A One Man mission to the moon using 1960-ish spacecraft (with better electronics)
First from Astronautix.com the Mercury Capsule data
Crew Size: 1.
Habitable Volume: 1.70 m3.
Structure: 340 kg (740 lb).
Heat shield: 272 kg (599 lb).
Reaction Control System: 40 kg (88 lb).
Recovery Equipment: 60 kg (132 lb).
Navigation Equipment: 40 kg (88 lb).
Telemetry Equipment: 50 kg (110 lb).
Electrical Equipment: 80 kg (176 lb).
Communications Systems: 20 kg (44 lb).
Crew Seats and Provisions: 80 kg (176 lb).
Crew: 72 kg (158 lb).
Environmental Control System: 50 kg (110 lb).
RCS Coarse No x Thrust: 6 x 107 N.
RCS Fine No x Thrust: 6 x 5 N.
RCS specific imulse: 220 sec.
RCS total impulse: 30 kgf-sec.
Electric System: 12.96 kWh.
Electric System: 0.54 average kW.
Gross mass: 1,118 kg (2,464 lb).
Unfuelled mass: 1,104 kg (2,434 lb).
Height: 3.51 m (11.51 ft).
Diameter: 1.89 m (6.20 ft).
1) If we assume an up-rated (cis-lunar capable) Heat shield weighs twice as much, we add 272kg (599 lbs) (This is based on kinetic energy of 11km/s ve 8 km/sec)
2) Next, this capsule was probably capable of 5 days in orbit. The last capsule flight landed when most systems had failed (electrical) but consumables were in good shape. Lets assume we double the 'crew seats and provisions' (it is hard to tell from this what this was) and add 80kg (176lbs).
3) RCS propellant would need to be increased similarly. 30 kgF-sec (???) is 66 lbf-sec at ISP of 220 sec this was only 0.3 lbs of propellant when the unfueled mass is 14 kg less than the fueled mass (??) double the 14 kg for RCS propellant, but we are guessing conservatively.
4) We assume electronic reliability, efficiency, and range have improved. This needs more detailed work, but I will bet that a meter of Solar cells could be added with no additional weight after trimming the radio alone down by a few of the 50kg. (no change to telemetry system)
5) Similarly the General Electrical and Navigation systems will be improved without weight gain.
This would give us a one person, cis-lunar mission capable capsule that weighed 1484 kg.
One man Lunar Lander from “Chariots For Apollo” circa 1961.
Although these two illustrations are not necessarily from the same concept, they are from the same era. If we take the Lunar Lander – One Man numbers as reasonable we can extrapolate the function.
1 man and life support 220 lbm Controls 50 lbm Structure 230 lmb Engine and tankage 220 lbm Fuel and oxidizer 2500 lbm
Total 3220 lbm (1460 kg) (remarkably close to the mercury capsule with its 11km/sec heat shield) Total without fuel 750 lbm (340kg)
With an assumed ISP of 300 seconds we get a DeltaV performance of 3540 m/s
( DV = 9.8 m/s * ISP * ln( full / empty ) )
From http://www.redyns.com/Reference/dvchart.jpg we see that 1.6 is the descent or ascent velocity required from low lunar orbit to and from the surface. This means that round trip is 3200 m/s leaving a nice healthy 340 m/s second for hover on the way down or rendezvous on the way back up.
Combining the one man lander and the extended mercury capsule from above in an apollo like stack, we have a leo mass of 2944 kg (6492 lbm). Note a space walk out of the mercury capsule would be needed and I make no promises about the utility of a mercury suit on the surface of the moon.
To get from low lunar orbit to the earth, assuming aerobraking, we need about 700 m/s for just the Mercury capsule. The sizing of a return propulsion stage gets a little iterational here, you assume you are using the engines and tanks from the trip out and account for burned propellants, but the size of the engines and tanks are dependent on the trip out, which includes the propellant for the trip back, which is dependent on the tanks …. time for a little iteration on a spread sheet. So to start with the rocket equation again. (remember y=e^x is the opposite of x = ln(y) )
700 = (300 s) * 9.8 m/s * ln (full/1484) rearrange is full = 1484 * e^(700/(300*9.8))
this implies a full mass of 1883kg or about 399 kg. (ignoring tanks etc)
Iterating for Engines Tanks and Structure at 10% of propellant, we wind up with 410 kg of propellant and 41kg of engines tanks and structure (for what it is worth here)
To get from low earth orbit to low lunar orbit with the lander and the mercury capsule, we need about 3900 m/s. We are using the propulsion calculations for the lander with tanks and engine and very little structure to be about 10% of the propellant to be burned again. so... from the rocket equation again...
3900 = 300 *9/8 *ln (full / (1484+410+41+1460) giving full = 3395 * e^(3900/(300*9.8) ) = 12973 kg, or 9578kg in propellants
iterating for structure we get.. a lot worse. The large deltaV with a 10% fraction drives the required propellant up to 13000 kg and 1300 kg of ETS. Staging is one solution, as is reducing the size of the engines. Cutting the ETS on this stage by half is quite possible and would reduce the propellant by about 2000 kg. We will use this number.
Extended Mercury capsule 1484 kg
Earth return Stage 41 kg
Earth return Propellant 410 kg
One man lander (mt) 340 kg
Descent and Ascent Propellant 1134 kg
Earth Departure Stage 545 kg
Earth Departure Propellant 10905 kg
Total Dry Mass 2410 kg
Total Propellant 12449 kg
Now raising the ISP of the Earth departure stage above 300 helps these numbers considerably. At 390 seconds, the entire stack weighs about 10500 kg, which happens to be the LEO throw weight of a SpaceX Falcon 9 (at $56M)
A reasonably small development program should be able to be run at $44M, giving a $100M total cost ?