### Author Topic: What are the most and least efficient rockets?  (Read 18946 times)

#### Hyperion5

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##### What are the most and least efficient rockets?
« on: 02/04/2013 06:25 pm »
Awhile back, for a class project, I dug into figuring out what the most efficient rockets were by payload mass fraction.  Although I surveyed only a limited field, I was surprised to find the biggest rockets were almost always the most efficient.  The bigger the rocket, the better overall it tended to do.  For instance, my chart was topped by large rockets like the Saturn V, Energia and Falcon Heavy, itself more efficient than the smaller Falcon 9.  So I've always wondered, if one did a comprehensive chart of rockets, which wind up top, and are larger rockets usually more efficient if you control for differing propellants?  If so, is there a law of physics that would explain bigger rockets being more efficient?

If you're doing a list, please state each rocket's payload mass fraction in percent and list off the propellants it uses if you can.  One last thing I noticed was that over time, the R-7 family has steadily gotten ever more efficient.  Is this trend seen everywhere over time or have we plateaued?

#### mlindner

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##### Re: What are the most and least efficient rockets?
« Reply #1 on: 02/04/2013 07:10 pm »
Awhile back, for a class project, I dug into figuring out what the most efficient rockets were by payload mass fraction.  Although I surveyed only a limited field, I was surprised to find the biggest rockets were almost always the most efficient.  The bigger the rocket, the better overall it tended to do.  For instance, my chart was topped by large rockets like the Saturn V, Energia and Falcon Heavy, itself more efficient than the smaller Falcon 9.  So I've always wondered, if one did a comprehensive chart of rockets, which wind up top, and are larger rockets usually more efficient if you control for differing propellants?  If so, is there a law of physics that would explain bigger rockets being more efficient?

If you're doing a list, please state each rocket's payload mass fraction in percent and list off the propellants it uses if you can.  One last thing I noticed was that over time, the R-7 family has steadily gotten ever more efficient.  Is this trend seen everywhere over time or have we plateaued?

There isn't a "law" of physics regarding this AFAIK. I believe it's just that when you double the amount of fuel mass, you don't double the amount of structure mass. The fuel volume (and thus the mass) scales roughly cubicly while the structure mass scales roughly quadratically. Thus as you get larger and larger rockets your fuel mass faction gets better and better, thus increasing your payload mass faction. The ideal rocket is a payload sitting on top of a giant lump of fuel.

#### Celebrimbor

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##### Re: What are the most and least efficient rockets?
« Reply #2 on: 02/04/2013 07:21 pm »
Awhile back, for a class project, I dug into figuring out what the most efficient rockets were by payload mass fraction.  Although I surveyed only a limited field, I was surprised to find the biggest rockets were almost always the most efficient.  The bigger the rocket, the better overall it tended to do.  For instance, my chart was topped by large rockets like the Saturn V, Energia and Falcon Heavy, itself more efficient than the smaller Falcon 9.  So I've always wondered, if one did a comprehensive chart of rockets, which wind up top, and are larger rockets usually more efficient if you control for differing propellants?  If so, is there a law of physics that would explain bigger rockets being more efficient?

If you're doing a list, please state each rocket's payload mass fraction in percent and list off the propellants it uses if you can.  One last thing I noticed was that over time, the R-7 family has steadily gotten ever more efficient.  Is this trend seen everywhere over time or have we plateaued?

There isn't a "law" of physics regarding this AFAIK. I believe it's just that when you double the amount of fuel mass, you don't double the amount of structure mass. The fuel volume (and thus the mass) scales roughly cubicly while the structure mass scales roughly quadratically. Thus as you get larger and larger rockets your fuel mass faction gets better and better, thus increasing your payload mass faction. The ideal rocket is a payload sitting on top of a giant lump of fuel.

I think this also affects the comparative effect of drag.  This is related to the problem of "What is the smallest rocket that could launch a paperclip into orbit?"
« Last Edit: 02/04/2013 07:24 pm by Celebrimbor »

#### Robotbeat

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##### Re: What are the most and least efficient rockets?
« Reply #3 on: 02/04/2013 07:24 pm »
Look at IMLEO to take-off mass ratio. That would tilt the deck in favor of high-Isp. If you look at IMLEO to take-off volume ratio, it'd tilt the deck in favor of lower-Isp but much denser propellants.
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#### go4mars

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##### Re: What are the most and least efficient rockets?
« Reply #4 on: 02/04/2013 07:24 pm »
Surface Area to Volume ratio is smaller for bigger containers of the same shape.  Also, there are some parts that can't be as realistically miniturized.  If every rocket needs a 'thingamabob' which can't be made much smaller, due to manufacturing accuracy constraints or physics, then the ratio of it to the fuel is smaller for bigger rockets.

All the silverbacks on this forum keep saying "tradeoffs".  So larger diameter tanks means they can be shorter (lower pressure differential inside) which is less structure and arguably easier handling, but then there is a lot more area to punch through the air, but the larger diameter for a "max height (if there were such a thing)" would allow more fuel to push air with...    and on it goes.

But yes, bigger is better.  Have a look at Truax expectations for Sea Bea/Sea Horse/ (and particularly Excalibur/Sea Dragon).
« Last Edit: 02/04/2013 07:41 pm by go4mars »
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#### R7

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##### Re: What are the most and least efficient rockets?
« Reply #5 on: 02/04/2013 07:25 pm »
The fuel volume (and thus the mass) scales roughly cubicly while the structure mass scales roughly quadratically. Thus as you get larger and larger rockets your fuel mass faction gets better and better, thus increasing your payload mass faction.

Incorrect. Propellant tanks are pressure vessels, mass directly proportional to volume.

See http://en.wikipedia.org/wiki/Pressure_vessel#Scaling

But you were onto something with cube/square law. Bigger vehicles benefit from it as lesser drag losses. Drag proportional to area, mass volume, then apply F = ma.

edit: oh well, several beat me to the cube/square thing..

But SeaDragon is interesting case, it was actually so big that the design took advantage of dynamic head during acceleration in fluid columns of several tens of meters high! Considerable pressure differential in the tank, upper wall sections were thinner than lower etc.
« Last Edit: 02/04/2013 07:31 pm by R7 »

#### Hyperion5

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##### Re: What are the most and least efficient rockets?
« Reply #6 on: 02/04/2013 08:44 pm »
Awhile back, for a class project, I dug into figuring out what the most efficient rockets were by payload mass fraction.  Although I surveyed only a limited field, I was surprised to find the biggest rockets were almost always the most efficient.  The bigger the rocket, the better overall it tended to do.  For instance, my chart was topped by large rockets like the Saturn V, Energia and Falcon Heavy, itself more efficient than the smaller Falcon 9.  So I've always wondered, if one did a comprehensive chart of rockets, which wind up top, and are larger rockets usually more efficient if you control for differing propellants?  If so, is there a law of physics that would explain bigger rockets being more efficient?

If you're doing a list, please state each rocket's payload mass fraction in percent and list off the propellants it uses if you can.  One last thing I noticed was that over time, the R-7 family has steadily gotten ever more efficient.  Is this trend seen everywhere over time or have we plateaued?

There isn't a "law" of physics regarding this AFAIK. I believe it's just that when you double the amount of fuel mass, you don't double the amount of structure mass. The fuel volume (and thus the mass) scales roughly cubicly while the structure mass scales roughly quadratically. Thus as you get larger and larger rockets your fuel mass faction gets better and better, thus increasing your payload mass faction. The ideal rocket is a payload sitting on top of a giant lump of fuel.

Found one!

http://en.wikipedia.org/wiki/Square-cube_law

The square-cube law (or cube-square law) is a mathematical principle, applied in a variety of scientific fields, which describes the relationship between the volume and the area as a shape's size increases or decreases. It was first described in 1638 by Galileo Galilei in his Two New Sciences.

This principle states that, as a shape grows in size, its volume grows faster than its area. When applied to the real world this principle has many implications which are important in fields ranging from mechanical engineering to biomechanics. It helps explain phenomena including why large mammals like elephants have a harder time cooling themselves than small ones like mice, and why there are fundamental limits to the size one can build a sand castle.The square-cube law (or cube-square law) is a mathematical principle, applied in a variety of scientific fields, which describes the relationship between the volume and the area as a shape's size increases or decreases. It was first described in 1638 by Galileo Galilei in his Two New Sciences.

This principle states that, as a shape grows in size, its volume grows faster than its area. When applied to the real world this principle has many implications which are important in fields ranging from mechanical engineering to biomechanics. It helps explain phenomena including why large mammals like elephants have a harder time cooling themselves than small ones like mice, and why there are fundamental limits to the size one can build a sand castle.

I think that law just about sums up why rockets benefit from this.  As was noted, their surface area relative to their volume drops as they get bigger and bigger.  So their drag losses should be dropping relative to their liftoff mass as they get bigger.  But that really only explains part of it. For instance, it doesn't explain why rockets' propellant mass fractions steadily climb as they get bigger.  I was trying to think of things on a rocket that scale more virtuously than pressurized propellant tanks.  Engines should be one area.  Let's face it, it should be easier to get a higher t/w ratio on a bigger engine than a smaller one, shouldn't it?  Are there other things that don't scale linearly with a rocket's growth in mass?  Structural?  I would think avionics has to be one area for sure.  Do you really need 2X as heavy of avionics to fly a 2X heavier rocket?  I think not.

So, does anyone know what LV holds current payload mass fraction top spot right now?

#### R7

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##### Re: What are the most and least efficient rockets?
« Reply #7 on: 02/04/2013 09:07 pm »
Let's face it, it should be easier to get a higher t/w ratio on a bigger engine than a smaller one, shouldn't it?

Why?

I propose that there are at least two additional factors, not related to cube-square law, which enable bigger LVs to have larger payload fraction.

1. big, really big LVs like Saturn V and Energia were government projects with almost unlimited funding. Using more expensive but lighter material here and there made sense because target was maximum payload size, not necessarily best economy.

2. big LVs tend to use hydrogen.

#### Robotbeat

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##### Re: What are the most and least efficient rockets?
« Reply #8 on: 02/04/2013 09:12 pm »
There's also the "minimum gauge" issue. For instnact some point, machining smaller and smaller tubes becomes nearly impossible.

Also, while it is true that you can get more thrust/weight from a smaller engine ideally, a lot of practical matters (which can also be expressed sort of like scaling laws) get in the way. Also, larger chambers can be more efficient... But large structures buckle more easily than smaller ones of proportional dimensions.

I once made a huge list of all the different scaling laws I could think of relating to rockets.
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#### Hyperion5

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##### Re: What are the most and least efficient rockets?
« Reply #9 on: 02/04/2013 09:45 pm »
Let's face it, it should be easier to get a higher t/w ratio on a bigger engine than a smaller one, shouldn't it?

Why?

Well if you go too small you start running into issues of things like your turbopump taking up more and more of the engine's weight in percentage.  This is one reason why the thrust/weight ratio on an RD-160 (staged combustion kerolox engine of approx. 4,000 lbf) was 16.6.  If you use pressure-fed engines instead you will similarly see lower t/w ratios.  The best example of the scale making a difference is the difference between the t/w ratio on the Merlin series versus the pressure-fed Kestrel series.  Now at what point does scaling backfire on improving engines' t/w ratio figures, I don't know.  But there definitely is an advantage of upping the scale from small engines.

I propose that there are at least two additional factors, not related to cube-square law, which enable bigger LVs to have larger payload fraction.

1. big, really big LVs like Saturn V and Energia were government projects with almost unlimited funding. Using more expensive but lighter material here and there made sense because target was maximum payload size, not necessarily best economy.

Spacex uses some pretty light material in their rockets, namely lithium-aluminum alloy, and they're not exactly funded on anything close to that scale.

2. big LVs tend to use hydrogen.

Ah, but I found when you control for propellants, the trend of bigger is more efficient tends to hold.  The Saturn V beats a Saturn IB, a Falcon Heavy beats a Falcon 9, the Atlas V tends to beat its smaller predecessors and so on.  So it isn't just that the big LVs are using hydrogen.  Even when you have vehicles using no hydrogen, the maxim is generally true, though not always.

#### Robotbeat

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##### Re: What are the most and least efficient rockets?
« Reply #10 on: 02/04/2013 09:47 pm »
You can make a much shorter engine bell with a lower thrust (at same pressure) engine.

Also, thrust scales as throat area, not as chamber volume. Thus, to get a good expansion ratio, at some point your engine is too big and you have to make your base wider to fit your engine...
« Last Edit: 02/04/2013 09:49 pm by Robotbeat »
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#### Celebrimbor

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##### Re: What are the most and least efficient rockets?
« Reply #11 on: 02/05/2013 07:18 am »
The 'efficiency' that counts of course is economic efficiency. And then there is a maximum efficient rocket that is not simply so tall that the payload start in GEO .
« Last Edit: 02/05/2013 07:20 am by Celebrimbor »

#### R7

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##### Re: What are the most and least efficient rockets?
« Reply #12 on: 02/05/2013 11:27 am »
But there definitely is an advantage of upping the scale from small engines.

True, one being the behavior of characteristic length L*. Once injected into the CC the propellants need a small but finite time to properly combust, and that time does not scale with engine. With bigger CCs you eventually reach a point where the CC length equals L*, after that even bigger CCs need only to scale diameter, not length. Examples F-1 and SeaDragon engines, almost no throat. Combustion stability becomes more challenging though.

Quote
Spacex uses some pretty light material in their rockets, namely lithium-aluminum alloy, and they're not exactly funded on anything close to that scale.

SpaceX benefits from being a late entry in the game. A lot has changed since Saturns. For instance titanium was rare hush-hush strategic material in the 60s, now Joe 6Pack can order it online.

Quote
The Saturn V beats a Saturn IB, a Falcon Heavy beats a Falcon 9, the Atlas V tends to beat its smaller predecessors and so on.

Saturn V is not just scaled up Saturn IB. Major differences in first stage.

F-1 outperforms H-1 in overall Isp (don't be fooled by the similar sealevel figures, F-1's higher pc and area ratio inevitably takes the lead at higher altitudes)

Bundling several long but thinner tanks (8 Redstones and 1 Jupiter) weighs more than equal volume on one big tank. This seems to contradict the pressure vessel scaling law present earlier in this thread, but does not. There's a geometry based constant in the mass equation. Also support structures become more challenging with a tank cluster.

F9H performance awaits actual demonstration.

I'll rather leave Atlas details to Jim, but clearly they enjoy even more impressive first stage engine performance upgrades.

#### R7

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##### Re: What are the most and least efficient rockets?
« Reply #13 on: 02/05/2013 01:39 pm »
Also, thrust scales as throat area, not as chamber volume. Thus, to get a good expansion ratio, at some point your engine is too big and you have to make your base wider to fit your engine...

Excellent point. problem especially to pressure-fed systems (until/unless advancements in CNTs produce composite materials with silly high specific strengths, fingers crossed...)

Below Truax's view how to handle it in SeaDragon using second stage nozzle extension, which wraps around first stage until stage separation, then expands.

(from http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19880069339_1988069339.pdf)

« Last Edit: 10/02/2013 05:22 pm by R7 »

#### Hyperion5

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##### Re: What are the most and least efficient rockets?
« Reply #14 on: 02/05/2013 04:52 pm »

Saturn V is not just scaled up Saturn IB. Major differences in first stage.

F-1 outperforms H-1 in overall Isp (don't be fooled by the similar sealevel figures, F-1's higher pc and area ratio inevitably takes the lead at higher altitudes)

Bundling several long but thinner tanks (8 Redstones and 1 Jupiter) weighs more than equal volume on one big tank. This seems to contradict the pressure vessel scaling law present earlier in this thread, but does not. There's a geometry based constant in the mass equation. Also support structures become more challenging with a tank cluster.

F9H performance awaits actual demonstration.

I'll rather leave Atlas details to Jim, but clearly they enjoy even more impressive first stage engine performance upgrades.

I get your points, but the maxim of "bigger is more efficient" still seems to hold up when you look at the overall trend.  So yes, there are differences between the Saturn V and Saturn IB, but I'd bet my house you could make a Saturn V-class rocket more efficient in terms of payload mass fraction than something the size of a Saturn IB.  I think the best example of scaling up out there is seen in the upgrade from the Falcon 1 to Falcon 9.  Sure the Falcon 9's got a more efficient upper stage, but that alone doesn't explain just how much better the Falcon 9 is than its predecessor.

The Falcon 9 is only 8.26X heavier than its predecessor, yet it can carry a payload 20X heavier with only 10X the thrust.  Sure it benefits from a more efficient upper stage engine, but the Falcon 9 is testament to the benefits of scaling up rockets.  Much of the design architecture on the Falcon 1 was simply modified and improved upon for the Falcon 9.  In turn, we can even see the benefits of scaling up the Falcon 9 with the v1.1 upgrade.  Propellant mass fraction?  Improved.  Payload jumps 53% while gross mass jumps only 51%.  Some of that's due to more Isp, but it doesn't hurt when you've got more thrust per square meter of frontal area.  In essence, the Falcon 9 benefits and gets more efficient both in cost per kg & payload mass fraction when it gets bigger.

#### R7

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##### Re: What are the most and least efficient rockets?
« Reply #15 on: 02/06/2013 12:51 pm »
I'd bet my house you could make a Saturn V-class rocket more efficient in terms of payload mass fraction than something the size of a Saturn IB.

With similar clean sheet designs for both, of course. As said the cube/square and CC geometries favor bigger.

One more thing to the list: tank insulation (if you require it)
You don't need thicker insulation with bigger tanks so your insulation mass scales with area. Actually you could even reduce the thickness if you don't need the reduction in the relative boil-off rate.

#### Robotbeat

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##### Re: What are the most and least efficient rockets?
« Reply #16 on: 02/06/2013 02:13 pm »
I'd bet my house you could make a Saturn V-class rocket more efficient in terms of payload mass fraction than something the size of a Saturn IB.

With similar clean sheet designs for both, of course. As said the cube/square...favor bigger....
Not /universally/. Again, because thrust is proportional to throat area, as you scale up too big, you run into constraints forcing you to either increase chamber pressure or become a squat rocket (negating any further benefit to proportional drag).
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#### R7

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##### Re: What are the most and least efficient rockets?
« Reply #17 on: 02/06/2013 03:40 pm »

Not /universally/. Again, because thrust is proportional to throat area, as you scale up too big, you run into constraints forcing you to either increase chamber pressure or become a squat rocket (negating any further benefit to proportional drag).

True, I was responding to discussion of specific classes where that is not yet a problem. Advancements since F-1 mean that using existing high pressure engines (RD-family etc) you'll get into ludicrous big class before available thrust/area becomes serious problem.

#### Robotbeat

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##### Re: What are the most and least efficient rockets?
« Reply #18 on: 02/06/2013 04:49 pm »

Not /universally/. Again, because thrust is proportional to throat area, as you scale up too big, you run into constraints forcing you to either increase chamber pressure or become a squat rocket (negating any further benefit to proportional drag).

True, I was responding to discussion of specific classes where that is not yet a problem. Advancements since F-1 mean that using existing high pressure engines (RD-family etc) you'll get into ludicrous big class before available thrust/area becomes serious problem.
That is just an example. There are other scaling laws.

I was just pointing out that the scaling laws can cut both ways. And there lots of them.
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#### R7

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##### Re: What are the most and least efficient rockets?
« Reply #19 on: 02/07/2013 11:27 am »

I was just pointing out that the scaling laws can cut both ways. And there lots of them.

Indeed. I for one would be interested to see that list of scaling laws you mentioned. Is it on the forum somewhere?

Actually all support structures take a performance hit with scaling, struts/beams etc? Generally their load bearing capacity is proportional to cross sectional area, cubesquare leads to their mass growing faster than strength, no?