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.