Cost of transportation

SpaceX Starship overflying the Valles Marineris

The cost estimates for transportation to Mars cover a large span. From extremely expensive (200 000$/kg) for one way scientific missions, to a more recent estimate of 130$/kg for the SpaceX Mars plans, and even less for future transportation systems(link).

The main cost parameter for launch systems cost is the number of flights per vehicle. Up till recently that number was one, but re-usability seems to be achievable soon, and should be expected for any large scale plan for Mars colonization. The cost of the energy required to prepare the return propellant is also important, with the development of in-situ fuel production is the key to low costs of transportation to Mars.

Propellant production costs

As far as propellant for launch vehicles on Earth is concerned, oxygen, hydrogen, kerosene and methane are all commercially available processes and are considered commodity goods for establishing the cost of transportation to Mars. The costs that were considered are in the following table:

Propellant costs for launch vehicles, 2016

Propellant	Density (kg/m3)	Cost ($/kg)	References
Oxygen	1140	0,16	NASA paid 67 cents per gallon for the shuttle, so about $0.16 per kg
Hydrogen	70	3	Hydrogen Production Cost Using Low-Cost Natural Gas, DOE projection, 2012
Kerosene	800	0,4	Commodity price for jet fuel, july 2016
Methane	420	0,2	0,1$/kg natural gas + delivery, refining and liquefaction

SpaceX Stainless Steel Starship reusable launch vehicle

Cost to LEO

The main cost of transportation is for the phase from Earth surface to LEO. The overall deltaV to orbit is about 9 000 m/s, more than for any other part of the trip. For re-usability, the vehicle must be able to return to Earth surface with the minimum amount of damage,

This analysis is done for unmanned vehicles. Use of unmanned vehicles greatly reduces the development costs and gives freedom of experimenting risky maneuvers without dramatic consequences.

The minimum value from the surface to LEO is the energy difference between the two positions: orbital velocity and elevation. With an electrical cost of 0.1$ per kWh, the difference in energy is about 33 MJ/kg, which corresponds to about 1 $ per kg. If energy costs can be reduces, the cost to orbit might be even lower.

Cost may eventually be reduced to nearly the base cost of energy when (and if) geostationary space elevators are finally developed and financed over long periods. Significant access to space based power systems might eventually reduce the cost for moving mass to orbit to a trivial amount.

Launch cost economics

Launch cost economics is a complex subject, source of endless debates.  We present a simplified analysis here, for transportation to LEO, using the following equation:
Pc	Payload cost  ($/kg)	Pc= (De+Co*Vg+In+Vg*Vf*(Ma+Fu))/Pm*Vg*Vf
De	Development	Research, management and testing.  Safety requirements for crewed vehicles.  Flight proofing.
Ma	Materials and manufacturing	person hours, testing.
Co	Construction of the vehicle	Materials and manufacturing, person hours, testing.
In	Infrastructure	Manufacturing plants, tooling and launch sites for a series of vehicles
Ma	Maintenance cost per flight	Clean up, repair, upgrades, fueling, set up on pad.
Fu	Fuel cost per flight
Vg	Vehicles per generation	Number of vehicles built per design generation.
Vf	Vehicle flights	Number of flights a vehicle can do over its lifetime
Pm	Payload mass (kg)	Payload mass per flight
Environmental impact is not included as a cost but needs to be taken into account in the overall analysis. This parameter doomed fission pulsed propulsion and exotic fuels using fluorine, and might become an issue at high flight rates. The table below gives the results for the above equation.  It is based on the transportation of 100 000 tonnes to LEO.

Comparison of various launch systems based on the above:

Launch system costs

Vehicle	Development (De)	Construc- tion (Co)	Infra- structure (In)	Flights (Vf)	Fuel cost per flight (Fu)	Mainten- ance/flight (Ma)	Vehicles per generation (Vg)	Payload (Pm)	Payload cost (Pc)
	Billions	millions	billions		millions	millions		kg	$/kg
Delta IV	0,5	300	0,2 B$	1	0,5	2	20	22 000	15 000
Falcon Heavy	0,3	70	0,2 B$	5	0,5	0,5	20	54 000	1 700
Falcon Heavy recoverable	0,7	90	0,2 B$	5	0,5	0,5	20	30 000	520
SpaceX Starship	10	600	2 B$	100	1,25	.5	20	300 000	40
REL Skylon	12	250	0,5 B$	200	0,1	0,1	200	15 000	48
Space gun	0,5	-	2 B$	20 000	0,05	0,01	20 000	1000	925
To achieve these figures ITS and Skylon need to transport about 100 000 tonnes. The firing rates requires for the space canon are very high and might not be achievable. These are base costs, without financing, subsidies, insurance or profit. The recoverable Falcon heavy is entirely speculative.

Solar powered Orbital Transfer Vehicle

Based on this, the cost to orbit in the nearby future might be as low as 40$ per kg.

Cost from LEO to Mars

The same analysis that was used to show the gains of re-usability can be used for orbital transfer to Mars.  Following the radical reduction in cost possible with high volume reusable launchers, the cost of moving cargo to Mars goes down significantly.  The solar electric or nuclear electric thrusters are clearly the most economical solution for the volumes needed for the development of a martian settlement, as long as the volumes are there. On the other hand, cheap orbital refueling can profit from the Obert effect for low ISP high trust chemical propulsion.

The main parameter for costs from LEO to Mars are deltaV and the use of atmospheric braking. Vehicles such as solar powered Orbital transfer vehicles (OTV)'s are unable to use either the Oberth effect or atmospheric braking. However, the mass of fuel required is so low that these loses are offset by the reduced overall mass. Interesting gains might exist with propellant produced on Mars, or in Mars orbit.

Orbital transfer vehicles

Vehicle	Development	Construction	Infrastructure	Flights per vehicle	Fuel cost per flight	Flights required	Payload per flight	Vehicles required	Total Flight costs	Payload cost ($/kg)
	Billions$	millions$	billions$		millions$				billions$
Chemical one way	1.0	10.0	0.0	1.0	0	16 667	6	16 667	2 666	26 657
ITS with refuelling	0.0	0.0	0.0	100.0	0	556	180	6	39	389
Beamed power Skylon()	0.0	0.0	1.0	200.0	0.0	6,667	15	33	57	567
Solar electric()	2.0	300.0	0.2	100.0	0	556	180	6	15	151
Nuclear thermal	4.0	300.0	0.0	20.0	0	556	180	28	24	243
Costs for 100 000 tonnes to high orbit. 2016$. The chemical one way is paired with the Delta IV vehicle.  For the purpose of this table solar electric is the same as nuclear electric. The payload  cost includes the cost of the Launcher flights required to carry up the propellant.

As for the launch vehicles, the OTVs are unmanned. This reduces cost and complexity tremendously, since there is no need to transport a crew and their living environment.  Docking, fuel and cargo transfer operations may be supervised and teleoperated, and the OTVs are provided with robot arms moving on rails, or similar active elements, that can be used for inspection and repair.  

• Low thrust vehicles follow very different trajectories than high thrust vehicles.  They cannot profit from the Oberth effect, and therefore require higher deltaV for the same mission.  Despite this, their reduced fuel use makes them more economical than high thrust vehicles. At least for most situations that concern the long term occupation of Mars.

• The lowest expected cost would be in the range of 130 $ per kg. The SpaceX Starship system might be possible at 3-400 $ per kg.

The Oberth effect, the gain from thrust deep in a gravity well

Δveff= Δv·√(2VE/Δv) where Δv= ve·ln(mo/mf)
Δveff	Effective Velocity change (m/s)
VE	Escape velocity (m/s)	Escape velocity of the body around which the vehicle is doing the Oberth maneuver
mo	Initial mass (kg)	Propellant, payload and vehicle structure
mf	Final mass (kg)	Payload and vehicle structure+remaining propellant

Cost to Low Mars Orbit (LMO)

Propellant production on Mars is mostly a factor of the cost of electrolysis of water. The embodied energy of Methane on Mars is about 127 MJ/kg. For an energy cost of 150$ per GJ, the cost per kg of Methane would be about 19 $ per kg. The price for oxygen is included in the cost of methane and hydrogen, as it is a byproduct of the electrolysis process required to produce methane.

Propellant costs for launch vehicles, on Mars

Propellant	Density (kg/m3)	Cost ($/kg)	References
Oxygen	1140	-	Included in hydrogen and methane costs. Oxygen is a byproduct of hydrogen separation
Hydrogen	70	28	Hydrogen from Electrolysis
Methane	420	19	Methane from Sabatier reaction of CO2 and hydrogen

BFS re entry with Space Shuttle to scale