of the ball is determined by its speed and the angle at which it is shot, relative to the ground. In this sports science fair project, you will explore the ballistics of paintballs, focusing on how drag and other factors affect the results.

## Objective

The objective of this sports science fair project is to compare the calculated vs. actual range and launch velocity of a paintball. The difference between the expected values, based on calculations, and the actual values, which are measured experimentally, is caused by drag and other real-world factors.

## Credits

David B. Whyte, PhD, Science Buddies

• Scotch® is a registered trademark of 3M.

General citation information is provided here. Be sure to check the formatting, including capitalization, for the method you are using and update your citation, as needed.

### MLA Style

Science Buddies Staff. "Paintball Ballistics." Science Buddies, 23 June 2020, https://www.sciencebuddies.org/science-fair-projects/project-ideas/Sports_p054/sports-science/paintball-ballistics?class=AQXOCUw4j7BdWk7O5AMEmiEvCSBZ1UHjenFj0Us46fx7MQui_nr89KWb8LSMKikkwgKaBUYlyukjBXqVs12aQGEllcO-bEIvLJSG1fS50B8Bcw. Accessed 6 Aug. 2020.

### APA Style

Last edit date: 2020-06-23

## Introduction

Paintball is a popular sport in which players eliminate opponents from the game by hitting them with pellets containing paint, usually shot from a carbon-dioxide-powered paintball gun (also known as a paintball marker). In this science fair project, you will explore how these projectiles fly through the air. The study of the flight characteristics of projectiles, such as paintballs, is called ballistics.

When the paintball leaves the gun barrel, there are two main forces that act on it: gravity and drag. Gravity is a constant (unchanging in space or time) downward force on the projectile. Drag is a force caused by the interaction of the projectile with the air molecules in its path. Drag acts to slow the projectile down. Drag force is not constant, since it depends on the velocity of the projectile, the density of the air, the surface texture of the projectile, and other complicating factors.

The range of the gun clearly depends on the angle at which it is shot. If it is shot straight up, the range will be nearly zero, since the ball falls back to the launch point. If it is held near the ground and fired horizontally, the range will be relatively short. Under ideal conditions, with no drag, the maximum range can be obtained when the gun is pointed at an angle of 45 degrees, halfway between the vertical and the horizontal. This is based on the physics of the projectile's flight path, or trajectory, and is true for any projectile. Several basic physics formulae for ballistic projectiles are shown below. The projectiles are assumed to be shot straight up at 90 degrees (for best height) or at a 45-degree angle (for best range). The formulas are approximations, because they assume there is no air resistance.

Equation 1 is used when launching straight up.

Equation 1:

 V = 1 2 × g × time of flight

The velocity of the paintball when launched vertically equals one-half of the product of the acceleration due to gravity and the time of flight.

• V = Launch velocity, measured in meters per second (m/s).
• g = Acceleration due to gravity, which is 9.8 meters/second squared (m/s2).
• Time of flight = The time it takes the projectile to return to the same level from which it was launched, measured in seconds (s).

Equations 2 and 3 are used when the projectile is shot at a 45-degree angle.

Equation 2:

 V = 0.71 × g × time of flight

The launch velocity at 45 degrees equals 0.71 times the acceleration due to gravity, times the time of flight.

• V = Launch velocity, measured in meters per second (m/s).
• g = Acceleration due to gravity, which is 9.8 meters/second squared (m/s2).
• Time of flight = The time it takes the projectile to return to the same level from which it was launched, measured in seconds (s).

Equation 3:

 Range = V2g

The range at 45 degrees equals the launch velocity squared, divided by the acceleration due to gravity.

• V = Launch velocity, measured in meters per second (m/s).
• g = Acceleration due to gravity, which is 9.8 meters/second squared (m/s2).

Note from Equation 1 that you can determine launch velocity if you know the flight time. Time of flight is easy to measure—just use the stopwatch to time the interval from launch to landing. You can also measure the launch velocity directly, using a measuring device, like the one referenced in the Materials and Equipment list, below. The calculated and measured values may or may not be in good agreement, depending on how drag and other real-world factors affect the ball's flight. Once you have calculated the launch velocity for a paintball fired at a 45-degree angle using Equation 2, you can calculate the range the paintball would fly using Equation 3. The difference between the calculated and measured ranges will depend on drag and other factors.

## Terms and Concepts

• Paintball gun
• Ballistics
• Force
• Gravity
• Drag
• Velocity
• Density
• Range
• Trajectory

### Questions

• What factors make the calculated values for the range of the paintball different than the actual value?
• What is the shape of the flight path of a projectile shot at 45 degrees without drag? How does the shape of the flight path change when drag is present?
• Based on your research, what is the best angle at which to shoot a projectile in order to get the maximum range?

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## Materials and Equipment

• Paintball gun (paintball marker), with all required safety accessories. Should be able to vary the launch velocity on the paintball gun.
• Paintball radar chronograph; such as the Paintball Radarchron by Sports Sensors, available at www.amazon.com.
• Scotch® tape
• Stopwatch
• Lab notebook
• String
• Small weight, such as a fishing sinker
• Tape measure, 100-ft.; available at hardware stores. You could also use string and a 25-foot tape measure.
• Protractor
• Orange cones (4); available at any sporting goods store
• Three helpers

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## Experimental Procedure

Important Notes Before You Begin:

• It is very important that you perform this procedure safely.
• Check with experienced paintball players if you have any questions about safety issues.
• Make sure you, and any helpers, wear all of your safety gear, including eye protection.
• Make sure there is no one in the area who is not wearing safety gear.
• Carry out the procedure in an area that is safe and that that allows paintball gun shooting.

### Firing the Gun Vertically

Note: In this section, you will compare the measured vs. the calculated launch velocity of the paintball when it is fired straight up. Have one helper record the velocity of the receding paintball, as measured by the chronograph, and another helper record the time of flight using a stopwatch. The procedure describes measuring velocity and time of flight separately, for the purpose of clarity, but you can also measure them at the same time.

1. First, adjust the vertical launch velocity on the paintball gun to 300 feet per second (fps), which is the recommended velocity for use in most tournaments.
2. When using the paintball radar chronograph to measure the velocity of the paintball when it is fired vertically:
1. Measure the speed at which the paintball moves away from the gun. Don't hold the chronograph in front of the barrel.
2. If the chronograph reads the velocity in feet per second, record this number in your lab notebook. Convert this to meters per second for your calculations.
3. You can attach the chronograph to the gun with tape, or have a helper hold the chronograph, pointing it in the direction of the paintball's path.
4. Fire the gun vertically.
5. Record the velocity in your lab notebook.
6. Repeat at least two more times and average your results.
7. Now measure the time of flight (with the stopwatch) of the paintball when it is shot vertically, which you will use to calculate the launch velocity.
1. Start the stopwatch when the gun is fired, and stop it when the paintball hits the ground. Technically, you should try to stop the watch when the paintball returns to the height from which it was shot, but if it proves too difficult, the difference should be minor.
8. If you are having trouble shooting straight up, you might use a plumb line to help determine the vertical line.
1. A plumb line is just a string with a weight on it. Make a plumb line about 18 inches (0.5 m) long, and have your helper hold it near the gun.
2. Align the gun with the plumb line, prior to firing.
9. Record the time of flight in your lab notebook, in seconds.
10. Repeat at least two more times and average your results.
11. Calculate the launch velocity based on the time of flight, using Equation 1 from the Introduction.
12. How does the calculated launch velocity that is based on the time of flight compare with the measured launch velocity, as determined with the chronograph?
13. Divide the calculated velocity (based on the time of flight) by the actual velocity, measured with the chronograph. Add this data to a data table in your lab notebook. It shows the effect of drag.
14. Now change the launch velocity. Read the instruction manual to learn how to adjust the velocity of the paintball gun. Adjust the vertical launch velocity, as listed below:
1. 200 fps
2. 250 fps
3. 350 fps
15. Repeat steps 1–14 at least two more times. This is to ensure that your results are accurate and repeatable.
16. Graph the measured launch velocity on the x-axis and the time of flight on the y-axis.
17. Calculate and graph the expected values (those discounting drag) on the same graph as the experimental values.
18. How does launch velocity affect the role of drag?

### Firing the Gun at a 45-degree Angle

1. Numbers the orange cones 1–4 with a permanent marker.
2. Attach the string to the protractor, in the middle of the flat section. Use clear tape. See Figure 1.

Figure 1. Mark the line at 90 degrees with a permanent marker. When the gun is pointing up at 45 degrees, the angle between the 90-degree line and the string will be 45 degrees.

1. Attach the weight to the other end of the string.
2. Mark the 90-degree line with a permanent marker.
3. Mark the spots on the protractor that are 45 degrees away from the 90-degree line, using a permanent marker.
4. Have helper #1 go to a spot down range where you will be shooting the paintball.
1. This helper's job is to determine where the paintball lands.
2. The helper should have on safety gear, including eye protection, and is also responsible for making sure everyone in the area is wearing paintball safety gear.
3. The helper should carry three orange cones, labeled 1–3, to mark where the paintballs have landed.
5. Place an orange cone (#4) on the ground directly in front of where you are standing. This marks the spot from where you are shooting.
6. Have another helper (helper #2) hold the protractor against the barrel of the gun.
7. The flat part of the protractor should be against the gun.
8. The string should hang down so that the angle of the gun can be read by looking at where the string is on the protractor.
9. Hold the gun at 45 degrees.
10. Have the helper with the protractor tell you when the gun is exactly at 45 degrees.
11. Have another helper (helper #3) hold the radar chronograph so that he or she can measure the launch velocity of the paintball. Caution: The helper should hold the chronograph behind the barrel opening and measure the speed of the paintball as it moves away from the gun.
12. Helper #3 should also start the stopwatch when the gun is fired and stop it when the paintball hits the ground. Helper #1 should raise his or her hand when the paintball hits the ground.
13. Fire the gun.
14. Adjust the velocity until the gun fires the paintball at 300 fps at 45 degrees.
15. The down-range helper (#1) should place an orange cone at the spot where the paintball hit the ground, not at the location where it rolled after landing. It may take several tries to get the range figured out.
16. Record the launch velocity, as measured by the chronograph.
17. Record the time of flight for each shot in your lab notebook.
18. Repeat steps 15–18 at least two more times, marking the landing spots with cones.
19. Measure the distance that the paintball traveled, using the 100-foot tape measure.
1. You could also use a piece of string, and then measure the length of the string in sections with a 25-foot tape measure.
20. Calculate the expected velocity, using the time of flight and Equation #2 from the Introduction.
21. Calculate the expected range using Equation 3. Use the value for the velocity from Equation #2.
22. Divide the calculated velocity (based on the time of flight) by the actual velocity measured with the chronograph. Add this data to your table.
23. Divide the calculated range with the measured range. Add this data to your table.
24. Repeat steps 16–24, and change the 45-degree launch velocity to the following values:
1. 200 fps
2. 250 fps
3. 350 fps
25. Graph the measured launch velocity on the x-axis and the range on the y-axis.
26. Calculate and graph the expected values (those discounting drag) on the same graph as the experimental values.
27. How does launch velocity affect the role of drag?
.

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## Variations

• Adjust the velocity to 300 fps and fire the gun at 15, 25, 35, 45, 55, 65, and 75 degrees. Graph the angle vs. the range.
• Try to use the chronograph to measure the speed of the paintball as it falls back to Earth after being shot straight up. How does its actual speed at the time it returns to Earth compare with the calculated speed? Is it moving fast enough to break on impact?
• In a paintball match, the gun is usually fired horizontally, or slightly higher than horizontally for more distant targets. Devise a way to use the chronograph to measure the change in speed of the paintball along a horizontal trajectory (for example, at 10, 20, 30, and 40 m). Graph the paintball's speed vs. distance from the gun. Graph the rate of change of the speed over time; that is, the deceleration due to drag.
• Look up the equations for the trajectory of a projectile fired from a certain height above the ground; for example, from a hill. Design a procedure to compare the actual data with the calculated data when the paintball is fired from an elevated position.

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