Launching into high orbit what's more efficient?

[paul23]

Well as per title, what is more efficient to get into a high orbit (600km):

 

1) launch to low orbit and then use a hohmann transfer

2) directly create a suborbital at around 600 km and circularize there?

[Streetwind]

Generally, approach 1 is more efficient, for a variety of different reasons. For example, if you aim for a higher initial apopasis, then your ascent angle will be higher. This means your engine is thrusting more towards the ground, less sideways; and at any time you are thrusting towards the ground, you have gravity losses. These will be made worse by the fact that you are spending more time not in orbit (because it takes time to reach that high apoapsis), and you are travelling at slower speed, which further increases the time spent not in orbit. Whenever you are not in orbit or landed, you have gravity losses. Another thing is the Oberth effect, which (simplified) states that burns executed while travelling faster and closer to a gravity well are more efficient. This doesn't really make much of a difference for a few hundred kilometers of apoapsis height, but it starts getting more and more noticeable the higher you go.

An ideal ascent is one that follows a natural gravity turn to end up at orbital velocity just a few kilometers above the edge of the atmosphere, while never coasting, always thrusting (and ideally at full throttle). In practical application, this is hard to achieve even with a computer-controlled autopilot unless the rocket itself is built specifically for the purpose. In manual flight, with typical player-built rockets, it is practically impossible to achieve. But you can practice and at least try to go somewhere near that.

Edited October 15, 2019 by Streetwind

[AHHans]

5 minutes ago, Streetwind said:

Generally, approach 1 is more efficient, for a variety of different reasons.

Well, in theory a direct burn to a high apoapsis is more fuel efficient, but it depends on the exact trajectory you are using. There are two competing effects: on the one hand you want to do your burns as low as possible to maximize the Oberth effect, and on the other hand you want to burn perpendicular to the gravity to minimize gravity losses. (You always only want to burn in the direction of your orbital prograde vector to minimize steering losses.) So on an airless body you'd want to give you a small kick to get clear of the ground, and then burn parallel to the ground (at 0 degrees elevation) until you get to your desired apoapsis. (Assuming that there is no terrain in the way...) Essentially doing a Hohmann transfer from the surface to the desired orbit. On Kerbin you have that pesky atmosphere, so you have to balance the Oberth effect against atmospheric drag and gravity losses. In addition trying to directly burn to the desired orbit to meet with e.g. a station (my gateway station is at 500 km, not 600 km ) means that you have a lot less time for navigation and being even slightly in the wrong plane can quickly eat up any gains from better use of the Oberth effect. If you are in a low parking orbit, then you can put your transfer burn at one of the nodes to your target orbit and thus minimize the losses for the plane change.

So my conclusion is: while a direct burn to high apoapsis might in theory be more efficient, in real life you probably do better to first get into some kind of parking orbit.

[Streetwind]

23 minutes ago, AHHans said:

Well, in theory a direct burn to a high apoapsis is more fuel efficient

According to which theory?

Your explanation appears to be advocating for the lowest apoapsis possible - either directly above the terrain on an airless body, or as close as you can get to that while avoiding an atmosphere in the process. That is consistent with what I said, but runs counter to the claim that burning to a high apoapsis is more efficient.

Remember, by burning really hard right away and pushing your trajectory way up, that burn will be performed at low speeds, under high gravity losses. Oberth cares about speed. Also, that's not an orbit insertion. You have to do another burn at apoapsis. And the higher up that apoapsis is, the steeper your trajectory becomes, and thus the slower you will be going at apoapsis, which is bad for Oberth, and it means that you'll be spending an increasingly larger share of your dV budget there.

As far as losses across a powered ascent from Kerbin go: roughly two thirds fo your dV budget goes to orbital velocity, another quarter goes to gravity losses, maybe 5% or so is lost to aerodynamic drag, and one percent to steering inefficiencies. Trying to optimize a trajectory for reduced drag is *always* a net loss, because  gravity is a far worse offender. You can fly steep, low drag trajectories when you have a raggy payload that would otherwise flip your rocket, but never to save dV. Turning over fast and burning hard is always better for pure dV expenditure concerns.

[paul23]

What he means is that if we suddenly remove the planetary body into a point mass, you will "fall" into an orbit anyways. - A highly eccentric orbit, wit hthe apoapsis at the radius of the body, and horizontal velocity due to the rotation velocity of the planet.

 

If, from such an orbit you wish to move to another orbit, it is most efficient to do that directly. So burn sideways until you have a (round) orbit at altitude of 0 meters. Then keep burning till you reach the desired final orbit. Instead of going first to an intermediate orbit at say 100km altitude circularize there, and then go for the final orbit.

[Streetwind]

Okay, I can see that, yes. That would work.

However, it only works by making the additional assumption that velocity changes are instantaneous, and therefore, gravity losses are nonexistant. Personally, I don't believe that this two-fold simplification is useful where launches are concerned. We can not approach it closely enough in practical application to employ it even as a first-order approximation; the result will always be far enough off to matter.

 

Edited October 15, 2019 by Streetwind

[magnemoe]

Burning up to 600 km AP is most efficient, however if this is an non equatorial orbit because of some contract. I always burn to low orbit first and try to match the plane. Then do an second burn who raise AP so I can both adjust plane and circulate at once. 

[Kryxal]

Better to burn immediately to 600 km, but there's no reason to change your usual gravity turn ... just don't stop thrusting to coast to LKO (or angle downwards, whichever you use).  A well-done gravity turn will have your periapsis above the surface anyway, and you're already thrusting as sideways as you would usually.

[AHHans]

9 hours ago, paul23 said:

What he means is that if we suddenly remove the planetary body into a point mass, you will "fall" into an orbit anyways. - A highly eccentric orbit, with the apoapsis at the radius of the body, and horizontal velocity due to the rotation velocity of the planet.

Yupp. I wouldn't have (thought to) put it in these words, but that's what I meant.

4 minutes ago, Kryxal said:

Better to burn immediately to 600 km, but there's no reason to change your usual gravity turn ... just don't stop thrusting to coast to LKO (or angle downwards, whichever you use).

Exactly, I was just about to write that with my own words: "Do your normal ascent avoiding gravity, steering, and atmospheric drag losses as well as possible. If you then would need to throttle down or coast (or steer down, I didn't think of that) to get into LKO, then it is more efficient to keep burning until you have your apoapsis at the height of your final orbit."

Edited October 15, 2019 by AHHans
fixed typo

[Pecan]

In the past I have vigorously argued for low-orbit circularisation-and-transfer but I have become convinced by the maths that burning directly to high orbit is more efficient.

Now I argue for low-orbit first because it's easier, allows for a good phasing orbit if you're rendezvousing with a space-station or similar and, frankly, consistent launches to 75km are something I do without thinking.

[AHHans]

54 minutes ago, Pecan said:

Now I argue for low-orbit first because it's easier, allows for a good phasing orbit if you're rendezvousing with a space-station or similar and, frankly, consistent launches to 75km are something I do without thinking.

You forgot: "the difference in efficiency is rather small".