#### RGClark

##### Mathematician

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All-Liquid: A Super Heavy Lift Alternative?

by Ed Kyle, Updated 11/29/2009

http://www.spacelaunchreport.com/liquidhllv.html

The reason for this is that it is cheaper to create new tanks of the same diameter as already produced ones by using the same tooling as those previous ones. This is true even if switching from hydrogen to kerosene in the new tanks.

However, I will argue that you can get super heavy lift launchers without using the expensive upper stages of the other proposals by using the very high mass ratios proven possible by SpaceX with the Falcon 9 lower stage, at above 20 to 1:

SPACEX ACHIEVES ORBITAL BULLSEYE WITH INAUGURAL FLIGHT OF FALCON 9 ROCKET.

Cape Canaveral, Florida – June 7, 2010

"The Merlin engine is one of only two orbit class rocket engines developed in the United States in the last decade (SpaceX’s Kestrel is the other), and is the highest efficiency American hydrocarbon engine ever built.

"The Falcon 9 first stage, with a fully fueled to dry weight ratio of over 20, has the world's best structural efficiency, despite being designed to higher human rated factors of safety."

http://www.spacex.com/press.php?page=20100607

We will use tanks of the same size as these other proposals but will use parallel, "bimese", staging with cross-feed fueling. This method uses two copies of lower stages mated together in parallel with the fueling for all the engines coming sequentially from only a single stage, and with that stage being jettisoned when it's expended its fuel. See the attached images below for how parallel staging with cross-feed fueling works.

Do the calculation first for the large 8.4 meter wide tank version. At the bottom of Kyle's "All-Liquid: A Super Heavy Lift Alternative?" article is given the estimated mass values for the gross mass and propellant mass of the 8.4 meter wide core first stage. The gross mass of this single stage is given as 1,423 metric tons and the propellant mass as 1,323 metric tons, so the empty mass of the stage would be approx. 100 metric tons (a proportionally small amount is also taken up by the residual propellant at the end of the flight.) Then the mass ratio is 14 to 1. However, the much smaller Falcon 9 first stage has already demonstrated a mass ratio of over 20 to 1.

A key fact about scaling is that you can increase your payload to orbit more than the proportional amount indicated by scaling the rocket up. Said another way, by scaling your rocket larger your mass ratio in fact gets better. The reason is the volume and mass of your propellant increases by cube of the increase and key weight components such as the engines and tanks do also, but some components such as fairings, avionics, wiring, etc. increase at a much smaller rate. That savings in dry weight translates to a better mass ratio, and so a payload even better than the proportional increase in mass.

This is the reason for example that proponents of the "big dumb booster" concept say you reduce your costs to orbit just by making very large rockets. It's also the reason that for all three of the reusable launch vehicle (RLV's) proposals that had been made to NASA in the 90's, for each them their half-scale demonstrators could only be suborbital.

Then we would get an even better mass ratio for this "super Evolved Atlas" core than the 20 to 1 of the Falcon 9 first stage, if we used the weight saving methods of the Falcon 9 first stage, which used aluminum-lithium tanks with common bulkhead design. It would also work to get a comparable high mass ratio if instead the balloon tanks of the earlier Atlas versions prior to the Atlas V were used.

So I'll use the mass ratio 20 to 1 to get a dry mass of 71.15 mT, call it 70,000 kg, though we should be able to do better than this. We'll calculate the case where we use the standard performance parameters of the RD-180 first, i.e., without altitude compensation methods. I'll use the average Isp of 329 s given in the Kyle article for the first leg of the trip, and 338 s for the standard vacuum Isp of the RD-180. For the required delta-V I'll use the 8,900 m/s often given for kerosene fueled vehicles when you take into account the reduction of the gravity drag using dense propellants. Estimate the payload as 115 mT. Then the delta-V for the first leg is 329*9.8ln(1 + 1,323/(2*70 + 1*1,323 + 115)) = 1,960 m/s. For the second leg the delta-V is 338*9.8ln(1 + 1,323/(70 + 115)) = 6,950 m/s. So the total delta-V is 8,910 m/s, sufficient for LEO with the 115 mT payload, by the 8,900 m/s value I'm taking here as required for a dense propellant vehicle.

Now let's estimate it assuming we can use altitude compensation methods. We'll use performance numbers given in this report:

Alternate Propellants for SSTO Launchers.

Dr. Bruce Dunn

Adapted from a Presentation at:

Space Access 96

Phoenix Arizona

April 25 - 27, 1996

http://www.dunnspace.com/alternate_ssto_propellants.htm

In table 2 is given the estimated average Isp for a high performance kerolox engine with altitude compensation as 338.3 s. We'll take the vacuum Isp as that reached by high performance vacuum optimized kerolox engines as 360 s. Estimate payload as 145,000 kg. For the first leg, the delta-V is 338.3*9.8ln(1 + 1,323/(2*70 + 1*1,323 + 145)) = 1,990 m/s. For the second leg the delta-V is 360*9.8ln(1 + 1,323/(70 + 145)) = 6,940 m/s, for a total delta-V of 8,930 m/s, sufficient for orbit with the 145,000 kg payload.

Now we'll estimate the payload using the higher energy fuel methylacetylene. The average Isp is given as 352 s in Dunn's report. The theoretical vacuum Isp is given as 391 s. High performance engines can get quite close to the theoretical value, at 97% and above. So I'll take the vacuum Isp as 380 s. Estimate the payload as 175,000 kg. Then the delta-V over the first leg is 352*9.8ln(1 + 1,323/(2*70 + 1*1,323 + 175)) = 2,040 s. For the second leg the delta-V will be 380*9.8ln(1 + 1,323/(70 + 175)) = 6,910 s, for a total delta-V of 8,950 m/s, sufficient for orbit with the 175,000 kg payload.

Bob Clark