Refined Kerbin delta-v Launch 1500 m/s Up, 3000 m/s Gravity Turn

[AuoroP]

Refined Kerbin delta-v Launch 1500 m/s Up, 3000 m/s Gravity Turn

Cross posted to r/KerbalSpaceProgram.

If you like to budget your designs on delta-v there are two outstanding questions about the delta-v you need to launch from Kerbin: how much deltaV for primary ascent and how much for a gravity turn.

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For the TLDR folks, the answer is in the title: a stage delta-v of 1500 m/s gets you moving straight up at terminal velocity and your fuel runs out around 12 km. The accepted answer for a Kerbin launch requires 4500 m/s so the gravity turn will require 3000 m/s = 4500 m/s - 1500 m/s.

So if you're still around you'll probably be interested in specifics about the methodology. Obviously, this is pretty easy. Design a single stage ship with just enough fuel to get it past the 12km lower atmospheres bar.

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Recipe: 6x OX-STAT solar panels (top and bottom) above a Stayputnik pod. Below that we add 3x Z-200 battery rings. Below that a TR-18A decoupler. Below that a FL-T100 fuel tank with Lv-909 engine. The atmosphere Isp for the LV-909 is 300 s. Then add another 6x Z-100 batteries. The total mass is 1.28 and the dry mass is 0.78. The stage delta-v is 1450 m/s.

I happened to conduct this research before I saw Scott Manley's adjustment video for gravity turn tutorials and learned that my target of waiting for barometric pressure to drop to 10% at 11.7 km for starting a gravity turn is too late. I did more testing and discovered that 1200 m/s gets you up to 8 km and it is possible to complete a lazy (did not move prograde fast enough) gravity turn into a circular 75 km orbit with only 3100 m/s in the second stage. 3000 m/s is enough to put you mostly in orbit and yet keep your second stage from turning into space junk.

[UmbralRaptor]

An efficient stock ascent will be <4400 m/s, though this is not possible for all craft (It's more like 4600 m/s for a rocket SSTO maxing out payload per engine). Actual gravity and aerodynamic losses will vary throughout the flight, and it's worth remembering that your Isp is lower deep in the atmosphere.

eg: from using MJ's ÃŽâ€V recorder, a rocket SSTO will have an average Isp ~= what you'd expect at 0.21 atm.

barometric pressure to drop to 10% at 11.7 km

Technically it's 11.5 km. Not a huge difference, but the sort of thing that can make someone look at you funny.

I'm slightly concerned about how you're using the term "gravity turn." Please describe how you perform one. (And please don't be one of those 45° at 10 km monsters)

[Superfluous J]

I'm slightly concerned about how you're using the term "gravity turn." Please describe how you perform one. (And please don't be one of those 45° at 10 km monsters)

Actually could you describe yours? I turn 45 degrees at 10-13km and then slowly follow my prograde marker, eyeing my apoapsis all the time. I end up having to cut the engines and burn at apoapsis a bit but I've usually got 90% of the burning done by that point. I'd love to do it more efficiently, but I simply don't know how. I've had launches use as little as 4700 dV and I think even dipped below that once, but if I could get down to actually 4500 or less I'd be ecstatic.

Edited November 9, 2013 by 5thHorseman

[UmbralRaptor]

Actually could you describe yours? I turn 45 degrees at 10-13km and then slowly follow my prograde marker, eyeing my apoapsis all the time. I end up having to cut the engines and burn at apoapsis a bit but I've usually got 90% of the burning done by that point. I'd love to do it more efficiently, but I simply don't know how. I've had launches use as little as 4700 dV and I think even dipped below that once, but if I could get down to actually 4500 or less I'd be ecstatic.

Fairly similar, except I start at ~5 km, with a ~5-10° turn. Beyond that, it's an aggressive pitch-over, often at the bottom of the prograde marker. Choosing a target orbit of 70-75 km also helps.

[AuoroP]

An efficient stock ascent will be <4400 m/s, though this is not possible for all craft (It's more like 4600 m/s for a rocket SSTO maxing out payload per engine).

The only craft which this won't work for are craft that don't have a high enough TWR to keep them limited to terminal velocity. But for these craft you get the great power of delta-v budgets and planning by breaking that one useless estimate up into two stages that you're going to know will get you out of the thick atmosphere and allow you to complete your gravity turn!

So if your SSTO still goes straight up and then does a gravity turn you can now budget delta-v for both phases: 1000 m/s for straight up to 5km and then probably 3200 m/s for the gravity turning part.

it's worth remembering that your Isp is lower deep in the atmosphere.

Thanks for pointing this out! I'm terrible at communicating because I assume people will see that I've used the atmosphere I_sp for the LV-909 and it would have been really helpful to point out that I made the assumptions that I could simplify I_sp to taking the atmosphere value under 12km and the vacuum above.

Technically it's 11.5 km. Not a huge difference, but the sort of thing that can make someone look at you funny.

Thanks for the correction. I obtained that value about a year ago via a single flight up while watching a barometer so I'm sure your value is more accurate.

I'm slightly concerned about how you're using the term "gravity turn." Please describe how you perform one. (And please don't be one of those 45° at 10 km monsters)

In the flight I mentioned, I started turning immediately after my second stage started at 8km. I kept my rocket pointing between the prograde circle and the outside of the cross. I didn't add any extra turning initially besides jumping right into that spot between the circle and cross

[AuoroP]

Actually could you describe yours? I turn 45 degrees at 10-13km and then slowly follow my prograde marker, eyeing my apoapsis all the time. I end up having to cut the engines and burn at apoapsis a bit but I've usually got 90% of the burning done by that point. I'd love to do it more efficiently, but I simply don't know how. I've had launches use as little as 4700 dV and I think even dipped below that once, but if I could get down to actually 4500 or less I'd be ecstatic.

I noticed that you didn't mention terminal velocity - this is the speed you want to be aiming for during your launch. I can attest that I've checked the Wiki's page on Kerbin's of altitudes and velocities and I believe they are all correct. I would advise you try a launch and pay special attention them especially during primary ascent (straight up) or you can use MechJeb's option to limit you to terminal velocity. MechJeb also has a (sandbox) window called Ascent Guidence that will allow you to watch MechJeb launch your rocket.

You can also watch three launches of Scott Manley in his YouTube video:

You may be disappointed to find that he does not explain what gravity turns are or how they should be done; he just seemed to be bothered that they didn't start early enough because they were waiting until they were out of the lower atmosphere bar (12km).

[Frederf]

A gravity turn is by definition a turn where all steering is done by gravity. If you or mechjeb is touching the controls in any way it is not a gravity turn. You'll see immediately that it is impossible to turn to orbit strictly via gravity if the rocket is radially symmetrical and starts vertical. An initial steer to "tip the domino" is required. A genuine gravity turn is done to utterly minimize steering losses in a very penny-pinching NASA manner. The KSP community grossly misuses the term.

What 99.999% of KSP users do is a generally prograde-ish turn where our small inaccuracies in technique dwarf the miniscule savings on steering losses that would have been saved by a true gravity turn if we did them, but we don't.

And this is OK. Our primitive attempts at optimization often get within 3% of the true optimum. The battle between aero drag and gravity drag steering losses be damned (if we stay within 10 deg AoA) is where the real fight is.

[Superfluous J]

I noticed that you didn't mention terminal velocity - this is the speed you want to be aiming for during your launch.

You are correct, I did not. Sorry about that.

I use Kerbal Engineer Redux and try to get to 90%+ atmospheric efficiency quickly, without ever getting above 100%, and then keep it right in the high 90s if I can the whole way to 10k when atmospheric pressure starts to drop rapidly enough that I can go full throttle without even worrying about it. I will cut the throttle if I need to, but whenever I do that I make a note to fix my rocket for next launch so I can do it at 100% throttle all the way.

A gravity turn is by definition a turn where all steering is done by gravity. If you or mechjeb is touching the controls in any way it is not a gravity turn. You'll see immediately that it is impossible to turn to orbit strictly via gravity if the rocket is radially symmetrical and starts vertical. An initial steer to "tip the domino" is required. A genuine gravity turn is done to utterly minimize steering losses in a very penny-pinching NASA manner. The KSP community grossly misuses the term.

Correct me if I'm wrong but you cannot do a "real" gravity turn in KSP due to the limitations of the simulation. I think it's fine to use the term to describe our attempts to simulate (both in flight path and fuel savings) what NASA does in real life.

Edited November 10, 2013 by 5thHorseman

[numerobis]

You can on atmospheric bodies, as long as there's draggier bits at the back than at the front. Fins, for example, will keep you pointing prograde without control input, so you'll perform that gravity turn just fine.