Throughout the series I referred several times to a reference design for a cargo tug. That was put together using what might kindly be described as rectal numbers, assuming a tankage factor of 6% and 1.5 tons of remaining structure.
I've gone back and run a preliminary estimation using a more detailed approach. In the process I created a spreadsheet that will allow users to enter their own values if desired. Errors are likely so use at your own risk; make a copy if you want to make changes.
My little tug ended up just under 5 tons dry mass, 6.5kW power, 62 tons fuel capacity. The initial estimate was pretty close.
Details after the jump.
I assumed the use of RL-10B-2 engines with modifications to allow unlimited restarts. Most of the mass estimation relationships came from a U of Maryland slide series with some references from TU Delft and http://www.braeunig.us/. My estimates for cryocoolers are primitive at best, but the mass and power values are for a real off-the-shelf unit and should be reasonably accurate for cis-lunar space in the 50-100 ton fueled mass range. I also adjusted the thrust structure value to account for strength in two dimensions plus lunar landing gear; a note in that cell explains how to omit either option.
Fuel hauling is assumed to use the craft's main propellant tanks. Cargo is assumed to be symmetrically attached to the thrust structure with low center of gravity. For cargo that is not being landed on the moon, attachment via a docking ring on the nose of the ship is also an option if a single bulky object is being transported.
This more precise model comes to 4.95 tons of dry mass and 62 tons of fuel. All payloads assume 5% dV margins. It can land a 20-ton payload on the surface of the Moon and return it. It can deliver 50 tons of cargo to low Mars orbit and return empty. A one-way trip from LEO delivers 39 tons to EML1 or 46 tons to EML2.
Fuel for a trip from EML1/2 takes two lunar surface fueling trips. Fuel for a trip from LEO takes three fueling trips from EML1/2 (requiring six surface trips). This is determined by engine Isp and the mass relationships used in the model, so the same is true if the vehicle is scaled up or down with similar thrust to weight ratio.
I included three alternate configurations. The most relevant is sized to fit a standard Falcon payload fairing; 2.06t dry mass, 24.6t fuel capacity and would be launched engine-up empty on a 9 or fueled on a reusable heavy. Two much larger craft (120t and 500t fuel capacity) are presented as examples; the large craft could be launched on an Ariane V, Proton M or SLS block 1 with diameter as the main constraint. This would be a reasonable propellant depot in its own right. The huge craft would require an SLS block 2 due to both diameter and mass, plus a substantial supply of guts, stupidity or cash.
Improvements to the model would be a better look at masses for a sunshield, cryocooler, payload hardpoints and docking system, as well as a frame with thermal/fragmentation protection between engines. A discrete tank model instead of a mass estimate based on volume is something I've done in another sheet and may migrate to this one in the future. A further set of refinements would be a look at ULA's integrated vehicle fluid management tech including gaseous H2/O2 lines for RCS thruster packs, combustion engine for reserve power and an electrolysis unit for converting waste water or payload water into additional fuel. I'd like to see a table or graph of total dV from surface to EML1/2 for a range of thrust to weight ratios as well. Lastly, some kind of mass estimate for a reusable (non-ablative) heatshield for the trip to LEO or LMO would be useful. I have not included estimates for any trip with aerobraking so the sheet would have to be reworked to account for that capability.