Breaking up long burns into multiple burns - How?

[CrashyMcCrashFace]

4 minutes is not too long. I've done 20+ minute burn with a xenon power probe.

PS, 20+ minutes wasn't by design but I wasn't giving up either.

Edited May 9, 2018 by CrashyMcCrashFace

[Norcalplanner]

Generally it's more trouble than its worth to split up a burn that takes less than 1/6 of the orbital period to accomplish.  If you do split it up, making the first burn so that the resulting orbit is precisely one day long (and making that first burn a day early) is usually a good way to go. My usual method is to simply give up some of the Oberth in exchange for a more accurate burn by departing from a higher orbit. Put the craft in a 300/600/1200/2400 km orbit, refuel with a tanker if needed, then make a single long ejection burn. One final tip - focus your view on the target planet as you get close to the end of the burn so you can stop burning at the correct instant.

[RizzoTheRat]

5 hours ago, OhioBob said:

It sounds like you misunderstood me.  I do not recommend two separate burns in the way that you describe.  It is most efficient to perform a single burn when near the planet.

I meant 2 steps to calculating the dV requirement, not to implementing it, but having reread my post I completely failed to explain it like that.  D'Oh

[Goody1981]

9 hours ago, Rauko said:

The more I think about it, the less I understand it

snip 

You think: wait! I will get advantage of oberth effect, I will raise my apoapsis to raise my speed at periapsis. I spend 1000 dv to get a eliptical orbit, and in my next periapsis I will burn. In the periapsis, the ship is now faster, say 3200m/s, and due to oberth, I will need less fuel to reach my desired destination, leaving me with, say, 200dv remaining in my KER readout.

I gained those 200dv because I was faster when I did the second burn. BUT when I finished my first burn I WAS ALREADY THAT FAST! (due to that velocity, my orbit was eliptical at that very moment), so I would have take advantage of Oberth just by not stoping my first burn. (IE, KER readout would have anyway ended showing 200dv remaining)

Where did I lost contact with reality?

The main reason to split up burns is not to get a different Oberth advantage, because as you say, you’re ALREADY that fast at the end of the first burn. Now if your burn is so long that you’re halfway to (your old) Ap and still burning, then I guess you do lose a bit from Oberth, but you lose much more by not burning prograde. E.g. if you need a 1000 m/s burn at Pe to complete a manoeuvre, but your low TWR makes it take so long that you’re a quarter of the way around your orbit and still burning, you’ll now be burning radial out. Or, if you kept pointing prograde through the whole burn, you’ll end up in a completely different orbit to the one you wanted. So splitting a long burn up is all about not thrusting in the wrong direction (ie your manoeuvre marker is prettt much aligned with the prograde marker)

 

9 hours ago, RizzoTheRat said:

Because the burn takes a finite duration, rather than the instant change in velocity that a manoeuvre node simulates, a lot more of the burn takes place at a higher altitude, and therefore lower speed.  Splitting the burn over 2 orbits means you're burning at a lower average altitude, and therefore higher average speed.

I think. 

Oberth is quite confusing.

 

7 hours ago, bewing said:

I think a better way of looking at it is more like:

When your orbit is not circular, you lose speed to gravity losses as you climb. The longer it takes you to climb, the more speed you lose. So the Oberth Effect is all about getting you out of the gravity well ASAP. This allows you to carry as much speed as possible along with you. So if you start with 700 m/s and add 2000 m/s and it takes you 20 days to leave the SOI, you will be going very slow once you are out. If you start with 2400 m/s and add 2000 m/s and it takes you 20 minutes to leave the SOI, then you won't lose much.

 

If I may (hi  ) a way that helps me to understand the Oberth effect is to think about it in terms of energy. How do you increase the size of your orbit? You add energy. And you get more energy added if you start your burn at a faster speed (at Pe), because kinetic energy is proportional to velocity squared.

Example: 

Imagine we have a 2kg spacecraft, with 1m/s dV, orbiting at 1m/s (ridiculous numbers, but makes the maths easy).

If we burn all our fuel in the right direction, we end up travelling at 2m/s. How much kinetic energy did we add?

start energy KE = 0.5mv^2 = 1 x 1 = 1J

—— 1m/s burn to increase velocity from 1 to 2

end energy KE = 0.5mv^2 = 1 x 4 = 4 J

...so we have added 4-1= 3 J of energy.

 

now,  see what would be different if we had started at 2 m/s orbital speed, with everything else the same:

start energy KE = 0.5mv^2 = 1 x 4 = 4 J

—— 1m/s burn to increase velocity from 2 to 3

end energy KE = 0.5mv^2 = 1 x 9 = 9 J

...so we have added 9-4 = 5 J of energy

 

(I realise this assumes the mass of the spacecraft doesn’t change through the fuel lost, so it may not be quite as cut and dried as this, but this still demonstrates the effect, and since KE is proportional to mass, but proportional to velocity SQUARED, the benefit of the increased velocity wins every time)

Scale up for actual rocket masses and velocities and you get quite an impressive benefit

Edited May 9, 2018 by Goody1981

[ibanix]

So what I'm reading is... break long burns into orbits of multiple integer days (1 day, 2 day, 3 day); or just burn to a higher circular orbit to begin with?

[Superfluous J]

There is no real reason to make your orbit an exact day, except maybe to ensure your ejection is right on time by starting exactly a day ahead of time. However, for any ejection to anywhere that isn't Mun or Minmus, being off by a day won't really affect the transfer enough to worry about it. I'm frequently off by several days and never have a problem.

The easiest way I know to "split the burn" is to make your maneuver node to do the full ejection, note the time it takes (Use BBT please or don't complain to me that the game lied to you), cut that time in half, thirds, etc noting that after about 950m/s you're going to have to just keep burning (because you'll be out of Kerbin's SOI), and then figure out what that smaller burn's time would be. Do that smaller burn, then delete the maneuver node and recreate it on the next orbit to make sure you're still on target. Repeat until you eject, usually just once.

And watch out for Mun. It likes to grab you on your way around.

[OhioBob]

42 minutes ago, ibanix said:

... break long burns into orbits of multiple integer days (1 day, 2 day, 3 day)

That has limitations, however.  The first burn (or the first two burns, or whatever) can't add up to more than escape velocity.  Once you hit escape velocity, that's it, you're never coming back.  In low Kerbin orbit escape velocity is about 940 m/s.  If you need a delta-v of, say, 1800 m/s, you might say I'll do it in burns of 600-600-600.  Well, that doesn't work because about halfway through the second burn you've hit escape velocity.  At that point you have no choice but to finish off the burn and send the spacecraft on its way.

I generally see no reason to do more than two burns.  With the first burn about 750-800 m/s to put the spacecraft in a 6-hour orbit.  And then the rest is done in the second burn.

[Laie]

EDIT: I've now made a short video tutorial. Hope it helps.

 

On 5/9/2018 at 10:10 AM, ibanix said:

Sure, that's a possibility. But it wastes more dV to get up into that orbit and then burn out. I know it's possible to use multiple burns, I just can't figure out the math involved. Hasn't *someone* done this?

Many have. Me too. It's trivial, you may possibly facepalm once you notice just how simple it is...

1. go into orbit some 6-10 hours before the scheduled departure (or more, but that'll do it in your case)
2. plan departure maneuver as usual
3. note the maneuver's position and magnitude (say 1000 prograde 150 normal) and time (I like to set a KAC alarm)
4. delete the maneuver, and replace it with a proportinally smaller node (e.g. 1/5th of the above, 200 pro /  30norm) to be executed ASAP. That maneuver has to be in the same place wher the (now deleteded) departure maneuver was.
5. After that burn, place another 1/5th maneuver at your PE (which now is where that node was, and where the departure node needs to be) and execute it.
6. repeat.
7. plan the fourth maneuver so that you will be back at PE just when the KAC alarm comes up (may allow for more than one orbit; be careful of not brushing up against the mun)
8. When you arrive at PE at departure time, do one last burn of however much dV still needs to be done.

That's it. Quick example here (I follow up with a munar assist, but that's beside the point -- the interesting bit is how I do three burns to get to the mun in the first place). If you want to (and have suitable tools) you can be very precise about it, but frankly, a well-calibrated eyeball is good enough for maneuver placement. Timing, too, can be rather lax -- give or take a few hours doesn't have much of an impact, you certainly don't need to fret about missing the window by minutes (unless you go for a munar assist, in which case a minute is a lot).

On 5/10/2018 at 1:57 AM, ibanix said:

So what I'm reading is... break long burns into orbits of multiple integer days (1 day, 2 day, 3 day); or just burn to a higher circular orbit to begin with? 

No, not a high circular orbit. Your PE stays low. All you do is a) rasing AP b) see to it that PE is in the right place c) you arrive at PE at about the right time. Integer days might make the maths easier, but isn't mandatory.

Edited May 13, 2018 by Laie

[Goody1981]

1 hour ago, Laie said:

No, not a high circular orbit. Your PE stays low.

Actually, being in a higher circular orbit to begin with removes the need to split a long burn, which I think is what he’s saying.

[Laie]

On 5/9/2018 at 3:00 PM, Rauko said:

But does is mean that it is beneficial to raise apoapsis and then burn again in your next periapsis? I dont see it.

The problem comes up because real burns take time (possibly a long time), and your vessel's vector is moving.

Experiment: Put vessel in low circular orbit. Place maneuver node going prograde. Now assume, for the sake of the argument, that your maneuver will need ten minutes to execute and you want to start the burn five minutes ahead of time. When you timewarp to T -5min, you will see that the maneuver marker on the navball doesn't point prograde but downwards by something like 45-60 degrees (depending on what you consider "Low" Kerbin Orbit).

The maneuver marker doesn't simply point to a fixed direction for the duration of the burn; I don't quite know how maneuvers are implemented, but they seem have an idea of the final vector you want to arrive at, and the marker on the navball will shift to compensate for (e.g.) steering errors. This works well enough for reasonably short burns -- you may use a little more dV than expected but will ultimately still go in the right direction after the maneuver is done. However, it can compensate for only so much.

 During ten minutes in LKO, you're doing about 1/3rd of an orbit and your vector changes it's direction by 100-120 degrees. That's definitely more than a single maneuver can still handle well. To repeat: the problem isn't the duration as such, but the changing vector.

On 5/9/2018 at 8:48 PM, Norcalplanner said:

Generally it's more trouble than its worth to split up a burn that takes less than 1/6 of the orbital period to accomplish. 

Quoted for truth. That's about as much a single maneuver can handle and still deliver good results.

An easy way of working around the issue is to start from a higher orbit, but this costs much more dV. Whereas periapsis-kicking can, in principle and for as far as it gets, be as efficient as an instantaneous burn.

Edited May 12, 2018 by Laie

[Norcalplanner]

3 hours ago, Laie said:

An easy way of working around the issue is to start from a higher orbit, but this costs much more dV. Whereas periapsis-kicking can, in principle and for as far as it gets, be as efficient as an instantaneous burn.

A lot of this comes down to play style as well. I play in upscaled systems with lots of infrastructure and will frequently use MJ to execute the maneuver nodes I've already created. Doing a 4 km/s burn is much more easily and accurately accomplished from a higher orbit, especially if there's an orbital refueling station also in a higher orbit to refuel the craft before it heads out.

Edited May 11, 2018 by Norcalplanner
Clarity

[ibanix]

On 5/10/2018 at 2:58 PM, Laie said:

Many have. Me too. It's trivial, you may possibly facepalm once you notice just how simple it is...

 

7. plan the fourth maneuver so that you will be back at PE just when the KAC alarm comes up (may allow for more than one orbit; be careful of not brushing up against the mun)

 

How? This is the one I have a problem with.

[Goody1981]

10 minutes ago, ibanix said:

How? This is the one I have a problem with.

If you literally want that last burn to happen the exact second of your departure window for super-duper-optimal dV, then I'm pretty sure the only way to do it is work backwards. Which means knowing the periods of the orbits you'll be in before you are in them. Which means a whole lot of maths!

E.g. say you have a 1000 m/s burn that you're gonna split into 4 x 250 m/s burns. Assume you're starting at orbital velocity of 2300 m/s (somewhere around 70x70 Kerbin orbit). So it goes first burn (+250m/s) -> wait until you're back at Pe -> second burn (+250m/s) -> wait until you're back at Pe -> third burn (+250/ms) -> wait until you're back at Pe -> fourth burn (+250 m/s) -> escape Kerbin system. You need to calculate those waiting times, add them up, and start your first burn that amount of time before your departure window.

1 - After your first burn, your velocity at periapsis is now 2550 m/s. Plug this number into the vis-viva equation to work out the semi-major axis of your orbit...

                   where v = orbital velocity, a = semi-major axis, u = universal gravitational constant, r = distance from centre of Kerbin (600km + current altitude)

2 - Once you have the semi-major axis, use it to work out the new orbital period of the orbit you'd be in...

                  where T = orbital period

3 - Now you know how long the first waiting period is...call it "OrbitTime1".

4 - Repeat 1-3 above until you have OrbitTime1, OrbitTime2 and OrbitTime3.

5 - Your departure window is T = 0. Therefore start your first burn at Tminus (OrbitTime1 + OrbitTime2 + OrbitTime3).

 

Note 1: If this sounds fun for you - go for it! But as many people have said in the answers above, if you just split the burn into manageable chunks, and start some time before your departure window, you won't miss by that much, and even if you miss by a week, it doesn't matter that much. By doing all the maths above you might be saving a couple of dozen dV.

Note 2: I didn't actually know all this stuff before 5 min ago....I wanted to give you a good answer so I did a bit of a delve into Wikipedia and found these equations. So thanks for encouraging me to educate myself! (and there is a chance I may be completely wrong haha...but it looks OK to me...I'm sure someone will quickly point out any errors I've made)

[Lego_Prodigy]

Not sure how I would be able to achieve this kind of lunacy, as I usually have extremely slow orbit speeds and pretty decent deceleration anyway.

[Laie]

52 minutes ago, ibanix said:

How [do I arrive at PE at a pre-determined time]? This is the one I have a problem with.

I simply place yet another maneuver node as a marker.

1. plop down maneuver-1 at PE (that's the last kick before departure)
2. put maneuver-2 further down the line (won't be executed, is just a marker)
3. adjust maneuver-2 so it's set to happen at the desired time (using tools)
4. tweak maneuver-1 and see how maneuver-2 shifts around on your orbit.

 

[ajburges]

Long burns have two inefficiencys: cosine lossess and lower average burn velocity (oberth). Separating the two is impactical (impossible?).

While there is little utility to do so, you can approximate your cosine thrust losses by taking the integral of cosine over your burn angle and time. A more complicated fuction can determine dV losses. The loss of work (by engines) is beyond what I care to derive.

[Laie]

I've now made a short video tutorial.  Updated my first post which has been voted to the first page, but poking the OP and the more active participants of this thread for good measure: @ibanix @Norcalplanner @bewing @Goody1981

[ibanix]

Thanks for this. I'll give this a try after I manage to remove enough mods to make my game playable again....

[Hotel26]

On 5/9/2018 at 1:29 PM, 4x4cheesecake said:

If your final burn is still very long, you will be limited by the altitude of your Pe.

I think this is the main take-away.  If you are doing a long burn, it's for efficiency (using nukes or ions), so you have to be willing to pay something in return.

@Bewing said if you are prograde, your Pe won't drop; but that's true only for an instantaneous burn[1].  If you're going to do a ten-minute burn, 5 minutes are before periapsis and it will lower your Pe[2], so you need to have enough altitude to allow for the atmosphere ceiling.  Easy enough, allow for it or stop burning when your Pe drops to atmosphere height; resume at Pe.  It's the last burn in the series that really counts.  Don't sweat the Oberth effect: (it is over-rated).

Hybrid strategies are also nice.  When I use ions (check my avatar), I am not zealous about it -- I also carry nukes or more to get the ball rolling.  Oberth works better with high thrust: more of a good thing is better, yeah?  Ions are for finishing off the job.  (Actually, my experience is that ions are for correcting for Mission Planning Laxity...  but we don't need to go there.)

On this subject, I don't fret mathematical exactitude.

[1] Bewing is probably right if you were pointed exactly prograde but the node manager tends to point you the prograde direction *AT* the node which direction is sub-prograde before you get there.  In practice, you can see the Pe drop...

[2] this is very like doing a MechJeb 90 degree inclination burn: you had better be sure you have the propellant to complete the burn because MJ does not care that it will drop Pe drastically by the middle of the burn and restore it perfectly only by the end of the burn.  (Many a vessel in the graveyard atop that hill, matey!)

Edited May 13, 2018 by Hotel26

[FleshJeb]

 

[ibanix]

That mod has not been updated since 1.2.2, fyi

[Superfluous J]

On 5/11/2018 at 7:42 PM, ibanix said:

How? This is the one I have a problem with.

If you burn (or place your maneuver node) slightly after Pe, it will tell you how long until you'll reach that Pe. Time that to match your ejection time. And remember there's no real good reason to make sure it's exact to the second, minute, or even hour.