Non-Dimensional Model for Optimal Horizontal Launch Efficiency

[GoSlash27]

High Isp test is in, and it's a bit inconclusive.

Same issue with the low Isp launcher on a light planet, the fuel mass is so low that it's hard to get an accurate read on the change in mass.

It also acted *exactly* like the low- Isp launcher on a light planet; poor inertia control and it spent nearly the entire launch pointed somewhere other than where I wanted to go.

Not because the mass was so high, but because the fuel was such a tiny percentage of it.

It stands to reason, since in the rocket equation treats Isp and Go exactly the same.

The result:

Launch from Mun using PB Ion at 1 G:

Thrust = 2kN

Initial mass-= 1.22t

T/w at launch= 1.01

Final mass= 1.19 t

Expended DV= 1,026 m/sec

Efficiency = 56.5% <-- that last reading is highly suspect due to granularity.

Again, the penalty in DV is high (as was expected), but it's a high percentage of a very tiny amount of fuel.

I think the model is good to go.

Best,

-Slashy

[arkie87]

High Isp test is in, and it's a bit inconclusive.

Same issue with the low Isp launcher on a light planet, the fuel mass is so low that it's hard to get an accurate read on the change in mass.

It also acted *exactly* like the low- Isp launcher on a light planet; poor inertia control and it spent nearly the entire launch pointed somewhere other than where I wanted to go.

Not because the mass was so high, but because the fuel was such a tiny percentage of it.

It stands to reason, since in the rocket equation treats Isp and Go exactly the same.

The result:

Launch from Mun using PB Ion at 1 G:

Thrust = 2kN

Initial mass-= 1.22t

T/w at launch= 1.01

Final mass= 1.19 t

Expended DV= 1,026 m/sec

Efficiency = 56.5% <-- that last reading is highly suspect due to granularity.

Again, the penalty in DV is high (as was expected), but it's a high percentage of a very tiny amount of fuel.

I think the model is good to go.

Best,

-Slashy

If readings are too small, just build a bigger lander?

But im glad to know you confirmed my model

[GoSlash27]

If readings are too small, just build a bigger lander?

But im glad to know you confirmed my model

The problem isn't the size of the lander, but rather the resolution of the math.

No result is more accurate than the resolution of the lowest resolution factor that feeds into it. That's why I limit my results to the first 3 significant digits.

If I ran a ginormous lander, I'd still have the same problem; the model predicts results to a much higher resolution than testing can confirm or refute.

But that said, there's nothing here that refutes anything your model has predicted, so I definitely call that a win.

If it's off, it's off by less than anyone would be able to notice.

So... what does this say about optimal t/w from an overall vehicle mass/ cost perspective? I think it shows that the optimal point is much lower than we all thought it was. A gee- and- a- half looks to be plenty efficient to get the job done according to the curve.

Best,

-Slashy

[arkie87]

The problem isn't the size of the lander, but rather the resolution of the math.

No result is more accurate than the resolution of the lowest resolution factor that feeds into it. That's why I limit my results to the first 3 significant digits.

If I ran a ginormous lander, I'd still have the same problem; the model predicts results to a much higher resolution than testing can confirm or refute.

But that said, there's nothing here that refutes anything your model has predicted, so I definitely call that a win.

If it's off, it's off by less than anyone would be able to notice.

So... what does this say about optimal t/w from an overall vehicle mass/ cost perspective? I think it shows that the optimal point is much lower than we all thought it was. A gee- and- a- half looks to be plenty efficient to get the job done according to the curve.

Best,

-Slashy

Well optimum TWR is still infinite, but practically speaking, optimum point depends on what efficiency we are comfortable living with.

Furthermore, in practice, it is not possible to vary all three variables independently i.e. increasing TWR increases FMR and/or TVR... etc...

To get more specific results, we need more details about the spacecraft. For instance, if we know that for a specific rocket TWR = c0- c1*FMR, we could plug that relationship in, and perhaps find the optimum point for it. I presume the optimum point wouldnt be on the boundary i.e. infinite TWR, but rather, somewhere in the middle.

[GoSlash27]

Well optimum TWR is still infinite, but practically speaking, optimum point depends on what efficiency we are comfortable living with.

Furthermore, in practice, it is not possible to vary all three variables independently i.e. increasing TWR increases FMR and/or TVR... etc...

To get more specific results, we need more details about the spacecraft. For instance, if we know that for a specific rocket TWR = c0- c1*FMR, we could plug that relationship in, and perhaps find the optimum point for it. I presume the optimum point wouldnt be on the boundary i.e. infinite TWR, but rather, somewhere in the middle.

Sorry, what I mean to say is this:

For massless engines, the optimal point is clearly infinity. For engines with mass, there's a point at which adding an engine adds more mass to the vehicle than the additional fuel and tankage you need for being underpowered. If seeking the lightest lander package (which is a common engineering goal) these curves would suggest that the ideal t/w for most launchers is a good deal lower than I had previously thought.

Even more so when looking at overall vehicle cost; fuel is much cheaper than engines. Overall cost, you're better off at 1:1 t/w at launch, even with massless engines.

What's the curve look like for a 4,200 m/sec Isp engine operating on Gilly? That would have to be the worst case scenario for a low- thrust lifter.

Thanks,

-Slashy

Edited December 22, 2014 by GoSlash27

[arkie87]

Sorry, what I mean to say is this:

For massless engines, the optimal point is clearly infinity. For engines with mass, there's a point at which adding an engine adds more mass to the vehicle than the additional fuel and tankage you need for being underpowered. If seeking the lightest lander package (which is a common engineering goal) these curves would suggest that the ideal t/w for most launchers is a good deal lower than I had previously thought.

Even more so when looking at overall vehicle cost; fuel is much cheaper than engines. Overall cost, you're better off at 1:1 t/w at launch, even with massless engines.

What's the curve look like for a 4,200 m/sec Isp engine operating on Gilly? That would have to be the worst case scenario for a low- thrust lifter.

Thanks,

-Slashy

Slashy,

I have updated the model, fixing some numerical problems (to make the graphs smoother, and in some cases, correct). I have also defined a new parameter DVR (delta-V-ratio i.e. deltaV of the craft divided by orbital velocity), as i think this is a more useful parameter for mission planning, and have found that performance is almost entirely independent of DVR, as long as DVR is large enough, given the efficiency, to actually get into orbit. I have put updated graphs which drastically simplify analysis and provide very useful information for mission planning. I have also described a very simple way to test my model!

Please check it out!

[GoSlash27]

Slashy,

I have updated the model, fixing some numerical problems (to make the graphs smoother, and in some cases, correct). I have also defined a new parameter DVR (delta-V-ratio i.e. deltaV of the craft divided by orbital velocity), as i think this is a more useful parameter for mission planning, and have found that performance is almost entirely independent of DVR, as long as DVR is large enough, given the efficiency, to actually get into orbit. I have put updated graphs which drastically simplify analysis and provide very useful information for mission planning. I have also described a very simple way to test my model!

Please check it out!

Will do, but, uhh... where is it?

Best,

-Slashy

[arkie87]

Will do, but, uhh... where is it?

Best,

-Slashy

I have updated the OP

[GoSlash27]

arkie,

Lookin' good, and DVR is clearly not a thing (which is what I was sayin')

Can you extend the plot out to beyond 4:1 t/w? That way I can plot my empirical results against it and see how it stacks up.

Thanks,

-Slashy

[arkie87]

arkie,

Lookin' good, and DVR is clearly not a thing (which is what I was sayin')

By "not a thing" you mean doest effect results? Then yes, you were right

But i dont think that was necessarily obvious...

Can you extend the plot out to beyond 4:1 t/w? That way I can plot my empirical results against it and see how it stacks up.

Thanks,

-Slashy

I can, but above 2.5, plot doesnt change much (maybe that's why you had a hard time getting significant results, since differences become small above TWR = 2.5). It's better if you give me your data points, and i run them to give you an exact number back; from the contour plots, you would be estimating the number from the color, and unless the colors changes, its impossible to get accurate results.

FYI: i ran some of my own tests (it took me forever because i kept messing SOMEthing up... eventually, i managed to get one craft with both Ion engines and LV-1R's capable of acheiving TWR = 1.1 at launch with enough deltaV to get into orbit and enough solar panels to power all the ion engines

Here are the results:

From my experience running the actual tests, the reason high ISP is worse for efficiency is because TWR remains more constant during the flight, thereby, requiring a steeper burn angle and more wasted time fighting gravity.

Data Used for Table:

Initial Mass:

Ion Test Results:

LFO Test Results

Edited December 23, 2014 by arkie87

[Duxwing]

O_O My head hurts...

What is the practical implication of these findings?

-Duxwing

[arkie87]

O_O My head hurts...

What is the practical implication of these findings?

-Duxwing

Efficiency is only a function of TWR and TVR (engine efficiency/planet size); it is not dependent on DVR (how much extra fuel you carry to use after you get into orbit), thus, optimum TWR is not a function of the mission (i.e. how much total deltaV you are carrying), but only of the planet and engine ISP

Smaller planets/higher efficiency engines need higher TWR to get the same efficiency i.e. on Kerbin you need TWR = 1.4 to get 90% efficient horizontal launch into orbit, while on Mun you need TWR = 1.6 (assuming your engines have the same ISP)

Edited December 23, 2014 by arkie87

[arkie87]

eta ~= 1-0.4221/TWR^2.313*(1-1/(1+TVR)^0.8) for TWR >= 1.1 (+/- ~1%)

[GoSlash27]

O_O My head hurts...

What is the practical implication of these findings?

-Duxwing

Duxwing,

Once we've got this pinned down, users will be able to more accurately predict how much fuel their ascent vehicles will consume. They will also be able to figure out the mass- optimal t/w ratio for a particular engine on a particular mission, thus enabling them to build lighter lifters, which makes for lighter ascent vehicles... which makes for lighter descent stages and so on.

Arkie was looking at the theoretical aspects of it, but the practical upshot of all this is already proving useful.

Best,

-Slashy

[GoSlash27]

Arkie,

I can, but above 2.5, plot doesnt change much (maybe that's why you had a hard time getting significant results, since differences become small above TWR = 2.5). It's better if you give me your data points, and i run them to give you an exact number back; from the contour plots, you would be estimating the number from the color, and unless the colors changes, its impossible to get accurate results.

When I was running the last series of tests, they were at 1:1 t/w ratio. I was trying to confirm the effect of TVR on efficiency.

The problem is that your FMR winds up being so tiny in those situations that it's hard to read the change in mass with sufficient accuracy.

Feel free to incorporate the test results I've provided upstream. I'm testing a Tylo lander and will relay the findings.

above 2.5, plot doesnt change much

That's kinda the info that I'm after. At some point, the improvement in efficiency is no longer worth the increase in mass and cost associated with adding engines.

Best,

-Slashy

[GoSlash27]

Arkie,

Could you do me a favor and post this contour plot slightly differently? y axis as a log scale from 1.5 to 1500 and x axis linear from 1 to 4?

Unless my math is off, there's no situation in KSP that exceeds these bounds (please confirm that).

I'm assuming the worst case is ions on Gilly and the best case is 0-10 engines on Tylo.

Thanks,

-Slashy

[arkie87]

Arkie,

Could you do me a favor and post this contour plot slightly differently? y axis as a log scale from 1.5 to 1500 and x axis linear from 1 to 4?

Unless my math is off, there's no situation in KSP that exceeds these bounds (please confirm that).

I'm assuming the worst case is ions on Gilly and the best case is 0-10 engines on Tylo.

Thanks,

-Slashy

Eve has TVR = 0.8, but yeah. Making TWR go up til 4 is still wasted space

Also, for TWR = 1, a good correlation to use:

eta ~= 1/log(2.488622+TVR^0.546581);

Out of curiosity, if you have been testing TWR = 1, how do you not crash and how long do your tests take????? They take long enough at TWR = 1.1....

Edited December 23, 2014 by arkie87

[GoSlash27]

Eve has TVR = 0.8, but yeah. Making TWR go up til 4 is still wasted space

True, but Eve also has an atmosphere, which overrides TVR as the primary driver of T/W choice. In all cases over the entire range of airless bodies and engines, it doesn't appear that going over 2:1 t/w is going to yield meaningful efficiency gains.

Out of curiosity, if you have been testing TWR = 1, how do you not crash and how long do your tests take????? They take long enough at TWR = 1.1....

Very carefully!

In the case of Tylo, I just wait until it's supporting itself, then adjust pitch to maintain zero climb rate until I've got some speed established. As fuel burns off, it gets easier.

In the case of Gilly, orbital velocity is only like 30 m/sec, so it's very difficult to crash. More likely to just bump up against something at like 3 m/sec. Shoulda seen that monster; a full Jumbo 64 getting nudged along by a single LV-1. It looked like it had sprung a pinhole leak!

Apologies, but I didn't record time of flight for my testing. I'll include that info in my next round.

Thanks!

-Slashy

P.S., that log layout is pimpin'! Much easier to read the trends that way IMO. Would you be able to double the contour lines for resolution? I think that'd help tremendously.

Edited December 23, 2014 by GoSlash27

[GoSlash27]

As an aside,

I've been using the experience I've gained over the past week to develop a new landing technique that's not only more efficient than suicide burning, but also much safer and more accurate. As a side- bonus, it doesn't require a crazy t/w ratio to work. This lander has had good results at just 1.2:1 initial t/w.

As you can see here, it works pretty good!

*edit* New variant is confirmed.

http://i52.photobucket.com/albums/g13/GoSlash27/TyloLander1_zpse6f985f2.jpg

Mass for the entire assembly is 13.85 tonnes and price is 15,791. Pretty respectable for Tylo.

I'll pass on my test results from the ascent portion.

Best,

-Slashy

[arkie87]

As an aside,

I've been using the experience I've gained over the past week to develop a new landing technique that's not only more efficient than suicide burning, but also much safer and more accurate. As a side- bonus, it doesn't require a crazy t/w ratio to work. This lander has had good results at just 1.2:1 initial t/w.

http://i52.photobucket.com/albums/g13/GoSlash27/Twinsies_zps765b618a.jpg

As you can see here, it works pretty good!

*edit* New variant is confirmed.

http://i52.photobucket.com/albums/g13/GoSlash27/TyloLander1_zpse6f985f2.jpg

Mass for the entire assembly is 13.85 tonnes and price is 15,791. Pretty respectable for Tylo.

I'll pass on my test results from the ascent portion.

Best,

-Slashy

Yes, K^2 has said that treating landings the same way as treating ascents is optimal since suicide burn is the same thing as vertical take off (though you do fall from a much lower height so it's kind of a hybrid approach).

That's just matching velocity at one point on trajectory. Instead, you maintain constant zero radial until you are on Hohmann. That's the same strategy as has been used for landings on many of the maximizing efficiency challenges. It beats suicide burn by a significant margin, even if the later is perfectly executed. And, needless to say, it's much easier to execute and much safer than a suicide burn.

Hohmann or bi-elliptical are clearly optimal under infinite TWR limit. But under finite TWR, getting to that initial Hohmann is a non-trivial optimization problem. I'm just wondering if anyone managed to actually solve it.

And K^2: isnt my work here the solution for finite TWR? I provide all the information you need to select optimum TWR

Finally, I was wondering what method you've come up with to improve landing technique? If it's just the opposite of horizontal ascent, i imagine its harder to perform (since you have to maintain zero vertical velocity while avoiding terrain) plus it would be very, very difficult to predict where your landing site will be.... ?

[GoSlash27]

Finally, I was wondering what method you've come up with to improve landing technique? If it's just the opposite of horizontal ascent, i imagine its harder to perform (since you have to maintain zero vertical velocity while avoiding terrain) plus it would be very, very difficult to predict where your landing site will be.... ?

Actually, it's a hybrid between the two techniques. The zero- vertical velocity technique is the reverse of the horizontal departure. Very good for efficiency, but bad for terrain avoidance and landing accuracy. The "suicide burn" is the reverse of vertical ascent with circularization burn. It'll put you into your desired ballpark, but is perilously dependent on precise timing, hogs fuel, and requires a very high t/w ratio.

What I'm doing is sort of a reverse gravity turn technique. medium efficiency, doesn't rely on high t/w, easy to execute, and will drop you precisely where you want to be every time.

I'll be writing up a tutorial shortly.

*edit* tutorial is up here.

After I'm done with that, what situations would you like me to test out?

Best,

-Slashy

Edited December 24, 2014 by GoSlash27

[arkie87]

Actually, it's a hybrid between the two techniques. The zero- vertical velocity technique is the reverse of the horizontal departure. Very good for efficiency, but bad for terrain avoidance and landing accuracy. The "suicide burn" is the reverse of vertical ascent with circularization burn. It'll put you into your desired ballpark, but is perilously dependent on precise timing, hogs fuel, and requires a very high t/w ratio.

What I'm doing is sort of a reverse gravity turn technique. medium efficiency, doesn't rely on high t/w, easy to execute, and will drop you precisely where you want to be every time.

I'll be writing up a tutorial shortly.

*edit* tutorial is up here.

After I'm done with that, what situations would you like me to test out?

Best,

-Slashy

Did you ever post your results for TWR = 1? A comparison between your efficiency and that predicted by my model would be cool to see...

[K^2]

And K^2: isnt my work here the solution for finite TWR? I provide all the information you need to select optimum TWR

You don't show that the strategy is optimal. You need to show that thrust vector must cancel gravity + centrifugal. That's the hard part, since it's calculus of variation.

[GoSlash27]

arkie,

I have conducted tests in the following situations:

Location/ Isp/ TWR / efficiency

Mun/ 290/0.91/ .526

Mun/290/1.84/ .883

Mun/290/3.68/ .921

Mun/290/7.37/ .928

Mun/4200/1.01/ .565*

Tylo/290/0.95/ .738

Tylo/290/3.78/ .970

*test results have an unacceptably high margin of error.

If you'd like me to test anything, just let me know.

Best,

-Slashy

[GoSlash27]

You don't show that the strategy is optimal. You need to show that thrust vector must cancel gravity + centrifugal. That's the hard part, since it's calculus of variation.

K^2,

I thought *you* were doing that?

Best,

-Slashy