Thorsten
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Hi to everyone.
Brief introduction - my name is Thorsten Renk, I'm a theoretical physicist by profession, and as part of my spare-time activities I'm part of the development team of the Flightgear OpenSource simulator, mainly doing weather simulation and coding OpenGL shaders. I am fascinated by all sorts of flight, which includes spaceflight, which is the reason why I'm currently looking into Orbiter as well.
Like probably others, I've been wondering about how to time de-orbit and re-entry burns correctly such as to bring a Shuttle onto the runway. On simply trying, I felt completely lost as to what exactly I had to control. I've been googling for tutorials and read some, but I feel they mostly skirt around the issues by providing a cooking recipe rather than a solid generally applicable checklist, or rely too much on 'need to practice'. At the same time, I prefer hands-on flying over an automated solution (it always seems a bit odd to me to have a simulated autopilot control a simulated plane...). I believe I've found a rather neat solution which I would like to share.
This solution applies to spacecraft with a controlled re-entry trajectory like the Shuttle or the Delta Glider - it won't work for a capsule like Vostok.
The key observation is that in such spacecraft, it is possible to control the deceleration rather precisely by controlling altitude - either with the elevator or with bank angle. Since the kinetic energy during reentry is so much more than the potential energy for a small altitude change, till the velocity drops to 1000 m/s, there's hardly any effect on velocity for going up or down in altitude, but the variation of air density with altitude allows a very precise control of the decelerating force if I can control altitude. So the only skill to master while flying re-entry is how to control altitude (which may differ from spacecraft to spacecraft) and then fly in such a way that the acceleration is stable around a given value.
The chief problem is to bring the spacecraft to a certain point with low velocity, say 20 km above Cape Canaveral with 1000 m/s. If I can control acceleration, there's a unique relation based on velocity and distance what *constant* deceleration will get me there. If my velocity for the final approach is v_end, my initial velocity is v0, the distance is d and the acceleration is a, that relation is
d = v0 * (v0-v_end)/a - (v0 - v_end)^2/(2*a)
If you're like me, you can't do this easily in your head, but a simple cue sheet with pre-tabulated values serves nicely:
v0 = 7000 - m/s
distance [km] - deceleration [m/s^2]
4500 - 5.3
4000 - 6.0
3500 - 6.8
3000 - 8.0
2500 - 9.6
2000 - 12.0
1500 - 16.0
1000 - 24.0
500 - 48.0
v0 = 5000 m/s
distance [km] - deceleration [m/s^2]
2250 - 5.3
2000 - 6.0
1750 - 6.8
1500 - 8.0
1250 - 9.6
1000 - 12.0
750 - 16.0
500 - 24.0
250 - 48.0
v0 = 3000 m/s
distance [km] - deceleration [m/s^2]
750 - 5.3
666 - 6.0
580 - 6.8
500 - 8.0
416 - 9.6
333 - 12.0
250 - 16.0
166 - 24.0
83 - 48.0
v0 = 2000 m/s
distance [km] - deceleration [m/s^2]
281 - 5.3
250 - 6.0
218 - 6.8
187 - 8.0
156 - 9.6
125 - 12.0
94 - 16.0
63 - 24.0
31 - 48.0
That's how it's used:
Fly a de-orbit and go through the messy zone when the air starts catching until you get low enough such that drag is appreciable and you velocity drops to 7000 m/s.
It is series of lookup tables based on distance to base while passing a certain value of the velocity - at the point your velocity reaches 7000 m/s, look at the distance to the base you want to reach and read off the deceleration you need to keep to get you there from the table. It doesn't matter precisely how you did your de-orbit burn, the table can accomodate a wide range of distances, the hardest limit is the structural stability of the spacecraft (I'd appreciate if someone can help me out with numbers here... I didn't find any maximal g-loads). If you're 4500 km away from the base, you just use a weak force, if you're 1000 km away you need to decelerate much harder. But the window to hit is huge - de-orbiting somewhere between 1000 and 4500 km from the base isn't a major problem I'd hope!
As you approach and the velocity drops, you make use of the follow-up tables to correct - say if you've been decelerating with 6 m/s^2 but by the time you reach 3000 m/s the distance to base reads 500 km, you know you need to ramp up acceleration to 8 m/s^2 for the next leg.
In this way, you can even accomodate curved approaches and similar corrections easily - the distance shown for a curved trajectory shown on the map will initially not be the true distance you have to fly, but you can nevertheless use the high velocity cue tables initially and you'll automatically get the relevant correction on the last leg if you keep using the distance shown in the map for the cue sheet.
Using this simple cue sheet I was able to get the Space Shuttle from ISS perfectly down to the runway on the first try with an entry trajectory that had a 90 degree angle in it, using no other instruments than the map (to know where I have to go and get distance readings) and surface MFD (to get the acceleration reading).
I believe this is how aerobraking in practice should be explained, planned and executed, because it's really simple that way and it can be done by a very general checklist which is pretty much independent of what spacecraft you're using and how precisely you control acceleration - it's just based on simple kinematic relations.
Brief introduction - my name is Thorsten Renk, I'm a theoretical physicist by profession, and as part of my spare-time activities I'm part of the development team of the Flightgear OpenSource simulator, mainly doing weather simulation and coding OpenGL shaders. I am fascinated by all sorts of flight, which includes spaceflight, which is the reason why I'm currently looking into Orbiter as well.
Like probably others, I've been wondering about how to time de-orbit and re-entry burns correctly such as to bring a Shuttle onto the runway. On simply trying, I felt completely lost as to what exactly I had to control. I've been googling for tutorials and read some, but I feel they mostly skirt around the issues by providing a cooking recipe rather than a solid generally applicable checklist, or rely too much on 'need to practice'. At the same time, I prefer hands-on flying over an automated solution (it always seems a bit odd to me to have a simulated autopilot control a simulated plane...). I believe I've found a rather neat solution which I would like to share.
This solution applies to spacecraft with a controlled re-entry trajectory like the Shuttle or the Delta Glider - it won't work for a capsule like Vostok.
The key observation is that in such spacecraft, it is possible to control the deceleration rather precisely by controlling altitude - either with the elevator or with bank angle. Since the kinetic energy during reentry is so much more than the potential energy for a small altitude change, till the velocity drops to 1000 m/s, there's hardly any effect on velocity for going up or down in altitude, but the variation of air density with altitude allows a very precise control of the decelerating force if I can control altitude. So the only skill to master while flying re-entry is how to control altitude (which may differ from spacecraft to spacecraft) and then fly in such a way that the acceleration is stable around a given value.
The chief problem is to bring the spacecraft to a certain point with low velocity, say 20 km above Cape Canaveral with 1000 m/s. If I can control acceleration, there's a unique relation based on velocity and distance what *constant* deceleration will get me there. If my velocity for the final approach is v_end, my initial velocity is v0, the distance is d and the acceleration is a, that relation is
d = v0 * (v0-v_end)/a - (v0 - v_end)^2/(2*a)
If you're like me, you can't do this easily in your head, but a simple cue sheet with pre-tabulated values serves nicely:
v0 = 7000 - m/s
distance [km] - deceleration [m/s^2]
4500 - 5.3
4000 - 6.0
3500 - 6.8
3000 - 8.0
2500 - 9.6
2000 - 12.0
1500 - 16.0
1000 - 24.0
500 - 48.0
v0 = 5000 m/s
distance [km] - deceleration [m/s^2]
2250 - 5.3
2000 - 6.0
1750 - 6.8
1500 - 8.0
1250 - 9.6
1000 - 12.0
750 - 16.0
500 - 24.0
250 - 48.0
v0 = 3000 m/s
distance [km] - deceleration [m/s^2]
750 - 5.3
666 - 6.0
580 - 6.8
500 - 8.0
416 - 9.6
333 - 12.0
250 - 16.0
166 - 24.0
83 - 48.0
v0 = 2000 m/s
distance [km] - deceleration [m/s^2]
281 - 5.3
250 - 6.0
218 - 6.8
187 - 8.0
156 - 9.6
125 - 12.0
94 - 16.0
63 - 24.0
31 - 48.0
That's how it's used:
Fly a de-orbit and go through the messy zone when the air starts catching until you get low enough such that drag is appreciable and you velocity drops to 7000 m/s.
It is series of lookup tables based on distance to base while passing a certain value of the velocity - at the point your velocity reaches 7000 m/s, look at the distance to the base you want to reach and read off the deceleration you need to keep to get you there from the table. It doesn't matter precisely how you did your de-orbit burn, the table can accomodate a wide range of distances, the hardest limit is the structural stability of the spacecraft (I'd appreciate if someone can help me out with numbers here... I didn't find any maximal g-loads). If you're 4500 km away from the base, you just use a weak force, if you're 1000 km away you need to decelerate much harder. But the window to hit is huge - de-orbiting somewhere between 1000 and 4500 km from the base isn't a major problem I'd hope!
As you approach and the velocity drops, you make use of the follow-up tables to correct - say if you've been decelerating with 6 m/s^2 but by the time you reach 3000 m/s the distance to base reads 500 km, you know you need to ramp up acceleration to 8 m/s^2 for the next leg.
In this way, you can even accomodate curved approaches and similar corrections easily - the distance shown for a curved trajectory shown on the map will initially not be the true distance you have to fly, but you can nevertheless use the high velocity cue tables initially and you'll automatically get the relevant correction on the last leg if you keep using the distance shown in the map for the cue sheet.
Using this simple cue sheet I was able to get the Space Shuttle from ISS perfectly down to the runway on the first try with an entry trajectory that had a 90 degree angle in it, using no other instruments than the map (to know where I have to go and get distance readings) and surface MFD (to get the acceleration reading).
I believe this is how aerobraking in practice should be explained, planned and executed, because it's really simple that way and it can be done by a very general checklist which is pretty much independent of what spacecraft you're using and how precisely you control acceleration - it's just based on simple kinematic relations.