News Elon Musk wants to put millions of people on Mars.

[RGClark]

Who are these experts? How did they calculate their estimates? Citation please.

Elon Musk on SpaceX’s Reusable Rocket Plans.
By Rand Simberg
February 7, 2012 6:00 PM

"The payload penalty for full and fast reusability versus an expendable version is roughly 40 percent," Musk says. "[But] propellant cost is less than 0.4 percent of the total flight cost. Even taking into account the payload reduction for reusability, the improvement is therefore theoretically over a hundred times."
A hundred times is an incredible gain. It would drop cost for Musk’s Falcon Heavy rocket—a scaled-up version of the Falcon 9 that’s currently rated at $1000 per pound to orbit—to just $10. "That, however, requires a very high flight rate, just like aircraft," Musk says. "At a low flight rate, the improvement is still probably around 50 percent. For Falcon Heavy, that would mean a price per pound to orbit of less than $500." Falcon Heavy is particularly amenable to reuse of the first stage—the two outer cores in particular, because they separate at a much lower velocity than the center one, being dropped off early in the flight.
http://www.popularmechanics.com/sci...musk-on-spacexs-reusable-rocket-plans-6653023

That low estimate would also require engines reusable hundreds of times. There is an engine development program that promises rocket engines capable of 200 uses at lowered maintenance costs:

Rethinking engines.
March 8, 2007
Stephen J. Mraz

"We're lowering temperatures by about 400°F and replacing them with more mass flow," says Vivro. "And we still get higher pressures in the gases coming out of the hydrogen and oxidizer preburners. And high pressures and more mass in the combustion chamber translates into more thrust.
"As far as maintenance, we wanted to go from a complete rebuild of the engine between uses to more of a ‘wash the windshields, check the oil, kick the tires' kind of approach," says Vivro.
...
The IPD should last for 200 missions, with overhauls needed only every 100 missions.
http://machinedesign.com/article/rethinking-engines-0308

This is for a hydrogen-fueled engine though. I don't know if similar developments are planned for hydrocarbon-fueled engines.


Bob Clark

 

[N_Molson]

For the price of electricity, lots of forces I would assume including the price of coal and fuel oil since many electric plants are run on them.

It is much worse than that. Global economics involves a nearly-infinite number of interdependancies. The price of cacao in Brazil or the price of bretzels in Germany can affect it as well. Butterfly (and domino) effect.

 

[RisingFury]

That's about 80 times higher than the numbers I've seen. What's your kilojoules to orbit per kilo, and your price per kilowatt-hour(kwh) for electricity?

Bob Clark

Kilojules per kg to orbit were the theoretical minimum possible. I just assumed the payload magically pops into orbit without having to deal with air drag, gravitational losses, orbit corrections.

Electricity prices I grabbed off the net.

Sorry I ruined your day.

 

[T.Neo]

Assuming a cost of 10.6 US cents per kilowatt-hour cost of energy*;

Kinetic energy at 7500 m/s (LEO orbital velocity)= ~28 000 kJ = 7.8 kW*h = $0.83

Kinetic energy at 9500 m/s (generic launch dV to LEO)= ~45 000 kJ = 12.5 kW*h = $1.33

Energy released by Falcon 9 during launch;
Stage one;
Vac ISP = 311 seconds
Vac thrust = 690 kN
Thrust power per engine = 1052 MW
Thrust power in total (9 engines) = 9468 MW
Burn time = 170
Total thrust energy = 447 100 kW*h

Stage 2;
Vac ISP = 340 seconds
Vac thrust = 448 kN
Thrust power = 747 MW
Burn time = 375
Thrust energy = 77 810 kW*h

Total energy expended in main propulsion for the vehicle = 524 910 kW*h = $55 640

Assuming 10 ton payload for F9, that's $5.56 per kilogram.

I am not sure why RisingFury's values are higher than my own. I am not sure what methods he used or what he factored into his calculations, but itt may be that I simply did something wrong here.

Of course, rockets are not launched with electricity. They are launched with propellant. Going by propellant costs;

F9 uses about 484 metric tons of propellant (this is not counting unburnt residuals). To my knowledge, the mixture ratio of the Merlin engines is unpublished. However, assuming a mixture ratio of 2.3**, that would be 338.8 tons of LOX and 145.2 tons of RP-1.

This page states that in the 1980s, kerosene cost $0.20/kg, and that in 1956, 24 years before, it cost only $0.05/kg (a growth rate of about 5.8% per year). It states that in the 1980s, NASA was paying $0.08/kg for LOX, and in 1959, LOX cost $0.04/kg (a growth rate of 3.3% over 21years).

Extrapolating this to today (32 years after 1980), we get a cost of $0.23/kg for LOX and $1.20/kg for RP-1. Note that this may be an underestimation.

Using these figures, we get a propellant cost of $252 000 for Falcon 9. Assuming a payload to LEO of 10 000 kg, that's $25/kg (over four times the highest figure based on energy and electricity costs).

The thing is, there is far more to launching rockets than propellant costs. Launch vehicles are very complex, demanding machines, who require a lot of people with a lot of expertise to operate. You can attempt to increase efficiency, for example through reusability, but getting the overall cost down to a few multiples of the propellant cost is a very difficult process.

* Average price for electricity for use in transportation in the United States.
** Similar to the F-1 engine value of 2.27.

Sources:
Prices and factors affecting prices of electricity - US Energy Information Administration
Space Launch Report - Falcon 9
Merlin 1D - Wikipedia
LOX/Kerosene - Astronautix
F-1 - Wikipedia

 

[RisingFury]

Found an error in your calculation, T.Neo:
Your initial energy estimate is not correct. I think you did not include mass into your calculation.

E = 0.5 * m * v^2. If I punch in 0.5 * (7600)^2 into my calculator, I get 28 800 kj / kg, which is what you displayed. For a 10 ton payload, you need to multiply that by 10 000.



My calculation:

K - cost per kW*h

Cos of energy:
C = K * E

Cost of energy per unit mass:
C/m = K * E/m

Energy per unit mass:
E/m = M*G*(1/(2 * (Re + h)) + h/R^2)

Cost:
C = K*M*G*(1/(2 * (Re + h)) + h/R^2)

Re - radius of Earth
h - height of orbit
M - mass of Earth
G - gravitational constant

First term is kinetic energy, second is potential energy. Unless I typed something into the calculator incorrectly twice, I stand by my estimate.

 

[T.Neo]

Cost per kilogram is total cost divided by total payload mass. If we're calculating the energy cost to put a single kilogram in orbit, neglecting other factors, I don't see why total payload mass would be relevant. I'm not sure what count account for the two order of magnitude disparity between our figures; I doubt the energy needed to lift something to the altitude of LEO could account for the difference.

 

[RisingFury]

Cost per kilogram is total cost divided by total payload mass. If we're calculating the energy cost to put a single kilogram in orbit, neglecting other factors, I don't see why total payload mass would be relevant. I'm not sure what count account for the two order of magnitude disparity between our figures; I doubt the energy needed to lift something to the altitude of LEO could account for the difference.

Yea, I realized that right after I posted and I couldn't edit the post...

 

[RGClark]

...
F9 uses about 484 metric tons of propellant (this is not counting unburnt residuals). To my knowledge, the mixture ratio of the Merlin engines is unpublished. However, assuming a mixture ratio of 2.3**, that would be 338.8 tons of LOX and 145.2 tons of RP-1.
This page states that in the 1980s, kerosene cost $0.20/kg, and that in 1956, 24 years before, it cost only $0.05/kg (a growth rate of about 5.8% per year). It states that in the 1980s, NASA was paying $0.08/kg for LOX, and in 1959, LOX cost $0.04/kg (a growth rate of 3.3% over 21years).
Extrapolating this to today (32 years after 1980), we get a cost of $0.23/kg for LOX and $1.20/kg for RP-1. Note that this may be an underestimation.
Using these figures, we get a propellant cost of $252 000 for Falcon 9. Assuming a payload to LEO of 10 000 kg, that's $25/kg (over four times the highest figure based on energy and electricity costs)...

Pretty good estimate. Elon Musk gives the propellant cost as $200,000 for the Falcon 9, and your propellant mass value is closer to that of the heavier Falcon 9 v1.1, which explains your higher estimate.

Bob Clark

---------- Post added at 02:17 AM ---------- Previous post was at 02:13 AM ----------

...
My calculation:
K - cost per kW*h
...

I suppose it's possible that some countries have 80 times higher electricity costs than the U.S. but that would be surprising.

Bob Clark

 

[RisingFury]

I suppose it's possible that some countries have 80 times higher electricity costs than the U.S. but that would be surprising.

Bob Clark

More likely explanation is that I I punched a wrong order of magnitude into my calculator somewhere.

 

[kamaz]

The problem is not getting the vehicle UP, it is getting the vehicle DOWN.

By the time the vehicle gets to orbit, it consists mainly of an empty fuel tank. If you want to reuse the vehicle, it obviously has to land in one piece. Here's the problem though: a reentering vehicle will be subject to a lot of thermal and mechanical stress. When you are going up, the tank is full, so the propellant inside supports the structure, but when you are going down, the aerodynamic forces will act to crush the empty tank. So this means that this tank has to be robust enough to withstand that, but such tank is heavier, so the mass ratio goes down.

There is a way around it, though; the weight of the tank scales with a^2, while the volume scales with a^3, so increasing the mass ratio is simply the matter of enlarging the vehicle. The problem with this approach is that the vehicle quickly becomes absurdly large.

But the vehicle not only has to survive the reentry, it has to survive the reentry well enough that it can be reused. While the Shuttle sort of got there, it was landing without the fuel tank and besides, it was essentially disassembled, carefully inspected, and reassembled again between flights. Not an option in airline economy, of course.

So the bottom line here is that achieving airline economy in spaceflight would require a vehicle that can survive reentry many times without catastrophic failure and without needing anything more than a quick inspection. This is very far from trivial.

Which is why Musk decided to start building rockets. They don't need to reenter, so they are much easier to build...

 

[icedown]

What if you design the tank to be one shot, but the engines to be reusable? Some how protect the engines and avionics so they can reenter undamaged, with tank taking the brunt of the reentry. I would figure the avionics and engines would be the the more expensive parts of the launch vehicle, comparatively with the tank.

 

[T.Neo]

To my knowledge, tank integrity does not depend as much as it does on the presence of propellant as it does on internal pressure; the F9 tanks utilise tank pressure to enable the structural integrity for flight loads (Centaur and the old 'balloon tank' Atlas stages required constant internal pressure to prevent them from collapsing in on themselves).

One would imagine that a propellant tank not loaded with fuel (and thus not subject to the extra weight/mass/inertia/slosh/etc) would, structurally, have an easier time. But generally lighter objects with a higher cross section will encounter lesser heat loads during reentry- so it's 'easier' for a less dense object (i.e. a rocket stage) to reenter safely than a denser object (i.e. a pack containing rocket engines).

Of course, there are all sorts of other issues, like providing adequate TPS for the entier stage, landing the structure safely, stabilising it during reentry, etc. In some cases it may be advantageous to devise a reusability scheme where the engines/avionics are recovered and the tankage is expended on each flight. It should be pointed out that most of the vehicle cost is in the engines and avionics.

Of course, reentry doesn't translate to needing to rebuild things from the ground up on each flight. The shuttle wasn't rebuilt from the ground up, and much of the maintainance done on it had little to do with the reentry systems (compare refurbishment of the SSMEs, etc) and was intrinsic to the system.

 

[RGClark]

Watching the retrospectives on Neil Armstrong on NASA TV, I saw he was a X-15 pilot. This reminded me we actually had reusable rocket engines from the very earliest days of manned rocket-powered flight. The XLR-99 engine used on the X-15 was reusable for 20 to 40 times before overhaul, after which it could be reused again:

XLR-99.
http://www.astronautix.com/engines/xlr99.htm

The 3 copies of the X-15 aircraft flew for a total of 199 flights. Can you imagine how expensive that program would have been if an entire new X-15 aircraft had to be used for each flight?

Bob Clark

 

[Urwumpe]

Can you imagine how expensive that program would have been if an entire new X-15 aircraft had to be used for each flight?

Well, first of all, why the whole new aircraft, if you could also replace only the propulsion system, which forms just a cylinder there? :lol:

Next, the difference is still, that the X-15 only had to reach Mach 3 for most of its flights or Mach 6.7 for its only record flight. While rocket-propelled, it was only slightly out of the envelope possible by jet engines at that time, and would today be even less likely to use rockets. Even for that time, it used rather ineffective, but robust and cheap rocket engines.

It isn't comparable to an orbital spacecraft, and still the X-15 was already a TSTO, with the B-52 being the first stage.

There had been many cost-saving options used in the X-15 and the task wasn't that much performance demanding, that reuseability was getting expensive. It was still closer to an aircraft than to a rocket in many aspects.

 

[RGClark]

Further on Elon Musk's Mars colonization plans:

NOVEMBER 23, 2012
Elon Musk talks about an 80,000 person Mars colony.
http://nextbigfuture.com/2012/11/elon-musk-talks-about-80000-person-mars.html


Bob Clark

 

[T.Neo]

An 80 000 person colony at $500 000 per person equals a $40 billion dollar market for immigration to Mars.

I'll believe it when I see a $40 billion dollar market for immigration to [ame="http://en.wikipedia.org/wiki/Baffin_Island"]Baffin Island[/ame] appearing for no better reason than a want to live in a frozen wasteland.

 

[Mader Levap]

Yeah, I cannot see colonization of Mars any time soon. We will be lucky if there will be permament manned scientific outpost by 2100.

 

[Cras]

conditions on this planet may be of such a degree that living on Mars suddenly becomes quite the appealing proposition.

And there will always those of us who want to go just to go, that sense of adventure and exploration.

Probably not in these numbers however.

 

[T.Neo]

conditions on this planet may be of such a degree that living on Mars suddenly becomes quite the appealing proposition.

It's quite difficult to overstate the environmental poverty of Mars compared to Earth. Nothing short of an utter planetary catastrophe, on a scale unprecedented in geological history, could make Mars and Earth comparable in terms of real-estate value.

If you have the sort of money necessary to emigrate to Mars, it would most probably be better spent on improving one's own lifestyle on Earth than moving to Mars. The wealthiest people in some of the worst places on Earth don't spend their money to emigrate to Baffin Island, after all.

 

[BruceJohnJennerLawso]

It's quite difficult to overstate the environmental poverty of Mars compared to Earth. Nothing short of an utter planetary catastrophe, on a scale unprecedented in geological history, could make Mars and Earth comparable in terms of real-estate value.

If you have the sort of money necessary to emigrate to Mars, it would most probably be better spent on improving one's own lifestyle on Earth than moving to Mars. The wealthiest people in some of the worst places on Earth don't spend their money to emigrate to Baffin Island, after all.

I would take the choice of going to Mars or Baffin Island. I find tremendous appeal in the idea of getting away from Earth, simply because society here reflects stagnation, stupidity, & arrogance. Currently being in my late teens, I would say the odds of surviving this century are fifty-fifty at best, given the challenges an Earth based society will have to deal with. Just my thoughts :shrug: