Rocket Science for Beginners

[elvum]

johnckirk said that he thought that horizontal takeoff for space-bound rockets sounded less efficient than vertical, so I was inspired to write a few words on the subject.

Conventional rockets don't take off vertically because space is "up". Thanks to angular momentum, orbital mechanics is strange and wonderful, and it's usually the case that to change your velocity in one direction, you have to fire your rockets in quite another. To get "up" into space (and stay there), you need to accelerate parallel to the surface of the earth, ie horizontally¹.

So, why take off vertically? This is because aerodynamic drag is proportional to the square of velocity. It therefore makes sense to get up into the low-density upper atmosphere at the start of a launch, while your rocket is still travelling relatively slowly. The optimal trajectory for a conventional rocket (ie the one that minimises fuel consumption for a given final orbit) is a curve that starts vertically and ends up horizontally. (Derivation of the formula describing this curve is left as an exercise for the reader.)

Now, as those of you who have seen aeroplanes, hot-air balloons, mountains or tall buildings may realise, putting people on top of a giant firework is not necessarily the most efficient way to get them to high altitudes. The most commonly considered alternative is a rocket that flies like an aeroplane to high altitude and then shoots like a rocket into orbit. BAe's HOTOL and its entirely exciting successor Skylon are prime examples of this concept.

The advantages of gaining altitude like an aircraft (ie using wings to create aerodynamic lift) can only really be obtained if air-breathing jet engines are used at the start of the flight. You lose all the benefits if you bolt both jet and rocket engines on your spacecraft (too much weight), or if you use rocket engines for the low altitude part of your flight (too much weight from carrying all your oxygen on-board). What you want is an engine that can work like a jet engine at low altitude, or like a rocket engine high up. To date the engineering complexity involved has prevented anyone from building such a spacecraft².

Also worth a mention is Burt Rutan's SpaceShipOne, which takes off strapped to an aircraft and then shoots up into space using its own rocket engines. Not into orbit though - that challenge is an order of magnitude harder.

¹Note that because the earth spins, you can get an additional boost by letting it "slingshot" you into space. Simplifying slightly, this is why most launch sites are near the equator, and why most rockets fly east.

²Although I hope to see Chinese Skylons flying before 2050 (this is a hint to any Chinese Intelligence agents that may be reading).


I hope you are all enjoying festive seasons of great amicability.

Comments

[johnckirk.livejournal.com]

Ah, interesting and informative (I think I follow most of it) - thanks for posting that.

Launching rockets

[(Anonymous)]

You might want to check out this game - http://www.globalspec.com/BrainStrainer/

[pozorvlak.livejournal.com]

Derivation of the formula describing this curve is left as an exercise for the reader

Eeek - that sounds rather hard. Have you read A Fall of Moondust? There's a bit in that where a ship takes off from the moon and lands less than a hundred miles away, something that nobody had bothered to do before. Arthur C. Clarke, in his narratorial voice, says that the mathematicians would probably have taken great delight in working out the optimal trajectory using the calculus of variations, but of course the captain doesn't do that - he goes 100 miles straight up, thus qualifying for deep space rates, and then orbits to the right point and drops straight down :-)

[elvum.livejournal.com]

I'm disappointed by ACC's lack of grasp of orbital mechanics, and by his lack of faith that computers would one day be able to calculate in microseconds an optimal trajectory with the constraint of a maximum altitude of 101 miles. ;-)

I wonder what "zero altitude" is on the moon? After all, you can't really measure it wrt sea-level...

[pozorvlak.livejournal.com]

I'm really not familiar with the mathematics, but is that actually computationally feasible? Presumably you could get a pretty good trajectory fairly quickly using numerical methods, but some of these problems turn out to be utter bastards if you want the optimal solution, IIRC.

Zero-altitude would probably be calculated wrt Armstrong and Aldrin's landing site, at a guess.

[elvum.livejournal.com]

It seems fairly simple to me. No air resistance, and you "know" that the optimal path will look pretty much like a parabola...

Skylons

[pozorvlak.livejournal.com]

That sounds uncomfortably like a race of Dr Who villains...