(Note: the following is one of various posts that were copied here from the Moonwards.com forum for the sake of preserving the early days of the project. It was originally posted there on April 22nd, 2016.)
A nuclear shuttle for transportation of ice from the pole to an equatorial base is limited by the thrust of its engine. That mass must accommodate the mass of the engine and all the other dry mass, and the propellant. What is left in the mass budget then is the payload. Note that fuel required for the return trip must be subtracted as well.
A reasonable delta-v budget for a one-way trip (including some gravity losses) is 3200 m/s.
For all my examples, I am going to use a hypothetical but realistic nuclear engine, at 2500kg, 100kN and an Isp of 950s
We can calculate the required mass ratio:
Also, using a thrust to weight ratio of 2, the launch mass of the shuttle can 30,800 kg. (Scale as desired by adding more engines).
From the mass ratio, we get that 21,800kg of that can be used for the dry mass, payload and return trip fuel.
First, why use water? After all, the Isp of water is only 45% of hydrogen. But, even though the mass ratio gets a lot worse, water allows us to get more thrust from the same engine. In a NTR, thrust is simply inversely proportional to the Isp.
So the same configuration with a T/W ratio of 2 allows us to increase the launch mass to 70,800kg. The mass ratio is 2.2, but that still gives us 32200kg for dry mass, etc. Absolutely an improvement.
But we can do better!
The extra thrust we get from the water is only required for the first part of the burn. After the shuttle has depleted some of its propellant, it is light enough that if you then switch to hydrogen, the T/W ratio is still good. (Also note that an high T/W ratio is not that important when you have gained a significant fraction of orbital velocity, making it even more favorable to switch propellant mid-burn.)
If, for instance, we use water for the first km/s of the ascent burn, and for the last 200 m/s of the landing burn, and hydrogen for the remaining 2km/s mid-flight. That results isn 37,300kg for the dry mass etc.
Thrust when needed, efficiency when possible.
This is great, Sigvart, you have started my day off quite well for me. And you have taught me an essential new emoticon :[)
That idea i talked to you about the other day, of moving the colony to Aristillus, is one i really didn't want to take on, at least not right now. This issue of transport of material between the pole and the base was what had driven me to consider it. Aristillus is at 33 degrees N latitude, meaning a one way hop would take about 10% less fuel than a trip to Lalande on the equator. As a double sub-orbital hop to get to Lalande and then fly back takes so much fuel, you and Russell had warned me very little space would be left for payload. But water (and carbon chemicals, and ammonia, and the rest) is so darned useful. Even though i think setting up a fuel depot is a low priority, i keep thinking of amazing things to do with water. Lots and lots of water. And those other things.
There are two things i think will make the colony flourish, especially once people are there. If you do it well, broadcasting can bring in 2 or 3 billion dollars a year. And you sell permanent residence in the colony for $100 million a pop. I see residence sales working in the early days mostly because it should be an international sponsorship process. You announce to the world that any nation can send permanent residents of their choosing for that price, and you focus on assembling an initial population that is as representative as possible. Those residents are then representatives of their countries, like Olympic athletes, like astronauts are today. Lots of countries would be attracted to the prestige of that - years and years of national pride and inspiration for one relatively low price, all things considered. And you'd get an almost ideal initial population as well. The best and brightest. The diplomats, the figureheads of a way of life, a way of seeing life and our place in the universe.
Yeah - so, water. For those things above to work, they must come to live in a beautiful place, a place just about anyone would be happy to live. People's impression of how worthwhile it is to live in space, how rewarding the experience could be, will be based on what they see in these broadcasts and the feeling they pick up from those residents. There are so many cool things you can do with water to make the colony more inviting, but you need a lot of it. There is, of course, the classic What If? lunar swimming pool scenario. There are water walls and water domes - 5 m of water is pretty good radiation shielding. There are natural ponds that both provide a sense of nature and do some of the work of recycling waste water.
To do those things on a proper scale requires several thousand tons of water. Some of it will therefore wait for the installation of coil guns at both the equator and the pole. Because really, you can't go too far with this idea. Lakes. A lunar lake, if you are putting in an actual town, you've gotta have one. A dome over a whole crater - good ol' Teacup Crater gets that treatment first. That will take 350,000 tons of water. After that you can stand below that dome and see the sky all around, and sort of feel like you are outside, unencumbered by a space suit, for the first time on another planet.
Oh - Aristillus. It is also a KREEP hotspot. Perhaps it can get the second full colony, but i think we are too far along to move the colony again, and actually, i think there is a decent argument against it. The likelihood of an ilmenite deposit is much higher at Lalande, based on Clemintine data of TiO2 on the surface. Concentration of TiO2 is much higher at Lalande than at Aristillus. ilmenite gets water and iron when reacted with hydrogen. Aristillus also looks a lot older and doesn't have the wonderfully clean walls that Lalande has, that look so very much like the digging depth to get to bedrock isn't much. And the equator has a big advantage if you start doing stuff with tethers, whether you go through EML1 or make a lunavator. So Lalande it is. Which is also nice because i've become quite fond of Lalande after looking at it so much.
Things are shaping up nicely :)