Design a spring-loaded gun to shoot a projectile to your worst enemy. The conceptual design of this gun is shown on the next page. It consists of a commercially available pipe (1), bottom cap (2) with an opening for the trigger pin, trigger pin (3), piston (4), threaded rod (5) with a machined groove (6) to engage the trigger pin, nut (7), projectile (8), helical spring (9) and aerodynamic projectile nose (10) of negligible weight. The projectile has a mass of 0.5 lbm. The target is located on the ground and 250 ft away. The gun will shoot from the ground level at an angle that maximizes the horizontal reach of the projectile. The spring must be preloaded (i.e. compressed) in order to install inside the gun and provide an initial compressive force. The force required to pull the trigger pin should be less than 50 lbf.
The spring is compressed to solid length by tightening the nut with a power wrench. The trigger pin is inserted through the bottom cap and into the groove to secure the gun in the loaded position. The nut is then backed up all the way and the trigger pin pulled by hand to shoot.
Specify all design parameters listed below. Make all necessary choices and assumptions, which should be listed along with your calculations. Use sound engineering judgement. Provide a professionally written calculation package and schematics to get full credit. Use Excel, MathCAD or MathLab to facilitate design iterations and provide detailed screenshots of inputs and outputs. Comply with all notes listed on the cover page.
1) Projectile velocity and angle when exiting the gun.
2) Stroke or distance traveled by the piston to shoot.
3) Distance that the spring should be preloaded or compressed when installed.
4) Outside diameter (OD) and length of the projectile knowing that it's made of aluminum 7075-T6 tubing having 1/8" wall thickness.
5) Diametral clearances between pipe and spring, and between pipe and projectile.
6) Internal diameter (ID) of the pipe.
7) Mean diameter, wire diameter, material choice, spring constant, spring index, number of active coils, total number of coils, solid length, free length, pitch, maximum spring force, minimum spring force, maximum stress, static safety factor, critical length, weight,
natural frequency and fatigue safety factor of the spring based on Gerber.
8) If necessary, consider the use of nested springs, in which case, all the parameters listed in item 7) should be specified for each spring.
9) Nominal diameter, thread type and material choice for the threaded rod.
10) Rod groove dimensions.
11) Safety factor against tensile yielding of the rod thread and rod body.
12) Use your knowledge of dynamics to estimate the force generated on the nut upon impact and to relate projectile velocity to spring constant.
13) Safety factor against shearing the rod and nut threads.
14) Torque required to turn the nut in order to load the gun.
15) Force to pull the trigger pin.
16) Safety factor against shearing the trigger pin.
17) Gerber fatigue safety factor for the rod.
