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I didn't include the answer to that last calculation:

311*9.81ln(1 + 375/(13 + 6.7)) = 9,145 m/s.

Dr. John Schilling has produced a payload estimation program:

Launch Vehicle Performance Calculator.
http://www.silverbirdastronautics.com/LVperform.html

It gives a range of likely values of the payload. I've found the midpoint of the range it specifies is a reasonably accurate estimate to the actual payload for known rockets.
Input the vacuum values for the thrust in kilonewtons and Isp in seconds. The program takes into account the sea level loss. SpaceX gives the Merlin 1D vacuum thrust as 161,000 lbs and vacuum Isp as 311 s:

FALCON 9 OVERVIEW.
http://www.spacex.com/falcon9.php

For the 9 Merlins this is a thrust of 9*161,000*4.46 = 6,460 kN. Use the default altitude of 185 km and the Cape Canaveral launch site, and a 28.5 degree orbital inclination, to match the Cape's latitude.
Input the dry mass of 13,000 kg and propellant mass of 375,000 kg. Then it gives an estimated 7,564 kg payload mass:

Launch Vehicle:      User-Defined Launch Vehicle
Launch Site:      Cape Canaveral / KSC
Destination Orbit:       185 x 185 km, 28 deg
Estimated Payload:       7564 kg
95% Confidence Interval:       3766 - 12191 kg

This may be enough to launch the Dragon capsule, depending on the mass of the Launch Abort System(LAS).

     Bob Clark

I think we can probably do better than that first estimate of the Falcon 9 first stage with Merlin 1D's as a SSTO. The Merlin 1D has a 147,000 lb sea level thrust:

Modified Merlin engine completes full duration firing.
BY STEPHEN CLARK
SPACEFLIGHT NOW
Posted: June 25, 2012
http://www.spaceflightnow.com/news/n1206/25merlin1d/

The gross mass of the Falcon 9 first stage with the Merlin 1D's and a 1.2 mT payload would be 250 + 11.8 + 1.2 = 263 mT, 578,600 lbs. This could be lofted by just 4 of the Merlin 1D's. But the thrust would be just a little over the gross mass resulting in high gravity loss. So let's use 5 Merlins. Subtracting off 4 Merlins makes the dry mass 11,800 - 4*450 = 10,000 kg.
The number of 30,000 fps delta-v for LEO is assuming a T/W ratio common for liquid fueled rockets, in the range 1.1 to 1.2. With all 9 Merlins the T/W ratio would above 2.2. This would result in a much reduced gravity loss. So the required delta-v would be less than the 30,000 fps number, and so actually higher than 1.2 mT could be sent to LEO even in that case.
But let's look at the case of using 5 Merlins. SpaceX has given a vacuum Isp of the Merlin 1D as actually 311 s. Then we could send 3.1 mT to LEO:

311*9.81ln(1 + 250/(10 + 3.1)) = 9,152 m/s.

  SpaceX has said though they want to move to a larger version of the Falcon 9 called the Falcon 9 v1.1, in accordance with the Merlin 1D's larger thrust. The Falcon Heavy will use this version's first stage for its core stage and side boosters. SpaceX expects the Falcon 9 v1.1 to be ready by the end of the year.
Elon Musk has said the version 1.1 will be about 50% longer:

Q&A with SpaceX founder and chief designer Elon Musk.
BY STEPHEN CLARK
SPACEFLIGHT NOW
Posted: May 18, 2012
http://www.spaceflightnow.com/falcon9/003/120518musk/

I'll assume this is coming from 50% larger tanks. This puts the propellant load now at 375,000 kg. Interestingly SpaceX says the side boosters on the Falcon Heavy will have a 30 to 1 mass ratio. This improvement is probably coming from the fact it is using the lighter Merlin 1D engines, and because scaling up a rocket actually improves your mass ratio, and also not having to support the weight of an upper stage and heavy payload means it can be made lighter.
So I'll assume for this SSTO version of the Falcon 9 v1.1 the mass ratio is 30 to 1, which makes the dry mass 13 mT. Then this version can lift 6.7 mT to LEO:

311*9.81ln(1 + 375/(13 + 6.7))

  Bob Clark

Just saw this interview of Elon Musk on NasaSpaceFlight:

Space X Heralds New Era of Travel.
http://www.youtube.com/watch?v=uZqN7351Z30

He mentions manned flights to Mars. He says initially they will be 6 month flights, but eventually they will come down to under a month.

  Bob Clark

Yes, I was wondering about the air pressure effects too. But there are a couple of factors that made it worse for those two examples you mentioned, and also for the Falcon 9 first stage which also falls apart on reentry.
The main one is that these spacecraft or stages were tumbling, which puts severe stress on the structure. The second is that these structures were so heavy they came down so rapidly that they reached high density air while still traveling very fast. However, for a very light structure for the wing area, the lift should be enough to make the descent much shallower so it will have burned off much of the speed when it gets down to the higher density air.
We could perhaps also add some strengthening members to resist the bending loads that would not add too much to the weight made of carbon composites materials. I saw this new carbon composite isotruss bicycle frame when searching on lightweight composites:

That thing just looks like it would be light for the strength doesn't it?

I get now what you mean about a "rough ride" by your comparison of a Piper Cub to a jumbo jet. Perhaps the reaction control system could keep it stable considering its lightweight.

   Bob Clark

How is this better than the usual suit? It is not for EVA but just when you are sitting inside the space ship like the suits astronauts wear during shuttle launch.
A low cost, lightweight, flexible EVA suit would really be something to look forward to.

   Bob Clark

Actually, we don't "know" that. To be more precise, we don't know how to do it now, but that is not the same as saying we know we can't do it.
The research on this is ongoing and I think multiple solutions will be available near term.
However, I'm not opposed to multiple small deliveries to the surface. One question that needs to be solved is landing them nearby each other, minimizing the landing ellipse in the parlance of the current Mars robot landers. Actually, a proposed solution to the question of landing large payloads has an influence on this question as well.
That's using a high lift/drag ratio lander. One of the selling points of the space shuttle was its high cross-range, enabling more precise landings. A high L/D ratio Mars lander would reduce the need for a large area aerobrake while at the same time enabling more precise landings.

    Bob Clark

Actually it would be even better than this. The X-33 had engines to liftoff from Earth fully fueled. For this purpose, these wouldn't be needed, or it would use much smaller engines just for landing the unfueled mass on Mars. The thrust for the X-33 given on the Astronautix page was 513,000 lbs.  vacuum. Reportedly the aerospike engines on the X-33 had a 40-to-1 T/W ratio. So their weight on the X-33 would be about 13,000 lbs. So the weight would be reduced to 35,000 lbs by removing them, and the wing loading to 35,000 lbs/1600 sq.ft = 22 lbs/sq.ft.
But another key factor would be the lift/drag ratio. For the X-33, the hypersonic L/D was about that of the space shuttle, in the range of 1 to 1.2. How does the L/D ratio affect the question of landing large masses on Mars?

  Bob Clark

This blog post shows the high mass ratio discussed in the "Low Cost HLV" blog post
is feasible by making a comparison to the Saturn S-IC stage:

MONDAY, MAY 7, 2012
Low Cost HLV, page 2: Comparison to the S-IC Stage.
http://exoscientist.blogspot.com/2012/0 … age-2.html

This blog post shows you can get an even higher mass ratio, close to 29 to 1,
by using modern materials and common bulkhead design. A mass ratio this high
makes possible a SSTO:

THURSDAY, JUNE 21, 2012
Low Cost HLV, page 3: Lightweighting the S-IC Stage.
http://exoscientist.blogspot.com/2012/0 … -s-ic.html

  Bob Clark

I read that report cited by the supporters of asteroid mining about moving a 500 mT asteroid to lunar orbit:

Asteroid Retrieval Feasibility Study.
2 April 2012
http://kiss.caltech.edu/study/asteroid/ … report.pdf

The news report were all about the solar electric ion propulsion used and that perhaps it would cost $2.6 billion to develop. But I was surprised in the report that it also discussed doing it with LH2/LOX chemical propulsion and how little propellant it would use. First it notes that an asteroid such as 2008HU4 at closest approach would require only a 170 m/s (!) delta-v to bring it to lunar orbit. Then in figure 19 on p. 43 is given a comparison between the propellant required for LH2/LO2, N204/MMH, and SEP propulsion for this asteroid at an assumed 1,000 mT mass. Surprisingly, for the hydrogen case it is less then 40 mT for a 1,000 mT payload! This is because of course it is only a 170 m/s delta-v. But this means for the 500 mT case that was cited in the news reports it would be less than 20 mT propellant load, and a LH2/LOX propulsion stage this size is already available in the Centaur.

Since the chemical propulsion would have greater thrust, the mission return time would also be significantly less than the 10 years for the SEP propulsion. The problem though is that you would need to get the return propellant from the asteroid. The report proposes using a carbonaceous asteroid which would have abundant H2O likely in chemically bound form, perhaps as much as 20%. So the question is are there simple methods known from ISRU studies to release H2O from say the carbonates and clays likely to be in carbonaceous asteroids?

You could enclose the ca. 7 meter diameter in a shroud and using a solar furnace either with a mirror or fresnel lens to release the volatiles, such as water, CO2 and methane. I'm thinking you could do this at low enough temperature that only the volatiles are released, and the solid material would not be vaporized. Then you would use the highest temperatures possible with a solar furnace, ca. 3,500 degress C:

Solar Furnace.
http://en.wikipedia.org/wiki/Solar_furnace

to do electrolysis to separate the hydrogen and oxygen. Another complication is that you would need cryogenic chilling equipment to liquefy the hydrogen and oxygen for the RL-10 engines on the Centaur. Probably you would also need to separate out the other volatiles such as the CO2 and methane, another complication.

Anyone know of research on this question of heating of water bearing minerals to remove the water all the way to the step of turning it separately into hydrogen and oxygen?

Another possibility if you are going to use a solar furnace is to use solar thermal propulsion. One particularly simple implementation of this would be to simply vaporize the asteroidal material without separating it out to say hydrogen as the reaction mass. At maximal temperatures of 3,500 C you would still get pretty good Isp even using high molecular weight materials. A disadvantage of this is that you would also lose some proportion of the valuable minerals.

Any of these possibilities I would estimate would cost far less than a billion dollars however.

   Bob Clark

I found the gun launch researchers by searching on the Mars Society conference for 2011:

Report on the 2011 Mars Society Annual Convention
posted Aug 16, 2011 10:36 AM by Michael Stoltz   [ updated Aug 16, 2011 10:46 AM ]
By Richard Obousy, Centauri Dreams (centauri-dreams.org), 08.16.11

Propellant Delivery to Orbit in Support of Mars Exploration with Hydrogen Gas Guns - Dr. John Hunter.
http://www.youtube.com/watch?v=s7RGSBOmsm4

  Bob Clark

Follow-up blog posts:

1.)Discussion of using the new Hubble-class scopes to search for nomad planets
and hypothesized large planets at the extreme fringe of the Solar System:

Low cost development and applications of the new NRO donated telescopes, Page 2.
http://exoscientist.blogspot.com/2012/0 … ns_12.html

and:

2.)Discussion of using distributed computing to allow the public to take part
in the asteroid, new planet, and brown dwarf search:

Low cost development and applications of the new NRO donated telescopes, Page 3.
http://exoscientist.blogspot.com/2012/0 … ns_13.html

   Bob Clark

Good point about gas gun launch being doable now for small payloads. Do you have a link to this teams research?
Railgun launch for small payloads is also doable now by scaling up the Navy research with their railguns:

It's real! Navy test-fires first working prototype railgun.
By Kelley Vlahos
Published February 28, 2012
http://www.foxnews.com/scitech/2012/02/ … e-railgun/

Small payload costs to orbit under $100/kg are possible then. When you consider the energy costs to orbit are less than a dollar a kilogram, this is well within the feasibility range.
Propellant costs to orbit at less than $100/kg makes possible a key advantage of SSTO's. If you calculate the delta-v from LEO to the Moon and back, then the total delta-v is less than that required to get to orbit. So if one did have his own private, SSTO vehicle, then with propellant depots, he would also have his own private lunar vehicle. Note this is NOT true of two-stage-to-orbit-vehicles where the upper stage might only get a delta-v of 6,000 m/s or so.
Then this is another reason why the fact that low cost SSTO's are doable now is so important:

The Coming SSTO's.
http://exoscientist.blogspot.com/2012/0 … sstos.html

  Bob Clark