The cannon symbolizes the gold ball's housing as well as the projectile launcher in our design, and this chapter emphasizes the design criteria used for the cannon's mechanisms, materials, and design. Material science and machine mechanics principles will be used in the analysis of the pipe and trigger mechanism.
Figure 1: Canon prototype
The following materials are required for the cannon:
springs from a pipe portion or several zip ties
A screw with a diameter of 4 mm
A bracket made of aluminum
Baseplate
Pipe
Figure 2: Machined pipe diagram
The pipe represents the mechanical launcher of the cannon and was machined to have a groove in which a screw was passed across, holes just above the bottom of the groove to attach the springs. The springs would then be attached to both ends of the screw to form a catapult for the golf ball.
Mechanical Characteristics
Several materials were considered in the construction of the pipe section, measuring 200mm in length, an inner diameter of 50 mm and a thickness of 0.25mm. Considerations to the material choice included the strength, friction, and weight.
Table 1: Pipe's Selection Materials Characteristics
Material Density (g/cm3) Young's Modulus (GPa) Tensile Strength (MPa) Yield Strength (MPa)
Aluminium (+ alloys) 2.69 - 2.71 68.9 90 - 572 34 - 505
Steel (+ alloys) 7.65 - 8.00 79.3 380 - 1790 170 - 1650
PVC (Polyvinyl Chloride) 1.30 - 1.58 2.4 - 4.1 40.7 - 51.7 40.7 - 44.8
*Data sourced from (Callister and Rethwisch 2010, Appendix B)
The interaction between the golf ball and the pipe is to be considered. From the properties of the possible pipe materials, the PVC pipe has the least weight, considering its density, is more resistant to the environments of weather, including rust, and is machinable (Callister and Rethwisch 2010, p.448). The metal components of the cannon shall be aluminium based, particularly the trigger. PVC for the cannon is able to handle the operational stresses from a spring with an 840 N/m K factor, even with the longitudinal notch across the pipe's diameter.
Table 2: Friction in cannon materials and golf ball in contact
Materials in contact Normal Force (N) Frictional Force (N) Frictional Coefficient (Static)
PVC on PVC 0.1962 0.0392 0.2000
PVC on Golf ball 0.4503 0.1351 0.3000
PVC on Aluminium trigger 1.6800 0.3192 0.1900
Calculations
The spring is our source of thrust, Kinetic Energy stored in the spring, (Cleghorn 2005, p.78) and using the manufacturer's catalogues, we were able to determine the 840 N/m K factor of several spring options, considering the requirements of the project's design. The K factor of the chosen spring was 840 N/m, and following the value, a number of calculations were done to determine the canon's angle of incline with respect to the barrier wall. In the results derived from the analysis, of the spring, the cannon's set up was drafted.
The following were the projected paths of the canon, through different angles of displacement, to generate the optimal outcomes of the design. The characteristics of the spring as supplied by the manufacturer are also provided for reference.
The energy in the spring was calculated using the equation:
(Cleghorn 2005, p.104)
Considering the average weight of a standard golf ball as 45.9 grammes, and the spring's compression (x) at 0.04m, then
U (840) (0.04)2 = 0.672 J
The motion of the expected projectile can be derived from:
(Ambekar 2007, p.78)
X - 270 mm distance, O = 70
References
Ambekar, A. G. (2007). Mechanism and machine theory. New Delhi: Prentice-Hall of India.
Callister, W. D., and Rethwisch, D. G. (2010). Materials Science and Engineering: An Introduction. Hoboken: John Wiley & Sons.
Cleghorn, W. L. (2005). Mechanics of Machines. New York: Oxford University Press.
