Is 75 km really an optimal launch orbit?

[ajburges]

Conventional wisdom on these forums suggest that launching to a minimum Kerbin orbit is best, but I am starting to question that.

Assuming you do most of circularizeation in atmosphere, an AP of less than 80 km means you spend a lot of time taking additional drag losses. Even 10 km of additional altitude can halve (or more) the arc you transcribe in the atmosphere! Furthermore such ballistic modifications don't require much additional velocity (important because drag force is directly proportional to the cube of velocity)

I have never seen a useful equation to describe Oberth gains or SoI transitions. I thus have no useful theoretical tools to explore the trade-off between greater drag losses and less optimal ejection burns caused by drag losses. Has this area been explored on these forums before? If not are there any derived equations that can help illustrate Oberth gains for ejection burns?

We already see examples that minimum Kerbin orbit is not the most efficient on the extreme end of the drag spectrum with large single launch stations.

Just to be clear: I don't dispute that low orbits are typically the most efficient for LKO access. I question if they are the most efficient for interplanetary expeditions.

[Raideur Ng]

If you're flying a drag-optimized SSTO into orbit (as it should be), then the last 10km is not really of any importance. Optimizing drag isnt hard to make very low drag rockets, specifically use of bays and fairings. That along with very low thrust requirements for re-entry profiles. I'd stick to 75km.

[WanderingKid]

I would agree with @Raideur Ng here.  The drag losses you encounter above 50km are minimal.  The extra 5-10k height for your orbit is also reasonably minimal.

However, as to your concern with larger space stations with weird/aggressive drag, my usual approach is less of a 'go for a higher orbit' than a 'bend harder at 30km where there's less atmo'.  Usually runs me ~200-500 d/v more for the technique (I don't MechJeb, so nothing's perfect) but it gets it done with a minimum of fuss.

There are no easy tools for determining the Oberth effect, but this article definitely helps to let you understand what's going on:

http://www.askamathematician.com/2013/01/q-how-does-the-oberth-effect-work-and-where-does-the-extra-energy-come-from-why-is-it-better-for-a-rocket-to-fire-at-the-lowest-point-in-its-orbit/

It all comes down to exhaust velocity vs. speed of the rocket and how much energy is left behind in the propellant vs. how much is transferred to the rocket.  I'm not sure KSP mimics this entirely, nor am I good enough to truly break apart the math underlying it, but this person does a great job explaining it in layman's terms.

EDIT: Doing a crossout (but not removing because it's referenced below) as the information is not helpful in understanding Oberth, as I thought it was originally.

Edited March 1, 2017 by WanderingKid

[FancyMouse]

1 hour ago, ajburges said:

can halve (or more) the arc you transcribe in the atmosphere

I don't know what the "halve" means for an arc, but the shape of the arc is actually deceptive - it only changes shape dramatically for the last couple hundreds of m/s. So the arc argument really says nothing but you're close to orbital speed, not telling anything about how much delta V is lost. You need some sort of "instrument flying" and the number you need is apoapsis speed (available in KER)

 

2 hours ago, ajburges said:

I question if they are the most efficient for interplanetary expeditions.

If you TWP plots a transfer with a large normal component (e.g. to basically everywhere but Duna), then obviously there's a better one, by starting the burn from the correct inclination to begin with. You could either carefully plan it, directly launch to that inclination. Another option, which is what I do, is first start from any equatorial LKO, burn to high elliptical with periapsis at the transfer point, do the inclination change at apoapsis (optionally drop a stage there), when coming back to periapsis, do the transfer burn.

[Foxster]

Nah, 605km is the optimal orbit height cos then you can use max warp to your burn time.  

[bewing]

For oberth purposes, it's best not to even bother establishing an orbit in the first place -- if you can time your launch so that your ejection burn starts right about the time you hit 50km altitude (and you're only a few seconds from your Ap), that'll pick you up another 100 m/s of oberth. However, on the other hand, see this: 

But OhioBob's calculation doesn't take into account the deltaV that you need to spend to establish that perfect ejection parking orbit -- which is a gigantic factor.

On the third hand, of course, his higher parking orbits make it much easier to create a very accurate ejection burn.

My choice is to just park and refuel at minmus, and then use a spacetug to give me the 80m/s I need to do a perfectly timed oberth dive to a 50km-to-60km Kerbin Pe for my final ejection burn.

Edited March 1, 2017 by bewing

[Snark]

5 hours ago, WanderingKid said:

It all comes down to exhaust velocity vs. speed of the rocket and how much energy is left behind in the propellant vs. how much is transferred to the rocket.  I'm not sure KSP mimics this entirely

KSP doesn't mimic it because it's irrelevant and has nothing to do with anything.  Exhaust velocity is relevant to how much dV you get out of the rocket equation, but it's irrelevant to Oberth effect per se.  It also has nothing directly to do with the inverse square law, or the particular nature of orbits.

Look, there's nothing mystical about Oberth.  You can do the math in a thought experiment.  You've got a projectile capable of, say, 20 m/s of total dV.  Let's say it can emit that in one giant bang, or two smaller bangs of 10 m/s each.

If you fire it straight up from the ground (let's say no air resistance, to keep it simple), the height it will go is v²/2g.  So, fire it upwards from the ground at 20 m/s on Earth, and it'll reach a height of 20.4 meters.  But if you fire it with a 10 m/s speed, it will only rise 5.1 meters.  So if you fire it upwards at 10 m/s, then when it reaches the apex you fire it again... you get a total height of only 10.2 meters.

In other words... you get a much better result if you use the whole oomph down low.  It comes from the fact that kinetic energy goes with the square of the velocity.

Talking about exhaust velocity and how much energy goes where and so forth may be useful in terms of understanding where the energy goes, but it's not useful in terms of working out what happens, and it's certainly not something that a computer program would need to "model".

[Blaarkies]

25 minutes ago, Snark said:

KSP doesn't mimic it because it's irrelevant and has nothing to do with anything.  Exhaust velocity is relevant to how much dV you get out of the rocket equation, but it's irrelevant to Oberth effect per se.  It also has nothing directly to do with the inverse square law, or the particular nature of orbits.

I am having real Déjà-vu over here... i have heard this before, the community explained Oberth to someone before, but they rejected the evidence and substituted it with their own...

 

@WanderingKid Please don't fall into the same trap he did, please please

[Snark]

44 minutes ago, Blaarkies said:

I am having real Déjà-vu over here... i have heard this before, the community explained Oberth to someone before, but they rejected the evidence and substituted it with their own...

Yeah, I remember that conversation.  Gee, thanks for dredging that memory up, Blaarkies...

Not to put too fine a point on it... if you're in an argument on a physics topic, and @OhioBob disagrees with you... you're almost certainly wrong. 

FWIW, here's my own how-Oberth-works rant from that thread:

 

[Kryxal]

There are more threads than that about Oberth, I have my own memories ... do the math on some "object on a hill" example and have it dismissed for no good reason I could tell.  It happens every now and then.

I like to launch to 80 km now, for a bit of extra room, higher if I'm going to be doing a low-TWR ejection burn.

[WanderingKid]

16 hours ago, Snark said:

Talking about exhaust velocity and how much energy goes where and so forth may be useful in terms of understanding where the energy goes, but it's not useful in terms of working out what happens, and it's certainly not something that a computer program would need to "model".

Fair enough.  That's twice this week you've helped keep me from leaving my foot in my mouth.  Thank you.

16 hours ago, Blaarkies said:

@WanderingKid Please don't fall into the same trap he did, please please

I'm really trying not to.    This has been a bad week for me trying to 'help', I see.  I'd honestly thought that a chunk of the dV effect had to do with the energy transfer due to other items (besides that one math post I dragged along for the ride) that I'd read before.  Note to self: Get away from the math papers and go figure out the physics ones.  I've wrapped my brain around the wrong ideas and need to dislodge those.

[Ultimate Steve]

For stations, though, I go 250km. somewhere below there the surface is unloaded and there is a lot less lag.

[Blaarkies]

On 3/1/2017 at 10:28 PM, WanderingKid said:

I'm really trying not to.    This has been a bad week for me trying to 'help', I see.  I'd honestly thought that a chunk of the dV effect had to do with the energy transfer due to other items (besides that one math post I dragged along for the ride) that I'd read before.  Note to self: Get away from the math papers and go figure out the physics ones.  I've wrapped my brain around the wrong ideas and need to dislodge those.

I bet we all were there at some time. I didnt want to believe the Oberth effect when I first heard of it(and i knew i was wrong because it is mathematically proven). My lightbulb moment happened when I realised this thought experiment:

A probe starts at the edge of Kerbin's SOI with almost no velocity (just enough to have a 70km Pe). Let's say this probe takes 10days to fall/reach Pe, it now has about 3200m/s speed which it received only due to gravity (10days of gravity acceleration causes this much speed).

Now do a tiny 100m/s burn towards prograde: This probe would have taken 10days to reach Ap, but this burn causes it to get there much faster. Gravity doesn't have that much time to slow it down by 3200m/s because it reaches Ap in just 7days. Naively we would expect the ending velocity to be 100m/s faster than what we had, but that is not the case...we exit Kerbin SOI with 500m/s.

If gravity only has 7days to slow us down again, there is no way it will get near -3200m/s again...that extra speed is ours now 

*these numbers are not exact, actual results will definately vary. This does not explain what causes the Oberth effect, it's just a local proof based on input/output of a few craft speeds

Edited March 3, 2017 by Blaarkies

[Kryxal]

The "real" answer has more to do with the change in speed vs the change in energy per unit mass.

[Norcalplanner]

10 hours ago, Ultimate Steve said:

For stations, though, I go 250km. somewhere below there the surface is unloaded and there is a lot less lag.

250 to 300 km is a great orbit for stations.  High quality textures for Kerbin are unloaded around 165 km, more time warp options open up above 240 km, and 300 km is the ideal "gate orbit" altitude for beginning a trip to Jool.

[Birdco_Space]

The answer is: It depends on what you are trying to accomplish.

If you are looking to build a station, higher orbits (within reason) have added value for greater ease of plotting maneuvers to get ships/components.  its hard to catch up with a station ahead of you in orbit if the station is at 75km.

For relatively high TWR interplanetary missions (talking around 0.5 TWR) with thin Delta V margins, the lowest possible parking orbit is desired, to make the most of Oberth effect.

For relatively low TWR interplanetary missions with ample delta-v, higher orbits allow longer burns to be made accurately (or without causing pe to dip into atmosphere during burn). 

If the final stage of your launch vehicle is very low TWR, higher orbits are easier to obtain, as there is more time before the vessel re-enters the atmosphere to add the required delta-v to obtain orbit.  I had a Whiplash/ Dawn powered SSTO that I couldn't get into orbit with a apoapsis below 100km, but it had all the delta V in the world to get anywhere.

Bottom line, there isn't one answer to the question, it depends on the entering argument.

Personally, I like 90km as my standard parking orbit.  easy to get to, Oberth is pretty good there, easy to set up Rendezvous there even if you botch the timing of the launch, it is tolerant to relatively low TWR interplanetary burns

[Snark]

10 hours ago, Norcalplanner said:

250 to 300 km is a great orbit for stations.  High quality textures for Kerbin are unloaded around 165 km, more time warp options open up above 240 km, and 300 km is the ideal "gate orbit" altitude for beginning a trip to Jool.

Not arguing about it being a good altitude for stations (which is, indeed, what you said), and "gate orbits" are indeed a handy thing to know about.

However, it's worth noting that this is getting a little off-topic, because @ajburges was asking about launching a ship to Duna from Kerbin's surface, not fueling it up at a space station and then departing.

And that's really important, because "gate orbit" isn't relevant, there.  If you launch from Kerbin's surface, circularize, and then depart for Duna, you'll get better dV efficiency from the lowest orbit possible.  Not to put too fine a point on it, you'd get better performance than if you circularize at the "gate orbit" first and then depart.  "Gate orbit" is a misleading concept for this scenario.

Why?  Because the "gate orbit" is all about minimizing dV requirements after you're already in a circular orbit.  Yes, it's cheaper in dV to get to Duna from the gate orbit than it is to get to Duna from a really low atmosphere-skimming orbit.  But you also have to consider how much dV does it take to arrive at that circular orbit in the first place, and the really low atmosphere-skimmer is a lot cheaper to get to than the gate orbit.

If you put them together, the total dV necessary is less for the circularize-really-low case, because that gets better Oberth benefit.

To summarize:

• Gate orbit gives best dV efficiency when starting from circular orbit.
• Low-as-possible orbit gives best dV efficiency when starting from planetary surface.

[Norcalplanner]

@Snark I totally agree. I didn't see where it was talking about Duna as a destination.

One thing I would add is that lower orbits can result in greater steering losses unless the craft's TWR is high enough to complete the burn within an arc of 60 degrees or so. You can get around this by splitting the burn into multiple periapsis kicks, but that isn't everyone's cup of tea.

[Snark]

3 minutes ago, Norcalplanner said:

@Snark I totally agree. I didn't see where it was talking about Duna as a destination.

Whoops, my bad. They didn't, I was mentally confusing this thread with another one. But the OP did mention "ejection", which I think is what put my brain into "Oberth mode".

[Spricigo]

 

For Oberth the optimal altitude is at sea level, unfortunately the drag will destroy the vehicle before anyone have a chance to think about cosine loses.

 

@Blaarkies Oberth already made some sense to me before, but mostly "because the math say so". Your example, talking about how much time the gravity have to steal the speed back made it crystal clear.

[ajburges]

Marking Bewing's first answer correct. The Oberth gains along with the larger radius atmospheric arc make insertion strait to target orbit seem optimal intuitively.

I now wonder if there is a more efficient (in dV) LKO target orbit height. However, if there was one of practical use, I imagine a lowest dV to orbit challenge would already have used it.