Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: chiralSPO on 10/09/2014 15:21:10
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Say we are launching an unmanned probe (~5000 kg) to some place in the inner solar system.
How much fuel could be saved if the rocket (let's say single stage, for simplicity) could be launched from an altitude of 50 km rather than from sea level? (this altitude could easily be achieved with a hydrogen-filled lighter-than-air vehicle, and I bet it would require less hydrogen to float to this altitude than to launch to it--plus, if one is clever enough this hydrogen could also be used as fuel after the buoyancy has been taken advantage of)
The 50 km change in distance is essentially negligible, but it is by far the most fuel-intensive 50 km of the trip (atmospheric drag, greatest gravitational force from Earth, and this is when the rocket is most massive).
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Say we are launching an unmanned probe (~5000 kg) to some place in the inner solar system.
How much fuel could be saved if the rocket (let's say single stage, for simplicity) could be launched from an altitude of 50 km rather than from sea level?
Not very much, that's for sure.
The 50 km change in distance is essentially negligible, but it is by far the most fuel-intensive 50 km of the trip (atmospheric drag, greatest gravitational force from Earth, and this is when the rocket is most massive).
That's not quite true. Drag is not a great deal of a problem and the gravitational force at the earth's surface is about the same as it is 50km above the surface. All the fuel being used to put a satellite into orbit goes into kinetic energy because we need the satellite to move quite fast when in orbit. Do yourself a favor and calculate the difference in energy between a change in potential associated with 50km above the earth's surface and the energy of motion of a satellite circling the earth.
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let's say single stage, for simplicity
One of the most significant fuel savings is to use a multi-stage rocket - once a fual tank is empty, you waste energy accelerating it - and the fuel tank to get off Earth weighs more than the payload. (...unless you have something useful to do with the fuel tank - the first US space station was essentially a repurposed fuel tank: Skylab).
launched from an altitude
This is sometimes done - the Virgin Galactic vessel is essentially a 2-stage vehicle, where the first stage is reusable and is an air-breathing aeroplane with a large wing area, making use of air pressure in the lower atmosphere to get above much of the atmosphere. The second stage is effectively a rocket - but it only has to reach 100km vertically; it does not attempt to reach the significant horizontal velocity needed to reach orbit.
Similarly, sounding rockets to explore the upper atmosphere and test-fly new types of telescopes (and potentially shoot down undesirable satellites in low-Earth orbit) are sometimes launched from military jets - but these are not attempting to reach orbital velocity.
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The fuel-intensive part of any flight is takeoff because you are having to accelerate the total fuel mass in addition to the hull and payload. A rocket has very little "wetted" area and atmospheric drag is not significant in the initial stages of flight - it varies with the square of speed, so it's minimal at the start.
Clearly there is an advantage in starting from a higher altitude but 50 km isn't a lot compared with the 6400 km radius of the planet. Flying balloons is a nontrivial exercise in meteorology and airmanship, and a balloon with an 800 ton payload (the launch mass of a small commerical rocket like an Ariane) would be one hell of a machine to build, inflate and control.
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launched from ... jets - but these are not attempting to reach orbital velocity
I take that back - last week the IRAS satellite was launched into Earth orbit from a plane.
There was a 3-stage rocket carried beneath the plane (the plane is effectively a 4th stage).
Getting into orbit is the biggest hurdle to getting into Sun orbit - but if you want to orbit Mars or a comet, you will need to carry far more fuel than for Earth orbit, since you must match orbits once you reach your destination.
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Has anybody ever compared the difference between a Saturn IV rocket and a Saturn V rocket? The fuel they carry is a lot different and hence the Saturn IV is much shorter than the Saturn V.
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the gravitational force at the earth's surface is about the same as it is 50km above the surface.
Yeah, I know that.
All the fuel being used to put a satellite into orbit goes into kinetic energy because we need the satellite to move quite fast when in orbit. Do yourself a favor and calculate the difference in energy between a change in potential associated with 50km above the earth's surface and the energy of motion of a satellite circling the earth.
Thanks! I had assumed that getting something out of the gravitational well would have the greatest energy requirement, but after crunching the numbers, it is obviously not...