Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: chris on 07/09/2018 09:34:05
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On this week's Ask! The Naked Scientists podcast (https://www.thenakedscientists.com/podcasts/ask-naked-scientists) someone enquired about the means by which rockets can be steered or guided as they ascend; his observation was that the craft goes straight up for a while then appears to flatten off.
He was wondering why and how this is achieved.
I thought this was an interesting point for discussion...
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By building and fuelling the rocket vertically, you avoid any problems of it bending or loading asymmetrically before takeoff, and you have optimum access to all parts of what is essentially an axially symmetric machine.You are thus constrained to a single "runway", pointing upwards.
Having left the runway in any sort of craft, the next task is point it where you want to go, which is rarely the same as the runway heading. Turning east gives you a useful 1000 mph contribution to speed in that direction, so the optimum initial heading may be a compromise between attaining orbital speed and final course.
A small asymmetry of the thrust vector will turn the rocket. This can be done with moveable vanes in the exhaust of a single motor, altering the thrust angles of multiple primary motors, or adding secondary steering motors with thrust vectors perpendicular to the primary drive.
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The optimum course is a compromise:
- the atmosphere is a real drag, so you want to go vertically to get above it as quickly as possible.
- attaining a stable orbit means that you need to be traveling horizontally at about 7.5km/second (for the ISS).
- so, in practise, they do more vertically at first, and then more horizontally later.
This has to be modified for air-launched space probes, which are already above most of the atmosphere when they are launched (eg at 50,000 feet), and already travelling horizontally. But they need a lot more altitude to reach space, and a lot more horizontal velocity to reach orbit.
Rocket motors are often mounted on gimbals, allowing the engine direction to be steered, which changes the direction of the whole spaceship.
Edit: Error pointed out by Chris...
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Thanks both.
the atmosphere is a real drag, so you want to go vertically to get above it as quickly as possible.
That's a really good point and I should have said that in passing. I'll commit that to memory.
attaining a stable orbit means that you need to be traveling horizontally at about 11km/second.
That sounds a bit fast, @evan_au - I had in my head that orbital velocity is about 7km/s and escape velocity is about 11km/s?
Turning east gives you a useful 1000 mph contribution to speed in that direction
Thanks for that @alancalverd - I did say this on the radio and I was relieved that you agreed with me!
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I'm not a rocket scientist, but I sometimes play one on Wikipedia (this is achieved by referring to actual rocketry textbooks- not making stuff up!)
The optimum trajectory isn't actually vertical initially, but it is quite steep- any time a rocket isn't firing at least slightly sideways it's wasting fuel because it needs to go sideways very fast to reach orbital speed. By Pythagorus, a rocket that is thrusting just off vertical gets little loss of vertical thrust, but gains a large amount sideways thrust.
In practice, a rocket will normally take off vertically and then quickly begin pitching once it clears the pad equipment. A lot of rockets then head east, because that gains the rotation of the Earth, but depending on the mission and launch site, most of them head not due east.
One interesting detail, rockets often don't follow the optimal trajectory initially, they do a gravity turn:
https://en.wikipedia.org/wiki/Gravity_turn
the difference is that with the optimum trajectory the rocket is angled to point upwards relative to it's trajectory somewhat to fight gravity, but that means it would get a lot of air drag and tends to buckle- a gravity turn means the rocket is always turned directly into the air until it gets past the point of 'maxQ' - the point of maximum air drag; and then it resumes the optimum trajectory. That means the rocket can be built more lightly, and this overall improves the amount of payload it can carry. Furthermore, the designers can put fins on the rear of the vehicle, these keep it mostly pointed in the right direction for a gravity turn, but don't work at low speeds, but they seem to be less common these days for some reason, but are very obvious on the Saturn V.
Evan's numbers are indeed a bit off, a low altitude (180km) orbit requires the rocket to achieve a horizontal velocity of about 7.8 km/s. However, it takes about 9.3-10 km/s of 'delta-v' to achieve that including gaining altitude and air drag (delta-v is the speed change the rocket would achieve if everything else was the same, but there was no air, and there was no gravity and it fired in a straight line) An escape orbit requires a velocity of 11.2 km/s, but because of having to fight gravity it will need more delta-v than that (about 13 km/s). These are pretty much minimal numbers from the equator, a lot of rockets have to work harder than this, it depends on the mission.
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Another factor is the inclination of the orbit - the highest latitude that it passes over.
- The ESA launch pad in Kourou is almost on the equator, and can launch due east to get a payload into geostationary orbit.
- The Russian launch pad at Baikonur is at 45 North, and this can launch to the ISS with its 52 degree inclination
- Some earth survey satellites are in polar orbits, and this requires little eastward velocity.
The purpose of the satellite determines its most useful inclination.
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From The Goon Show - Rocket to the Sun
Ned: We need a pilot. Eccles - can you drive?
Eccles: Which way are we going?
Ned: Up
Eccles: Good. I know that way.
Like the man said, rocket science is easy, rocket engineering is extremely difficult.
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Another type of launch trajectory is where they don't go into Earth orbit first, but launch with greater than Earth escape velocity; but this takes a powerful rocket and a light payload.
New Horizons launched with 16 km/s initial velocity, headed for Jupiter; after a gravity assist from Jupiter, it headed beyond Pluto, having exceeded escape velocity from the Sun.
https://en.wikipedia.org/wiki/New_Horizons
The Parker Solar Probe is heading in the opposite direction, and after a series of gravity assists from Venus will approach quite close to the Sun.
See: https://en.wikipedia.org/wiki/Parker_Solar_Probe#Trajectory
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The optimum trajectory isn't actually vertical initially, but it is quite steep- any time a rocket isn't firing at least slightly sideways it's wasting fuel because it needs to go sideways very fast to reach orbital speed.
So your point is that because an orbit is a circle around the Earth, and the rocket needs to be describing this trajectory eventually and it won't be achieved by firing perpendicularly away from the planet surface, you might as well have a small vector component that imparts this from the get go?
Presumably this is at odds with the point made above about getting above as much atmosphere as possible - as rapidly as possible - to avoid drag? Thus there must be an optimal solution which would be to head up vertically to a point where the drag is tolerable, and then apply the sideways trajectory?
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To be optimal, the trajectory has to be smooth (otherwise you could have cut the corner and made it more optimal), and you can show that nearby optimal trajectories (going to slightly different orbits) can't branch from it in mid flight. That means that all the trajectories are slightly different going right back to the take-off point, so a rocket optimally takes off at slightly different angles to end up at different orbits.
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On this week's Ask! The Naked Scientists podcast (https://www.thenakedscientists.com/podcasts/ask-naked-scientists) someone enquired about the means by which rockets can be steered or guided as they ascend; his observation was that the craft goes straight up for a while then appears to flatten off.
He was wondering why and how this is achieved.
I thought this was an interesting point for discussion...
The rockets used on fighters containing explosives use flight surfaces (fins). Rockets going into orbit steer the thrust which steers the rocket motion and accomplished by movable nozzles on the space shuttle. Some solid boosters have fixed nozzles with a cold liquid injected into the exhaust through a ring of injectors around the throat of the nozzle reducing the force on that side of the nozzle thus changing the vector. I don't think vanes are used anymore. The A4 used them in WWII.