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Greetings and Salutations:

From: davem@ee.ubc.ca (Dave Michelson)
>I've been corresponding with Ken about this point and I think he was confused
>by the way "injection velocity" is described in Fundamentals of Astrodynamics.
> 
>I, for one, agree that TLI from LEO only requires a velocity increment some
>something less than 7500 mph or just over 2 miles/sec.  Ken was under the
>impression that TLI required an *additional* (rather than a net) velocity of
>of 25,000 mph...

It is very kind of you to explain my confusion on the matter (I usually just
let the audience wonder ;->) I understand now where the complete confusion came
from, and I have gotten better data.  Reference McDonnell Douglas Astronautics
Company - West - Propulsion engineering manual - Development engineering -
Manual M8069.ACD.  For a 100 NM orbit, we require 25,581 ft/second velocity. 
For lunar missions (depending on how much time you wish to be in transit to the
moon) 90 hour transfer = 35,850 to 35,910 ft/sec with 8,310 ft/sec additional
velocity to land.  50 hour transfer orbit is 36,070 to 36,160 ft./sec. with
9,410 ft/sec. additional velocity to land.  Note that the Apollo missions never
reached true Earth escape velocity (36,178 ft./sec.) but would have been in a
highly elliptical orbit if something had gone badly wrong.

Now for the confusion factor.  Here is the original post:

From: ritley@uimrl7.mrl.uiuc.edu
>Would it be possible for the Space Shuttle to journey to the Moon?
>
>Obviously it could not easily land there, but could it at least make
>the trip?
>
>If so, would it be possible to fit the Shuttle with equipment which
>would permit it to land there --- possibly some sort of rocket
>engine located in the cargo bay?  Or possibly a second landing
>vehicle could be taken up (perhaps on a second flight) and
>``shuttled" to the Moon in the cargo bay?

My reply was, essentially, that it would take at least twice (if not more)
ENERGY to get to the moon than the shuttle expends for launch into low earth
orbit.  I got wrapped around the axle when energy was  equated with velocity in
some of the other posts.  This is like discussing apples & pineapples.  They
are somewhat related, but not directly.  You must expend energy to get more
velocity, but that energy expenditure can be an efficient expenditure or not so
efficient.  Once again my McDonnell reference gives a graph of "Rocket vehicle
payload fraction versus velocity relationship".  When you get into the
approximately 35,000 ft/sec range, the ratio gets pretty nasty.  The first hint
is that the payload fraction side of the scale is logarithmic.  Basically you
burn an exponential amount of fuel for linear velocity increase.  Even with an
Isp of 460, you get only about 0.0025% payload into 34,000 ft/sec orbit,
assuming the "good" step structure factor of 0.10, of course.

To put it differently, Reference "Rocket Propulsion Elements", Sixth edition,
George P. Sutton.  Assuming you have enough thrust to put 100% payload in orbit
(300 nautical miles), to soft land that on the moon, you would only be able to
get about 10% to 20% of the payload there.  To land and return, you can only
get about 1% to 4%.

By the way, as a matter of general interest, even if you run the OMS system dry
you only get about an additional 1,500 ft/sec extra boost with no payload. 
I.e. The OMS will get you about 10% of the way to the moon...

Now, I can see how far off my SWAG (Scientific Wild Ass Guess) was.  I am going
to go for pure numbers.

Lets, just for grins, go for a empty Orbiter.

  171,205 = Orbiter weight (dry, with engines)
1,655,600 = External Tank with propellants
1,300,000 = SRB (Each)
1,300,000 = SRB #2
----------
4,426,805 Lbs total

  171,205 = Orbiter weight (dry, no OMS propellants, with engines)

Payload fraction = Payload weight/launch weight.  This gives us a payload
fraction versus 25,000 ft/sec fraction of 0.038 to low Earth orbit.

The SSMEs have a Isp of 453.5 at altitude.  The SRBs have a Isp of 265.5.  One
SRB has 3 million Lbs thrust, but is optimized for atmosphere.  One SSME has
470,000 Lbs thrust in vacuum at 100% thrust and is optimized for upper
atmosphere / vacuum.

To get a payload fraction of 0.0025% into 34,000 ft/sec orbit (as mentioned
above) it looks like you would have to have about:

171,205 / 0.0025 = 68,482,000 Lbs total.  That is assuming a Isp of somewhere
around 460, and a GREAT step structure factor.  This is also neglecting the
weight of the propellant tank(s) that are required.

Gee.  Looks like I was off by a factor of 5 (conservatively).  You would need
about 11 times the amount of propellants, and have it all lifted by SSMEs, no
SRBs.  That still doesn't get you to the moon.

Now if you wish to discuss refueling options in low earth orbit, to get an
additional 10,000 ft/second for moon injection, you make life a little easier. 
But that would be cheating.  You STILL have to send the propellant up, and
count that as total energy.

The absolute best case would be where you had an infinite number of propulsion
filling stations all long the flight path to the moon, but that sort of
thinking starts getting ridiculous.

-- 
-----------------------------------------------
Ken Hollis  INTERNET: HOLLIS@TITAN.KSC.NASA.GOV
            SPAN/HEPnet: KSCP00::HOLLIS
Due to additional budget constraints, the light at the end of the tunnel
will be turned off until further notice...