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# How far can you shoot a melon?

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

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## How far can you shoot a melon?

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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

14. 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 (M0) 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, M0 is defined as: • 1550g total mass • 1741 mL volume • 150mm diameter

18. The Melon Model Air cavity Pulp Skin

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)

21. 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

22. 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.

23. Future Improvements • Non-linear dynamic analysis. • More accurate tissue modelling. • More samples for the M0 relations. • Testing of results in measured simulated scenarios. • More accurate modelling of melon tissue mechanics at high speeds.

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