1. How far can you shoot a melon? Andrew Jessup Physics TSP Project 2001, The University of Sydney

2. Punkin’ Chunkin 1986-2001 Delaware, USA Rules of competition: –The pumpkin must weigh 8-10 pounds –The pumpkin must leave the barrell intact –The launcher must not use explosives

3. The Second Amendment Gas powered cannon - Two Kaeser nitrogen gas compressors deliver up to 800 each psi per blast. Weighs 9 tons. Can shoot a pumpkin 4,496 ft (1.37 kilometers)

4. The Second Amendment (cont.)

5. How far can we go? Muzzle velocity of the Second Amendment is 268 m/s. The upper distance limit is set by the maximum momentum imparted to the pumpkin before it leaves the barrel. This in turn is limited by the maximum instantaneous force that can be applied without vaporising it.

6. Modifications Originally 2nd year U.Del. Students made pumpkin cannons. We studied honey dew melons (Cucumis melo.) not pumpkins –Easier to model the aerodynamics –Less variation in post-harvest size –More homogenous physiology We couldn’t actually shoot the melons to test theory.

7. How can you measure the force? The force is applied from one end only, and is opposed by the inertia of the melon. Cannot simply compress a melon to work out it’s maximum tolerance. Could shoot, hit or drop the melon - but then it would be difficult to derive the force without knowing the precise impact duration.

8. The Virtual Melon Finite Element Analysis (FEA) - this project used the STRAND package. Process for FEA simulations –Build a simple model –Compare against known data –Build the complex model (the melon) –Test findings (if budget permits)

9. The Simple Model From previous data - aluminium bending Result is 0.027 m deformation.

10. The Simple Model This is modeled in STRAND (different scale on diagram): Result is 0.025 m deformation, within 9% of the expected value.

11. The Melon Model - Physiology Tough elastic outer skin Spongy saturated pulp Inner seed capusle (mostly air in ripe fruit)

12. The Melon Model - Physiology For each material, FEA requires: –Young’s modulus (force per unit cross section / corresp. length increase) –Poisson’s Ratio (the lateral expansion/the distance stretched - usually < 0.5). –OR: stress/strain curves Also need to know the maximum strain the skin can take.

13. The Melon Model - Physiology

15. The Melon Model - Structure Melon size, mass and water content is quite variable. Makes repeatability difficult, or to draw general conclusions. Logically, many characteristics such as mass and length should have roughly linear relationships. The Standard Melon (M 0 ) is needed.

16. The Standard Melon Looked for linear relations between weight, volume, length, width, dimensions of the seed capsule and the mass of pulp and capsule. Found several reasonably strong mass-relations between melons of similar ages.

17. The Standard Melon Mean mass of 20 supermarket melons was 1550g. From this, and our relations, M 0 is defined as: –1550g total mass –1741 mL volume –150mm diameter

18. The Melon Model Skin Air cavity Pulp

19. The Tests 1. Pressure applied by a flat face Maximum force: 50000 N (25MPa)

20. The Tests 2. A cup of even pressure behind Maximum force: 3.1 MN (170MPa) 2. A cup of even pressure behind Maximum force: 3.1 MN (170MPa)

22. How does this compare? 2nd Ammendment uses 800psi (5.51GPa), only delivers 1271N (2x0.5s shots, 10lb pumpkin, 280m/s) Forces are high because: –Static analysis –Tissue is strong –Shape and structure distributes axially symmetric pressure well

25. Conclusions The maximum force that we can apply to a melon is: 3.05 MN, distributed evenly over the back surface. Practical relevance: –Damage mechanics of food transport –Accuracy of FEA in modeling fruit flesh –“The Stealth Melon”/”Smart Fruit” - World Aid in shooting food at hungry people.

26. Future Improvements Non-linear dynamic analysis. More accurate tissue modelling. More samples for the M 0 relations. Testing of results in measured simulated scenarios. More accurate modelling of melon tissue mechanics at high speeds.