arkie87

http://forum.kerbalspaceprogram.com/threads/103890-Non-Dimensional-Model-for-Optimal-Launch-Efficiency?p=1613079#post1613079

[tl:dr]To obtain efficiency greater than or equal to 90%, a thrust-to-weight ratio (TWR) of at least 1.4 at launch on an atmosphereless, Kerbin-sized body (like Tylo) is required with standard ISP engines; but for planets with smaller orbital velocity or more efficient engines (nuclear or Ion), TWR at launch to obtain efficiency greater than 90% increases. [/tl:dr] I have made a computer model in Matlab (also available in Excel now! Click here to get it) to simulate optimal TWR (thrust-to-weight ratio), TVR (thrust-velocity-ratio), and DVR (delta-V-ratio). I provide non-dimensional contour plots to show results which are globally applicable for the same non-dimensional parameters. Link to The Paper: https://www.dropbox.com/s/qud778opmyp4fis/OptimalHorizontalLaunch.pdf?dl=0 Some sample results: This graph shows the independence of efficiency on DVR. The slope of the curve is zero, until efficiency drops to zero instantly when delta-V-ratio no longer provides enough deltaV to get into orbit due to efficiency. Since efficiency is not a function of DVR (i.e. how much extra fuel you carry into orbit), we only need to vary TWR and TVR. The above plot contains all the information a player needs when designing craft. First, increasing TWR increases efficiency while increasing TVR decreases efficiency. Increasing TWR increases efficiency by allowing the craft to aim more horizontal, thereby, using more of its fuel to accelerate into orbit instead of fighting gravity. Increasing TVR decreases efficiency since, for a given DVR, less fuel is burned. This, in turn, results in a more constant TWR during the flight, and therefore, a longer flight as well as a steeper angle above vertical, causing more fuel to be wasted fighting gravity. Second, for low TVR, lower TWR are needed for a given efficiency; similarly, for a higher TVR, a higher TWR is needed to obtain the same efficiency. This is the direct result of the trends described above, and is the most important result of the simulation: thus, for two crafts with the same ISP engine, the craft on Minmus will require a higher TWR for the same efficiency as a craft on Mun, and so on. Finally, this model should be easy to test. Since efficiency is not a function of DVR (i.e. size or scale), two craft with the same TWR can be compared on the same planet with different ISP engines or on different planets with the same engine, and the craft with the larger ISP engine or equivalently on the planet with a smaller orbital velocity should have reduced efficiency. And in case you dont believe that efficiency is independent of DVR for all TWR and TVR:

Ok. so there were a lot of bugs/errors in my program. Do not look at that first graph. Almost positive it is correct now after reviewing and checking everything. I also came up with a definition of "efficiency" which is basically deltaV_min/deltaV_spent, so, if you have an efficiecny of 90% with your craft, an orbital velocity is 900 m/s, then you need 1000 m/s. Pretty straightforward calculation, and dimensionless (meaning it applies to all craft/planets etc... with the same dimensionless or relative parameters). LOTS of interesting things from new graphs... Will start a new thread in Science Lab, and paste a link here so you can find it

That is very true-- good point. Though, given my track record, i feel like if i did that test, people would tell me that I didnt need to climb up to 10 km, misunderstanding that i'my pretending there was a cliff in the way... But like i said. I'm sick of debating by now. I wan't to just play. And kill Kerbals. The way the game was meant to be played. Maybe after i play through everything 0.9 has to offer, i'll revisit Hmm, Idk if i can give it to you in that form.... but, Did you see this: http://forum.kerbalspaceprogram.com/threads/102947-Vertical-Ascent-vs-To-LXO-First?p=1612130&viewfull=1#post1612130 The final form of the dimensionless equation is very useful. And the contour plots it can provide are applicable to ANY craft taking off from that planet with that TWR, FMR, and ISP (though i think the contour plot i provided with it is wrong... im still working on the objective function a bit). I can definitely use the model to provide you with contour plots of extra (dimensionless) velocity requirements. btw: the normalizing factor for velocity isnt escape, it's orbital, for convenience (and since one you are in orbit, TWR doesnt matter...) Incidentally, the dimensionless form indicates the need to define FMR (fuel to mass ratio i.e. fuel mass to total mass), which Rocketeer used. I'll probably start a new thread once I am sure about the results. I have asked numerobis to verify my work... but like i said, i'm pretty sure my objective function for fuel is wrong, since TWR * dimensionless time is not fuel, but dimensionless fuel. I need to multiply by t0 to turn it into actual fuel... and when i do that, the graphs all change... Hopefully i'll post soon, but probably in the science labs, not here.

Is it just me, or is the new SAS wonky... If you click any of the directions (prograde, retrograde etc...) the SAS moves close to it, but never actually points dead center (perpetually about 25 degrees off). This even happens in sandbox mode. Is this a bug, or "intentional"... what use is SAS if it wont point where it should?

No, the cliff doesnt have to exist. It's theoretical. Sure. pick away...

That is true, but it might illustrate what the planet would have to look like before it becomes relevant, which is, once again, what I'm after. In the OP, i've shown that a 10km cliff is more than enough to make vertical ascent more fuel efficient. 10 km out of a 200 km radius, is about 5% roughness. The roughness on gilly is much more than 5%. And I obviously cannot test this experimentally because no such place exists (that i know of) in KSP. Anyway, I'm gonna get back to playing KSP instead of talking about it

I'm getting sick of repeating myself. This is a theoretical question.

Exactly. For it to be practical in the Kerbol system, it is an astrogeographical question (is that a word? astro=star, geo=earth... lol); however, it is interesting to find out under what conditions it could exist in theory... And what about Gilly? Is it tidally-locked?

Well, one thing we can agree on, is that we are all dysfunctional at communicating with each other...

I understand that my case is astonishingly specific. My point is simple: Until we explore the math and/or do tests, it's not obvious how common or uncommon it is. If we do that math, and find out it's not important, then that is a result as well.

Brief paper describing nondimensionalization and differential equation.

For the case presented in the OP, i did prove it with math (and not experiment). For the case of Gilly it's just a hypothesis, but i really do not care to prove or disprove it. Do you doubt that it is the case anyway?

I dont think he is assisting anyone. He is just clarifying some confusion. The case i presented in the OP mathematically showed that an ideal vertical burn is more efficient than a 10 km hop followed by a horizontal burn. However, this thread has made it abundantly clear that a vertical 10 km hop is extremely inefficient if you plan to do a horizontal burn, thus, the math in the OP was a bit biased...

I can understand in specific cases, like the Mun example, it is not the most efficient, but the Mun case was just an example. Admittedly, in the OP, i thought i specifically asked if there are other known cases that anyone knows of where it might be more efficient, but i think i either deleted it or decided against it, since i thought it would be better to focus on this specific example. So i will take credit for that confusion My bad. That said, you haven't addressed this case, where horizontal method doesnt work: Once again, think of my threads are more scientific exploration, rather than me suggesting one approach is right. If someone tells me X wont work, when i have provided math or video to show it will, i expect at least a math or video in return

Ok, had you specified "heavier more expensive but higher ISP engine" i would have understood the logic

I was using FAR with aerodynamic disassembly disabled (or equivalently, NEAR with Mach effects). Right. But that can happen just the same with a "proper" (i.e. low) TWR.

( is a lot easier to simulate. I already have a matlab code that does that I can vary TWR and ISP and show the optimum TWR for a given ISP...

I trust your results, since you said you optimized it in the game... If i doubted your results, or asked you to prove it, then i expect you to provide data But thanks for the data; data makes Kerbals happy I assume by optimize, you mean, dumped all excess fuel? Out of curiosity, were you optimizing for cost or deltaV? Is this KSP or Portal? Now you lost me again -- can you explain this logic?

I assume by optimization you mean starting fuel in the lander? It's good to know that you are willing to do so many tests to find the optimum... I'll be sure next time i need something rigorously tested to get you interested in the problem so that you will perform the tests

I have learned a few things as well, particularly, just how bad it is to raise apoapsis at all by going vertical at all if you plan to go horizontal to get into orbit. From now on, i will tap throttle to get off surfaces and then aim as horizontal as possible Also, the only reason the cheapest (in terms of kerbucks) Mun lander also happens to have high TWR and more deltaV then lightest Mun lander is due to the way squad balanced the game. So perhaps one could argue that this result is unrealistic. In the real world, higher thrust, more efficient engines should be more expensive... but my point was that we arent in the real world, we are in KSP, and the optimum solutions must be constructed from the parts that are available, however unrealistic or imbalanced they might be-- and this might result in *interesting* solutions. I still think Rocketeer's last post is missing the point. This was a theoretical scientific discussion (admittedly, the science labs is a better place than "gameplay questions and tutorials" for that, but like i said, a mod moved this thread to this sub-forum), so, it doesnt matter how unlikely it is. I wanted to know what to do in this scenario, and i think it should be obvious that i want a reason/justification (though, i think most people felt they didnt need to give a reason because this was in "gameplay questions and tutorials" sub-forum, where people are usually just asking what to do, not looking for scientific discussion). In the OP itself, i even ask if there are even any better scenarios that people are aware of where the two approaches might be similar. I assume Rocketeer will categorically assert: "no, never". (don't mean to put words in your mouth if you wouldnt say this... so feel free to correct me) But that is clearly not the answer I am looking for, since that answer, based on orbital mechanics, doesnt account for real-world problems. There could easily be an example in the Kerbol System where one is inside a deep crater somewhere, where, given how much distance they have to go vertically, it will pay to just continue. Or there can be another place in the Kerbol system, where, due to reasons I am unfamiliar with, it would pay to go vertical. This is what i was asking for in the OP-- if others were aware of any or could calculate any. The only example that comes to mind is Gilly-- since it is so misshapen (surface roughness-to-diameter ratio is the largest of any body in the Kerbol System), that you can rarely launch east without also climbing. However, you could also throw a ball into orbit around it, so any deltaV savings would be minimal. This is a much better answer than a categorical "no" because it illustrates how ugly the planet/moon would have to be for this effect to dominate, and since it is only likely to occur on smaller bodies, any deltaV savings would be minimal anyway. This is what i was looking to investigate-- if there are any other cases in the Kerbol system where this would be practical-- and in examining the Mun problem with you guys, I think it made the Gilly answer clear.

I fully understand this, but i specified in the problem statement in the OP that aerodynamic disassembly feature of FAR is disabled (though perhaps i should have highlighted this fact a bit more). People, who use stock aerodynamics, have mocked my disabling of this feature because it's unrealistic, which for obvious reasons, is ironic. I like FAR with aerodynamic dis-assembly disabled because it gives spaceplanes more ability to actually control where they go, and the ability to bounce off the atmosphere during re-entry i.e. the control over where you re-enter and how steeply. However, since I'm using a keyboard, and not a joystick, it is wayyyyyyy too easy to increase G load wayyyyy too fast even with a quick tap. Even if i play with quicksaves, it still a huge pain.... thus FAR with aerodynamic dis-assembly disabled is more realistic than stock, but less than FAR. Alternatively, it's like playing with NEAR but with Mach effects... Thus, i was wondering if aerodynamic dis-assemblies arent a problem, what optimum TWR for FAR was (which was discussed in another thread), and I arrived at this craft... I can test this rocket with dis-assembly enabled and see if it would have been a problem. If it is, then I obviously,reducing thrust on SRB's even is beneficial. Furthermore, I and 5thHorseman have tested getting it into circular orbit around Kerbin and it seems performing a somewhat good gravity turn with apoapsis around 200 km is possible. I can try reducing thrust to see if that makes performing the gravity turn easier, and therefore, saves fuel, despite the wasted atmospheric efficiency (velocity/terminal-velocity). Props to Ferram on being able to calibrate his correlations so accurately that they force players to match real-world rocket TWR pretty well.

Oh wow. That is very good to know. I tried doing it in map mode, but it wouldnt let me, like you said. Didnt know i could do it in staging screen. Thanks!

We were never arguing over which was more efficient, but rather, if the difference is significant for this case, which it clearly is not. If Slashy had taken a more balanced approach and said "yes, horizontal is more efficient, but under certain conditions, efficiency gains would be marginal" acknowledged even once that horizontal is not even always possible from within a deep crater, and in general actually addressed the logical arguments that were provided instead of (condescendingly) dismissing them with literally no reason given, then this thread would never have made it past 3 pages... Anyway, I think it's time to label this question answered. Thank you LethalDose and Slashy for building and testing ships and providing results to us here for all to see. I think in the future, I will post my theoretical questions in the Science Labs, rather than here, since here, I tend to get more advice of what to do (after all, this sub-forum is about gameplay questions so it is usually noobs asking for advice from experts) rather than a discussion, which is what i am after (in my defense, I think a Mod moved this discussion to this sub-forum).

The challenge was about if a craft with high TWR can be cheaper than one with a low TWR, since that was a highly contested point by Slashy (see LethalDose's post on page 21). Not necessarily about which method of returning to Kerbin used less deltaV, though admittedly, the horizontal burn approach seemed better than i would have imagined given he got into LMO first. I assume he burned straight horizontal to raise apoapsis, stayed low, burned hard, and was very very careful not to overshoot. Either way, now i know that i really shouldnt climb at all when launching from the Mun horizontally unless i have to. So let him optimize it, if he cares... there are only a finite number of ways to combine the parts... and ive tested every other engine, and the one LethalDose used is the best for both TWR and deltaV.