Transcript 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
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)

The Second Amendment (cont.)
QuickTime™ and a
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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.

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.
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.

The Virtual Melon
Finite Element Analysis (F EA) - 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)
The Simple Model

From previous data - aluminium
bending

Result is 0.027 m deformation.
The Simple Model

This is modeled in STRAND (different
scale on diagram):

Result is 0.025 m deformation, within
9% of the expected value.
The Melon Model - Physiology
Tough elastic
outer skin
 Spongy
saturated pulp
 Inner seed
capusle (mostly
air in ripe fruit)

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.
The Melon Model - Physiology
The Melon Model - Physiology
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.

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.

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
The Melon Model
Air cavity
Pulp
Skin
The Tests

1. Pressure applied by a flat face

Maximum force: 50000 N (25MPa)
The Tests

2. A cup of even pressure behind

Maximum force: 3.1 MN (170MPa)
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
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.
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.
