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How big should your stages be?


he77789
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26 minutes ago, herbal space program said:

It's kind of hard for me to fathom how taking 30-50 seconds to get to 100m/s rate of climb can be the most mass-efficient solution even on Kerbin.

herbal,

 Check out the "cheap and cheerful rocket challenge", you'll see it at work. Perhaps the best way to explain it is to simply have you prove it to yourself. Simply take a rocket engine and load it with enough fuel tanks to launch at 2G. The mass of fuel/o2 remaining (plus tank mass to contain it) that remains when you hit the staging point represents the mass of the payload.

 Now just add some fuel to get it down to 1.8G, rinse and repeat. 1.7G, 1.6G, etc.

What you will find is that more dv is wasted as gravity losses, but not as much fuel is consumed in total as has been added. This payload fraction is maximized when T/W is around 1.4G off the pad.

 And for the record, the Twin Boar is actually cheaper to operate than SRBs from Kerbin. My personal best disposable lifter was able to place (IIRC) 137 tonnes into orbit at less than $650/tonne.

Best,

-Slashy

Edited by GoSlash27
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On 7/25/2021 at 10:10 AM, GoSlash27 said:

herbal,

 Check out the "cheap and cheerful rocket challenge", you'll see it at work. Perhaps the best way to explain it is to simply have you prove it to yourself. Simply take a rocket engine and load it with enough fuel tanks to launch at 2G. The mass of fuel/o2 remaining (plus tank mass to contain it) that remains when you hit the staging point represents the mass of the payload.

 Now just add some fuel to get it down to 1.8G, rinse and repeat. 1.7G, 1.6G, etc.

What you will find is that more dv is wasted as gravity losses, but not as much fuel is consumed in total as has been added. This payload fraction is maximized when T/W is around 1.4G off the pad.

 And for the record, the Twin Boar is actually cheaper to operate than SRBs from Kerbin. My personal best disposable lifter was able to place (IIRC) 137 tonnes into orbit at less than $650/tonne.

Best,

-Slashy

So I did a version of what you suggested, using vertical lifting of a 20t payload to an AP of 100km as my benchmark,  since actually flying to orbit involves too many variables. The test vehicles all had a single Mainsail engine and a variable number of 2.5m tank segments between it and the payload. In each case, the test craft remained at full throttle for the entire duration of the burn, except for small corrections at the end. I also only accepted runs in which the AP after reaching 70km was between 100km exactly and 100.05km. In this test, a TWR of 1.4 did not result in the optimal mass ratio between what was launched and what arrived at 100km. The mass ratios I observed ranged continuously upwards from 0.4868 for a Saturn V launch TWR of 1.21 to 0.569 at a launch TWR of 2.1.  The mass ratio at 1.4 was 0.518, and although above TWR 1.75 the returns diminished fairly sharply, I never found the point at which they became negative.  In short, I think your statement about TWR1.4 is based on an outdated aero model. Between 1.1x (when the cheap and cheerful challenge happened) and the more recent versions, they  have nerfed the effects of drag quite considerably, especially in the upper atmo. That has made re-entry a somewhat dicier proposition than it used to be, but it has also significantly changed the calculus of when to initiate gravity turns and also significantly expanded the capabilities of SSTO space planes. I also spent some time testing single-stage flight-to-orbit in this setup with a reduced payload, and although standardizing that readout is pretty difficult, everything I saw suggested the same answer, because the larger cross-section of atmo you have to fly through is more than offset by the more aggressive gravity turn profile that having a higher TWR at launch allows. And this is without even getting fancy about asparagus staging or throttling back for max-Q. Anyway, what you might consider the best lifter is obviously a subjective question because different people have different criteria, but as far as getting the best mass ratio for a single stage using the available heavy lift rocket engines, a TWR of 1.4 at launch is more like the floor than the sweet spot IMO.

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Edited by herbal space program
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33 minutes ago, herbal space program said:

So I did a version of what you suggested, using vertical lifting of a 20t payload to an AP of 100km as my benchmark,  since actually flying to orbit involves too many variables.

A better (but harder) set of experiments to run would be delivering a 20t payload to an AP of 100km with enough remaining delta-V to circularize.  And then compare the cost of each.

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8 minutes ago, Jacke said:

A better (but harder) set of experiments to run would be delivering a 20t payload to an AP of 100km with enough remaining delta-V to circularize.  And then compare the cost of each.

No, that is not a better experiment to answer the question I wanted to answer. I was interested in mass ratios, not cost. 

Edited by herbal space program
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herbal,

 Your method has been tried before and has shown similar results to yours. It's a fine method for determining the effects of t/w on rockets that just go straight up, but is not applicable to boosters in a gravity turn. Try it again and follow a gravity turn.

Best,

-Slashy

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2 hours ago, GoSlash27 said:

herbal,

 Your method has been tried before and has shown similar results to yours. It's a fine method for determining the effects of t/w on rockets that just go straight up, but is not applicable to boosters in a gravity turn. Try it again and follow a gravity turn.

Best,

-Slashy

I have tried it, with the same rig carrying a 16t dead mass payload going to orbit, and doing best-of-three, what I've gotten so far is 0.31 at TWR 1.08, 0.34 at TWR 1.2, 0.35 at TWR 1.3, 0.36 at TWR 1.4, and 0.37 at TWR 1.67.  But I'm not ready to stand by that result yet, because every trip to orbit is a little different.  Exactly how you execute your gravity turn is a very important  and rather inconsistent variable if you're flying by hand, even with my very experienced hands, and it's also easy to fall victim to unconscious bias if you have a personal interest in the outcome. Also, single-engine stages with dVs of >2km/s are really never the way I do things. I always set my launch stacks up so that  I start off with a bang, getting to a ~200m/s rate-of-climb at a brisk TWR, but then I'm also dropping radially mounted boosters frequently, to shed excess dry mass and keep my TWR in the 1.4-2.0 range until I have gotten my Ap to ~50km. After that, I'll generally use my high-ISP, low TWR transfer stage to get the rest of the way to orbit. I'll also often throttle down temporarily during the middle of the gravity turn to minimize cosine losses from boosting below my prograde vector. It's very hard to create a consistent testing platform with all those variables in play.

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6 minutes ago, herbal space program said:

I have tried it, with the same rig carrying a 16t dead mass payload going to orbit, and doing best-of-three, what I've gotten so far is 0.31 at TWR 1.08, 0.34 at TWR 1.2, 0.35 at TWR 1.3, 0.36 at TWR 1.4, and 0.37 at TWR 1.67.  But I'm not ready to stand by that result yet, because every trip to orbit is a little different.  Exactly how you execute your gravity turn is a very important  and rather inconsistent variable if you're flying by hand, even with my very experienced hands, and it's also easy to fall victim to unconscious bias if you have a personal interest in the outcome. Also, single-engine stages with dVs of >2km/s are really never the way I do things. I always set my launch stacks up so that  I start off with a bang, getting to a ~200m/s rate-of-climb at a brisk TWR, but then I'm also dropping radially mounted boosters frequently, to shed excess dry mass and keep my TWR in the 1.4-2.0 range until I have gotten my Ap to ~50km. After that, I'll generally use my high-ISP, low TWR transfer stage to get the rest of the way to orbit. I'll also often throttle down temporarily during the middle of the gravity turn to minimize cosine losses from boosting below my prograde vector. It's very hard to create a consistent testing platform with all those variables in play.

Most of us do it the same way you do. Just model it as a standardized booster stage. I aim for 30° pitch, 25 km altitude, and around 750 m/sec. That's generally 1,800 m/sec.

 And you don't want to use a fixed mass and adjust the throttle to get the different t/w ratios. You want to add mass to achieve the t/w ratios. Otherwise *obviously* the higher t/w will perform better.

Best,

-Slashy

Edited by GoSlash27
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8 minutes ago, GoSlash27 said:

Most of us do it the same way you do. Just model it as a standardized booster stage. I aim for 30° pitch, 25 km altitude, and around 750 m/sec. That's generally 1,800 m/sec.

Best,

-Slashy

Wait, you're only going 750m/s at 25km in what you consider an optimal run to orbit?  I'm generally going closer to 1,200m/s by the time I'm at that altitude, and if things are going to plan I'm usually at closer to 20° pitch by then. I'll actually throw away runs where my prograde marker is still at  30 degrees at 25km, because I know I'll end up with less dV on orbit that way.

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1 minute ago, herbal space program said:

Wait, you're only going 750m/s at 25km in what you consider an optimal run to orbit?  I'm generally going closer to 1,200m/s by the time I'm at that altitude, and if things are going to plan I'm usually at closer to 20° pitch by then. I'll actually throw away runs where my prograde marker is still at  30 degrees at 25km, because I know I'll end up with less dV on orbit that way.

Yes, but as we have already established "dV on orbit" is a useless marker for lifter efficiency. What matters for the end user is cost per tonne (in career), payload fraction, reliability, and ease of use for all cases including career. If you run a hot launcher blazing through the stratosphere, you'll get to orbit with minimum dV expended, but no practical gains for having done it and a launcher that is likely as not to explode or flip on staging and mediocre payload fraction.

 To be very clear, yes: Launchers that are optimized for minimum dV to orbit *will* benefit from cleaner aerodynamics and higher t/w.

Best,

-Slashy

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...And having said all of that, I actually do agree that a TWR of 1.4 at launch for Kerbin rocket lifters is a good starting point.  That was after all what I suggested as a minimum value  at the beginning of this thread. I just don't think that lower than that confers any benefit except for pure SRB stages, and that higher than that with the current aero, especially in the first 30-60 seconds, can have real benefits beyond that if what you are after is ultimate payload fraction to orbit.

Just now, GoSlash27 said:

Yes, but as we have already established "dV on orbit" is a useless marker for lifter efficiency. What matters for the end user is cost per tonne (in career), payload fraction, reliability, and ease of use for all cases including career. If you run a hot launcher blazing through the stratosphere, you'll get to orbit with minimum dV expended, but no practical gains for having done it and a launcher that is likely as not to explode or flip on staging and mediocre payload fraction.

 To be very clear, yes: Launchers that are optimized for minimum dV to orbit *will* benefit from cleaner aerodynamics and higher t/w.

Best,

-Slashy

"dV to orbit" and "dV on orbit" are different things. The latter, which is what I was talking about, is essentially proportional to payload fraction. 

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Just now, herbal space program said:

...And having said all of that, I actually do agree that a TWR of 1.4 at launch for Kerbin rocket lifters is a good starting point.  That was after all what I suggested as a minimum value  at the beginning of this thread. I just don't think that lower than that confers any benefit except for pure SRB stages, and that higher than that with the current aero, especially in the first 30-60 seconds, can have real benefits beyond that if what you are after is ultimate payload fraction to orbit.

And I repeat: Lower than that *can* actually have certain benefits, particularly for stages that employ (even partially) SRBs. This is mainly for aero stability issues, but also overspeeding at the end of the boost stage and inherent aerodynamic instability during staging into the sustainer phase.

 As a pure "efficiency" measure, you are correct in that going much below 1.4 will only hurt you, but if you want cheap you'll probably have SRBs involved and it's probably wise to rein it in a bit. Other than that... it's a 'quality of life' improvement.

Best,

-Slashy

9 minutes ago, herbal space program said:

"dV to orbit" and "dV on orbit" are different things. The latter, which is what I was talking about, is essentially proportional to payload fraction. 

It's not proportional, though. Literally. It's inverse logarithmic. You can saddle the same engine with more payload and get it (and the attendant fuel) up there at a more leisurely pace for less cash. Up to a point...

Best,

-Slashy

 

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7 minutes ago, GoSlash27 said:

As a pure "efficiency" measure, you are correct in that going much below 1.4 will only hurt you, but if you want cheap you'll probably have SRBs involved and it's probably wise to rein it in a bit. Other than that... it's a 'quality of life' improvement.

I will definitely admit that the higher your starting TWR and the concomitant mid-atmosphere aero forces go, the more your flying skills become essential to achieving the desired outcome. I have spent thousands of hours honing those skills in this silly game, so maybe my perception of that type of difficulty is distorted.

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Just now, herbal space program said:

I will definitely admit that the higher your starting TWR and the concomitant mid-atmosphere aero forces go, the more your flying skills become essential to achieving the desired outcome. I have spent thousands of hours honing those skills in this silly game, so maybe my perception of that type of difficulty is distorted.

herbal,

 I was just about to comment on that difference, but I wasn't going to use an inflammatory word like 'distorted'. :D

Yes, for a person that launches like you do, higher t/w is beneficial. For the lazy buggers like myself tho' (and I daresay most players), the higher t/w is actually a hinderance to our efficiency and an even bigger 'ease of use' nuisance. We generally build our rockets to fly themselves after the initial gravity kick while we go grab a beer. :D

 We find that our rockets are actually *more* efficient in that profile with lower t/w.

So just 2 different perspectives. ;)

Best,

-Slashy

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Here are some old plots I made years ago that are relevant to this question. They are a figure of merit (payload fraction x dv) on the x axis by dv on the y axis for various engines. 

WBL0Z7H.jpg

This first one shows that for a sustainer stage (t/w of 0.7), the Swivel can never compete with a dedicated vacuum engine in terms of payload fraction or dv. It has an optimal dv range of 1500-2700 m/sec.

EGyXRip.jpg

This one compares the Poodle to the Aerospike as an interplanetary stage (0.5 t/w) and shows virtually identical performance. Ideal dv range would be between 1600 and 3000 m/sec.

llyIYU9.jpg

Same comparison as a sustainer stage, same result more or less. 

vps0Uko.jpg

LV-N and Dawn compared for an interplanetary stage at 0.5g. Note that the Dawn's mass calculation doesn't include the mass of equipment required to generate and store the electricity, which is substantial. Ideal stage size for the LV-N in this regime is between 2700 and 5000 m/sec, while the Dawn is (theoretically) best between 3300 and 6700 m/sec.

u37Kf8t.jpg

The LV-909 vs LV-N as a sustainer stage. Generally, a sustainer will have 1,600 m/sec to attain LKO, so this illustrates how much further than that you need to go before it's more efficient to use the LV-N. 

Finally...

wPnRPCm.jpg

The dramatic difference between a chemical vacuum engine vs the Nerv for interplanetary travel.

These charts give a rough idea of how big a stage should be for optimal efficiency, and how much leeway you have... which is quite broad.

HTHs,

-Slashy

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39 minutes ago, he77789 said:

Wouldn't say jet engines with low TWR be better than a high thrust low efficiency SRB in the atmosphere?

Certainly... but that's a apples/ barn owls comparison, especially when you factor in wings. We're just talking ballistic rockets on a gravity turn. Jet engines get their efficiency gains from their high Isp, not their low twr.

Best,

-Slashy

 

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45 minutes ago, he77789 said:

Wouldn't say jet engines with low TWR be better than a high thrust low efficiency SRB in the atmosphere?

As Slashy said, we were just talking about the stock LF/O lifting engines, and I was specifically talking about what TWR at launch makes for the best payload fraction to orbit.  Jet engines are another beast entirely because of their insanely higher ISPs, which let you give up a whole lot of impulse to gravity early on without it making a very big dent in your fuel supply.  The other thing about the high-end jet engines however is that they also get a much more favorable TWR when they are operating at high speeds, comparable to the best LF/O engine TWRs, and it's really that phase of their profile  (i.e. from ~380 m/s to  ~1,400 m/s) that does 90% of the work in the air-breathing part of your run.  All the low-TWR stuff at the beginning is just about getting you to that point.

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1 hour ago, GoSlash27 said:

Here are some old plots I made years ago that are relevant to this question. They are a figure of merit (payload fraction x dv) on the x axis by dv on the y axis for various engines.

I think you have those backwards, especially considering the labelling of the later graphs.  On the horizontal x-axis, you have delta-V.  On the vertical y-axis, you have the figure of merit, payload fraction multiplied by delta-V.

This is the first time I've seen that figure of merit, payload fraction multiplied by delta-V.  Why is it the value desired to be maximized?

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2 hours ago, Jacke said:

I think you have those backwards, especially considering the labelling of the later graphs.  On the horizontal x-axis, you have delta-V.  On the vertical y-axis, you have the figure of merit, payload fraction multiplied by delta-V.

This is the first time I've seen that figure of merit, payload fraction multiplied by delta-V.  Why is it the value desired to be maximized?

Thanks for the correction :)

 The two things desired for any stage are dv and payload fraction. As one goes up, the other goes down. I just multiply them together to give equal weighting (double the dv is just as desirable as double the payload fraction).

 Others may prefer to combine them differently, say by raising e to the power of dv to express them both in linear terms.

Best,

-Slashy 

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