A couple of general physics questions

[crashedintothesun]

Hi,

So I recently started to wonder two things:

1. If the Oberth effect causes your burns to be more effective at higher speeds, why does everyone burn at apogee, when the speed is lowest? Wouldn't burning when you're lower/deeper in the gravity well be more effective?

2. Why does a rocket with one engine go farther than a rocket with three engines? I tested this just now. I put a rocket with one engine and a rocket with one engine on a rocket that would carry it to an altitude of 70km (to avoid the atmospheric drag getting in the way). To my surprise, the rocket with three engines (tricoupler -> three aerospikes) got to ~2 million meters, while the rocket with one engine escaped kerbin's gravity! I guess what I'm trying to ask is, why does the three-engine rocket have a lower dV than the rocket with a single engine?

Thanks!

[Bluejayek]

1. The Oberth effect causes burns to be more effective when you have a higher orbital energy. Your orbital energy is the same at all points in a given orbit, therefore the apogee/perigee distinction is not effected. People burn at apogee for inclination changes, as you have less kinetic energy at this point to burn away to change to a different inclination.

2. Two reasons: First, you are often wasting delta V in low atmosphere when you have too high of a thrust on the initial stage. Drag scales as velocity squared, so it is often beneficial to keep velocity down while in the lower atmosphere. Second, once you are in orbit, you need only a miniscule amount of thrust applied over time to move your ship, your maximum thrust essentially doesnt matter. This makes those extra two engines simply dead weight that has to be carried. A lighter ship can achieve a higher delta V.

EDIT: I misread the part about getting out of the atmosphere. Part two of my response to 2. still applies.

[Nibb31]

1) Apogee is the best place to burn prograde to raise your Perigee, and therefore to turn a ballistic trajectory into an orbit. If you burn at a lower altitude, you will necessarily have to burn at a different angle than prograde to circularize, which is less efficient.

2) dV depends on thrust and mass. A 3 engine rocket with tanks will weigh 3 times more. For the same reason, a setup with 1 engine and 2 tanks is more efficient than a setup with 1 engine and 4 tanks. You will burn 4 times longer, but you will accelerate 5 times slower because of the extra mass.

[melaus]

I thought the Oberth effect was caused by high velocity, not neccesarily higher orbital energy. since kenetic energy is 1/2*M*V^2 a change in velocty at a higher velocity adds more kenetic energy to the system ie. your ship (because velocity is squared). and conservation of energy is maintained because your exhaust loses more kenetic energy at higher velocities.

as far as the more engines being worse, its the mass of the engines. you basically have the same stored energy (fuel) so your potential is the same. with 3 engines you burn for 1/3 as long for 3 times the force. which is the same energy. however your acceleration is your force divided by your mass, more engines=more mass. you'll find that this distinction does not exactly hold up in high gravity situations because if you have a thrust/weight ratio of 1.1 (barely enough to lift the ship) you're spending 10/11ths of your energy just fighting gravity. but too much thrust/weight ratio when in an atmosphere will cause the wind resistance to pick up exponentially too. the key is to find the right balance of thrust/weight in the atmosphere, and to have almost no engines when far from gravity (one nuclear is ideal).

Edited October 16, 2012 by melaus

[Millitron]

Well, the Oberth effect actually is more effective when you have higher kinetic energy, which is not necessarily the same as higher orbital energy.

In any case, it is easier to change inclination at low kinetic energy, because of the way vectors work. When you make a burn, you're essentially adding another vector into the sum that normally makes up your velocity vector. When you're moving slower, i.e. your velocity vector is shorter, your burn doesn't need as much energy to turn your velocity vector. Think of it with triangles. In the picture I attached, the Red line is your original velocity vector, the blue and green lines are your burn vectors, and the purple line is your new velocity vector. In each triangle, the burn vector is the same length, i.e. same delta V. Notice that when your original velocity vector is shorter (lower speed), the same length of burn will provide a wider angle between your original vector and your new vector.

As for your other question, as long as we are talking about space-flight, i.e. no atmosphere, thrust doesn't matter when it comes to delta V. The extra engines do nothing but add weight, decreasing the delta V a given amount of fuel will provide.

Edited October 16, 2012 by Millitron

[crashedintothesun]

All right, guys, thanks!

This will hopefully help a lot with my rocket designs.