Optimal TWR with Stock vs. FAR Aerodynamics

[arkie87]

I was wondering what people thought optimal TWR was for stock and FAR.

It seems to me that with stock souposphere (as i've heard it called), it's very easy to reach terminal velocity (which is optimal ascent velocity). Thus, smaller/lighter engines are of great benefit since you dont need high TWR.

However, with FAR, since terminal velocity is essentially unreachable (see

and http://forum.kerbalspaceprogram.com/threads/32033-FAR-and-Mechjeb-terminal-velocity?p=894880&viewfull=1#post894880), it would make sense that optimal TWR is higher, since every second spent fighting gravity is ~10 m/s deltaV wasted. Now clearly, the extra weight required to increase TWR must be factored into the decision-- i.e. to choose mainsail or skipper engine, since skipper is lighter-- this makes sense. However, what doesn't make sense is if one is using boosters, what is the advantage of reducing their maximum thrust when using FAR? You do not reduce your weight, like you do when you switch from a mainsail to a skipper, so what is the advantage? What am i missing?

Also, i've seen people post that having TWR=2 is terminal velocity. This is clearly silly. What they meant to say is this: having TWR =2 will ensure that your velocity will approach (exponentially) terminal velocity, but is guaranteed never to exceed it, since: m*a = T - Drag - m*g; at terminal velocity, Drag = m*g, and a=0, so T=2*m*g i.e. TWR = 2.

Edited December 14, 2014 by arkie87

[OhioBob]

I'm not familiar with FAR so I can't comment about that. In stock, however, I've actually done some research/simulations to try to pinpoint the optimum TWR. There's no way I could test every possible configuration, so I just concentrated on a simple two-stage launch vehicle. My simulations revealed that the ideal TWRs are 1.64 for the lower stage and 1.31 for the upper stage. I've used these same TWRs for more complex vehicles (strap-on SRBs, etc.) and have found good results there as well. I've had no problem obtaining payload fractions of about 0.16 using these numbers.

(ETA) These are, of course, the TWR at initial stage ignition.

Edited December 14, 2014 by OhioBob

[Starman4308]

Muuuch lower TWR in FAR/NEAR: the sweet spot is usually 1.2-1.6, probably optimal around 1.4. While increased TWR reduces atmo drag, you also need engine mass to get that TWR, and that engine mass will reduce your available dV. Reduced atmo drag also means that, to some extent, you can get away with it: there's not so much pressure to get out of the super-duper-drag zone (roughly 0-10km) as quickly.

There's also a consideration vis-a-vis pulling off your gravity turn: if your TWR is too high, you generally wind off shooting up to space and lose too much to gravity, whereas a lower TWR helps you manage a good, tight gravity turn. I make too many 1.6-ish TWR boosters, and I curse and struggle and scream trying to bring the rocket's pitch down.

You can also look at real-world boosters, which tend to be in the 1.2-1.6 TWR range. Saturn V came in at around 1.17-ish, while Proton-K came in around 1.55. I've heard of some with around 2.0-ish, but that is only on account of SRBs which last maybe 30 seconds before being discarded.

EDIT: I think the reason you see so much "2.0 to terminal velocity" is that, for the crucial first stage of ascent in stock aero, 2.0 TWR is a very good approximation of hitting terminal velocity, and it's roughly the upper bound of what you should be aiming for (particularly in asparagus-staged designs).

Edited December 14, 2014 by Starman4308

[arkie87]

Interesting response.

Muuuch lower TWR in FAR/NEAR: the sweet spot is usually 1.2-1.6, probably optimal around 1.4. While increased TWR reduces atmo drag, you also need engine mass to get that TWR, and that engine mass will reduce your available dV.

I understand the trade-off between TWR and deltaV when it comes to selecting a different engine, and the optimum solution is dependent on the particular values that the parts in KSP have. Clearly, if they weighed the same, higher TWR would always be the most efficient choice, but for all other cases, a more complicated analysis must be conducted based on the particular numbers (i.e. we would need the mathematical relationship between TWR and total mass, so that we could differentiate it w.r.t. TWR and set it equal to zero as is done to find the optimal solution). Accordingly, this is not what i want to debate...

Reduced atmo drag also means that, to some extent, you can get away with it: there's not so much pressure to get out of the super-duper-drag zone (roughly 0-10km) as quickly.

Quite the opposite -- reduced drag means you want to get out of the atmosphere faster, since it costs little in terms of drag force/deltaV and every second you spend in your initial climb, you are wasting fuel fighting gravity. If your TWR is 1.2-1.6, you are wasting between 63-83% of your thrust fighting gravity... According to your logic, optimal TWR on the mun is lower still since there is even less drag

There's also a consideration vis-a-vis pulling off your gravity turn: if your TWR is too high, you generally wind off shooting up to space and lose too much to gravity, whereas a lower TWR helps you manage a good, tight gravity turn. I make too many 1.6-ish TWR boosters, and I curse and struggle and scream trying to bring the rocket's pitch down.

This is true. But the alternative, for a given vehicle design which has too much TWR, is to reduce throttle or limit SRB thrust, both of which hurt your deltaV... This is the case i am interested to discuss and kind of the point i wanted to get across.

You can also look at real-world boosters, which tend to be in the 1.2-1.6 TWR range. Saturn V came in at around 1.17-ish, while Proton-K came in around 1.55. I've heard of some with around 2.0-ish, but that is only on account of SRBs which last maybe 30 seconds before being discarded.

That makes little sense to me. I think i am still missing something. It is always most fuel efficient to ascend at terminal velocity, and TWR will have a much harder time getting you there.

EDIT: I think the reason you see so much "2.0 to terminal velocity" is that, for the crucial first stage of ascent in stock aero, 2.0 TWR is a very good approximation of hitting terminal velocity, and it's roughly the upper bound of what you should be aiming for (particularly in asparagus-staged designs).

What do you mean is a good approximation of hitting terminal velocity? For the reason i gave, it is impossible to go faster than terminal velocity as long as TWR = 2. By "upper bound", i think you are saying what I was saying.

Edited December 14, 2014 by arkie87

[Starman4308]

-stuff-

The short version is that in FAR, you aren't getting to terminal velocity, so you shouldn't bother trying. In stock, terminal velocity is crucial, because for the first 10 km of your ascent, you're basically fighting gravity every step of the way at a sluggish 100 m/s-ish pace. You are taking 9.8 m/s^2 of gravity drag every second for ~100 seconds for that first part of ascent.

In FAR, that consideration is gone. You can heel over almost right off the pad, so the primary consideration is exactly where it is that adding more engine mass reduces delta-V faster than the increased TWR reduces gravity losses. There is also consideration for atmospheric stresses: a high-velocity rocket in low atmosphere is going to be under a lot of aerodynamic stress, something which affects a significant number of real-world rockets.

As to the 2.0 TWR approximation: for that first 10km, terminal velocity requires only a tiny bit more than 2.0 TWR, and most rockets will get that tiny bit anyways from burning fuel. 2.0 is a good approximation, and conveys the point of "one gravity of acceleration to fight gravity, one gravity to fight atmosphere". When explaining it, I usually add "and a bit more for accelerating as terminal velocity goes up".

EDIT: In short, rocket designers trade off almost horrific gravity losses in the first minute or so for improved performance during the rest of the ascent. Don't forget that body lift is a thing in FAR and the real-world: you can get away with a bit lower TWR than would otherwise be necessary because of that. Also, real-world fuel tanks and engines are much lighter than KSP, so there tends to be a bigger difference in TWR between the start and end of a stage.

Edited December 14, 2014 by Starman4308

[Wanderfound]

Also keep in mind that a lot of FAR flyers are spaceplaning, where the most fuel efficient TWR is whatever is the minimum number of jets required to get up to flight speed before the end of the runway.

[OhioBob]

But the alternative, for a given vehicle design which has too much TWR, is to reduce throttle or limit SRB thrust, both of which hurt your deltaV... This is the case i am interested to discuss and kind of the point i wanted to get across.

I found that in stock the sweet spot for first stage TWR is about 1.6-1.7. One of the reasons for not using a higher TWR is to save mass on smaller engines. However, if for some reason you are forced to use a larger engine, I've found that throttling back to the 1.6-1.7 range doesn't necessarily achieve the best result. I didn't do extensive research on this, but I did find for one example that throttling back to about 1.85 gave the best result. I guess the moral is, use smaller engines when you can, but when you can't, you don't necessarily want to force a big engine behave like a little one. You might have to throttle back, but it might not be necessary to throttle back as far as you think.

[GoSlash27]

Honestly...

The more I experiment in stock, the more I'm convinced that the optimal t/w at engine start is 1.

Crazy, but there it is...

But disclaimer, all of my launches the last couple months have been hyper- efficient SSTOs, so that's probably skewing my results.

Best,

-Slashy

[arkie87]

The short version is that in FAR, you aren't getting to terminal velocity, so you shouldn't bother trying. In stock, terminal velocity is crucial, because for the first 10 km of your ascent, you're basically fighting gravity every step of the way at a sluggish 100 m/s-ish pace. You are taking 9.8 m/s^2 of gravity drag every second for ~100 seconds for that first part of ascent.

In FAR, that consideration is gone. You can heel over almost right off the pad, so the primary consideration is exactly where it is that adding more engine mass reduces delta-V faster than the increased TWR reduces gravity losses.

Ok, so that's pretty much what i was saying. Makes sense.

There is also consideration for atmospheric stresses: a high-velocity rocket in low atmosphere is going to be under a lot of aerodynamic stress, something which affects a significant number of real-world rockets.

That is definitely true and could explain the low TWR that you reported for real-world rockets. Personally, i disable aerodynamic disassembly

As to the 2.0 TWR approximation: for that first 10km, terminal velocity requires only a tiny bit more than 2.0 TWR, and most rockets will get that tiny bit anyways from burning fuel. 2.0 is a good approximation, and conveys the point of "one gravity of acceleration to fight gravity, one gravity to fight atmosphere". When explaining it, I usually add "and a bit more for accelerating as terminal velocity goes up".

I don't see why it needs a tiny bit more? It will exponentially approach terminal velocity if TWR is maintained through the flight. However, this is only true in practice for stock aerodynamics, since other than blasting off to 100 m/s as fast as possible, the increase in terminal velocity with altitude is relatively mild such that it is manageable with even small TWR. In FAR, you will never reach terminal velocity with TWR=2 as it starts off too high and increases too fast to keep up with; you'll need like TWR = 10, and if so, i hope your kerbals have exoskeletons

EDIT: In short, rocket designers trade off almost horrific gravity losses in the first minute or so for improved performance during the rest of the ascent. Don't forget that body lift is a thing in FAR and the real-world: you can get away with a bit lower TWR than would otherwise be necessary because of that. Also, real-world fuel tanks and engines are much lighter than KSP, so there tends to be a bigger difference in TWR between the start and end of a stage.

Yeah, i was thinking about body lift, so gravity losses can be managed that way, especially if lift/drag ratio is large.

[arkie87]

Honestly...

The more I experiment in stock, the more I'm convinced that the optimal t/w at engine start is 1.

Crazy, but there it is...

But disclaimer, all of my launches the last couple months have been hyper- efficient SSTOs, so that's probably skewing my results.

Best,

-Slashy

The space shuttle seems to launch with TWR = 1... which, since playing this game, has confused the hell out of me since it cannot be the most efficient.

Do you have mathematical reasons for your conclusion or just personal experience?

[Bryce Ring]

Drag = Cd * 1/2 air mass * V * V * Surface area (that's the basic formation without looking at length and Reynolds numbers.

Cd increases as you near the speed of sound. it then decreases from that maximum value as you pass the sound barrier but it will still be higher than a lower subsonic value.

Terminal Velocity will change due to weight only based on its potential to push a Cd value with this area through air mass at this level. Basing a climb on terminal velocity is just a way to reduce the compound effect of Velocity on the Cd to form drag.

here is a very important thing to remember.

if you double the velocity with given area and Cd value and atmosphere density. not changing any other value, just velocity to double, you will increase your drag 4 fold.

all that aside.

I am curious what is the BC value in that video.

and where is the Drag loss recorder or indicator.

Bryce.

[OhioBob]

The space shuttle seems to launch with TWR = 1

Are you talking about the real world Space Shuttle? The real Space Shuttle had a liftoff TWR of about 1.7.

[kujuman]

Yeah, this debate is hard to develop a simple answer for (which is why it constantly rages ) because it's very hard to develop a single set of assumptions. Riding the border of terminal velocity makes sense for the straight up portion of the launch, which in stock may be 5-15km depending on TWR. In NEAR/FAR this portion might be...200m tall? And you're probably (hopefully) not getting to terminal velocity that quickly. In stock, terminal velocity is attitude independent, but in NEAR/FAR craft orientation is a consideration. Too much dynamic pressure may make control of the rocket impossible (either too stable or too unstable), or your rocket may disintegrate; an "optimal TWR" rocket which can't control itself through launch or breaks apart isn't optimal

Then there's the question of TWR when? Asking for optimal initial TWR based on initial conditions is pretty unhelpful as stages have differing average TWRs, differing extremes of those TWRs, and different burn times. Also, with engines becoming more fuel efficient higher up, saving reaction mass for later in launch by not having a high initial TWR may allow you to develop more total delta-V, even if it costs more delta-V to perform this maneuver.

The "best" TWR for a launcher in stock is relatively similar because the atmo model leaves launch profiles to be pretty consistent. In FAR there are more variables to factor in, and there are concerns outside of pure fuel savings. Besides, in FAR, drag losses are very small, so even a pretty "unoptimized" TWR and launch profile (for minimizing drag losses) isn't going to cost that much.

And Kraken help you if you're also trying to figure out an optimal launcher in career mode, having to pay for things...

Edited December 14, 2014 by kujuman

[arkie87]

Drag = Cd * 1/2 air mass * V * V * Surface area (that's the basic formation without looking at length and Reynolds numbers.

Cd increases as you near the speed of sound. it then decreases from that maximum value as you pass the sound barrier but it will still be higher than a lower subsonic value.

http://upload.wikimedia.org/wikipedia/commons/0/0e/Qualitive_variation_of_cd_with_mach_number.png

Terminal Velocity will change due to weight only based on its potential to push a Cd value with this area through air mass at this level. Basing a climb on terminal velocity is just a way to reduce the compound effect of Velocity on the Cd to form drag.

here is a very important thing to remember.

if you double the velocity with given area and Cd value and atmosphere density. not changing any other value, just velocity to double, you will increase your drag 4 fold.

Not really sure what you were saying here.

all that aside.

I am curious what is the BC value in that video.

and where is the Drag loss recorder or indicator.

Bryce.

What is a "BC value"?

The drag loss is the Cd-- coefficient of drag indicator.

[arkie87]

Are you talking about the real world Space Shuttle? The real Space Shuttle had a liftoff TWR of about 1.7.

But it always seems to lift off so SLOWLY!

Edited December 14, 2014 by arkie87

[arkie87]

Honestly...

The more I experiment in stock, the more I'm convinced that the optimal t/w at engine start is 1.

Crazy, but there it is...

But disclaimer, all of my launches the last couple months have been hyper- efficient SSTOs, so that's probably skewing my results.

Best,

-Slashy

TBH, I'm kinda surprised you use stock aerodynamics. You seem too technically-literate to be satisfied with the completely unrealistic stock aerodynamics...

[GoSlash27]

The space shuttle seems to launch with TWR = 1... which, since playing this game, has confused the hell out of me since it cannot be the most efficient.

Do you have mathematical reasons for your conclusion or just personal experience?

Just experience and a fuzzy theory.

In stock KSP, the gravity turn doesn't begin until 7K or so. And from the gravity turn on, the ideal curve seems to favor much lower t/w than the conventional wisdom suggests.

I think it's because "terminal velocity" isn't what matters, but rather the "delta terminal velocity".

It's not a matter of matching the terminal velocity itself, but rather accelerating at the same rate at which your terminal velocity is increasing.

If your rate of climb is about 100M/sec, you don't have to accelerate at 2G to match your terminal velocity.

So since the Vt wall doesn't take much acceleration to match, the thrust requirement is greatly reduced over most of the flight. Ditching the excess thrust seems to save more DV over the course of the launch than more rapid acceleration in the vertical phase and then throttling back.

tl;dr...

The DV savings from carrying powerful engines in the early going winds up getting wiped out in the later going by carrying more engine mass than I need.

So I start very close to 1 and let the fuel burnoff increase my acceleration.

I don't know if my explanation is sound or not, but I *do* know it seems to work. I just launched a payload into orbit that weighed more than the ship that put it there. I don't know if that's ever been done before or not, but I do know that that sort of thing doesn't happen with inefficient launch profiles.

Scratchin' mah head,

-Slashy

Edited December 14, 2014 by GoSlash27

[GoSlash27]

TBH, I'm kinda surprised you use stock aerodynamics. You seem too technically-literate to be satisfied with the completely unrealistic stock aerodynamics...

Well... (sheepish grin)

I like helping folks and most folks who need help are running stock. So I focus on gaining as much knowledge and experience as I can in the unmodified engine. Plus, altering my setup from stock just seems wrong somehow.

Weird, I know

-Slashy

[arkie87]

Just experience and a fuzzy theory.

In stock KSP, the gravity turn doesn't begin until 7K or so. And from the gravity turn on, the ideal curve seems to favor much lower t/w than the conventional wisdom suggests.

I think it's because "terminal velocity" isn't what matters, but rather the "delta terminal velocity".

It's not a matter of matching the terminal velocity itself, but rather accelerating at the same rate at which your terminal velocity is increasing.

If your rate of climb is about 100M/sec, you don't have to accelerate at 2G to match your terminal velocity.

Yes, for stock, achieving terminal velocity is easy and doable, since at sea level, its only 100 m/s. Thus, maintaining terminal velocity as you get high is what matters, and that is relatively easy to do even with low TWR until you get to 10 km or so. I actually once made a spreadsheet that calculates required acceleration needed to maintain terminal velocity vs. altitude:

(The initial high value at 1 km is based on some assumption of how fast we want to get to terminal velocity from a standing start). Thus, i think you are right. We can save weight by keeping a small TWR in stock aerodynamics, and still be efficient by flying at terminal velocity.

In FAR, achieving terminal velocity is impossible (read: not possible without very large TWR), thus, there are potential benefits of higher TWR that might outweigh added weight of more engines...

Edited December 14, 2014 by arkie87

[arkie87]

Well... (sheepish grin)

I like helping folks and most folks who need help are running stock. So I focus on gaining as much knowledge and experience as I can in the unmodified engine. Plus, altering my setup from stock just seems wrong somehow.

Weird, I know

-Slashy

Once you go FAR, you never look back

The main reason i switched to FAR is because it enables "skipping" off the atmosphere during re-entry. With stock, i dont think that's possible-- once you start falling, its hard to use lift/AoA to bring your craft back up again.

However, i am thinking of switching back to stock, since it's drag simplifications will make this mod (http://forum.kerbalspaceprogram.com/threads/93685-0-24-0-25-Trajectories-v1-0-0-%282014-11-17%29-atmospheric-predictions-FAR-NEAR) that predicts aerobreaking (and with a beautiful GUI!) more accurate/deterministic and less prone to variation due to piloting.

FAR makes flying planes more fun and realistic; all it does for rockets is cause them to tumble around during lift off albeit, more realistically. When flying rockets, i'd rather have stock drag; when flying planes, i'd rather have FAR.

[Bryce Ring]

What is a "BC value"?

The drag loss is the Cd-- coefficient of drag indicator.

The value just under the terminal Velocity value in the video. it is units of kg/m^2

Cd is not drag loss. I was thinking more along the lines as what MechJeb has. total ⌂V lost due to drag.

[arkie87]

The value just under the terminal Velocity value in the video. it is units of kg/m^2

Cd is not drag loss. I was thinking more along the lines as what MechJeb has. total ⌂V lost due to drag.

Oh, havent a clue what BC is Ask Mr. Ferram

Oh i see. I dont have that information, but terminal velocity is always optimum.

Perhaps i should try again with mechjeb...

[arkie87]

Yeah, this debate is hard to develop a simple answer for (which is why it constantly rages ) because it's very hard to develop a single set of assumptions. Riding the border of terminal velocity makes sense for the straight up portion of the launch, which in stock may be 5-15km depending on TWR. In NEAR/FAR this portion might be...200m tall? And you're probably (hopefully) not getting to terminal velocity that quickly. In stock, terminal velocity is attitude independent, but in NEAR/FAR craft orientation is a consideration. Too much dynamic pressure may make control of the rocket impossible (either too stable or too unstable), or your rocket may disintegrate; an "optimal TWR" rocket which can't control itself through launch or breaks apart isn't optimal

Then there's the question of TWR when? Asking for optimal initial TWR based on initial conditions is pretty unhelpful as stages have differing average TWRs, differing extremes of those TWRs, and different burn times. Also, with engines becoming more fuel efficient higher up, saving reaction mass for later in launch by not having a high initial TWR may allow you to develop more total delta-V, even if it costs more delta-V to perform this maneuver.

The "best" TWR for a launcher in stock is relatively similar because the atmo model leaves launch profiles to be pretty consistent. In FAR there are more variables to factor in, and there are concerns outside of pure fuel savings. Besides, in FAR, drag losses are very small, so even a pretty "unoptimized" TWR and launch profile (for minimizing drag losses) isn't going to cost that much.

And Kraken help you if you're also trying to figure out an optimal launcher in career mode, having to pay for things...

Yes, i think your analysis is spot on.

So, you are saying with FAR, i should begin turning instantly? Interesting...perhaps i will experiment with that...

And career mode is sort of what sparked this question for me, since the only thing we care about is cost. And SRB's are dirt cheap, but have no throttle or thrust vectoring, making turning them difficult in FAR for that gravity turn, especially before you unlock reaction wheels and control surfaces... so i considered whether it was cheaper/easier to just launch vertically to the mun by strapping on cheap SRB's that didnt NEED to be steered...

[WuphonsReach]

At low tech levels, I get reliable launches by keeping the TWR at around 1.2-1.5 at the pad for the first stage. Past 8-12km of altitude and it no longer matters. But if I try and push a TWR > 1.8-2.0 off the pad with FAR, you'll hit mach speed and things tend to break from the aero-stresses.

For unstable rockets, starting with a TWR of 1.2 works well. You can ease your way up past 15-25km to where you can start a turn without things going to pieces. For well designed rockets, 1.5-1.8.

[John FX]

In FAR I wait until I have enough speed for control surfaces to start working (around 50m/s) then bank over. Depending on TWR (bank more for high TWR) I settle on an angle and wait until I reach mach 1 (around 330m/s) at which point I should be at about 45 degrees (less for high TWR). I remove SAS and let the craft control itself. I then adjust throttle to keep the Ap around 50 secs away. When my Ap is the desired one I set a node to circularise and execute it (normally about 100m/s)

Whether a very low TWR makes sense depends on how you get it. Obviously the low TWR should be due to large amounts of fuel not weak engines...

Here is a chart for which engine you should use for TWR=1 to TWR=3 in atmosphere for a range of payloads and Dv requirements (the chart assumes you will be using a single engine) from this thread.

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Edited December 14, 2014 by John FX