Friday, December 03, 2010

Apollo 8 Solo


In 1927 Charles Lindbergh flew non-stop from Long Island to Paris. He was catapulted to instant fame by doing so and won the Orteig Prize. He didn't have a co-pilot. He didn't have an army of engineers monitoring his plane or a flight surgeon monitoring his heart rate, it was just him and his trusty single-engine monoplane, the Spirit of St. Louis. His achievement is heralded today as kick-starting the commercial aviation industry and opening up the skies to the everyman.

But what of space? Could a modern Lindbergh fly an impossible journey and change the way we look at spaceflight forever? I think it can be done, and for cheaper than you might imagine.

In 1968 the first humans left the vicinity of Earth, flew 6 days and nearly a million miles to the Moon and back. Their mission not only was the first, it also proved the feasibility of the missions to follow. Apollo 8 would have been much easier to achieve had they only wanted to swing-by the Moon, and still a significant achievement. Instead, they entered lunar orbit, circling it 10 times before returning home.

If the flight is to be attempted today, the cheapest available launcher is the Falcon 9 from SpaceX. It can put 10,450kg into LEO. The Dragon capsule is also available - they say the crew configuration is not much different from the cargo configuration - and after removing the 310kg Common Berthing Mechanism, and another 60kg of miscellaneous mass savings, a dry mass of 1926kg is achievable.

For a single crew member, assumed to be less than 90kg, the consumables requirements for one week are: 11.839kg cabin air and pressurization, 25.83kg oxygen candles, 52.71kg LiHo CO2 scrubbers, 45kg food and water. Adding this to the dry mass gives a final mass to run the rocket equation on: 2152kg.

The delta-v required to leave Earth orbit and head towards the Moon is a whopping 3107m/s. Entering low Lunar orbit requires another 837m/s, and returning home requires another 837m/s. So we need a grand total of 4781m/s.

All the propulsive maneuvers are achieved using the Draco thrusters on the Dragon capsule, which I estimate to have a specific impulse of 309 seconds. dv = 9.8 * 309 * ln(10450 / 2152) gives us an uncomfortable 4m/s of margin. :) [edit: it occurs to me that the Dragon dry mass already includes a life support system, and a 78.54kg reduction in mass has a massive effect on delta-v. So this is more like 115m/s of margin, which should make anyone happy.]

In order to win the Orteig, Lindbergh had the Spirit built custom for his needs. Benjamin Mahoney is said to have built it for cost. Perhaps Elon Musk could be similarly persuaded, but at current prices it'll cost around $130M.

11 comments:

  1. Unless I missed something, you left out the modified heat shield to take the delta v coming from lunar transfer orbit.

    But the concept is certainly interesting.

    ReplyDelete
  2. Anonymous4:47 AM

    I think you forgot the mass to add Radiation shields to Falcon capsule and a composite debris shield.

    Although I remember the Apollo capsule never had a frontal debris shield, so this one can be left out.

    But nothing prevent a double DragonX launch with LEO rende-vous and flying the complex to the moon, but then you double the figure ... so lets stick to the Apolo 8

    ReplyDelete
  3. Anonymous5:13 AM

    Just as a thought, what would happen if you
    used 2 to 4 Falcon 1/1e first stages as strap
    on boosters for a Falcon 9 core? I realize there are structural, software, and other infrastructure issues, but this is intended as a "what if" type
    question.

    ReplyDelete
  4. Anonymous5:38 AM

    According to Wikipedia, 'In 2010 SpaceX's Elon Musk stated that the "Dragon is capable of re-entering from a Lunar velocity, or even a Mars velocity with the heat shield that it has."'

    ReplyDelete
  5. Anonymous6:24 AM

    You would not use the dragon capsule for all these maneuvers. Instead, you would use the falcon 9 upper stage to get the dragon to a highly elliptic orbit (similar to GTO), or perhaps even through TLI. Then you would use the draco thrusters for entering and leaving lunar orbit (LOI/TEI).

    That changes the numbers a bit in your favor, since the merlic vacuum engine on the 2nd stage of the falcon 9 has a better Isp.

    ReplyDelete
  6. The Falcon 9 can only put 2585kg into LTO. Carrying a big second stage through TLI makes no sense at this scale. If you're using a Falcon 9 Heavy, that's a different story. There's a tradeoff there.

    Dragon has more radiation protection than the Apollo CM had. It has more debris protection too. The heat shield is adequate for an Apollo 8 style reentry.

    I'm now thinking about how feasible a single person lander under 511kg is.. cause that's what Falcon 9 can deliver to the lunar surface with enough delta-v to get back to Earth. If you have mass to throw out along the way, like tanks, it could be a little heavier too.

    ReplyDelete
  7. rklaehn9:29 PM

    Using the second stage to send the dragon all the way to TLI is not the way to go. But if you want to use a mostly unmodified dragon to do a circumlunar flight, you have to be aware that it has only a limited amount of propellant (I got 1290kg from some dragon brochure, but the real amount might be slightly different). Adding propellant tanks sounds easy, but it isn't. This is NTO and MMH, so you do _not_ want to have it inside the pressurized volume.

    So the best way to go is to make the dragon as light as possible without having to do major modifications, and then send it to a highly elliptic earth orbit using the falcon 9 2nd stage. This would probably be around the 28° "pseudo-GTO" described in the falcon 9 users guide.

    Then you would use the dragon propulsion system itself to add another ~800m/s and send it to a free return translunar injection (TLI)

    ReplyDelete
  8. Great initial discussion point. I did some research into multiple F9 launched Dragon/Bigelow modules leading to single burn flyby trips of the moon (there's a very cool trajectory which takes a craft out to the moon, flies by to change inclination, passes above the Earth-Moon system to another lunar flyby 2 weeks later, then a return to Earth), a NEO and Mars, but this is much simpler.

    Maybe Elon will weigh in...

    ReplyDelete
  9. In an interview, I saw Elon say that the Dragon's escape system would be a pusher unit, using the propellants on board already. Has anyone heard whether the tanks need to be enlarged to do so? That may provide some delta-v margin.

    ReplyDelete
  10. Tom, more importantly, it would mean they have to increase the thrust of the thrusters *significantly*. Currently the Draco thrusters are 90lbf weaklings - literally, they produce only 400N of thrust each. This is good for the Dragon-to-the-Moon scenario because it means you can deliver the LEO impulse in a single shot, meaning less total delta-v required and less time spent by astronauts in the radiation belts.

    ReplyDelete