Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: David Compton on 25/10/2008 12:25:52
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David Compton asked the Naked Scientists:
In an earlier Podcast (http://www.thenakedscientists.com/HTML/podcasts/show/2008.10.12/) Dr. Dave mentioned that 11.2 kilometres / second was the value of escape velocity.
I was wondering how that applies in the real world? The discussion was about firing a bullet into space. If the speed of the bullet was 11.2 kilometres / second when it left the barrel of the gun, would that be fast enough to reach space?
That bullet will immediately begin to slow down due to air resistance and gravity. Would that 11.2 kilometres / second have to be increased to account for these forces?
I figure that a small .50 calibre bullet weighs 647gr (41.9g), which typically has a velocity of 928 meters/second. So my question is this: How fast would a 41.9g projectile have to going when it leaves the barrel to make it into space?
Thanks!
What do you think?
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Escape velocities do not take air resistance into account.
Escape velocities are independent of mass: any object, whether a bullet or a bus, would have to be travelling at 11.2Km/s in space
(outside Earth's atmosphere) to escape Earth's gravitational field.
The speed a bullet leaves a gun (muzzle velocity) is no where near Earth's escape velocity...
A gun's muzzle velocity is the speed at which the projectile leaves the muzzle of the gun. Muzzle velocities range from subsonic (below 330 m/s / ~1080 ft/s) for some pistols to more than 1,800 m/s (~5910 ft/s) for tank guns firing kinetic energy penetrator ammunition. The latter velocity is close to the limit achievable with chemical propellants.
http://en.wikipedia.org/wiki/Muzzle_velocity
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Take a look here
http://en.wikipedia.org/wiki/Project_HARP
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This was the big gun thing that some people though Saddam Hussein was trying to build at one time.
The problems are enormous. The muzzle velocity has to be very high indeed and the payload has to withstand both the huge acceleration in the barrel (even though this has to be made very long to minimise this) and the huge rise in temperature due to air friction. In the reverse situation when space craft return from orbit the thermal problems, even in the thin upper atmosphere, are extreme. I suspect this would be an impossibly difficult problem at ground level, although it may be possible to get some sort of object (maybe ceramic) that could withstand the heat and acceleration. The question would be "why?".
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There's a limit to how fast you can get soemthing using a gun. The projectile is driven by the hot gasses produced by the explosion but the gas is made of molecules and they have a range of velocities. The hotter the gas the higher the average velocity. To a fair aproximation the average speed of the molecules is the speed of sound in the gas. Once the projectile is moving faster than that, the gas molecules get left behind they can no longer push on the projectile and make it go faster.
By fudging the issue and using hot light gases you can get a bit faster but there's no way you will get to escape velocity this way.
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I think you can get to about 3x the velocity of sound, BC, but not much more with conventional explosive type propulsion. There is no such limit with the "rail gun" electromagnetic propulsion though. It is not exactly a "muzzle" you would have then, but I guess the idea is the same in that all the propelling force equipment stays on the ground.
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Listen to the answer to this question on our podcast. (http://www.thenakedscientists.com/HTML/podcasts/show/2009.02.22/)
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Ummm there's a big difference between 'reaching space' and escape velocity.
For a spacecraft to reach space (the Von Karman line at 100km) needs a delta-v of about 3km/s, including air drag. Bullets are draggier though and will need somewhat more delta-v than that (depending on their length, longer is better).
11.2 km/s (PLUS air drag) is needed to escape entirely from the Earth, but that's much too fast; you don't need to go that fast to just to reach space.
And the idea that a bullet can't go faster than the molecular motion (speed of sound in the gas to be precise) isn't quite right either- Project Harp involved injecting the gas in sideways with an angled boat tail on the projectile. This squeezes the bullet like squeezing a pip between your fingers and it can go significantly faster than the molecular motion/speed of sound. Note that Project Harp actually fired at 3.6km/s (about Mach 10) and actually reached space (180km in this case).
There's also something called a 'multistage light gas gun'. Basically this is a way to make gas go at supersonic speeds, and this supersonic gas can be used to push on a projectile. They've achieved over 7km/s (about Mach 25).
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Very interesting wolfekeeper.