Delta-V for "direct descent" to the lunar surface?

[Robert Clark]

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

[Enthalpy]

Hi Robert, nice to see you here!

 

The delta-V should not differ if you make a stop on a low orbit. The only difference lies in the Oberth effect, where the additional energy you put to reach the transfer path is added at the speed of the low orbit, instead of possibly at a marginally higher speed if the push is done at a slightly lower altitude (measured from the planet's centre). So if you get a difference, I expect some unclear data lead to misinterpretation.

 

In any case, keeping the return vessel in Lunar orbit is an excellent choice, one that made Apollo possible, because then you save the mass of the return vehicle (and fuel) from your Lunar descent-ascent module. This makes a huge difference, much more interesting than 360m/s.

 

Remember Wiki's table gives minimum speed increments, but in a real mission you wouldn't choose a lengthy Hohmann transfer. A few 10m/s more cut the transfers by several days and are the normal choice.