…and I’m trying to get a manned vehicle into orbit using the railgun concept; the ship will be pulled along a rail accelerated by magnetic fields until it is flung out the end up into the air, where scramjets will take over to get the ship up to near orbital velocity; then rockets will finish the job.
My question: I want no more than 3g’s on the passengers and a terminal rail speed of 5000mph. How long should the rail be? If I base the Slingshot in the Rocky Mountains would the altitude be high enough so I wouldn’t have to worry about air friction?
If no one wants to do the math, at least I’d like an equation that could help me. Thanks.
First, forget miles per hour, and go with kph. Lets say 10,000 kph rather than 5000 mph. Rounding, I know.
Now, what is g? 9.8 m/sec^2. Round to 10, 3 g’s is 30 m/sec^2. 10000 kph is 2.7 kps or 2700 meters per second. (2700 mps)/(30 m/sec^2) is 90 seconds. It will take 90 seconds at 3 gees to reach the velocity you want. The average speed will be 1350 m/sec, (1350 m/sec)*(90 sec) is 121500 meters, or 121 kilometers. Your track will have to be 121 kilometers long.
The Rocky Mountains definately aren’t high enough to neglect friction, which I did. Besides, the best launch site is on the equator where you get maximum advantage from earth’s angular momentum.
Why are you limiting it to only 3Gs? There would be no problem accelerating them much faster unless one of the passengers has a serious heart condition. I know people can take up to 8 without blacking out, and that’s when the G forces are pulling blood down from the head, if the passengers were laying flat, perpendicular to the vector of acceleration, they could maintain consciousness with more acceleration than that, it would be a lot quicker, and you’d need a much shorter track.
IRL, these things are driven more by what the marketing people want than what the techies say is possible.
Back in the late-80’s / early-90’s, there was a proposal for a commercial hypersonic vehicle, the “Orient Express”, that would do Mach 7 or so between LA and Tokyo. Two of the main criticisms which scuttled the project were not technical:
the marketing people believed that there was no way to convince the general public that having the wings glowing red was normal and expected (cooled internally by hydrogen slush fuel).
the marketing people believed that people paying what these tickets would cost would expect a great meal, but the proposed trajectory left little time to serve drinks, much less food.
Basically, the techies were hot to go because they wanted someone to fund their scramjet engines, but the marketing types who had to approve the funding thought a Mach 4 plan would be much more sellable. Go figure…
So, limiting your launch railgun to 3g’s to keep grandma from puking up her Earl Grey is probably realistic (at least as realistic as putting grandma in orbit in the first place).
The trouble with keeping to low gees is that you dramatically increase the length of the railgun line, which dramatically increases the investment needed to build the damn thing.
But I agree that 3 g’s is pretty close to the limit for regular traffic. Any more than that and only healthy people are going to be able to use the launcher. A launcher that can put grandma and the kids in space is a different sort of thing than one that can only launch astronauts and military personel.
The rail gun can be horozontal for a part then bend up - you whould have to stop ‘forward’ accereration to counteract the angular acceleration and the joint and still maintain 3 g’s.
That being said you could accelerate at any rate (10g, 1.001g (you need >1g to overcome the 1 g of gravity) and get to orbit - it would just take longer (or shorter). for very low acceleration rates it would require a tremendous amount of fuel to accelerate at 1.001g all the way into space but possible.
I think the OP was talking about a railgun just to attain scramjet speed, so the entire rail can be laid out on the ground. I think there are a few places where this is feasible. The bigger problem might be whether anyone will let you do a routine Mach 8 launch from the ground.
Situation the “terminal” of the rail-launcer begin in the Great Basin, where it’s (relatively) level terrain. Have the vessel travel approximately have the distance while traveling level… after which it begins to curve upwards for the trip into the upper atmospher. It’d have to have a very sharp-angled launch point - in the realm of 60-70 degrees from horizontal - so describe the launch point as being set atop a mountain peak.
Additionally, I would suggest having a disposable “cocoon” cover up the front of the ship to help insulate it from the heat it would build up. Upon launch, the cocoon would be discarded, and recovered, polished, and set up again for the next launch.
I’m assuming you’re setting you SF story in the not-too-near-yet-not-too-far future…
Why would the heat shield suddenly become unnecessary after the spacecraft leaves the rail? You’d want it till you get out of the atmosphere, not to mention the return trip. (I assume it’s a reusable spacecraft - if you want an expendable rocket you don’t need linear accelerators, rockets work just fine.)
Just a note on terminology, the disposable cocoon used to hold a body in a barrel is called a “sabot”. We used to use them when launching aerodynamic test bodies out of large gun barrels. In this case, they were used to provide a body which conformed to the barrel dimensions and insulate the payload from the charge behind it, and the sabot was scored longitudinally so it just peeled away when the payload left the barrel.
A sabot could be used in a railgun to provide the E/M and structural properties the railgun requires without adding that additional weight to the actual launch vehicle.
Thanks for all the replies. For what you have said:
Lemur866:
You’re right; I should have used KPH. I’ts just that my physics class was 26 years ago and I got out of the habit of thinking metric.
Batz Maru:
3Gs is what the Shuttle uses, and since my heroines are two teenaged girls, I wanted to keep the launch strains down to what the average healthy civilian could stand. In the interest of shortening the track, though, I think I’ll up the G’s to 4 or 4.5.
K2dave, SPOOFE:
Good idea. I could have the launcher start a 3Gs, cut acceleration for the upward bend, then slam it at 5 or 6 G’s for the last few thousand meters. I’ll have to do the math. thanks.
scr4:
Yeah, I was trying to find the most godforsaken real estate I could; I imagine that the thunderclap of a launch would carry for hundreds of square miles.
SPOOFE, micco:
A sabot would be useful for the reasons stated, and also be armor against impact with foreign bodies (birds, etc.)
I had thought about putting the bulk of the launcher underground like a linear accelerator, but the problems of overpressure or on the other hand evacuating all of the air from the entire launch tunnel gave me a headache. So I decided just to put the whole thing in the open air.
