Author Topic: Fuel costs for routine travel to Mars  (Read 17552 times)

Offline aero

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Fuel costs for routine travel to Mars
« on: 12/20/2012 01:27 pm »
I asked about this question before but the discussion evolved toward estimates of the number of passengers aboard Elon's Mars transit vehicles. So let me ask again.

The assumptions are:
150 passengers at 500 kg each = 75 tonnes of payload
Guesstimate transit vehicle at 25 tonnes
ALL vehicles are FULLY reusable from surface to surface.
Mass ratios per vehicle are given by the rocket equation.

My question is, "How much will the fuel cost?"

Of course there are still other questions to be answered before this one. Eg. Where are the fuel depots for refueling, How much fuel will be needed and what fuel is used? I speculate LOX and Methane but that is debatable.

If the Mars Transit Vehicle is refueled only twice, in LEO and on the surface of Mars, then "How much fuel will be used and how much will it cost?"

I will work on my guess and post it later.


Edit - Orgionally posted in SpaceX general section, moved by moderator. This thread is to question Elon Musk's proposal of $500,000 USD ticket price for colonists to Mars.
« Last Edit: 12/20/2012 05:56 pm by aero »
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Offline IRobot

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Re: Fuel costs for routine travel to Mars
« Reply #1 on: 12/20/2012 03:06 pm »
The assumptions are:
150 passengers at 500 kg each = 75 tonnes of payload
Guesstimate transit vehicle at 25 tonnes
ALL vehicles are FULLY reusable from surface to surface.
Mass ratios per vehicle are given by the rocket equation.

The transit vehicle will weight much more than 25 tonnes... that is the weight of a normal ISS module. Do you think you can fit 150 passengers there?? Better, name an earth vehicle where you can fit 150 passengers and weights less than 50 tonnes!

Offline aero

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Re: Fuel costs for routine travel to Mars
« Reply #2 on: 12/20/2012 05:00 pm »
The assumptions are:
150 passengers at 500 kg each = 75 tonnes of payload
Guesstimate transit vehicle at 25 tonnes
ALL vehicles are FULLY reusable from surface to surface.
Mass ratios per vehicle are given by the rocket equation.

The transit vehicle will weight much more than 25 tonnes... that is the weight of a normal ISS module. Do you think you can fit 150 passengers there?? Better, name an earth vehicle where you can fit 150 passengers and weights less than 50 tonnes!

Well, your most likely right, but to name a vehicle, the Boeing 727 dry weight is 37.5 tonnes and has a capacity of 149 people. But I agree, those are seated passengers and do not mass 500 kg each.

On the other hand, the passenger density of the Mars transit vehicle should be higher than that of the ISS so using the ISS as a basis will give an unrealistically high estimate of vehicle mass, IMO. I think a better estimate can be derived by scaling the Dragon Crew or the ORION capsule.

Argument could be made that the Mars transit vehicle will also transport drygoods and machinery and so will be larger and heavier than just a passenger carrier. I'm looking for a low but realistic mass estimate of the transit vehicle and so want to limit it to a passenger carrier to ovoid an open ended debate about the vehicle type.
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Offline guckyfan

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Re: Fuel costs for routine travel to Mars
« Reply #3 on: 12/20/2012 05:31 pm »
On the other hand, the passenger density of the Mars transit vehicle should be higher than that of the ISS so using the ISS as a basis will give an unrealistically high estimate of vehicle mass, IMO. I think a better estimate can be derived by scaling the Dragon Crew or the ORION capsule.

Argument could be made that the Mars transit vehicle will also transport drygoods and machinery and so will be larger and heavier than just a passenger carrier. I'm looking for a low but realistic mass estimate of the transit vehicle and so want to limit it to a passenger carrier to ovoid an open ended debate about the vehicle type.

You can hardly have people in such cramped quarters for half a year. These are not slave transports and the transfer takes longer than sailing fom Africa to America. Also rigorous exercise is necessary for everybody to stay fit.

About the fuel, maybe you turn the calculation the other way around. Assume that half of the cost (500,000$) goes for fuel. How much fuel will thay get you? How much is a metric ton of Methane/LNG at the moment?

That will give you ~ an upper limit for the needed fuel, assuming the price can be achieved.

Offline aero

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Re: Fuel costs for routine travel to Mars
« Reply #4 on: 12/20/2012 05:52 pm »
On the other hand, the passenger density of the Mars transit vehicle should be higher than that of the ISS so using the ISS as a basis will give an unrealistically high estimate of vehicle mass, IMO. I think a better estimate can be derived by scaling the Dragon Crew or the ORION capsule.

Argument could be made that the Mars transit vehicle will also transport drygoods and machinery and so will be larger and heavier than just a passenger carrier. I'm looking for a low but realistic mass estimate of the transit vehicle and so want to limit it to a passenger carrier to ovoid an open ended debate about the vehicle type.

You can hardly have people in such cramped quarters for half a year. These are not slave transports and the transfer takes longer than sailing fom Africa to America. Also rigorous exercise is necessary for everybody to stay fit.

About the fuel, maybe you turn the calculation the other way around. Assume that half of the cost (500,000$) goes for fuel. How much fuel will thay get you? How much is a metric ton of Methane/LNG at the moment?

That will give you ~ an upper limit for the needed fuel, assuming the price can be achieved.

I could do that but my hidden agenda is to apply rocket physics to estimate the number of passengers needed to pay for the fuel. I don't have much confidence in the 150 passenger number but if the rocket equation shows that Isp is reasonable for the mass of fuel purchased from ticket revenue, then I will be more confident in the SpaceX proposal.

Edit - No, people cannot sit in cramped quarters for 6 months, even though it seems that some airlines would like to think so.

The Mars transit vehicle will probably be internally configured more like a cruise ship or passenger train than an airliner but the mass/volume ratio will be for a spacecraft.
« Last Edit: 12/20/2012 06:05 pm by aero »
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Offline Jim

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Re: Fuel costs for routine travel to Mars
« Reply #5 on: 12/20/2012 05:56 pm »

On the other hand, the passenger density of the Mars transit vehicle should be higher than that of the ISS so using the ISS as a basis will give an unrealistically high estimate of vehicle mass, IMO. I think a better estimate can be derived by scaling the Dragon Crew or the ORION capsule.


No, the ISS would a better basis.  Dragon or ORION are only manned for days, the ISS is manned for months

Offline Jim

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Re: Fuel costs for routine travel to Mars
« Reply #6 on: 12/20/2012 05:57 pm »
I don't have much confidence in the 150 passenger number but if the rocket equation shows that Isp is reasonable for the mass of fuel purchased from ticket revenue, then I will be more confident in the SpaceX proposal.

Propellant costs will be in the noise compared to the vehicle costs.

Offline aero

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Re: Fuel costs for routine travel to Mars
« Reply #7 on: 12/20/2012 06:13 pm »
I don't have much confidence in the 150 passenger number but if the rocket equation shows that Isp is reasonable for the mass of fuel purchased from ticket revenue, then I will be more confident in the SpaceX proposal.

Propellant costs will be in the noise compared to the vehicle costs.

Jim - I know that - but I am shooting at the $500,000 ticket price, so my unrealistic assumption is that the vehicles have magically been paid for already. After fuel costs are known, and if there is a cash balance, then take out the magic and apply that balance to retire the debt.
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Offline Jim

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Re: Fuel costs for routine travel to Mars
« Reply #8 on: 12/20/2012 06:16 pm »
I don't have much confidence in the 150 passenger number but if the rocket equation shows that Isp is reasonable for the mass of fuel purchased from ticket revenue, then I will be more confident in the SpaceX proposal.

Propellant costs will be in the noise compared to the vehicle costs.

Jim - I know that - but I am shooting at the $500,000 ticket price, so my unrealistic assumption is that the vehicles have magically been paid for already. After fuel costs are known, and if there is a cash balance, then take out the magic and apply that balance to retire the debt.


which segment propellant costs?  Earth to LEO or LEO to Mars?


Food, oxygen, water, etc are going to cost more than the propellant.  You can't apply airline cost factors to this problem.
« Last Edit: 12/20/2012 06:21 pm by Jim »

Offline aero

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Re: Fuel costs for routine travel to Mars
« Reply #9 on: 12/21/2012 03:07 am »
Quote
which segment propellant costs?  Earth to LEO or LEO to Mars?

Both of course. If we fail to look at the fuel costs for the LEO to Mars leg we totally miss the point, which I illustrate with the following.

I have used Elon's quoted 2% mass to LEO for reusable launch vehicles, Jim's suggestion that I use the ISS to estimate mass and small cruise ship cabin space to estimate volume. Twenty cubic meters for a cabin for four persons is a small cruise ship cabin and requires 750 m^3 of cabin space for 150 people. The ISS pressurized volume is 837 m^3,  leaving 87 m^3 for common areas in the Mars transit vehicle. The ISS masses 450 tonnes. Let me ignore fuel tanks and engines on the Mars transit vehicle for the moment.

Note that for fuel costs to launch, it doesn't matter whether the Mars transit vehicle is constructed on Earth or in space, it takes a GLOW of 50 times the payload to get the vehicle mass into orbit and that mass is 450 tonnes vehicle +75 tonnes colonists. Fuel mass to LEO therefore is ~ 26,000 tonnes and at current LNG import prices ($0.14 per kg LNG) and guessing LOX costs the same, then fuel to launch the Mars transit vehicle into LEO costs $3,279,967 that is, three and one quarter million dollars. Quite affordable but the Mars transit vehicle is empty of fuel.

It takes about the same delta V to get from LEO to the Mars surface as it does to launch from Earth to LEO, so it will take about the same amount of fuel. Where will that fuel come from if not from Earth. Sure, there are solutions such as Moon ISRU for LOX, but that is expensive, too. Methane is available from Earth but it will take 50 times as much fuel to launch the Mars transit vehicle fuel load-out as it took to launch the Mars transit vehicle in the first place. Plus the cost of the fuel load-out, of course. That is 51 times the cost of the fuel to launch the Mars transit vehicle in the first place. That is 51 * $3,279,967 = $167,278,301.19 and adding in the origional fuel costs above gives $170,558,268 in fuel costs to get the Habitat (Mars transfer vehicle) from LEO to Mars. That does not include the mass of tanks and engines for the Habitat.

It looks to me like the $500,000 ticket price is not even close if chemical rockets are used. One hundred fifty tickets is only $75M, and not close to the $170.5M cost of fuel required.
 
Edit: Restated GLOW and payload relationship above and added note.
Note - I have my calculations on Excel so if other fuel costs are proposed, I can easily recalculate. (LOX costs, in particular.) I could add life support mass, shielding, engines and tanks to the Habitat if anyone cares at this point.

« Last Edit: 12/21/2012 04:48 am by aero »
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Offline Patchouli

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Re: Fuel costs for routine travel to Mars
« Reply #10 on: 12/21/2012 06:51 am »
The cheapest option looks to be to go with a Mars cycler.
http://en.wikipedia.org/wiki/Mars_cycler
That way the massive and expensive Earth to Mars transport craft can be reused multiple times and little propellant is used.
Even though fuel is just a tiny fraction of the cost of a launch it becomes expensive once it's hauled up out of the gravity well.
« Last Edit: 12/21/2012 06:56 am by Patchouli »

Offline Andrew_W

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Re: Fuel costs for routine travel to Mars
« Reply #11 on: 12/21/2012 07:37 am »
You probably should start by working out the propellant mass ratios for the trip using an optimum travel time, make a case for the ship tonnes dry mass/passenger, and assume cheap LOX, LH2 fired from the moon, and a similar H2O source on Phobos. Then you need to guess how much that infrastructure including producing the energy in space to split the H2O is going to cost, and can you really ignore the capital cost, not just of the ship, but of the systems supporting it?

http://www.gdnordley.com/_files/Going_to_Mars.html
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Offline Alexsander

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Re: Fuel costs for routine travel to Mars
« Reply #12 on: 12/21/2012 12:19 pm »
What if Elon is thinking USD 500,000 for LEO-Mars (surface) one-way ticket only? If he assumes the passenger is already on orbit (at a Bigelow's hotel, for example), the fuel need will be quite different.

In a flourishing space travel market, there's room for Earth-LEO tickets, LEO-LagrangeN tickets, LEO-Moon tickets... with competing hotels/stations in each of these places -- and maybe Moon colonies. In that scenario, LEO-Mars tickets and Mars colonies would be plausible.

Offline guckyfan

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Re: Fuel costs for routine travel to Mars
« Reply #13 on: 12/21/2012 12:29 pm »
What if Elon is thinking USD 500,000 for LEO-Mars (surface) one-way ticket only?

He mentioned in a speech recently, that the flight is intended one way to Mars. But as the ships go back for reuse anyway, he said the return would be free if anyone needs to go back. That would imply if for some reason all need to go back, the cost would not be covered.

If he assumes the passenger is already on orbit (at a Bigelow's hotel, for example), the fuel need will be quite different.

In a flourishing space travel market, there's room for Earth-LEO tickets, LEO-LagrangeN tickets, LEO-Moon tickets... with competing hotels/stations in each of these places -- and maybe Moon colonies. In that scenario, LEO-Mars tickets and Mars colonies would be plausible.

That would be a sematics trick. I understand that price is meant to be for the ticket Earth-Mars. If it is realistic though, I doubt.

Offline Alexsander

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Re: Fuel costs for routine travel to Mars
« Reply #14 on: 12/21/2012 01:28 pm »
That would be a sematics trick. I understand that price is meant to be for the ticket Earth-Mars. If it is realistic though, I doubt.

There's a separation of phases (Earth-LEO and LEO-Moon surface) in the movie "2001", with private companies (PanAm) and space stations. Maybe something like that could exist in the future.

Offline aero

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Re: Fuel costs for routine travel to Mars
« Reply #15 on: 12/21/2012 11:21 pm »
The cheapest option looks to be to go with a Mars cycler.
http://en.wikipedia.org/wiki/Mars_cycler
That way the massive and expensive Earth to Mars transport craft can be reused multiple times and little propellant is used.
Even though fuel is just a tiny fraction of the cost of a launch it becomes expensive once it's hauled up out of the gravity well.


That's the point. You can't afford to haul chemical fuel out of the gravity well for use in propelling a large chemical rocket ship to Mars at the ticket price being bandied about. You are limited by the rocket equation which can be stated as: (pardon the tutelage)

MR = exp(delta V/g0*Isp) where

MR is the mass ratio, = full mass/empty mass
delta V is the change in velocity required to reach orbit
Isp is your rocket engine efficiency, and
g0 is a constant = 9.8065 m/s^2
and of course full mass = empty mass + propellant (fuel)

To send the colonists to Mars there are only three adjustments that can be made to the rocket equation.

1. Reduce the mass of the Habitat or payload (mass will be optimized)
2. Use more efficient rocket engines (but then fuel becomes more expensive)
3. Go somewhere that takes less delta V (for example, a fly-by trajectory without stopping, thereby saving fuel)

Buzz Aldrin's cycler uses a twist on 1. above plus point 3. An Aldrin Cycler could be a very large Habitat orbiting around both the Earth and Mars on a regular and frequent basis. Buzz Aldrin proposed using 2 habitats in the same orbit, one outgoing and one incoming relative to Earth. The Habitat could be large because it accelerates by gravity with only orbit control (maneuver) thrusting needed. That minimizes the delta V required for the Habitat, reducing it to near zero.

But of course the colonists still need to accelerate and decelerate to catch the cycler and stop off at Mars. Aldrin proposed the use of space taxi's for this. A minimum of 3 taxi's are needed, like this.

The Habitat approaches the first planet, either Mars or Earth, and a taxi undocks, decelerating to orbit the planet and land (or descend directly using aerocapture depending on design). Simultaneously a second taxi departs the first planet (or low orbit) to rendezvous and dock with the Habitat. Colonists and consumables transfer to the habitat and ride to the vicinity of the second planet where they get back in the taxi which then it undocks and decelerates to the planet. Landing is achieved per taxi design. Simultaneously, a third taxi departs the second planet for rendezvous with the Habitat and the ride back to the first planet. The third taxi arrives at the first planet and the first taxi launches to rendezvous with the Habitat, continuing the cycle.

With the cycler Habitat approach, only the mass of the taxi need be accelerated and decelerated out of and into the planet's gravity wells which will much reduce the empty mass and payload needing to be accelerated although the delta V of that mass will be the same as always. I note that if it would be more efficient, two types of taxis could be designed, one human rated for colonists, and one for cargo. Further, these taxis have only a very short mission duration, on the order of hours, similar to the time needed for a Mars probe to reach TMI. As soon as TMI is achieved, the taxi docks with the Habitat.

One concern raised by those who have studied the cycler approach is that if a taxi fails to rendezvous with the Habitat then it is lost with all hands. The Habitat cannot maneuver to rescue it. Of course the Habitat could carry a rescue tug in case the rendezvous was only a near miss. (Study needed) If a seperate cargo taxi were used, perhaps it could follow and rescue if the passenger taxi were to experience the failure.

For the cycler approach, the fuel needed by the taxis is all that needs to be purchased and lofted to orbit. This is much less than before, but is it enough less? As for additional hardware, a minimum of three taxis are needed, three spacecraft that were not needed before. The Habitat itself can be larger and more "user friendly" since its mass is no longer a concern beyond initial orbit insertion.

Back to the rocket equation above. The final variable to adjust is Isp, engine efficiency. Electric propulsion comes to mind with Isp potentially of 5000 seconds or greater (compare this to LOX/Methane engine Isp in the range of 360 to 370 seconds.) Unfortunately, as we know, high thrust electric propulsion has not been developed, and the propellant used currently is quite expensive so fuel costs may or may not be reduced by its use.

Edit: Word choice and grammar
« Last Edit: 12/21/2012 11:29 pm by aero »
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Offline aero

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Re: Fuel costs for routine travel to Mars
« Reply #16 on: 12/22/2012 12:09 am »
Considering the above, I calculated the Methane/LOX fuel costs assuming a 75 tonne taxi carrying 150 passengers at 500 kg each, for a total dry mass of 150 tonnes. The fuel cost now comes out to be less than $49 million.

I guess it depends then on how far down the road into the future Elon is projecting. 75 - 49 gives $26 million remaining to pay for all of the non-fuel costs.

Oh well.

Edit add: In all this I overlooked the fuel consumed by the reusable launch vehicles while returning to the pad. The rocket equation as applied here does not address this function. I think I recall that the fuel burned by reusability equals 2% of the lofted mass, but I'm not sure. Whatever the amount of fuel needed for reuse, there are 51 launches with reusable stages returned to the launch pad. That constitutes an additional cost of fuel added to the above numbers.
« Last Edit: 12/22/2012 02:24 am by aero »
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Offline guckyfan

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Re: Fuel costs for routine travel to Mars
« Reply #17 on: 12/22/2012 06:15 am »
A cycler does not make sense for cargo except if the cargo is live animals as it does not need a habitat and the delta-v required to reach the cycler is higher than going directly.

Assuming the cycler hast an very efficient life support and even grows much of the required food, the payload per passenger could however be much lower than the assumed 500kg. Maybe as low as 200kg. Food and oxygen production using algae is efficient with low space requirement so may be possible, depending on how the algae are processed into usable food.

Offline IRobot

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Re: Fuel costs for routine travel to Mars
« Reply #18 on: 12/22/2012 03:05 pm »
Considering the above, I calculated the Methane/LOX fuel costs assuming a 75 tonne taxi carrying 150 passengers at 500 kg each, for a total dry mass of 150 tonnes. The fuel cost now comes out to be less than $49 million.
I still think 75 tonnes is too small. I would think on something over 200 tonnes dry.

Offline aero

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Re: Fuel costs for routine travel to Mars
« Reply #19 on: 12/22/2012 03:39 pm »
Considering the above, I calculated the Methane/LOX fuel costs assuming a 75 tonne taxi carrying 150 passengers at 500 kg each, for a total dry mass of 150 tonnes. The fuel cost now comes out to be less than $49 million.
I still think 75 tonnes is too small. I would think on something over 200 tonnes dry.

Maybe, but 158 tonnes dry mass plus 75 tonnes colonists for 233 tonnes uses all of the $75 million for fuel. And remember, the passengers will only ride in the taxi for a few hours beyond LEO, so shield mass can be reduced.

As for cargo taxis, I was thinking to use them for the colonists personal effects and to top off consumables for the duration of the trip.  Again very little shielding needed. The purpose was to reduce the mass and cost of the man rated taxis. Sure heavy machinery destined for Mars would take the slow, efficient trajectory.

Just a thought, but would orbital mechanics allow, say 10 or more cyclers along the same trajectory? That way, Elon could transport his million colonests to Mars within the century.
« Last Edit: 12/22/2012 03:48 pm by aero »
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Offline colbourne

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Re: Fuel costs for routine travel to Mars
« Reply #20 on: 12/23/2012 12:00 am »
For a half year trip , putting the passengers into some form of hibernation would be a good idea and will probably be possible by the time this colonization is planned.

This way passengers will not need so much food and will take less space.


I think Musk should first plan on getting a handful of people to Mars first before he starts worrying about mass colonization. I guess he wants to see a large Mars base in his own lifetime, so is pushing this concept.

Offline guckyfan

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Re: Fuel costs for routine travel to Mars
« Reply #21 on: 12/23/2012 07:14 am »
For a half year trip , putting the passengers into some form of hibernation would be a good idea and will probably be possible by the time this colonization is planned.

I think it is possible alredy. I had thought about an induced coma with lowerered body temperature and intravenous feeding. With water-recycling that would cut way back on their nutrition needs.

But what would be their shape on arrival? How much would their muscles decrease without training? Probably they would need some treatment and training after arrival. The low gravity may help at the start.

Offline alexterrell

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Re: Fuel costs for routine travel to Mars
« Reply #22 on: 12/23/2012 12:42 pm »
I've assumed the first Mars ships is 2 BA-330 capsules, a heat shield, and a service module. It can take 18 passengers, which is 50% more than the Bigelow advertise the BA-330 more. The mission leaves from L1 (SEP modules are used to raise the fuel and modules - only humans go there in CEV.

Including 40 tons of supplies, it masses 120 tons. The first mission needs enough fuel to come back, and therefore delta V is 3360 (including aeiocapture at both ends). So that's 185 tons of LOX and Methane.

Subsequent missions however get refuelled at Phobos. Fuel needed is 108 tons, plus about 63 tons for tug operations at Phobos, so 172 tons in total for 18 people.

It would be a similar amount to fuel at L1, but I assume that fuel at Phobos is cheaper than fuel at L1.

For second generation craft I assume 440 tons (with supplies) for 90 crew. This is basically allowing an outer wall of about 100kg/m2. This one takes a lot of fuel (1750 tons) and goes all the way to Low Earth Orbit, where is spends 18 months as a hotel, before heading back to L1, for refuelling with 125 tons, and then to Phobos.

A key point is that Delta V LEO to L1 is the biggest requirement.

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