Scaling up a test cannon to a life sized cannon

[FredGirl13]

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!

 

[haruspex]

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.