I was reading this article about railguns, coilguns and some of the technical problems involved and it mentioned that (theoretically) an operational rail gun could fire a projectile 250 miles in about 6 minutes. If you really could fire a projectile this fast and this far how hot would it be when it reached it’s target.
Assume the projectile is made of tungsten and is the size and shape of a 12 oz can of soda. At that speed and considering atmospheric resistance how hot would it be when it got to the target?
If I haven’t missed something in my math, this comes out to be 2,500 miles per hour which equals about 3,600 feet per second. You most definitely could–and a lot of off the shelf rifles do–fire a projectile (bullet) this fast. The projectiles are much smaller and lighter than the one you propose, of course, around 50-150 grains in weight.
I keep thinking I must have bothed the equation, my result is not a very amazing speed. (250 miles in 6 min = 2500 miles per hour [which divided by 3600 secs in an hour]= .69444… miles per second which times 5280 feet per mile = 3666 feet per second)
No idea about the actual answer to your question, though. I know the SR-71 at speed (~ Mach 3 or so), did get its exterior skin very hot, but I don’t know just how hot, sorry.
I think you missed the point. To send a projectile 250 miles in 6 minutes you have to fire it much faster than the average speed, because the projectile will be constantly decelerating due to air resistance.
250 miles = ~402,000 meters
6 minutes = 360 seconds
1,116 meters/sec
Thats slightly faster than a NATO 5.56mm round, which reaches 267C. So lets pretend this is a linear relationship (I dont see why not), then that coil gun bullet is going ~10% faster than the 5.56mm bullet, so it has 10% more heat. So 290C or so.
OK… forgetting about the heat and the soda can shape for the moment… to have enough momentum to travel 250 miles approximately how fast does a slug of tungsten weighing say, 10 kilograms, have to be traveling when it exists the barrel of the railgun?
Well if its trajectory reached 200km of altitude it could. Of course at those altitudes we are pushing orbit and gravity would be significantly reduced I would imagine. Calculations there would be way out of my league/math/physics skills.
The maximum range for a projectile, assuming even ground and optimum firing angle, and neglecting air resistance and the curvature of the Earth, is d = v[sup]2[/sup]/g. 250 miles is just about 400 km, and g is about 10 m/s[sup]2[/sup], so we’re looking at a launch speed of 2000 m/s. Of course, air resistance will mean that the initial speed will actually have to be much greater than that, and at those kinds of speeds you really can’t ignore air resistance, but that’s a lot more complicated to calculate.
The OP simply requires an average velocity of 2500 MPH over 250 miles. I don’t want to do the math (mainly because I don’t remember all the details of how to account for air resistance), but my gut feeling tells me that there should be a launch angle for a small bullet-like projectile with a launch velocity of ~100,000 MPH that would yield just that sort of result. I could be way wrong though.
Not that it adds much to the discussion at hand, but it’s not really the case that gravity is significantly reduced in such close quarters – at 200km height, it’d be around 94% of what it is on the surface of the Earth, if I have my figures right. That you’re weightless in orbit is just because you’re in a freefall situation and gravity accelerates everything around you equally, like when you’re in a crashing lift; you just keep missing the ground (hopefully).