Muzzle Velocity of Spring Loaded Musket Ball: 64.26m/s

[howdybilly]

disclaimer: bizarre question from physics novice

Using a smooth bore classic musket (approximately 1m length of barrel, musket ball (.0173m diameter)), what would the potential muzzle velocity of the musket ball be if the powder charge were replaced with a compressed spring?

PE=1/2kx^2

KE=1/2mv^2

Using a spring with k=128 Nm (used a calculator on engineer's edge where modulus of ridgity G was 25x10^6, wire diameter d was .2 inches, mean coil diameter D was .48 inches and number of active coils n was 40). Not sure if this is kosher or not.

Assuming friction and gravity are negligible - the musketeer keeps the weapon well lubed and is on the moon, if he pulls the trigger which releases the "charged" spring, what will the muzzle velocity be of the musket ball when it leaves the musket? Let's also assume that the spring when uncompressed, is the full length (1m) of the barrel.

PE=1/2*128*1^2=64 joules?
KE=64=1/2*.031v^2 so v=64.26m/s

64.26m/s, long way from a 1700's .69 caliber musket firing around 310m/s

Could that be right? What am I messing up?

 

[JaredJames]

64.26m/s, long way from a 1700's .69 caliber musket firing around 310m/s

Could that be right? What am I messing up?

Given you know the exit velocity of the rifle, you may want to work it backwards - get the KE, stick it into the PE equation and see what spring you would need.

Then you can see if the required spring matches what you've got now.

 

[howdybilly]

Given you know the exit velocity of the rifle, you may want to work it backwards - get the KE, stick it into the PE equation and see what spring you would need.

Then you can see if the required spring matches what you've got now.

I did it backwards and entered the new spring constant k as 2979.1 Nm, plugged it into the spring calculator on the engineering website and keeping the diameters and modulus of ridgidity the same, I came up with a change in the number of active coils from 40 to 5.82.

I think there are probably some nature of elasticity issues that I'm neglecting but not sure.

so, rewritten - given a 1m long musket, standard .69 cal musket ball (approx .031kg) and a spring under compression with a constant of 1489 Nm (modulus of ridgitity 25x10^6psi, .25in wire diameter, .43 mean diameter and 5.82 active coils), a muzzle velocity of the musket ball could match the 310 m/s of a traditional powder musket.

PE=1/2*2979*1^2=1489.5 joules
KE=1489.5=1/2*.031v^2 so v=310 m/s

?? not sure if I'm using the right calculations. is a spring constant of 2979 Nm possible?

thanks

 

[JaredJames]

?? not sure if I'm using the right calculations. is a spring constant of 2979 Nm possible?

Not sure, but I'd say definitely not with the dimensions you're talking about.

 

[PJC01]

I would first like to commend you for your curiosity and effort in attempting to calculate the muzzle velocity of a musket ball using a compressed spring. However, I must point out that your calculation may not be entirely accurate.

Firstly, the equation you used for potential energy (PE) is correct, but the equation for kinetic energy (KE) should be KE=1/2mv^2, where m is the mass of the musket ball and v is the muzzle velocity.

Secondly, the value of k that you used for the spring constant may not be accurate for this specific scenario. The value of k depends on the material and dimensions of the spring, and may vary depending on the specific spring used in the musket.

Additionally, neglecting friction and gravity may not be entirely accurate as they will have some impact on the muzzle velocity of the musket ball.

Furthermore, the assumption that the spring, when uncompressed, is the full length of the barrel may not be accurate. The spring may not be able to fully compress to the length of the barrel, and this will affect the potential energy and ultimately the muzzle velocity.

In conclusion, while your calculation may give a rough estimate of the muzzle velocity, it may not be entirely accurate due to the various assumptions and approximations made. To accurately determine the muzzle velocity, further experimentation and testing would need to be conducted.