Question about conserving Delta V.

[IllicitMedic]

Ok, quick question. I've been on a quest to rebuild all my rockets to be more efficient now that I'm fairly "skilled" at this game.

The question...would it be more efficient (delta v/fuel wise) to launch, lets say a communications satellite, into a low orbit (80km), circularize and THEN raise to the final orbit of, lets say 500km, or would it be better/just the same to launch straight to 500km and then circularize?

[rryy]

I'm pretty sure going directly into a 500 km orbit is more efficient.

[trepnick]

Technically it's more fuel efficient to head straight for the final orbit, but its easier to build a standard launch stage that goes to 80k and then give your payload enough dV to get to its final orbit. It's also a wee bit easier to fly that ascent profile too, simply because you've probably already done it a few dozen times by now

[CCKinnison]

Get to your exo-atmosphere point, then move the far side of your orbit to desired point, THEN circularize. That should be the "cheapest".

[Caelib]

I believe a gravity turn is more efficient (complete your turn between 10km and 70km -- burn until you reach your desired apoapsis, then circularize). Wikipedia explains it pretty well:

A gravity turn or zero-lift turn is a maneuver used in launching a spacecraft into, or descending from, an orbit around a celestial body such as a planet or a moon. It is a trajectory optimization that uses gravity to steer the vehicle onto its desired trajectory. It offers two main advantages over a trajectory controlled solely through vehicle's own thrust. Firstly, the thrust doesn't need to be used to change the ship's direction so more of it can be used to accelerate the vehicle into orbit. Secondly, and more importantly, during the initial ascent phase the vehicle can maintain low or even zero angle of attack. This minimizes transverse aerodynamic stress on the launch vehicle, allowing for a lighter launch vehicle.

[arq]

Based on the Oberth effect, I would suspect that the most efficient way would be to do a normal ascent profile and just keep burning prograde horizontal near the fringe of the atmo until you reach the desired apo, then raise the peri to match. So, 'no, don't circularize' (though at some point in the transfer it will become roughly circular). Though it is possible that a bi-eliptic transfer *could* be more efficient than the standard Hohmann, depending on the final altitude. If I recall correctly, that is useful if you're changing your orbital radius by more than a factor of ~13, but you'd need to read up on that more thoroughly (though the savings are small at best and prob not worth the extra effort).

[K^2]

There are precisely three quantites you should be aware of for every maneuver. Energy, angular momentum, and delta-V resource of your rocket.

First, lets look at a simpler case. Suppose your ship is in parking orbit at 70km. Is it cheaper to go directly to a 500km operational orbit, or to make a stop at a 200km intermediate orbit? In terms of energy and angular momentum chnage, the two maneuvers are equivalent. So which one requires greater delta-V? Turns out, the answer is very simple. A reaction engine, such as conventional chemical rocket, is more efficient at higher speeds. If your rocket went from velocity V to V + dV, then the energy went from MV²/2 to M(V+dV)²/2. So dE = M(dV² + 2V dV)/2. The higher your velocity, the more energy you get from the same burn. So if you want to go from a 70km orbit to a 500km orbit, you want to get as much of the needed energy as possible when you are moving the fastest, which is at your lowest point. In other words, direct transfer to 500km is your best choice.

Now, suppose you are taking off from the planet's surface. What is your priority? Well, if it wasn't for atmosphere, your best ascent would be equivalent to circularizing at minimum safe altitude and transfering from there to your operating orbit. However, you are operating in the atmosphere. That means you have to start with ascent, transition to gravity turn, and then either park at 70km or burn directly to operating orbit at 500km. It turns out that at altitudes of about 50km the atmosphere is thin enough that you are not saving much by operating bellow orbital speeds. Obviously, you can't have a stable orbit there, but if you burn directly to 500km, it works as if you have circularized at 50km and then transfered to 500km. In other words, you get a bit more dE out of direct transfer to operating orbit over parking at 70km first. This isn't much. Difference between 50km and 70km is pretty small, in terms of energy gain. So if it's a matter of convenience, parking at 70-80km is not a bad option. But if you do wish for the most fuel-optimal way to reach the operating orbit at 500km, you do go for direct ascent.

Finally, I mentioned that there is also the angular momentum to watch. While you get most delta-E for your delta-V at the lowest point, you get most delta-L for delta-V at the highest point. This is why you want to circularize all in one go at the apoapsis, and not start early or make adjustments mid-transfer. Obviously, if you have to make corrections to catch up with your target, or whatever, you have to make corrections. But that will always cost you extra delta-V. Hence the optimal transfer between two circular orbits is a Hohmann Transfer. The low burn optimizes delta-E, the high burn optimizes delta-L, and the combination gives you the least delta-V needed for transfer. Understanding of these simple rules behind it will help you design more fuel-efficient maneuvers.

Edited July 6, 2013 by K^2

[Flixxbeatz]

Parking orbits to give you a huge breathing room for the final burn (in which in my case, a geostationary orbit).

That is, if you will fly the rocket in a way that you won't cut the engines off at any point during the ascent (just throttling down to the lowest possible without losing speed). Circularization is all up to you (it's part of my launches, a trait that I've carried over from version 0.11).

[Cheaterman]

Waste & space ecology is a bigger deal in general so you'd want your periapsis to stay under 20km until your apokee matches destination orbit's apoapsis (which doesn't mean you'll burn only upwards), then get rid of the waste and circularize. This is pretty fuel efficient as well.