Going the Distance: Launch Angles & Projectile Trajectory

Abstract

Objective

The goal of this project is to determine which launch angle results in the greatest distance for a projectile.

Credits

Andrew Olson, Ph.D., Science Buddies

Sources

This project is based on an entry to the 2007 Monterey County Science Fair:
Freedman, D. and T. Winick, 2007. "Calculating a Projectile's Trajectory."

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Introduction

This project is about projectile motion, specifically, how the launch angle affects the distance that a projectile will travel. You'll build a spring-powered mechanical launcher using pieces of PVC pipe, a wood frame, and fastening hardware, so this is a project for someone who is handy with tools.

Before you start designing and building your launcher, you should do some background research on the physics of projectile motion. The Bibliography section has some good resources to get you started. Think about the forces that act on a projectile in flight, and make a prediction about the launch angle that will result in the longest flights. The student-written "Water Balloons" site (Terrence and Jason, 1996) has a great balloon-launching simulation that you can use to make some preliminary tests.

To test your hypothesis in the real world, you'll want a launcher that will make it easy to change the launch angle while keeping the other variables (e.g., projectile mass, force used to launch the projectile) constant. The instructions below will assist you with your design. Remember to have an adult present when you do the test launches to make sure that they are done safely. Then it's bomb's away and may the best launch angle win!

Terms and Concepts

To do this project, you should do research that enables you to understand the following terms and concepts:

• Mass
• Velocity
• Range
• Launch angle
• Gravity
• Projectile motion

Questions

• What forces act on a projectile in flight?

Bibliography

• This is a good, student-written, introduction to the history and physics of projectile motion:
  Terrence and Jason, 1996. "Water Balloons: The Physics of Projectile Motion," ThinkQuest Library [accessed September 17, 2007] http://library.thinkquest.org/2779/.
• This is a high-school level tutorial on the physics of projectile motion:
  Henderson, T., 2004. "Projectile Motion," The Physics Classroom and MathSoft Engineering [accessed September 17, 2007] http://www.physicsclassroom.com/Class/vectors/U3L2a.html.
• This webpage has information on the mathematics of projectile motion:
  Nave, C.R., 2006. "Trajectories," HyperPhysics, Department of Physics and Astronomy, Georgia State University [accessed September 17, 2007] http://hyperphysics.phy-astr.gsu.edu/hbase/traj.html.
• A fun website with some cool animations:
  Zobel, E.A., 2006. "Projectile Motion," Zona Land, Education in Physics and Mathematics [accessed September 17, 2007] http://id.mind.net/~zona/mstm/physics/meachanics/curvedMotion/projectileMotion/projectileMotion.html.

Materials and Equipment

To do this experiment you will need the following materials and equipment:

• 1-1/2 in diameter PVC pipe (main body of launcher), 75 cm length
• 1 in diameter PVC pipe (launcher barrel), 45 cm length
• Wooden dowel, 77 cm length, diameter to fit inside plastic sleeve
• 9/16" ball bearings (projectile)
• 2 U-bolts with nuts and washers for attaching launcher to launch frame
• Spring (fits over dowel, provide driving force, 20 Newtons)
• Large washer (attach to dowel to push against spring, must fit inside launcher barrel)
• Wood screws (to hold washer in place)
• Copper sleeve (to keep launcher barrel fixed inside main body)
• Plastic sleeve (to keep dowel from wobbling in barrel)
• Pipe cap with hole (allows ball bearing to be launched, but holds dowel inside the barrel)
• 1 in × 4 in lumber for launcher frame (approx. 8 ft required)
• Hinge and wood screws for mounting
• PVC cement
• Tools:
  • Drill and bits
  • Saw
  • PVC pipe cutter
  • Screw driver
  • Tape measure
  • Protractor

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Experimental Procedure

1. Do your background research so that you are knowledgeable about the terms, concepts, and questions, above.
2. The illustration below shows an example of the kind of launcher you can build for this project.

   The projectile launcher is made from PVC pipe mounted on a wood frame. The frame is hinged at the base so that the launch angle can be easily adjusted.

   1. The launcher is made from PVC tubing. An outer tube (1-1/2 in diameter) is attached to the wood frame using two U-bolts. (Note: it should also be possible to omit the outer tube and attach the barrel directly to the frame.)
   2. The barrel of the launcher is the inner tube of PVC (1 in diameter). It fits inside the outer tube, held snugly in place with some short lengths of copper sleeve.
   3. A wooden dowel is placed inside the barrel, with a large washer attached near the midpoint, and a spring around the dowel below the washer. A string is firmly attached to the dowel in order to pull against the spring to "cock" the launcher.
   4. The lower end of the outer tube is covered with a PVC cap, cemented in place. The cap is drilled so that the dowel passes through, but not the spring (see detail photo, below).

      Detail view of the base end of the projectile launcher. A PVC cap holds the spring in place inside the barrel. The dowel passes through a hole in the cap. The string is used to pull the dowel back against the spring to "cock" the launcher.

   5. The launcher frame can be fashioned from 1 in × 4 in lumber and a hinge.
   6. Prop the frame open with short pieces of 1 × 4 to achieve different launch angles.
3. Be safe when using the launcher!
   1. The apparatus described for this experiment should only be operated with adult supervision.
   2. Injury is possible if adequate safety precautions are not followed.
   3. Make sure no one is near the projectile's path!
   4. Test fire with only partial spring compression, and build up gradually to full power to make sure that you have sufficient space.
4. Measure the distance that the ball bearing travels for several different angles, e.g. 15°, 30°, 40°, 45°, 50°, and 60°.
   1. Use at least 10 trials for each angle.
   2. Use the same spring compression for every shot, i.e., pull the dowel back the same distance each time.
   3. Use the same projectile for each test.
5. Calculate the average distance traveled for each angle.
6. More advanced students should also calculate the standard deviation of the distance traveled for each angle.
7. Which launch angle resulted in the greatest distance traveled?

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Variations

• You could extend the experiment by testing additional launch angles.
• How does the mass of the projectile affect the distance it will travel, when the same force and launch angle are used? Design an experiment to find out.

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Related Links

• Science Fair Project Guide
• Other Ideas Like This
• Physics Project Ideas
• My Favorites

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