Author Topic: LOX/LH2  (Read 20357 times)

Offline DonPMitchell

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LOX/LH2
« on: June 22, 2008, 12:53:15 AM »
I've been reading K.E. Tsiolkovsky's actual 1903 paper (not later revisions).

First (cue violins) let me say what a pain it has been to find and read that work.  I found the Russian version, but writing at the turn of the century, he used a bunch of old-slavonic letters that nobody uses today, as well as some old-fashion spellings involving a lot more hard signs and soft signs than modern Russian.  This is  bad when you are using OCR and computer language translation, but I massaged his antique Russion into mostly modern form.

So, Konstantin Eduardovich considered the heat of combustion and mass of various fuels and concluded that liquid oxygen and liquid hyrogen was the way to make a rocket.  He derived the "rocket equation" and then calculated the idea exhaust velocity for LOX/LH2, by converting the heat of combustion into kinetic energy, he came up with 5700 meters/sec for the specific impulse.

I looked up current values for heat of combustion of hydrogen (141.9 megajoules per kilogram).  Since it takes 8 kilograms of oxygen to burn a kilogram of hydrogen, I divided by (1+8) and get an equivalent kinetic energy of 5615 m/s, so he seems to have done the math right (I assume he just used an older and slightly different heat-of-combustion value).

The SSME is a closed cycle engine of great efficiency, and it's exhaust velocity is 4500 m/s.  I guess we should be impressed that it comes that close to 100 percent efficiency of converting chemical energy into exhaust kinetic energy!  I get 64% efficiency.

Oddly enough, Goddard claimed to have measured 64 percent efficiency in 1915, working with black powder engines and de Laval nozzles.  I wonder if that was really possible?

Oh Tsiolkovsky mentions that he ignored the extra energy needed to account for the coldness of the liquified gases.  I ignored that too.
« Last Edit: June 22, 2008, 12:56:32 AM by DonPMitchell »
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Offline DonPMitchell

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Re: LOX/LH2
« Reply #1 on: June 23, 2008, 07:06:22 PM »
I checked Goddard's math in his 1919 paper "Method of Reaching Extreme Altitudes".  He got his sums right too.

He used two brands of nitrocellulose smokeless powder, and measured their heat of combustion himself in a calorimeter.  The numbers he cites are consistent with smokless powder figures I looked up.

"Infallible" shotgun powder has a heat of combustion of 1238.5 calories/gram or 5.1819 megajoules per kilogram.  The ideal exhaust velocity would then be 3219 meters/sec.  Using a De Laval nozzle, Goddard measured exhaust velocities of 2434 meters/sec, which is 57.16 percent efficient conversion of chemical into kinetic energy.  He published 57.25 percent, and likely was using a different number of digits of precision or a slightly older value for the mechanical equivalent of heat.

So Goddard and Tsiolkovsky both seemed to know what they were doing, which is more than I can say for many papers I've seen on NASA's Advanced Concepts website.  :-)
Never send a human to do a machine's job.
  - Agent Smith