Scaling up a test cannon to a life sized cannon

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SUMMARY

The discussion focuses on scaling a model cannon to accommodate an 80 kg clown for a projectile launch. Key calculations include determining the bore and barrel length of the life-sized cannon based on the model's dimensions, specifically using a diameter of 60.96 cm for the clown and a launch distance of 30 m at a 25° angle. The model cannon's specifications include a 7 cm diameter ball, a 21.5 cm barrel length, and 2.6 mL of methanol used for fuel. The challenge lies in estimating the fuel required for the life-sized cannon, which must be scaled according to the kinetic energy principles.

PREREQUISITES
  • Understanding of projectile motion and basic physics principles
  • Familiarity with scaling laws in physics
  • Knowledge of fuel energy calculations and combustion principles
  • Experience with mathematical modeling and dimensional analysis
NEXT STEPS
  • Research "Projectile motion equations" to understand the dynamics of launching objects.
  • Study "Scaling laws in physics" to grasp how physical properties change with size.
  • Learn about "Kinetic energy calculations" to determine the energy needed for the clown's launch.
  • Investigate "Combustion energy of methanol" to estimate fuel requirements accurately.
USEFUL FOR

This discussion is beneficial for physics students, engineering students, and hobbyists interested in projectile design and scaling models for practical applications.

FredGirl13
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Homework Statement



Your task is to determine:

a.the length and bore of cannon that is required to accommodate an 80 kg Clown with an over-arm measurement of 48 inches

b.the amount of fuel that is required to launch the Clown at the same angle as you did with your model cannon .

c.the amount of fuel that is required to launch the Clown at the same angle as you did with your model cannon onto a foam mattress 30 m away.

Test Cannon
Diameter of Ball: 7cm
Length of Cannon Barrel: 21.5cm
Length of Compression Chamber: 6.5cm
Amount of Fuel Used: 2.6mL of Methanol
Distance Travelled: 1.256m

Life Size Variables
Diameter of Life Sized Clown: 60.96cm
Distance Clown Must Travel: 30m
Mass of Clown: 80kg
Angle: 25°


The Attempt at a Solution



a. (Diameter of Clown/Diameter of Ball)xBore of Model Cannon=Bore of Real Cannon
(62.661cm)
(Bore of Life Sized Cannon/Bore of Model Cannon)xLength of Model Cannon= Barrel length of real cannon (185.653cm)

(length of model compression chamber/length of model barrel)xLength of life sized Cannon Barrel= Compression chamber of life sized cannon (56.122cm)

And I have no idea where to start with the estimating fuel part :(


This is a group project but its due tomorrow and I've been left with trying to finish it all by myself so I really really need help!
 
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I'm not sure whether artillery scales as simply as that, but I don't know anything to the contrary.
For the fuel, you could assume the fuel energy has to be scaled up the same as the kinetic energy at muzzle exit.
 

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