Oberth Effect - Landings too?

[ErikTheAngry]

I was thinking earlier about landing with suicide burns.  I know they're not as efficient as constant altitude landing, especially at lower TWRs.  But then I got to thinking.. the Oberth effect makes a rocket burn more efficient effective(?).  Constant Altitude burns generally feel like they take longer, perhaps because you maintain a low altitude while you kill horizontal velocity, which suggests to me that as they decelerate over a longer period of time, the net Oberth effect would be lower.  Otoh, a suicide burn would accelerate you to the highest speed before you hit the LFO brakes (and hopefully not the lithobrake, unless your experiment is to find out how big of a hole you can make - which would be wicked fun in a destructible environment).

On a scale of something like the Mun or Minmus it's not really relevant, but for something like Moho, where you come in nail-bitingly fast with no atmosphere (or at least... I did the one time I tried - my landing attempt turned into a very fast low altitude flyby followed by many years of floating around in space lol) if you had a sufficiently high TWR to do a meaningful suicide burn from a transfer whose periapsis barely impacts the surface, would it exceed the efficiency of a circularization and constant altitude landing?

It would probably never be more efficient if you look at the whole mission (for example, you'd need to heave around a bunch of very heavy engines to try and dump out 3000m/s or so in 20-30s which would be more costly to send in the first place) but it's still a question that came up.  Also using something like mechjeb with a sucide burn timer so you don't bugger it up (which you'd have little room for error at those speeds).

Edited December 30, 2015 by ErikTheAngry

[Yasmy]

A suicide burn is the most efficient landing, and the higher the TWR, the more efficient, in terms of delta-v. Note that a proper constant altitude landing is a suicide burn. You touch the ground just as you bring your surface speed to zero. But like you said, if you want to do a quick, high TWR suicide burn, you have to pay the upfront cost of heavier engines, more fuel and larger launch platforms.

The reason why high TWR suicide burns are more efficient is because they allow you to spend less time fighting gravity.  The constant altitude burn is designed to likewise minimize gravity losses by preventing gravity from accelerating your rocket vertically. If you can't beat a constant altitude burn, then I would argue that your TWR is really not all that high.

Edited December 30, 2015 by Yasmy

[Superfluous J]

From what I've seen, the point of a constant altitude burn is to slow down for a landing in spite of having poor TWR. Usually, having poor TWR means your ship is more efficient, either on fuel, or on price, or both. THIS is what makes the maneuver more "efficient."

Optimizing for raw dV is not optimizing at all, remember. You can do something for 100 less dV while burning 2x the fuel.

[wumpus]

I must be missing something.  Constant altitude burns should require more TWR than less efficient routes.  In fact, the higher the TWR, the more efficient you can make your route.  I can see why you rant may be applicable, but I typically find TWR much more useful (and increases *real* deltaV) in atmospheric ascents (of course if you just visited Tylo, I can really see your point).  Low TWR on non-atmospheric landing doesn't seem to be much of an issue.

[Snark]

31 minutes ago, wumpus said:

I must be missing something.  Constant altitude burns should require more TWR than less efficient routes.  In fact, the higher the TWR, the more efficient you can make your route.  I can see why you rant may be applicable, but I typically find TWR much more useful (and increases *real* deltaV) in atmospheric ascents (of course if you just visited Tylo, I can really see your point).  Low TWR on non-atmospheric landing doesn't seem to be much of an issue.

Having high TWR improves launch and landing efficiency by minimizing gravity losses. That's true regardless of whether you're in atmosphere or a vacuum.

I'd guess that if "low TWR on non-atmospheric landing doesn't seem to be much of an issue," that's because TWR is actually a lot higher than you think.    Bear in mind that what matters for efficiency, gravity loss, etc. is local TWR, i.e. using a weight calculated using local gravity.  Assuming you're not landing on Tylo, that generally means a local gravity much less than Kerbin's, which means your TWR is probably really high.  Typical local TWR for a Mun lander can easily be 5, 10, or even more, without requiring much engine mass.

When your TWR is that high, it doesn't matter much what it is.  Going from a TWR of 5 to a TWR of 10 doesn't buy you all that much.  It's going from a TWR of 1.5 to a TWR of 2 or 3 that makes a much bigger difference.

Edited December 30, 2015 by Snark

[Plusck]

On 30/12/2015 at 8:44 AM, 5thHorseman said:

From what I've seen, the point of a constant altitude burn is to slow down for a landing in spite of having poor TWR. Usually, having poor TWR means your ship is more efficient, either on fuel, or on price, or both. THIS is what makes the maneuver more "efficient."

Optimizing for raw dV is not optimizing at all, remember. You can do something for 100 less dV while burning 2x the fuel.

 

On 30/12/2015 at 8:34 PM, wumpus said:

I must be missing something.  Constant altitude burns should require more TWR than less efficient routes.  In fact, the higher the TWR, the more efficient you can make your route.  I can see why you rant may be applicable, but I typically find TWR much more useful (and increases *real* deltaV) in atmospheric ascents (of course if you just visited Tylo, I can really see your point).  Low TWR on non-atmospheric landing doesn't seem to be much of an issue.

I think the problem is one of definition. I've read an old reddit post where the first definition of "suicide burn" is, IMHO, utterly wrong.

So to define:

A suicide burn is one where your initial trajectory touches the surface. Your ship points due retrograde. You don't touch the controls until precisely the time before hitting the ground that you need to kill all velocity. Then you burn retrograde at full thrust. As your horizontal speed falls, "retrograde" will lift to the vertical and you follow it, so that you come to a dead stop just inches off the ground. It's called a suicide burn because if you leave it just a couple of seconds too late or fail to calculate the timing correctly, you will hit the ground at dozens or even hundreds of m/s and there is virtually nothing you can do to save yourself at that point.

A constant altitude burn starts off like a suicide burn, preferably with a trajectory which is virtually flat at the point that it touches the surface (or even not quite touching the surface), except you start a little earlier and point slightly up from retrograde. Therefore, while you are reducing your horizontal velocity you are also preventing the addition of a vertical velocity component. This makes it far safer than a suicide burn because - especially with a low TWR craft - you can vary your inclination on-the-fly to stop yourself falling while shedding horizontal velocity. The disadvantage is that very slight changes in inclination will make a very big difference to the exact point that you land.

I personally don't see how it is possible to consider the "constant altitude burn" to be efficient. You are necessarily burning off retrograde, therefore chucking propellant at an angle to your trajectory (which is always, always less efficient). And you are increasing the length of time that gravity is pulling on your ship, therefore necessarily increasing gravity losses.

And I also don't see why people make a distinction between a suicide burn and a reverse gravity turn. They necessarily come to the same thing if they are done properly. The higher your TWR, the sharper the turn at the end as retrograde slides towards the vertical, and the more efficient the manouvre.

[Superfluous J]

4 hours ago, Plusck said:

I personally don't see how it is possible to consider the "constant altitude burn" to be efficient. You are necessarily burning off retrograde, therefore chucking propellant at an angle to your trajectory (which is always, always less efficient). And you are increasing the length of time that gravity is pulling on your ship, therefore necessarily increasing gravity losses.

I will again reiterate what you quoted.

Constant altitude burn allows for more efficient CRAFT. You can do a CAB for far cheaper if you build your craft so it can only land doing a CAB.

I've seen videos of someone landing on Mun with a craft that starts with less than 1.0 local TWR.

Is that an extreme? Sure. Especially on Mun. But on Tylo, it can make a difference especially if you're carrying that Tylo ship along with all the other stuff you're bringing along for a Jool-5 mission.

Edited January 3, 2016 by 5thHorseman
My brain made me type "Titan" when I wanted to type "Tylo"

[Plusck]

Sure, I wasn't disputing what you were saying at all. Rather, reconciling your post wth wumpus's since I feel that there is some confusion about the actual terms.

And yes, when I was talking about "CAB being efficient" I was talking about raw fuel usage of a given design that is capable of both types of approach. Of course, if your TWR is very low then you need to stop yourself from gaining any vertical speed as you slow horizontally, and the ship as a whole might well be more efficient than one with bigger engines.

As you said, you can do something for 100 dv less while burning 2x the fuel. There are a couple of circumstances I can think of that correspond to that. One is changing to a higher orbit by burning to a much higher orbit then raising Pe then circularising: bound to be less efficient due to the long initial burn even if the sum of dv requirements is slightly less than a straightforward transfer. The other is what you're talking about here: you add engines to make a suicide burn possible, but the dv savings will not cover the fuel cost of slowing down those same extra engines.

Edited January 3, 2016 by Plusck

[ErikTheAngry]

Just wanted to chine in and say thanks for the very interesting discussion.  I have been reading it silently as I have not had anything meaningful to contribute but also want you to know your answers are not going to an op-abandoned thread.

[Plusck]

That's kind of you to say. But I'm sure some people here could contentedly discuss this sort of thing without anybody but themselves reading their posts. Almost.

[Yasmy]

19 hours ago, Plusck said:

I personally don't see how it is possible to consider the "constant altitude burn" to be efficient. You are necessarily burning off retrograde, therefore chucking propellant at an angle to your trajectory (which is always, always less efficient). And you are increasing the length of time that gravity is pulling on your ship, therefore necessarily increasing gravity losses.

What people mean by efficient is that it is about the cheapest delta-v landing you can make with a low TWR vehicle. Using a pure retrograde suicide burn trajectory with a low TWR vehicle will cost more in gravity losses and more in total delta-v (but less in cosine losses) than a constant altitude trajectory, because you spend more delta-v to counteract a large vertical velocity. Yes, burning off-retrograde is less efficient at changing your total orbital energy than burning retrograde, but not by as much as you may think. Burning 10 degrees off retrograde is only about 1-cos(10) = 1.5% less efficient than burning retrograde at reducing your retrograde velocity.  That's tiny.  Even at 20 degrees off retrograde, you are still getting 94% of your thrust directed retrograde. Gravity losses are kept low by keeping your vertical velocity low. Gravity losses are proportional to the time integral of your vertical velocity times the difference in your vertical thrust and local g. Going to longer times, but with lower vertical velocity and vertical thrust means lower total gravity losses.

And a low TWR vehicle is usually a lighter vehicle, which means much cheaper launch cost. You didn't define efficiency. For some people on these forums, total cost or part count or total mass are considered the primary factors in efficiency.  Of course, once you are orbiting something with some particular vessel, then efficiency is usually in terms of delta-v. But don't ignore the considerations that caused you to be in orbit with a vessel with a certain TWR vs fuel budget.

Edited January 4, 2016 by Yasmy

[Plusck]

5 hours ago, Yasmy said:

What people mean by efficient is that it is about the cheapest delta-v landing you can make with a low TWR vehicle. Using a pure retrograde suicide burn trajectory with a low TWR vehicle will cost more in gravity losses and more in total delta-v (but less in cosine losses) than a constant altitude trajectory, because you spend more delta-v to counteract a large vertical velocity. Yes, burning off-retrograde is less efficient at changing your total orbital energy than burning retrograde, but not by as much as you may think. Burning 10 degrees off retrograde is only about 1-cos(10) = 1.5% less efficient than burning retrograde at reducing your retrograde velocity.  That's tiny.  Even at 20 degrees off retrograde, you are still getting 94% of your thrust directed retrograde. Gravity losses are kept low by keeping your vertical velocity low. Gravity losses are proportional to the time integral of your vertical velocity times the difference in your vertical thrust and local g. Going to longer times, but with lower vertical velocity and vertical thrust means lower total gravity losses.

And a low TWR vehicle is usually a lighter vehicle, which means much cheaper launch cost. You didn't define efficiency. For some people on these forums, total cost or part count or total mass are considered the primary factors in efficiency.  Of course, once you are orbiting something with some particular vessel, then efficiency is usually in terms of delta-v. But don't ignore the considerations that caused you to be in orbit with a vessel with a certain TWR vs fuel budget.

I freely admit to having been a bit short on the "definition of efficiency" bit, and I tried to correct that in my response to 5thHorseman. The overall efficiency (in mass, part count, cost, and/or fuel usage) of a vessel that needs to do a constant altitude burn may easily exceed a more powerful one that can do a suicide burn.

However, although your arguments based on the relatively minor losses on burning off-retrograde are entirely convincing - and it is an interesting point to bear in mind in future missions, I cannot agree with your conclusion because it seems to confuse two different issues:

1 - suicide burn angle of impact.

When you deorbit, you bring your trajectory down to touch (or nearly touch) the surface. If the body is a perfect sphere without any hills, then a steep descent with a high impact angle (a) costs more in the deorbit burn, (b) adds a greater vertical component to your velocity and (c) requires a higher TWR.

However, on the plus side, (a) it makes your final landing spot far more accurate and (b) the horizontal component of your velocity will be lower.

I may be wrong on this (but I don't think so...) but it seems clear that the horizontal velocity savings of a high impact angle will never compensate for the vertical velocity increase. Therefore, for any suicide burn the more acute the angle, the better.

What is true of a perfect sphere remains true for a hilly terrain, except that an extremely shallow angle may be impossible. Therefore in any event, the most efficient suicide burn is going to be the most shallow-angled approach possible within the constraints of the body you're landing on.

2 - how constant is a constant altitude burn.

The only possible situation where you have zero vertical velocity before starting your burn is if your trajectory barely grazes the surface. On a perfect sphere this is fine, inasmuch as you can be mere metres above the surface when you start the burn and then simply stick to a virtual orbital path as you follow the surface while slowing. However in that case your burn has to start off with being purely retrograde anyway (and even radially out from retrograde, since otherwise you'll rise until you've slowed enough to bring Ap down to the same as Pe). I can agree that this will probably be the most efficient landing on a perfect sphere, but then again this is merely an extension of the previous point: this is just taking the suicide burn at its most efficient (very shallow impact) and then taking it one step further (i.e. no impact).

On any other surface than a perfect sphere, you have to add height. This means either starting higher (Pe hundreds or thousands of metres above the surface) or actively negating your vertical velocity at the start of your burn.

And this is where I can't agree with your statement that "Going to longer times, but with lower vertical velocity and vertical thrust means lower total gravity losses".

Because the two assumptions - "lower vertical velocity" and "lower vertical thrust" - cannot both be true. On any given deorbiting trajectory, you start your burn by negating almost exactly the same vertical velocity component that the suicide burn negates, but at an altitude and not on approaching the surface. For every second that you remain at that altitude you are adding 1.6 m/s (for the Mun) or whatever to the vertical velocity that you are effectively countering. And if there are any hills in the way, then you're going to accumulate another 30s or a minute or so of vertical velocity at that same 1.6 m/s (or whatever) as you fall into that (most inefficient of all) vertical landing.

 

This confusion of the issues it what I was originally trying to address with my "definitions", and I should have added an "efficiency" definition while I was at it. However, separating the issues still (IMHO) leads to the inescapable conclusion that a suicide burn at the shallowest possible angle for a given terrain will always be more efficient (for a given vessel that is capable of it) than any other approach for that same landing site.

 

Edit: I just checked back to the beginning of the thread, and I think I've found where I really can't agree with you:

Where you said "The constant altitude burn is designed to likewise minimize gravity losses by preventing gravity from accelerating your rocket vertically", I just cannot agree.

Say you are hanging motionless in space above the Mun, and you have 10 m/s delta-v left in your rocket, and you have 6 seconds in which you can decide when to spend it. If you spend it at a constant rate, you stay exactly where you are. If you wait 6 seconds then spend it all at the same time, you will be hanging in space once again but about 30m lower down. Over those 6 seconds gravity will have accelerated your rocket by exactly the same amount, and your rocket will have pushed against gravity by exactly the same amount, but in the second case you're closer to where you want to be.

Edited January 4, 2016 by Plusck

[Superfluous J]

1 hour ago, Plusck said:

Say you are hanging motionless in space above the Mun, and you have 10 m/s delta-v left in your rocket, and you have 6 seconds in which you can decide when to spend it. If you spend it at a constant rate, you stay exactly where you are. If you wait 6 seconds then spend it all at the same time, you will be hanging in space once again but about 30m lower down. Over those 6 seconds gravity will have accelerated your rocket by exactly the same amount, and your rocket will have pushed against gravity by exactly the same amount, but in the second case you're closer to where you want to be.

But during the bulk of the constant-altitude burn, you are NOT hanging over the Mun. You are flying across its surface first at orbital speeds, then at sub-orbital-but-still-pretty-high speeds. You travel a significant distance horizontally and the Munar surface falls away from you a significant amount, causing you to not lose as much thrust to gravity as you'd think.

Sure, once you get slower maybe you want to rethink things. But if your local TWR is 1.1 at that time, you're still going to need to go about it pretty gingerly.

[Yasmy]

4 hours ago, Plusck said:

Where you said "The constant altitude burn is designed to likewise minimize gravity losses by preventing gravity from accelerating your rocket vertically", I just cannot agree.

I agree that this statement was imprecise. Local gravity always accelerates you vertically by the same amount no matter your current velocity. But like 5H said, at nearly orbital velocity, due to the curvature of the body, that gravitational acceleration does not add significantly to your total velocity, therefore it doesn't add significantly to your total energy. In the extreme case of a stable circular orbit, gravity constantly accelerates objects towards the center of the body you are orbiting, but doesn't increase your vertical velocity at all, because the local direction of vertical has changed. Additionally, your total energy has not changed.

Issues of accuracy are a different consideration, and may be the deciding factor for many people, but are not the issue at hand.

[Plusck]

Of course, you are both right. I had taken curvature and horizontal velocity into consideration but didn't think it was necessary to state that I was making an abstraction for the purpose of clarity whan I was giving the "10 m/s over 6 s" example.

However, I still don't get where you see CAB as being more efficient than SB for a given craft on a given terrain.

At orbital velocity, you arrive at ground level. If you just miss the ground (and hills) then your vertical component is zero, it is all horizontal. Then you decrease your horizontal velocity and the vertical acceleration starts to increase as you fall below orbital velocity. Of course it is very gradual at first but in any event, by the time you've shed your horizontal speed, vertical acceleration will be 100% local gravity.

Therefore it is bound to be a sine function of sorts as horizontal velocity falls. You start at zero, and then at the end you have full vertical acceleration (so for the Mun, 1.6 m/s) affecting your craft. However, you have not been losing altitude during this time. Therefore in any event, you are necessarily fighting gravity for longer at the end, even if you were able to avoid fighting gravity at the start of your burn.

And even if you make some sort of compromise (starting at constant altitude then letting altitude fall as horizontal speed falls) you cannot avoid the conclusion that you are adding two vectors to your deceleration over time, and making the vertical vector gain in length over a longer time, than if you were simply to burn directly retrograde.

 

Unfortunately I don't see an end to this discussion until somebody steps up to the task and does the actual maths... and I'm pretty sure it isn't going to be me

[Faghti]

If you define efficiency in terms of required delta V for a given craft then a constant altitude burn is always more efficient than a suicide burn (using the definitions of Plusk above).

This thread has a particularly good video that illustrates a constant altitude burn, and some maths as well, for those that want it.

Here is another thread that reaches the same conclusion: http://forum.kerbalspaceprogram.com/index.php?/topic/36960-how-to-calculate-optimal-descent-profiles/#comment-509383

Yes, the contstant altitude burn has steerage losses.  Conversely, the suicide burn has gravity losses.  Which are greater ?

As Yasmi points out, a suicide burn has gravity losses.  When burning close to vertical, most delta V is going into counteracting gravity, not reducing orbital velocity.  It may not seem very much, but the difference is pronounced with a craft with low TWR.  In the video in the link above by Cosmo-not (it is well worth watching !) the craft has a TWR of 1.1 at the start of the burn, increasing to 1.36 by the end.  It would be very expensive to try to perform a suicide burn with such a craft, not to mention hazardous.  Without doing the maths, I expect you'd have to begin at a great height in order to be able to burn long enough.

One way of thinking about it is to recognise that much more energy is in orbital velocity than gravitational potential energy.  Therefore we might expect that the method that most effectively reduces (or adds for take-off) orbital velocity is a good candidate.  In the video you can see that as long as the burn is, most thrust is expended on reducing the orbital velocity to zero - with only enough vertical thrust to avoid crashing into the surface.

But thought experiments don't answer the quesiton.  The above threads refer to calculations concluding that the constant altitude burn is the most efficient.  I haven't followed the maths.

I did try an experiment - I found it much easier to experiment with takeoffs to orbit rather than landings.  In particular, when taking off, a good compromise alternative to a constant altitude is to adjust your angle of flight so as to remain a few seconds away from apoapsis.  In the limit, a constant altitude burn should be always exactly at the apoapsis.  In practice, a few seconds off means that the craft is pushing the apoapsis forward and up, while remaining close to it.  This allows the craft to gain height, and is easier to control than a perfect constant amplitude.

If terrain means you need to climb more steeply, then aim for more seconds to apoapsis during your climb.  The standard interface doesn't give you seconds to apoapsis, but mechjeb and Kerbal engineer do.  I use the HUD view of Kerbal engineer to give me the read-out constantly.

Here are some results from a trial that I performed on the Mun.  The craft comprised

1 OCTO, 1 Z-200 battery, 2 Oscar-B fuel tanks, 1 LV1 Ant engine, 4 OX-Stat solar panels, 4 LT-05 landing struts, 2 MK1 illuminators, and a Mechjeb controller.

Mass at landing site:  524 kg; TWR on surface:  2.45

I experimented with two styles of take-off:

1)  As close to gravity turn as possible:  turn to 20 deg at 20 m/s;  Thrust prograde until apoapsis is at 10000 m.  Cut thrust.  burn at apoapsis to circularise.  Total delta V:  651 m/s.

2)  Immediately after take-off, turn over to the point where the time to apoapsis is neither increasing nor decreasing.  That is approx 60 deg for this craft.  At this point, time to apoapsis is a few seconds.  The time to apoapsis will gradually increase - allow it to increase to five seconds - which means that the apoapsis is rising in height as the craft gains velocity;  Progressively turn towards prograde in order to keep time to apoapsis approximately 5 sec.  On reaching horizontal, progressively throttle down in order to remain close to the apoapsis (but always behind it).  Orbit eventually becomes circular at around 5000 m.  Increase to a 10000 m orbit in the usual fashion.  Total delta v:  594 m/s.

Not a big difference between the two - but it does refute the idea that thrusting along prograde is always the most efficient.

I did try experiments on landing as well.  Difficult to get a decent comparison, since landing sites for every experiment I tried ended up with landing sites at different heights - and the difference in delta V wasn't great anyway:  With both approaches, most delta V is expended thrusting essentially retrograde, while travelling at high speed above the surface.

Unfortunately method (2) above is more difficult to execute for landings.  I don't have a readout that gives me seconds since apoapsis.  And in any case, I'd have to descend steadily as well.  In practice I prefer to be able to control where I land.  I use a method that I think was published here:  Use low thrust for most of the descent, with more vertical than retrograde thrust, to reduce descent rate and bring apoapsis down steadily during the descent.

 

Edit:  I also meant to add:  Aesthetics is a big reason why we play KSP.  For me, one of the most sublime parts of the game is skimming mountain peaks with a craft at sunrise over an alien landscape.  Low TWR craft with low take-off and descent profiles maximise that.  Why would you take off vertically from the Mun (or anywhere else) with a high TWR craft ?

Edited January 5, 2016 by Faghti