Spacecraft economy of scale

[DarkenedOne]

Something I have been wondering recently is how much can the cost of sending people into space be reduced by using larger spacecraft.  Now lets set aside the problems of investment, cost, and etc. for now.

It seems that in practically every transport sector there exist for a number of both physics and economics reasons.  Planes, ships, cars, and etc. all get more cost effective as they get bigger (assuming full use).   


The Soyuz only carried 3 people, and able to deliver them to the ISS at about $30 million.  Now the Dragon and the CST-100 are being designed to carry 7 people.  As I understand the Dragon will be able to cost less than the $30 million price tag of the Soyuz. 

In the satellite launch sector we can see that effect of economy of scale in the fact that the cost going from the Falcon 1e to the F9H is an order of magnitude.

Personally I believe that an order of magnitude reduction in cost could come from increasing the payload (in humans) of spacecraft assuming no new technology. 

[Robotbeat]

Quantity is just as (or perhaps more) important. There is no physics holding reusable launch vehicles (and spacecraft) back, just quantity of flights.

Best of both worlds would be large reusable launch vehicles flying several times a day per vehicle with fleets all over the world.

[DarkenedOne]

Quantity is just as (or perhaps more) important. There is no physics holding reusable launch vehicles (and spacecraft) back, just quantity of flights.

Best of both worlds would be large reusable launch vehicles flying several times a day per vehicle with fleets all over the world.

Physics are even less of an impediment with large rockets.  Larger rockets have higher mass fractions and reduced drag per unit mass.

But you are right that it is only one aspect of many.  I am saying though that this one aspect can result in an order of magnitude cost reduction. 

[Robotbeat]

Quantity is just as (or perhaps more) important. There is no physics holding reusable launch vehicles (and spacecraft) back, just quantity of flights.

Best of both worlds would be large reusable launch vehicles flying several times a day per vehicle with fleets all over the world.

Physics are even less of an impediment with large rockets.  Larger rockets have higher mass fractions and reduced drag per unit mass.

But you are right that it is only one aspect of many.  I am saying though that this one aspect can result in an order of magnitude cost reduction. 

There are a host of other problems with large rockets, especially with large engines. People make a simplifying assumption that bigger is always better, when that is most certainly not always the case. For instance, the taller your rocket (same width, propellant density, pressure), then the wider your throat has to be for the same T/W ratio. At some point, it becomes ridiculous. Saturn V's engines had no choice but to be high pressure because of that. I've heard estimates that cost for building a rocket engine is proportional to the chamber pressure to the fourth power or something like that.

Plus, large rockets generally mean even larger ground infrastructure costs. This is true for both rockets and spacecraft. There is, for instance, no real ground infrastructure in place for processing payloads larger than EELV-class.

Somewhere, I have a very long list of pros and cons of scaling up or scaling down rockets. Another is that if you have a big engine, the bell nozzle ends up ridiculously huge, which has structural issues and can cause mass to increase disproportionately compared to smaller engines.

Something real important to keep in mind:
"Akin's Laws of Spacecraft Design"
http://spacecraft.ssl.umd.edu/akins_laws.html
"8. In nature, the optimum is almost always in the middle somewhere. Distrust assertions that the optimum is at an extreme point."

It also reminds me of one of Richard Feynmann's talks where he related a story about when he worked in a job which required him to pick out and buy a kind of gear. It turns out that the optimum number of gear teeth is somewhere in the middle of the catalog. Too few teeth, and the gear is more likely to break. Too many fine teeth are pretty expensive to produce, so the optimum is somewhere in the middle.

At some point with rockets (scaling either up or down), you get to a scaling relationship which just blows up on you, like the "cost proportional to the fourth power of pressure" relationship I showed earlier. That part of the equation is inconsequential at low pressures, is only moderately important at moderate pressures, but makes things very quickly unfeasible at higher pressures. Same thing if you try to scale down too far, where you run into "minimum gauge" issues.

One consequence of the issue of the chamber pressure and throat diameter limitations of big rockets is that they tend to have low T/W ratios, which means much higher gravity losses. So while, yes, drag losses are much less, that is often dwarfed by the increase in gravity losses. The optimum is somewhere in the middle.

[QuantumG]

I remember hearing Jeff Greason at ISDC dismiss building a vehicle as big as Space Ship Two because there's no proven market, and so much immaturity when it comes to RLV design. SS2 is tiny by your definition. Just like the aircraft industry, slow steady growth is the way to get to mature designs and high density seating.

[Robotbeat]

Quantity is just as (or perhaps more) important. There is no physics holding reusable launch vehicles (and spacecraft) back, just quantity of flights.

Best of both worlds would be large reusable launch vehicles flying several times a day per vehicle with fleets all over the world.

Physics are even less of an impediment with large rockets...

As a physicist that has read several spacecraft systems engineering and rocket science textbooks, I strongly disagree.

[go4mars]

the taller your rocket (same width, propellant density, pressure), then the wider your throat has to be for the same T/W ratio. At some point, it becomes ridiculous. Saturn V's engines had no choice but to be high pressure because of that. I've heard estimates that cost for building a rocket engine is proportional to the chamber pressure to the fourth power or something like that...  That part of the equation is inconsequential at low pressures, is only moderately important at moderate pressures, but makes things very quickly unfeasible at higher pressures. One consequence of the issue of the chamber pressure and throat diameter limitations of big rockets is that they tend to have low T/W ratios, which means much higher gravity losses. So while, yes, drag losses are much less, that is often dwarfed by the increase in gravity losses.

Aside from ground handling/infrastructure, this suggests to me that the ideal 1st stage would be larger diameter and shorter than what is common.  Is that correct? 

[Robotbeat]

the taller your rocket (same width, propellant density, pressure), then the wider your throat has to be for the same T/W ratio. At some point, it becomes ridiculous. Saturn V's engines had no choice but to be high pressure because of that. I've heard estimates that cost for building a rocket engine is proportional to the chamber pressure to the fourth power or something like that...  That part of the equation is inconsequential at low pressures, is only moderately important at moderate pressures, but makes things very quickly unfeasible at higher pressures. One consequence of the issue of the chamber pressure and throat diameter limitations of big rockets is that they tend to have low T/W ratios, which means much higher gravity losses. So while, yes, drag losses are much less, that is often dwarfed by the increase in gravity losses.

Aside from ground handling/infrastructure, this suggests to me that the ideal 1st stage would be larger diameter and shorter than what is common.  Is that correct? 

Not necessarily. What's "ideal" depends on an enormous number of systems engineering factors that need to be carefully weighed and evaluated.

I was just pointing out that at an extreme, if you keep chamber pressure constant, you have to start making your rocket fatter instead of just taller... Things get complicated.

[JohnFornaro]

Somewhere, I have a very long list of pros and cons of scaling up or scaling down rockets.

As is well known, SLS will scale to 130 tons to orbit.  Somewhere on the forum is a thread where they speculate on 200 to 400 tons to orbit.  Would that be at the middle of this theoretical range?  Or would 1000 tons be the middle?  About where is that middle range?

[DarkenedOne]

There are a host of other problems with large rockets, especially with large engines. People make a simplifying assumption that bigger is always better, when that is most certainly not always the case. For instance, the taller your rocket (same width, propellant density, pressure), then the wider your throat has to be for the same T/W ratio. At some point, it becomes ridiculous. Saturn V's engines had no choice but to be high pressure because of that. I've heard estimates that cost for building a rocket engine is proportional to the chamber pressure to the fourth power or something like that.

Never heard of this being a problem.  Your welcome to provide a link.

Plus there is nothing that stops you from using many small engines to propel the rocket. 

Plus, large rockets generally mean even larger ground infrastructure costs. This is true for both rockets and spacecraft. There is, for instance, no real ground infrastructure in place for processing payloads larger than EELV-class.

True in all transportation industries.  However infrastructure generally has high capital, but low recurring costs.

Somewhere, I have a very long list of pros and cons of scaling up or scaling down rockets. Another is that if you have a big engine, the bell nozzle ends up ridiculously huge, which has structural issues and can cause mass to increase disproportionately compared to smaller engines.

"increase disproportionately compared to smaller engines" - generally this is not the case with engines in general. 

Something real important to keep in mind:
"Akin's Laws of Spacecraft Design"
http://spacecraft.ssl.umd.edu/akins_laws.html
"8. In nature, the optimum is almost always in the middle somewhere. Distrust assertions that the optimum is at an extreme point."

It also reminds me of one of Richard Feynmann's talks where he related a story about when he worked in a job which required him to pick out and buy a kind of gear. It turns out that the optimum number of gear teeth is somewhere in the middle of the catalog. Too few teeth, and the gear is more likely to break. Too many fine teeth are pretty expensive to produce, so the optimum is somewhere in the middle.

At some point with rockets (scaling either up or down), you get to a scaling relationship which just blows up on you, like the "cost proportional to the fourth power of pressure" relationship I showed earlier. That part of the equation is inconsequential at low pressures, is only moderately important at moderate pressures, but makes things very quickly unfeasible at higher pressures. Same thing if you try to scale down too far, where you run into "minimum gauge" issues.

One consequence of the issue of the chamber pressure and throat diameter limitations of big rockets is that they tend to have low T/W ratios, which means much higher gravity losses. So while, yes, drag losses are much less, that is often dwarfed by the increase in gravity losses. The optimum is somewhere in the middle.

I highly doubt this is the case, and if it is it would be the first case in transportation I know of where bigger vehicles did not result in lower costs. 

Secondly you are clearly not evaluating the greatest contributor to cost, and that is labor.  An Airbus 380 carries at about 4 times as many people as the Boeing 737, yet both are crewed by 2 people.  In the same way launch teams do not scale linearly with the rocket.  I do not believe that the size of manufacturing teams scale linearly either.

[Robotbeat]

You are thinking about this wrong. To start: Why aren't there ships ten times the largest ship ever? Obviously, it'd be a lot cheaper according to your simplistic thinking, right? So why isn't it done? Are people just stupid?


Another HUGE issue is sound energy, which scales very quickly with rocket take-off thrust. You put the payload at serious risk of damage, not to mention the ground infrastructure and the rocket itself.

And no links are needed about the T/W ratio issue, because it's basic rocket physics. You've read your Sutton, right?

[Robotbeat]

...
I highly doubt this is the case, and if it is it would be the first case in transportation I know of where bigger vehicles did not result in lower costs.

Spruce Goose. 

Secondly you are clearly not evaluating the greatest contributor to cost, and that is labor.  An Airbus 380 carries at about 4 times as many people as the Boeing 737, yet both are crewed by 2 people.  In the same way launch teams do not scale linearly with the rocket.  I do not believe that the size of manufacturing teams scale linearly either.

Rockets are pilot-less.

Larger rockets tend to have a harder time getting a high launch rate. Fundamentally, this is for the same reason that motorcycle engines can operate at tens of thousands of RPMs while giant ship motors operate at hundreds of RPMs. Thus, the motorcycle engines can have a far higher specific power than the ship motors, because the same volume can be used many times more per second to produce power.

Maintaining the infrastructure is expensive, too. Perhaps if large and small vehicles could somehow get the same launch rate, you'd be right, but they can't and won't (partially because of physical limitations... large objects have a lower natural frequency... moving them around must be done at a slower cycle rate). Thus, because small launch vehicles are capable of a higher launch rate, you can get proportionately a lot more use out of that infrastructure than the big launch vehicles. Your capital investment gets proportionately a lot more use.

Heck, even moving the vehicles can take hours just for the crawler (or whatever) to move back and forth.

As I said, the equations of scale meet in the middle somewhere. They always do. Not too small, not too big.

Another issue is boarding (or payload integration) time... It takes a lot longer to board an A380 than it does a bunch of smaller vehicles, since you can do the smaller ones in parallel across multiple terminals.

[DarkenedOne]

You are thinking about this wrong. To start: Why aren't there ships ten times the largest ship ever? Obviously, it'd be a lot cheaper according to your simplistic thinking, right? So why isn't it done? Are people just stupid?

1.  The ship building industry is limited by the size of the shipyards, ports, and canals.  That why they use terms like Panamax class to designate ship size.  Same things with the Airline industry where the A380 is as big as most airports can handle.  Same thing with trucks which are limited in both size and weight by what the roads can handle.

2.  While physics allows bigger vehicles to be able to transport matter at a lower cost per unit, economics states they also cost more to develop and development is risky. 

3.  Lastly vehicles grow to the size they need to most efficiently serve demand.  It would make no sense to design a 30 person space capsule right now when the only destination in space can only handle 7.  That is why all the new human launch vehicles going to LEO are being designed to handle 7 people.

Another HUGE issue is sound energy, which scales very quickly with rocket take-off thrust. You put the payload at serious risk of damage, not to mention the ground infrastructure and the rocket itself.

I believe that problem has already been solved by Apollo and the Shuttle programs.

Look I am just trying to say I wonder what the economics for a space that could take 50 people into space at a time rather than the current 3. 

[Robotbeat]

Without really much more infrastructure, you can launch 7 times more often with the smaller vehicles to get the same passenger numbers.

The ideal spacecraft size, like you said, depends on the market size.

But an important thing to consider is that a reusable launch vehicle offers an enormous improvement in potential safety, since you can afford 10-30 times more test flights before operations. This is partly why you don't see enormous disposable airplanes... Well, that and it's a heck of a lot cheaper at higher flight rates (which is what you're talking about).

I'm convinced that in the 10-30 mT payload range and 400+ mT or more in LEO per year, adding reusability (starting with first stage) would have a FAR greater impact on reducing costs than increasing vehicle size (since you're already clear of the worst effects of minimum-gauge and large drag that affect small vehicles disproportionately). (Rule of thumb is partial reusability has no leg to stand on under 8 flights per year and full reusability needs at least 40-50 flights per year.)

Anything much larger would be more than what our existing spacecraft-related ground infrastructure can handle... You stop being able to fit under bridges, etc. Thus, there's a disproportionate increase in infrastructure cost if you scale up in that direction too much.

[go4mars]

Not necessarily. What's "ideal" depends on an enormous number of systems engineering factors that need to be carefully weighed and evaluated.

I was just pointing out that at an extreme, if you keep chamber pressure constant, you have to start making your rocket fatter instead of just taller... Things get complicated.

So Sea Dragon, UR-700M, and other "tall" rocket designs are unlikely compared to shorter, larger diameter ones (for payloads in the 500+ tonnes to LEO range)?  Is that a fair generalization?

Spruce Goose. 

It never got the follow-on contract.     
Shipping, cruise ships, and tankers are basically getting stopped from growing by constraints of average port size. 

And it seems to me that eventually, reusable "busses" to space would be cheaper per person than reusable "cars or motorcycles".