LKO and then hohmann to final orbit vs. straight to final orbit

[Gooru]

I´m mostly interested in the answer for rockets, but feel free to talk about spaceplanes too.

What is the better launch option?

Is it better to go for LKO first and then do a hohmann transfer to the final orbit?

Or is it better to raise straight to the final AP and establish an orbit when you reach it?

[Gaarst]

I think that due to the Oberth Effect (and possibly other orbital mechanics), it would be better to set your apoapsis straight at the final orbit height. Don't quote me on that though.

Edit:

Actually I don't think I understood your post correctly; but as said below you'd still have to do your gravity turn, not go straight upwards.

The difference between the two solutions would arise in high atmosphere: either to set your rocket to circularise (first option, usually head 0°), or you continue burning with a small angle wrt the horizon before reaching LKO apoapsis (else it will essentially be the same as the first solution).

Edited October 5, 2015 by Gaarst

[Empiro]

It depends on what you mean by straight to final AP. If you're burning straight up to get to the desired AP, and then burning horizontally, then no, you shouldn't do that.

If you're performing a good gravity turn while continuously firing your engines until the AP gets to where you want and then circularizing, then that's better, though highly dependent on your trajectory.

[Van Disaster]

For pure rockets: it would *probably* be better to burn to your final AP: burning to LKO means you'd be in atmosphere longer & that's extra loss due to drag ( assuming an atmospheric launch - if there's no atmosphere then it doesn't matter ), although the upper atmosphere isn't all that draggy.

Spaceplanes: you want to spend as much time where wings & jet engines work as possible, and then as little time in atmosphere again; however in this case I'd probably set AP to just outside the atmosphere and then raise AP to it's final point once I exit, because spaceplanes have considerably more drag inducing bits and you want to be as slow as possible in atmosphere to keep drag down - and even when there is almost no air the wings are still contributing *some* lift.

[Tatonf]

If you performed a good gravity turn you're almost in orbit anyway, so the difference won't be huge between the two options.

Just remember that bi-elliptical transfer is better if your orbit is above 7 500 000m.

[FyunchClick]

For pure rockets: it would *probably* be better to burn to your final AP: burning to LKO means you'd be in atmosphere longer & that's extra loss due to drag ( assuming an atmospheric launch - if there's no atmosphere then it doesn't matter ), although the upper atmosphere isn't all that draggy.

I have seen the case being made that gravity losses outweigh drag losses most of the time (e.g every second you burn straight up you waste 9.8 m/s of dV) so I wonder if a gravity turn isn't preferred regardless.

[jlcarneiro]

I think the OP question is: If I intend to get to a 250x250 orbit, should I:

• set my AP to 250 and when I reach it, I circularize?
  
• set my AP to 71, circularize and THEN do Hohman transfer to 250x250?
  

Unfortunately, I don't know the answer either... I'd very like to learn it from you guys...

[Empiro]

I think the OP question is: If I intend to get to a 250x250 orbit, should I:

• set my AP to 250 and when I reach it, I circularize?
  
• set my AP to 71, circularize and THEN do Hohman transfer to 250x250?
  

Unfortunately, I don't know the answer either... I'd very like to learn it from you guys...

Definitely option 1 for most rockets with modest TWR and reasonable aerodynamics. However, the difference isn't that huge.

Edited October 6, 2015 by Empiro

[Sampak]

I admit this took me a second to wrap my head around. As Tatonf mentioned, you're almost in orbit already, as soon as Peri passes higher than atmosphere. However, in the process of accelerating from there, you are already creating, then passing a circularized orbit.

The other option would be to create a suborbital flight with an insanely high Peri, which is the equivalent of blasting straight up until you get there, then turning sideways. VERY bad idea in terms of efficiency.

Don't you mean insanely high Apoapsis?

In any case, I am no expert at this but I thought about this question as OP mentioned. And I came to the conclusion that aside from some technical stuff I may not be aware of, one would spend the same amount of energy/Delta V to get to the Mun regardless of first circularizing orbit. If you setup your launch so that you can launch directly to the Mun, you could "skip" circularizing, but you would simply be burning up to, and past some sort of LKO and still need a certain amount of dV.

Only difference I can see is instead of stopping for a bathroom break in orbit around Kerbin before burning off toward the Mun as per a typical flight plan, instead you just happened to launch at the right window to be able to keep burning from launch until you intercept the Mun.

I hope I made sense with all that rambling.

[Van Disaster]

I have seen the case being made that gravity losses outweigh drag losses most of the time (e.g every second you burn straight up you waste 9.8 m/s of dV) so I wonder if a gravity turn isn't preferred regardless.

You would always do a gravity turn; where your trajectory aims at, AP at LKO vs AP somewhere higher will shape the trajectory, and the higher the AP target the less of that trajectory will be spent in atmosphere. There's a lot of corners depending on TWR and burn time of each stage, but aside from low down drag losses from a rocket should be pretty low so it doesn't matter *that* much - but given the choice of burn to low AP and raise vs burn to high AP, seems sensible to go straight to high AP.

[jlcarneiro]

Thank you all!

Thinking of it, it makes sense!

About spaceplanes, I THINK the same rule applies, I should aim for the highest AP that doesn't interfere (much) with the speed run phase, right?

[GoSlash27]

I always do LKO first if I'm rendezvousing with something. If it's just a plain ol' sat contract, I launch right into it.

Going to LKO first costs some DV (usually marginal) but gives a lot of flexibility. Shooting direct saves some DV, but it demands a tight launch window.

For spaceplanes... I go to LKO first every time. They take longer to get to orbit, so there's more variation in their time to orbit. This means it's less likely you'll launch directly into a rendezvous.

Best,

-Slashy

Edited October 5, 2015 by GoSlash27

[Van Disaster]

Thank you all!

Thinking of it, it makes sense!

About spaceplanes, I THINK the same rule applies, I should aim for the highest AP that doesn't interfere (much) with the speed run phase, right?

No, other way round - for spaceplanes use the atmosphere as much as possible, go as slow as you can get away with in atmosphere which means as low AP as possible until you're out of it - then start raising AP, you don't have to circularize at that point. Rockets are very slippery shapes - things with wings are not.

[Jason Patterson]

I admit this took me a second to wrap my head around. As Tatonf mentioned, you're almost in orbit already, as soon as Peri passes higher than atmosphere. However, in the process of accelerating from there, you are already creating, then passing a circularized orbit.

Not really. If you're burning prograde prior to apoapsis (or really any direction other than radially) then you're never going to create a circular orbit, as your apoapsis is always going to be higher than your current position, which can't be lower than periapsis. To get a circular orbit you either have to burn at one of the apses to alter the other or burn radially to make your current position an apsis and alter the other side of the orbit. It's 100% possible to do a proper gravity turn and burn hard enough to exceed Kerbin's escape velocity without ever having a periapsis above the planet's surface.

I think the OP question is: If I intend to get to a 250x250 orbit, should I:

• set my AP to 250 and when I reach it, I circularize?
  
• set my AP to 71, circularize and THEN do Hohman transfer to 250x250?
  

Unfortunately, I don't know the answer either... I'd very like to learn it from you guys...

The first option is superior. You're taking advantage of your high launch velocity (the well know Oberth effect) to increase your ship's energy enough to reach a high altitude. At that high altitude you can then make a relatively small adjustment in velocity to increase your periapsis to circularize. To circularize at 71 km you need to add significantly more velocity as well as lose velocity to reach periapsis (i.e. waste Oberth effect.) At this point you then step up to 250km, then increase your periapsis to 250km. Though this second periapsis increase would be less than the first version, the savings on that step would not outweigh the losses at other steps. I might try to set up a test later to try this out, but it's going to vary somewhat depending on the particulars of your launch anyway.

ETA: Better, I just did the math. I'm assuming burns are instantaneous for sanity's sake. Real burns take time, so the difference is slightly less, but if your burns are taking a significant fraction of an orbital period, you really ought to increase your TWR (or be using a crazy efficient engine to compensate for the loss.)

I ran a quick launch to see where my periapsis would be with a reasonable 71km apoapsis, and it happened to be right at the surface (321 meters below it, but that's close enough for government work.) I hit that periapsis at about 40km. Let's assume that you've burned to a 71km apoapsis with a 0 km apoapsis and your ship is at 40km. You're now going 2340 m/s. You now follow one path or the other.

A) Circularize at 71km, burn to 250km, circularize at 250km.

1. Coast to apoapsis = 0 m/s delta-v

2. Burn to circular orbit: At apoapsis your velocity will now be 2229 m/s. A 71km circular orbit has a velocity of 2294 m/s. 65 m/s delta-v (This does not include additional losses in this launch due to prolonged time in the atmosphere, perhaps 10m/s total delta-v difference between the two.)

3. Burn to 250km apoapsis: This requires an increase to 2425 m/s at periapsis. 131 m/s delta-v

4. Burn to circular orbit: At apoapsis your velocity will now be 1914 m/s. A circular 250km orbit has a velocity of 2038 m/s. 124 m/s delta-v

Delta-v total for this burn from the starting orbit: 65 + 131 + 124 = 320 m/s

Burn to 250km, circularize at 250km.

1. Burn to 250km apoapsis: Doing the math here is rough. If you simply increase your speed here without changing direction you would raise both periapsis and apoapsis. You'd have to intentionally orient your ship at some wonky angle to force your periapsis to remain at 0km. Doing a horizontal burn to avoid gravity drag gives me a new periapsis of 35km, and apoapsis of 250km, all at 40km altitude. Your mileage may vary, of course. In any case, this yields a new velocity of 2507 m/s. 167 delta-v

2. Burn to circular orbit: At apoapsis your velocity will now be 1887 m/s. Again a circular orbit has a velocity of 2038 m/s. 151 m/s delta-v

Delta-v total for this burn from the starting orbit: 167 + 151 = 318 m/s

You save a whopping 2 m/s by my calculations! Totally worth it!!! Contrary to my expectations, there's just not enough difference between a 71x71 orbit and a 71x0 orbit to make a difference here. I'm sure that the difference would increase for a larger destination orbit (say a Mun encounter) and for a more aggressive gravity turn than I made, but it's not going to be much for a typical launch of mine, as a fraction of total delta-v required.

Edited October 6, 2015 by Jason Patterson

[Tatonf]

The best way would be a reapetable launch with mechjeb for comparison.

[OhioBob]

I think the OP question is: If I intend to get to a 250x250 orbit, should I:

• set my AP to 250 and when I reach it, I circularize?
  
• set my AP to 71, circularize and THEN do Hohman transfer to 250x250?
  

Unfortunately, I don't know the answer either... I'd very like to learn it from you guys...

#1 is better but the difference is insignificant. Below is a numerical example. The effects of the atmosphere have been ignored and all ÃŽâ€v are assumed to be applied instantaneously.

Let's say we're launching into a 71 km circular on way to eventually establishing a 250 km circular orbit. Let's say that during ascent we cut our engine at an altitude of 45 km, leaving us in a temporary orbit with an apoapsis of 71 km and a periapsis of 0 km. By the time we coast up to our apoapsis, we require a burn of 65.0 m/s to circularize at 71 km. We then perform a second burn to boast our apoapsis to 250 km, and then a third burn to circularize at 250 km. These second and third burns require ÃŽâ€v of 131.2 m/s and 123.7 m/s respectively. That's a total ÃŽâ€v of 319.9 m/s to establish the 250 km orbit, not counting what it took to get up to our initial 45 km cutoff point.

Let's now say we travel up to the exact same cutoff point as before, but instead of stopping we continue to burn prograde until we boost the apoapsis all the way up to 250 km. This takes an additional ÃŽâ€v of 167.9 m/s, leaving us in a temporary orbit with Ap = 250 km and Pe = 37.3 km. After coasting up to apoapsis, we require a burn of 151.4 m/s to circularize at 250 km. That's a total ÃŽâ€v of 319.3 m/s.

So you can see in this example that the difference is a negligible 0.6 m/s. I would recommend that you just do what is most comfortable to you and what best suits the circumstances. There is really no big advantage one way or the other in terms of ÃŽâ€v.

[FancyMouse]

And I'm actually interested in how many newbies are interpreting #1 as "I don't have to do a proper gravity turn"?

[OhioBob]

ETA: Better, I just did the math. I'm assuming burns are instantaneous for sanity's sake. Real burns take time, so the difference is slightly less, but if your burns are taking a significant fraction of an orbital period, you really ought to increase your TWR (or be using a crazy efficient engine to compensate for the loss.)

I ran a quick launch to see where my periapsis would be with a reasonable 71km apoapsis, and it happened to be right at the surface (321 meters below it, but that's close enough for government work.) I hit that periapsis at about 40km. Let's assume that you've burned to a 71km apoapsis with a 0 km apoapsis and your ship is at 40km. You're now going 2340 m/s. You now follow one path or the other.

A) Circularize at 71km, burn to 250km, circularize at 250km.

1. Coast to apoapsis = 0 m/s delta-v

2. Burn to circular orbit: At apoapsis your velocity will now be 2229 m/s. A 71km circular orbit has a velocity of 2294 m/s. 65 m/s delta-v (This does not include additional losses in this launch due to prolonged time in the atmosphere, perhaps 10m/s total delta-v difference between the two.)

3. Burn to 250km apoapsis: This requires an increase to 2425 m/s at periapsis. 131 m/s delta-v

4. Burn to circular orbit: At apoapsis your velocity will now be 1914 m/s. A circular 250km orbit has a velocity of 2038 m/s. 124 m/s delta-v

Delta-v total for this burn from the starting orbit: 65 + 131 + 124 = 320 m/s

Burn to 250km, circularize at 250km.

1. Burn to 250km apoapsis: Doing the math here is rough. If you simply increase your speed here without changing direction you would raise both periapsis and apoapsis. You'd have to intentionally orient your ship at some wonky angle to force your periapsis to remain at 0km. Doing a horizontal burn to avoid gravity drag gives me a new periapsis of 35km, and apoapsis of 250km, all at 40km altitude. Your mileage may vary, of course. In any case, this yields a new velocity of 2507 m/s. 167 delta-v

2. Burn to circular orbit: At apoapsis your velocity will now be 1887 m/s. Again a circular orbit has a velocity of 2038 m/s. 151 m/s delta-v

Delta-v total for this burn from the starting orbit: 167 + 151 = 318 m/s

You save a whopping 2 m/s by my calculations! Totally worth it!!! Contrary to my expectations, there's just not enough difference between a 71x71 orbit and a 71x0 orbit to make a difference here. I'm sure that the difference would increase for a larger destination orbit (say a Mun encounter) and for a more aggressive gravity turn than I made, but it's not going to be much for a typical launch of mine, as a fraction of total delta-v required.

Holy crap! Your example is virtually identical to mine. The only difference is that I figured an initial burnout altitude of 45 km while you used 40 km.

It looks like I beat you to it by 6 minutes. But seriously, it's great that we got the same result and arrived at the same conclusions.

[magnemoe]

I always do LKO first if I'm rendezvousing with something. If it's just a plain ol' sat contract, I launch right into it.

Going to LKO first costs some DV (usually marginal) but gives a lot of flexibility. Shooting direct saves some DV, but it demands a tight launch window.

For spaceplanes... I go to LKO first every time. They take longer to get to orbit, so there's more variation in their time to orbit. This means it's less likely you'll launch directly into a rendezvous.

Best,

-Slashy

For satellites in high orbit and not in plane I tend to launch to 500 km, circulate then raise Ap, do plane change while raising Pe, then do final adjustment burn

[Gooru]

I think the OP question is: If I intend to get to a 250x250 orbit, should I:

• set my AP to 250 and when I reach it, I circularize?
  
• set my AP to 71, circularize and THEN do Hohman transfer to 250x250?
  

Yes, exactly this was my question.

My testlaunches up to around 200km did not show any significant difference, so i asked :-)

[Van Disaster]

For satellites in high orbit and not in plane I tend to launch to 500 km, circulate then raise Ap, do plane change while raising Pe, then do final adjustment burn

Plane changes are kinda anti-Oberth, the slower you are the better. If you need to do a big plane change for anything it is worth testing if raising AP a lot, doing the change there and then recircularizing at the unchanged PE is cheaper than the direct burn(s) you'd need otherwise. Setting up synched polar satellite networks has to be the most awkward thing.

[cantab]

If you're flying an efficient ascent it's slightly better to go straight to your target orbit. During an efficient ascent you'll normally pass through something like a 50x50 or 60x60 orbit. From there you carry on burning, and you may as well carry on until your final apoapsis instead of first reaching some intermediate orbit. Plus if you stop on something like a 60x70 orbit you'll be in the upper atmosphere for ages and get your apo slowly dragged down, whereas if you get into a 60x250 orbit you'll get out of the atmo quickly and suffer no more drag.

[Kelvin Kerbin]

For satellites in high orbit and not in plane I tend to launch to 500 km, circulate then raise Ap, do plane change while raising Pe, then do final adjustment burn

I'm curious, why don't you wait until the launch site is on the satellite orbit plane and then launch directly into that plane (as opposed to launching into the equatorial plane and then changing orbital planes)?

I've always launched directly into the satellite orbital plane and found there is a slight dV cost (over launching into an equatorial plane) but it didn't seem anywhere near the dV cost of actually making a plane change, especially for polar orbits. Then again, it just made sense so I've not run a proper scientific test of the idea.

[OhioBob]

I'm curious, why don't you wait until the launch site is on the satellite orbit plane and then launch directly into that plane (as opposed to launching into the equatorial plane and then changing orbital planes)?

I've always launched directly into the satellite orbital plane and found there is a slight dV cost (over launching into an equatorial plane) but it didn't seem anywhere near the dV cost of actually making a plane change, especially for polar orbits. Then again, it just made sense so I've not run a proper scientific test of the idea.

You are correct. Any time you can combine a plane change with an altitude change, you save considerable dV over performing the two maneuvers separately. It is simply a matter of how the vectors are added.

(ETA) For example, let's say you are making a 100 m/s altitude change and a 100 m/s plane change. If you do them separately it's 100+100 = 200 m/s. If you combine them it's (100²+100²)^0.5 = 141.4 m/s.

Edited October 6, 2015 by OhioBob

[OhioBob]

I'm very surprised by this result.. I assumed that max efficiency (in theory) would involve establishing a small LKO orbit, and gradually expanding it from each side in small increments.

Burning straight to a high Apoapsis sounds like it would involve much more gravity losses, due to the higher AoA relative to the planet... How is this not the case?

In the numerical example that Jason and I presented (independently but essentially identical), we're suggesting that the rocket follows the exact same ascent profile in both the low apoapsis and the high apoapsis scenarios (the AoA doesn't change). The only difference is that in the high apoapsis scenario, the rocket must burn its engine a little longer (probably about 6 seconds or so). This makes virtually no difference in the gravity losses because the extended burn comes near the end of the ascent after we're essentially already in orbit.