Delta-V For "direct Descent" To The Lunar Surface?

[RGClark]

I was trying to get a lower roundtrip delta-V for lunar missions by flying

directly to the lunar surface rather than going first into lunar orbit then

descending, the "direct descent" mode. Here's a list of delta-V's of the

Earth/Moon system:

 

Delta-V budget.

Earth–Moon space.

http://en.wikipedia.org/wiki/Delta-v_budget#Earth.E2.80.93Moon_space

 

If you add up the delta-V's from LEO to LLO, 4,040 m/s, then to the lunar

surface, 1,870 m/s, then back to LEO, 2,740 m/s, you get 8,650 m/s, with

aerobraking on the return.

I wanted to reduce the 4,040 m/s + 1,870 m/s = 5,910 m/s for the trip to the

Moon. The idea was to do a trans lunar injection at 3,150 m/s towards the Moon

then cancel out the speed the vehicle picks up by the Moons gravity. This

would be the escape velocity for the Moon at 2,400 m/s. Then the total would

be 5,550 m/s. This is a saving of 360 m/s. This brings the roundtrip delta-V

down to 8,290 m/s.

I had a question though if the relative velocity of the Moon around the Earth

might add to this amount. But the book The Rocket Company, a fictional

account of the private development of a reusable launch vehicle written by

actual rocket engineers, gives the same amount for the "direct descent"

delta-V to the Moon 18,200 feet/sec, 5,550 m/s:

 

The Rocket Company.

http://books.google.com/books?id=ku3sBbICJGwC&pg=PA174&lpg=PA174&dq=%22direct+descent%22+Moon+delta-V&source=bl&ots=V0ShEuXLAv&sig=QIpkcV9Gtu-rYMOYJpLOmWwsy54&hl=en#v=onepage&q=%22direct%20descent%22%20Moon%20delta-V&f=false

 

Another approach would be to find the Hohmann transfer burn to take it from

LEO to the distance of the Moon's orbit but don't add on the burn to

circularize the orbit. Then add on the value of the Moon's escape velocity.

I'm looking at that now.

 

Here's another clue. This NASA report from 1970 gives the delta-V for direct

descent but it gives it dependent on the specific orbital energy, called the

vis viva energy, of the craft when it begins the descent burn:

 

SITE ACCESSIBILITY AND CHARACTERISTIC VELOCITY

REQUIREMENTS FOR DIRECT-DESCENT LUNAR LANDINGS.

http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19700023906_1970023906.pdf

 

The problem is I couldn't connect the specific orbital energy it was citing

to a delta-V you would apply at LEO to get to that point. How do you get that?

 

With the lower delta-V number, I can carry more payload with low cost

proposals for manned lunar missions:

 

SpaceX Dragon spacecraft for low cost trips to the Moon.

http://exoscientist.blogspot.com/2012/05/spacex-dragon-spacecraft-for-low-cost.html

 

The Coming SSTO's: Applications to interplanetary flight.

http://exoscientist.blogspot.com/2012/08/the-coming-sstos-applications-to.html

 

 

Bob Clark

[CraigD]

Being a fan of brute-force calculation over competent orbital mechanics calculations, I did a rough-guess simulation (using XGRAVSIM2) of half a tweaked Hohmann transfer from a LEO of r=6578137 m (200 km altitude) to r=384400000 (the moon’s SA). The bottom delta-V for such a Hohman transfer should be about 3131.34 m/s, the top about 831.50. Via trial and error (I kept trying, varying its start time and duration, ‘til I hit the moon), I used a 321 s burn at 9.788 m/s/s for a bottom delta-V of about 3141.95. The impact speed with the moon was 2660.63 m/s. So, assuming a last-moment burn enough for a soft landing, the total delta-V for this LEO to Moon maneuver is about 5802 m/s.

 

This is substantially lower than the 8650 m/s you cited, Robert.

 

I fiddled around with trying to actually pull said soft landing, but gave up after getting disoriented. I need to enhance my simulator a bit to use it in such a seat-of-the-pants way.

 

I’ve taken a few amateurish liberties with the sim’s inputs (I started with the Earth at velocity = 0, rather than the correct velocity for the Earth-Moon system), but think my numbers are close enough for purposes of estimation to address this thread’s question.

[RGClark]

Being a fan of brute-force calculation over competent orbital mechanics calculations, I did a rough-guess simulation (using XGRAVSIM2) of half a tweaked Hohmann transfer from a LEO of r=6578137 m (200 km altitude) to r=384400000 (the moon’s SA). The bottom delta-V for such a Hohman transfer should be about 3131.34 m/s, the top about 831.50. Via trial and error (I kept trying, varying its start time and duration, ‘til I hit the moon), I used a 321 s burn at 9.788 m/s/s for a bottom delta-V of about 3141.95. The impact speed with the moon was 2660.63 m/s. So, assuming a last-moment burn enough for a soft landing, the total delta-V for this LEO to Moon maneuver is about 5802 m/s.

This is substantially lower than the 8650 m/s you cited, Robert.

I fiddled around with trying to actually pull said soft landing, but gave up after getting disoriented. I need to enhance my simulator a bit to use it in such a seat-of-the-pants way.

I’ve taken a few amateurish liberties with the sim’s inputs (I started with the Earth at velocity = 0, rather than the correct velocity for the Earth-Moon system), but think my numbers are close enough for purposes of estimation to address this thread’s question.

 

Thanks for taking the time to do the calculation. Remember the 8,650 m/s number was the total round trip delta-V from LEO to the lunar surface and back to LEO. The number to compare to was 5,910 m/s, which is just the one-way delta-V from LEO to lunar orbit and then to the lunar surface. You were able to reduce this number by about 100 m/s.

Note after a web search I found this lunar landing proposal from the early 90's called 'Early Lunar Access' that used the "direct descent" method:

 

Lunar Base Studies in the 1990s.

1993: Early Lunar Access (ELA).

by Marcus Lindroos

To save fuel, the LEV makes a direct landing rather than enter an intermediate lunar parking orbit as Apollo did. The vehicle retains sufficient propellant to perform a later ascent burn to return the crew to Earth. For unmanned cargo missions, the LEV carries a heavier payload and uses up all its fuel for landing.

http://www.nss.org/settlement/moon/ELA.html

 

I still need to find out how much they were able to save with their trajectory.

 

Bob Clark

Edited October 30, 2012 by Robert Clark