Question for the material engineering types

[Garibaldi]

Let's say you have a spring about the diameter of a hula hoop. What material would this spring have to be made of, and how long and tightly compressed would it need to be, in order to be able to launch a 200lb man to the moon? Assume that accuracy and the survival of the launchee aren't issues.

[Darth Wong]

Oooh, an interesting question!

Before one can look at the materials requirements, one must first look at the physics requirements. This is a "back of envelope" calculation, so let's just approximate the minimum necessary energy as escape velocity. Technically, moving an object to the Moon could be done with less energy than that because you are not actually escaping Earth's gravity entirely (in fact, it would be slightly less than the energy required to reach the Moon's orbital altitude, because the Moon's gravity could theoretically take over and accelerate you toward it when you get close enough).

Nevertheless, escape velocity is much simpler, so let's go with that for now (we'll also ignore atmospheric drag). Escape velocity means that the hypothetical spring needs to accelerate you to roughly 11 km/s by the time it uncoils. Or, to put it another way, it must impart roughly 60 MJ per kg of the man's body. Let's assume the man is 80kg; this would mean that the imaginary spring must be compressible to the point that it has 4.8 GJ of potential energy.

Spring force is generally approximated by a linear function F=kx, where k is the spring constant and x is deformation from zero, so the potential energy of a spring would be calculated with the equation U=½kx². Therefore, you can simply use the equation kx²=9.6E9 in order to determine the necessary values for k and x (where x is in metres and k is a dimensionless constant).

Mind you, these calculations are sort of irrelevant because it's impossible to make a metal spring which can coil or uncoil at a peak velocity of 11 km/s, since that is higher than the speed of sound in those materials and deformations at such velocities would take the form of destructive shock waves which would shatter or melt the metal. They would, however, allow you to determine the necessary values for an imaginary piece of technology which acts like a spring by observing the simple linear F=kx function.

[Serafina]

What "imaginary piece of technology" are we talking about?
Was that just a random idea like "well, we might find something one day", or are there any actual ideas how this could be achieved?

Regards
Fina

[Darth Wong]

What "imaginary piece of technology" are we talking about?
Was that just a random idea like "well, we might find something one day", or are there any actual ideas how this could be achieved?

Regards
Fina

Technically, a giant gun would behave in a manner not unlike a hypothetical spring, although it's obviously not a perfectly linear curve. The pressure is greatest at max deformation, ie- when the projectile is at the breech of the barrel. If PV is constant for the trapped gas body (again, obviously a pretty loose approximation since n and R are constant but T is not), then P will drop linearly as the projectile moves through the barrel, because V for a cylinder is πr²h.

[Serafina]

Technically, a giant gun would behave in a manner not unlike a hypothetical spring, although it's obviously not a perfectly linear curve. The pressure is greatest at max deformation, ie- when the projectile is at the breech of the barrel. If PV is constant for the trapped gas body (again, obviously a pretty loose approximation since n and R are constant but T is not), then P will drop linearly as the projectile moves through the barrel, because V for a cylinder is πr²h.

Well, thats certainly interesting.
I suspected that we are talking about some hokey sci-fi tech here - but if it's something as "simple" as giant gun, that question is certainly more interestin.

[Garibaldi]

The question came to me in the form of a dream in which I was launched into space by something resembling a giant mattress spring, so I wasn't really envisioning any sort of sci-fi technology.

[Adam Reynolds]

Technically, a giant gun would behave in a manner not unlike a hypothetical spring, although it's obviously not a perfectly linear curve. The pressure is greatest at max deformation, ie- when the projectile is at the breech of the barrel. If PV is constant for the trapped gas body (again, obviously a pretty loose approximation since n and R are constant but T is not), then P will drop linearly as the projectile moves through the barrel, because V for a cylinder is πr²h.

Wouldn't temperature also decrease as the bullet travels down the barrel, causing pressure to decrease more slowly?

[Wyrm]

Wouldn't temperature also decrease as the bullet travels down the barrel, causing pressure to decrease more slowly?

More quickly. For a given sample of (ideal) gas, PV/T = constant. If T is falling and V is rising, then V/T is really rising, so P must fall in step to keep PV/T constant, so P is really crashing. In order to make P fall linearly as the man travels down the barrel, T must be kept constant: the gun has blowtorches around it to keep the gas constant temperature as the projectile is fired.

Incidentally, a gun is how Jules Verne got his passengers to the moon.

[madd0ct0r]

Could not a large enough resivoir of compressed gas (air say) keep P from dropping too fast?


Use the different size hydralic ram trick - a ram the size of a gas resoivoir would cause a ram the size of a dustbin lid to move pretty damn quickly.

Heat issues in the transfer pipes though.

[Sea Skimmer]

If you want to make a very large very high velocity gun then you can just employ multiple firing chambers. The Germans built such weapons called Hochdruckpumpe (also known as the V-3) in WW2 and Saddams super gun which could have fired a shell almost into orbit (it could reach orbit with rocket assist) was the same thing. By employing multiple chambers spread down the length of the barrel average pressure can be uniformly high, without an excessive peak pressure at the breach end. As the shell passes each chamber fires in turn. Its hard to make the shell seal in the bore, but other then that such weapons are very straightforward engineering exercises.

An alterative means of obtaining extremely high velocity from a cannon is a light gas gun. With this sort of device a power charge or other source of energy drives a piston which is already holding back highly compressed gas. The piston massively increases the pressure, which flows into a sub caliber barrel. However hard to make a light gas gun of high caliber, the largest I know of is only a 203mm bore. Saddams multi chamber Babalon supergun meanwhile had a modest bore of 1000mm which would have made it the highest caliber cannon ever had it been assembled. It’s primarily purpose would have been to launch a small rocket assisted satellite into space, making Iraq the first Muslim space power.