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Glom
2003-May-01, 10:28 PM
We did a practice Physics paper today. One of the questions was about the feasibility of using a spacecraft powered by two 10kmē solar sails that generate a thrust of 10N each to get to the outer planets. I went into a two body calculation about the delta-v for a Hohmann transfer to Jupiter just for the sake of being arrogant.

The question is, would that be a viable spacecraft?

QuagmaPhage
2003-May-04, 11:03 AM
It's been some years since I tried to study astronomy, but I seem to remember that a to enter/exit a Hohmann transfer orbit you apply a short burst of acceleration to achieve the delta-v needed to change orbit. This is what makes a Hohmann transfer orbit cheap because of the low fuel consumption. But with solar sails you have a continual acceleration so the actual orbit would not be a Hohmann orbit.

But of course that depends on the design of the spacecraft. So whether the spacecraft is viable I really can't say. When the spacecraft's acceleration is constant (depending on the distance from the sun of course) there must be a way to change the direction of the acceleration vector i order to change orbit.

daver
2003-May-05, 08:40 PM
We did a practice Physics paper today. One of the questions was about the feasibility of using a spacecraft powered by two 10kmē solar sails that generate a thrust of 10N each to get to the outer planets. I went into a two body calculation about the delta-v for a Hohmann transfer to Jupiter just for the sake of being arrogant.

The question is, would that be a viable spacecraft?

Did your solar sails have a mass associated with them? 1 gm/sq meter gives ten tons/sail.

Why two sails?

Did you assume 10 N constant acceleration, or 10 N at 1 au?

How close can your sails get to the sun (if they're getting 10 N at 1 au it seems there are reflectivity losses, or else your sails have holes in them). Close approaches to the sun will boost your acceleration and cut your trip time, but that doesn't help if it melts your sail. Icarus would probably be a bad name for a solar sailer.

Glom
2003-May-05, 09:27 PM
Those are very good questions, but those kinds of details are way over the heads of the people at Edexcel. That's the problem I had with the question. They said 10N from two sails of each 2kmē and that's it. I couldn't answer the question with just that information, which is why I gave a very 'arrogant git' answer.

daver
2003-May-05, 11:09 PM
The arrogant git answer seems the proper answer in this case.

I don't know anything about Edexcel. Setting up the DiffEqs for a hypothetical solar sail doesn't seem to be all that difficult, but i haven't done it. I thought at first that Edexcel might be some sort of iterative diffeq engine built on top of an excel spreadsheet, but that no longer seems very likely.

Anyway, you could assume that your salis produced a net acceleration of 1 milli-g at 1 au and proceed from there (for extra credit, you could adjust your sail angle depending on your orbit). It wouldn't have been hard to phrase the problem in that way; the fact that they didn't makes me think that perhaps the "Ed" part of "Edexcel doesn't stand for "education".

Wyvern
2003-May-05, 11:52 PM
A couple years ago, I was in a class in which we had to calculate an orbit to Jupiter. One of the first engines we considered was one designed along the lines of a throttled nuclear powered ion propulsion engine (I don't remember for sure, but I think it was called a Vasmir engine).

We decided not to go with the engine because the constant thrust produced by the engine makes the orbit calculation really difficult, to say the least (particularly for the undergraduate project that it was). The orbital calculation for a constant thrust trajectory essentially becomes an optimization problem - you have to optimize the direction of your thrust at all points in the orbit. Like I said, really hard.

However, if you can solve that problem, it's viable, assuming you have a way to produce the required delta-V once you reach Jupiter. It'd take a much larger sail to produce the required thrust due to the lower light intensity. You might not even be able to get the direction right with a solar sail - I'm not sure about that though.

daver
2003-May-06, 01:35 AM
A couple years ago, I was in a class in which we had to calculate an orbit to Jupiter. One of the first engines we considered was one designed along the lines of a throttled nuclear powered ion propulsion engine (I don't remember for sure, but I think it was called a Vasmir engine).

We decided not to go with the engine because the constant thrust produced by the engine makes the orbit calculation really difficult, to say the least (particularly for the undergraduate project that it was). The orbital calculation for a constant thrust trajectory essentially becomes an optimization problem - you have to optimize the direction of your thrust at all points in the orbit. Like I said, really hard.

However, if you can solve that problem, it's viable, assuming you have a way to produce the required delta-V once you reach Jupiter. It'd take a much larger sail to produce the required thrust due to the lower light intensity. You might not even be able to get the direction right with a solar sail - I'm not sure about that though.

I assumed that the best bet for a low thrust engine was to thrust as much as possible along your direction of flight. Vasimir has even more degrees of freedom--you can choose high thrust or high Isp. My guess is high thrust to get to a fairly eccentric orbit, then high Isp for a bit to make it even more eccentric. Coast in the middle (acceleration then won't speed things up by much).

For the solar sail, instead of throttling the engine, you tilt the sail. Presumably you want to decelerate at first, to bring your perihelion closer to the sun (there's going to be a minimum distance here--too close and your sail melts). I'm guessing that a solar sail might be ok for flyby missions to the outer planets, but it's not going to do too way for orbiters much past Jupiter.

Wyvern
2003-May-06, 03:51 AM
I assumed that the best bet for a low thrust engine was to thrust as much as possible along your direction of flight. Vasimir has even more degrees of freedom--you can choose high thrust or high Isp. My guess is high thrust to get to a fairly eccentric orbit, then high Isp for a bit to make it even more eccentric. Coast in the middle (acceleration then won't speed things up by much).

For the solar sail, instead of throttling the engine, you tilt the sail. Presumably you want to decelerate at first, to bring your perihelion closer to the sun (there's going to be a minimum distance here--too close and your sail melts). I'm guessing that a solar sail might be ok for flyby missions to the outer planets, but it's not going to do too way for orbiters much past Jupiter.

The lowest energy trajectory with a constant thrust engine didn't have the thrust vector aligned with the flight path. Here is one reference, although this is not the one I originally used: http://gps.csr.utexas.edu/~gaylor/gaylor_pub/project.pdf. One of the variables in the problem is the normal vector of the thrust which is independent of the velocity vector for the lowest fuel transfer.

Actually, I did remember a way to do an insertion maneuver with a constant-thrust engine. By turning around at roughly the halfway point of your mission and using your engine to decelerate, you can actually get the correct delta-V to do an orbital insertion. For a solar sail, you'd have to turn around somewhat before the half point due to the lower intensity of the sun. Of course, another way would be to use aerobraking, but this is just a tad bit risky, not to mention that you have to get enough delta-V out of the maneuver in the first pass to get into some kind of orbit around the planet. :-?

roidspop
2003-May-06, 03:52 AM
I haven't done a google to see if I can re-discover it, but a year or so ago I found (probably on BABB) a link to some freeware that did a nice job of simulating the performance of a solar sail. I should look, but I'm too lazy just now. Good luck.

Glom
2003-May-06, 12:18 PM
Sorry, daver. Maybe I should elaborate on exactly what Edexcel is. In the education system in England and Wales, students take excessive amounts of exams. These exams are adminstered by different private exam boards, or at least after Maggie privatised it. Edexcel is one of them. Their Physics course is diabolical. They seem to operate on the premise that no maths is required for A-level physics. You ask someone at Edexcel what a differential equation is and you'll just get a blank look.

Mainframes
2003-May-06, 12:35 PM
Sorry, daver. Maybe I should elaborate on exactly what Edexcel is. In the education system in England and Wales, students take excessive amounts of exams. These exams are adminstered by different private exam boards, or at least after Maggie privatised it. Edexcel is one of them. Their Physics course is diabolical. They seem to operate on the premise that no maths is required for A-level physics. You ask someone at Edexcel what a differential equation is and you'll just get a blank look.

Add to that their tendancy to screw up exam papers, for instance the maths exam with a question that was impossible to answer because the exam hadn't been properly proof read before being sent out....

Glom
2003-May-06, 12:39 PM
Or the security breaches.