Non-Dimensional Model for Optimal Horizontal Launch Efficiency

[K^2]

I *think* I can verify local optimum. That is not the same thing. There could still be better solutions. But arkie's solution simply assumes the strategy to be a correct one.

[GoSlash27]

I *think* I can verify local optimum. That is not the same thing. There could still be better solutions. But arkie's solution simply assumes the strategy to be a correct one.

As an engineer, I don't have a problem with that. I can reason that it's optimal and don't require proof.

I can understand if you do as a mathematician, but he didn't set out to prove that the strategy is correct, he set out to show the effects of t/w on the strategy's efficiency.

Merry Christmas,

-Slashy

[arkie87]

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

I had to revise my model to accept TWR < 1

Was quite simple though, just said theta = 90 degrees if argument into arcsin function is greater than one (so it burns fuel but does not move horizontally).

Tylo tests seem spot on.

Mun tests with TWR >> 1 seem significantly under-performing compared to model. Perhaps it is more difficult to properly aim completely horizontal and you wind up climbing too high?

Mun tests with TWR <~= 1 are higher than model predicts is possible...

[arkie87]

As an engineer, I don't have a problem with that. I can reason that it's optimal and don't require proof.

I can understand if you do as a mathematician, but he didn't set out to prove that the strategy is correct, he set out to show the effects of t/w on the strategy's efficiency.

Merry Christmas,

-Slashy

Yeah, basically, what Slashy said. I do not prove that this strategy is optimal, but i do provide the optimum TWR if you choose this strategy. I am an engineer, not a mathematician, so I do not need a rigorous mathematical proof, but the only alternatives i can think of is vertical for some distance and then horizontal, which for the case of infinite TWR, requires more deltaV than horizontal, so I see no reason why/how it would/could be better...

[K^2]

Which is fine. But it is a boring problem otherwise. Good exercise, I suppose, but nothing conceptually difficult about it.

If you are having problem maintaining attitude, consider writing a plugin. That is a proper engineering solution.

[arkie87]

Which is fine. But it is a boring problem otherwise. Good exercise, I suppose, but nothing conceptually difficult about it.

If you are having problem maintaining attitude, consider writing a plugin. That is a proper engineering solution.

Not sure where any of this is coming from? Nobody said it was a "conceptually difficult" problem, I was just providing the solution. And who said i was having trouble maintaining altitude?

Though i would agree, a plugin (i was thinking about writing a kOS code http://forum.kerbalspaceprogram.com/threads/68089-0-25-kOS-Scriptable-Autopilot-System-v0-15-2-2014-11-19) would be ideal to always follow the orientation to produce zero vertical velocity. Alternatively, a plugin to put a marker on the navball would be pretty sweet....

EDIT: actually, i think K^2's point is that in the OP title, i said "optimal launch efficiency" rather than "optimal horizontal launch efficiency." I have revised OP title to reflect this.

Edited December 24, 2014 by arkie87

[GoSlash27]

I had to revise my model to accept TWR < 1

Was quite simple though, just said theta = 90 degrees if argument into arcsin function is greater than one (so it burns fuel but does not move horizontally).

http://i.imgur.com/VjyRydN.png

Tylo tests seem spot on.

Mun tests with TWR >> 1 seem significantly under-performing compared to model. Perhaps it is more difficult to properly aim completely horizontal and you wind up climbing too high?

Mun tests with TWR <~= 1 are higher than model predicts is possible...

For Mun tests, I can't go perfectly horizontal for climbout since there's terrain. That would explain the inefficiency there. And also, higher t/w ratios become increasingly difficult to control precisely in the early part of the launch. I hadn't thought about it before, but that sets a practical upper bound on increased efficiency from higher t/w as well. Not any way that I know of to integrate that into a formula.

The Mun test with ions really needs to be taken with a grain of salt. Total fuel consumed in that test was only 2.5% of total vehicle mass, and with the margin of error for final mass, it could've been anywhere between 23% and 80% efficiency.

The result at Isp=290s is a legit result and should be accounted for.

Incidentally, LD is trying to derive a solution for the same problem. You may want to check in with him.

Best,

-Slashy

Edited December 24, 2014 by GoSlash27

[arkie87]

For Mun tests, I can't go perfectly horizontal for climbout since there's terrain. That would explain the inefficiency there. And also, higher t/w ratios become increasingly difficult to control precisely in the early part of the launch. I hadn't thought about it before, but that sets a practical upper bound on increased efficiency from higher t/w as well. Not any way that I know of to integrate that into a formula.

The Mun test with ions really needs to be taken with a grain of salt. Total fuel consumed in that test was only 2.5% of total vehicle mass, and with the margin of error for final mass, my calculation for DV could be off by as much as 41%.

The result at Isp=290s is a legit result and should be accounted for.

Incidentally, LD is trying to derive a solution for the same problem. You may want to check in with him.

Best,

-Slashy

Yeah, he PM'ed me and i check out his thread, but he neglects centripetal lift

[GoSlash27]

My low TWR result at 290s Isp launch out-performing the model troubles me.

Just to verify, it was to an orbital velocity of 547m/sec.

I wonder what's behind this... *scratches head*

[GoSlash27]

Which is fine. But it is a boring problem otherwise. Good exercise, I suppose, but nothing conceptually difficult about it.

If you are having problem maintaining attitude, consider writing a plugin. That is a proper engineering solution.

K^2,

All due respect, but we're not doing this for the entertainment value. We're doing this to answer questions.

Best,

-Slashy

[GoSlash27]

Arkie,

The contour plot you posted earlier agrees with with my findings.

If I'm reading it right, it predicts a high 50% efficiency for t/w=1 and TVR of 5.2. That's in line with my result.

*edit* And also the predicted efficiency for Mun at 1.0 TWR with 290s Isp vs. Mun at 1.0 TWR with 4,200s Isp shouldn't be anywhere near each other, yet your table upstream predicts about 48% efficiency for both cases.

The way I read your contour plot, 290s Isp should get me high 50% efficiency, while 4200s Isp should get me high 30% efficiency.

I'm thinkin' there was a transcription error somewhere.

Best,

-Slashy

Edited December 25, 2014 by GoSlash27

[arkie87]

My low TWR result at 290s Isp launch out-performing the model troubles me.

Just to verify, it was to an orbital velocity of 547m/sec.

I wonder what's behind this... *scratches head*

Try starting out at TWR > 1. If you start below 1, you must be standing still until you burn off enough weight? How does that work? It's also possible you started high enough above sea level such that you began falling...

[GoSlash27]

Try starting out at TWR > 1. If you start below 1, you must be standing still until you burn off enough weight? How does that work? It's also possible you started high enough above sea level such that you began falling...

arkie,

the series of Mun tests were conducted using the same vehicle in the same location.

It was an RCS tank with selectable banks of O-10 engines. I landed it, created a save point, and then repeatedly launched it into orbit at various t/w ratios.

There was no change in the initial state that would account for the discrepancy.

Best,

-Slashy

[arkie87]

Arkie,

The contour plot you posted earlier agrees with with my findings.

If I'm reading it right, it predicts a high 50% efficiency for t/w=1 and TVR of 5.2. That's in line with my result.

*edit* And also the predicted efficiency for Mun at 1.0 TWR with 290s Isp vs. Mun at 1.0 TWR with 4,200s Isp shouldn't be anywhere near each other, yet your table upstream predicts about 48% efficiency for both cases.

The way I read your contour plot, 290s Isp should get me high 50% efficiency, while 4200s Isp should get me high 30% efficiency.

I'm thinkin' there was a transcription error somewhere.

Best,

-Slashy

Your table doesn't have mun with twr of 1 at isp 290. It has twr if 0.91....

[GoSlash27]

Your table doesn't have mun with twr of 1 at isp 290. It has twr if 0.91....

No, Sir, *your* table.

It doesn't go down that far, but I'm interpolating.

Point being that low TWR shouldn't be anywhere near the same in the two instances I cited according to the contour plot, but are nearly identical in the table. I think the table is hosed, 'cus the contour plot agrees with the empirical results, plus the table disagrees with your math.

Best,

-Slashy

[arkie87]

No, Sir, *your* table.

It doesn't go down that far, but I'm interpolating.

Point being that low TWR shouldn't be anywhere near the same in the two instances I cited according to the contour plot, but are nearly identical in the table. I think the table is hosed, 'cus the contour plot agrees with the empirical results, plus the table disagrees with your math.

Best,

-Slashy

Confused. Here is your table:

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.

y

I don't see a Mun TWR = 1 @ ISP = 290... there is only one @ TWR = 0.91 (in bold).

EDIT: I see what you are saying-- that in my table TWR = 0.91 @ISP=290 ~= TWR 1.01 @ ISP = 4200, which shouldnt be possible since ISP =4200 should perform worse than ISP 290 (for the reasons we've discussed).

However, that is only at constant TWR. In our case, TWR < 1 is really bad, since it means we are burning fuel until TWR = 1 before we can start moving... if TWR started at 1 (instead of 0.91) then the results would be much different.

As a side note, if TWR was 0.91 with ISP = 4200 i imagine efficiency would be zero, since due to high ISP, TWR would never go above 1 to allow the craft to actually move...

Edited December 25, 2014 by arkie87

[GoSlash27]

Confused. Here is your table:

I don't see a Mun TWR = 1 @ ISP = 290... there is only one @ TWR = 0.91 (in bold).

EDIT: I see what you are saying-- that in my table TWR = 0.91 @ISP=290 ~= TWR 1.01 @ ISP = 4200, which shouldnt be possible since ISP =4200 should perform worse than ISP 290 (for the reasons we've discussed).

However, that is only at constant TWR. In our case, TWR < 1 is really bad, since it means we are burning fuel until TWR = 1 before we can start moving... if TWR started at 1 (instead of 0.91) then the results would be much different.

As a side note, if TWR was 0.91 with ISP = 4200 i imagine efficiency would be zero, since due to high ISP, TWR would never go above 1 to allow the craft to actually move...

No Sir, that's not what I'm saying...

Hang on a sec; let me try something...

What I'm saying is that these numbers

do not agree with these numbers

If you go with the values from the contour plot, then I'm not out- performing the model at 290s Isp. I am at 4200, but the margin of error is so huge that my result may well be in conformance with the model and the resolution is masking it.

I need a way to get a more accurate read for ions. The expended mass is so frustratingly tiny...

Hope you had a great Christmas!

-Slashy

[arkie87]

No Sir, that's not what I'm saying...

Hang on a sec; let me try something...

What I'm saying is that these numbers

http://i52.photobucket.com/albums/g13/GoSlash27/table_zpsd08564ad.jpg

do not agree with these numbers

http://i52.photobucket.com/albums/g13/GoSlash27/plot_zps24bd7e96.jpg

If you go with the values from the contour plot, then I'm not out- performing the model at 290s Isp. I am at 4200, but the margin of error is so huge that my result may well be in conformance with the model and the resolution is masking it.

I need a way to get a more accurate read for ions. The expended mass is so frustratingly tiny...

Hope you had a great Christmas!

-Slashy

You cannot plot the first data point on the contour plot because the TWR for this point is 0.91 but the contour plot starts from TWR of 1....

You can however plot your numbers on this contour plot:

[GoSlash27]

Arkie,

Wow, I see what you mean. I didn't realize the numbers would fall off so sharply under 1:1.

In that case, there is a problem. I am outperforming the model at very low t/w ratios on the Mun.

This would be a problem...

BTW, I really like that expanded plot. I'm gonna see if I can't make it just a little more user friendly and repost it here.

Best,

-Slashy

[GoSlash27]

Hope that doesn't butcher it!

Best,

-Slashy

[arkie87]

Arkie,

Wow, I see what you mean. I didn't realize the numbers would fall off so sharply under 1:1.

In that case, there is a problem. I am outperforming the model at very low t/w ratios on the Mun.

This would be a problem...

BTW, I really like that expanded plot. I'm gonna see if I can't make it just a little more user friendly and repost it here.

Best,

-Slashy

Of course it should! All fuel spent while TWR < 1 is completely wasted! You are basically jettisoning mass to get your TWR >=1... Is that not what happened during your tests?

[GoSlash27]

arkie,

yeah, it is... but that's not the point.

The point is I'm outperforming the model at very low t/w and I shouldn't be. Especially not with terrain in the way (which is very tough to dodge at low t/w)

Gotta be something the model's not accounting for.

Maybe initial launch altitude above "sea" level, or sidereal rotation?

What do you think?

Best,

-Slashy

[arkie87]

arkie,

yeah, it is... but that's not the point.

The point is I'm outperforming the model at very low t/w and I shouldn't be. Especially not with terrain in the way (which is very tough to dodge at low t/w)

Gotta be something the model's not accounting for.

Maybe initial launch altitude above "sea" level, or sidereal rotation?

What do you think?

Best,

-Slashy

Yes, both of those the model does not account for.

Can you confirm that when you launch with TWR < 1, you dont move for a while (until TWR >1)?

[arkie87]

What is your initial altitude? I can revise model to adjust g based on altitude.

On the Mun, landing 5 km above sea level results in 5% change in gravity...

[GoSlash27]

Sorry, I'll get to your question in a moment. Just wanted to post this for you first.

I hope that works for you. Let me know if there are any errors.