1. Gao Guangyan Desmond Chan Ng Kia Boon Daniel Yip Raffles Institution NUS Physics Open House Projectile Competition

2. Objectives To create a device – propelling a projectile With a target range of 80 metres Furthest possible distance for the maximum points Device must be: Accurate Consistent Method Consider options and conduct experiments Analyse and evaluate them

3. Design Consideration Factors to Consider 1. Distance (Enough power for a range of 80m) 2. Projectile Size (Must consider projectile dimensions) 3. Cost (Feasible to build financially) 4. Portability (Not too bulky and easy to transport) 5. Consistency (Consistently hit 80m accurately) 6. Elegance (No unnecessary sophistication)

4. Design Consideration Medieval Siege Weaponry k 1. Trebuchet Able to propel projectile far if made correctly Not consistent due to nature of propulsion (sling) 2. Onager Similar to Trebuchet / but uses torsion bundle Powerful yet small in size But not consistent Small-scale onager model constructed to test for feasibility

5. Design Consideration Medieval Siege Weaponry k 3. Ballista Cross between a crossbow and an onager However, large model needed for 80m target 4. Crossbow Powerful crossbow required Projectile subjected to external influences (wind) Small-scale crossbow model constructed to test for feasibility

6. Design Consideration Electro-Magnetic Acceleration 1. Repulsion Several Options: Thomson’s Coil Gun, Railgun etc.. Most common: Railgun Requires: Strong Rail system Extremely High Pulsed Current Pulse Capacitors Not suited for small scaling Very expensive Loud and Noisy operation

7. Design Consideration Electro-Magnetic Acceleration 1. Attraction Coil Gun: Linear Asynchronous Motor Model Constructed Previously Powered by 729J at 450V Only 4.35% peak efficiency Relatively Expensive Projectile size too large Consistent and accurate But Large model required for 80m target – too expensive to build

8. Design Consideration Pressure Powered Propulsion 1. Water Rocket Safe and relatively powerful device Difficult to hit our targeted 80m consistently Large body – affected greatly by wind Operators might get wet Design commonly used Difficult to construct reliable watertight launcher

9. Design Consideration Pressure Powered Propulsion Final Design: Air Cannon Safe and relatively powerful device Similar to handgun or rifle, but pressures are lower Powered by compressed air (bicycle pump) Simple and elegant Original Design and completely self constructed Easy Operation and easy handling Comparatively Cheaper than other options Powerful, consistent, accurate.

10. Accelerator Design Pressure Powered Propulsion Final Design: Air Cannon

11. Accelerator Design Construction Materials Final Design: Air Cannon High Pressure Industry Class AW(VP) PVC pipes (rated 283psi) 1” Brass Ball Valve Bicycle Pumps Bicycle Tyre Valves Waterproof Plywood boards for stand

12. Accelerator Design Main Design Final Design: Air Cannon 2 2’ long 2” dia. Air tanks A 5’ long 1” dia. Barrel Wooden base essential Gives accelerator stability and supports entire structure Projectile: solid aluminium Less affected by wind due to mass

13. Accelerator Design Operation Pumped using bicycle pumps Simple and easy to operate Device is muzzle loaded Flight Path Both Ballistic and Line of Sight paths possible due to power of the system. Low ballistic trajectory chosen Less affected by wind and other external influences

14. Accelerator Design

15. Physics Involved Calculation of Output energy and projectile velocity Air Tank Dimensions: 2"dia * 24" * 2 Barrel Dimensions: 1"dia * 12" * 5 The barrel cross section is therefore Pi * r 2 = 0.7854" 2 Using Pi * r2 * h, we can calculate the volume of the chambers: Air Tank Volume = 150.7964"3 > 0.002472m 3 Barrel Volume = 47.12400"3 > 0.00077225m 3 Total Volume = 197.9204"3 > 0.00324425m 3

16. Physics Involved Calculation of Output energy and projectile velocity We take the pressure to be 100psi, projectile mass of 0.1kg The pressure changes since air fills up the barrel which changes the pressure. Since the volume of air does not change, We can use the formula P1 * V1 = P2 * V2 100 PSI * Air Tank Volume = P2 * Total Volume Therefore, P2 = 76.19635 PSI, and there is a pressure drop of 23.80365 PSI Knowing these values, we can calculate the force acting on the projectile throughout the barrel.

17. Physics Involved Calculation of Output energy and projectile velocity The force acting on projectile = Pressure * Area 100 PSI (start of barrel), 100 * 0.7854" 2 = 78.54lb = 357N 76.19635 PSI (end of barrel), 76.2 * 0.79" 2 = 59.845lb = 272N The average force acting on the projectile in the barrel is therefore (357+285.6)/2 = 314.5N When there is force and mass, there is acceleration. And where there's a lot of force, there is a lot of acceleration! Using the formula F=ma, 314.5 = 0.1 * a a = 3145ms -2

18. Physics Involved Calculation of Output energy and projectile velocity And using the formula d = ½ at 2, 1.524 metres = ½ * 3145 * t 2 Therefore, t = 0.0311313s Time taken for the projectile to travel out of the barrel Hence, using these values, Velocity = Acceleration * Time, Therefore v = 3145 * 0.0311313 Velocity = 97.90791ms -1 > 352.4685km/h! And because K.E. = ½mv 2, Energy = ½ * 0.1 * 97.907912 Energy = ~479.29Joules.

19. Difficulties & Limitations Lack of funding Could not construct more sophisticated device Lack of time Could not carry out more experiments Lack of testing grounds Difficult to test out projectile device (large area, at least 80m long required)

20. Thank you.