ENGINES AND MCD
Well, last issue I said that I had finished my study of Minimum Cost Design, but I found one more item to analyze. As engines drive rockets into space, and as we saw in the MCD analysis of staging, engines also drive the cost and size of each stage, choosing the cheapest rocket engine will effect the entire cost of the rocket.
Basically there is one big problem with a rocket engine, keeping it from melting. The temperatures inside the engine approach 5000 degrees F, and the combustion rate and forces are intense. If you run a rocket engine for just a few seconds you can just absorb the heat in the structure of the engine. There are materials which will take the heat and force for a few seconds. These are called refractive materials. Graphite and furnace cement in a steel casing are the materials we use for our short burn hybrids. Plain steel can also be used for a couple of seconds. The longer the burn duration the heavier the engine becomes. Now, if you want to run for longer periods of time, then you have to figure out how to cool the engine. This is not a simple process. Active cooling of an engine requires lots of equations and lots of testing, and is therefore very expensive. The simplest active cooling system is called ablative cooling. Think of a wet towel. it's cool to the touch because the water in the fibers is evaporating and removing the heat. In ablative rocket engines, silica cloth is used to make up the material and plastics are used to melt and evaporate and thereby cool the material. Ablative engines, once tested and verified, are simple and can be run for long durations. They are heavy though. The best way to cool a rocket engine is regenerative cooling. The liquid fuel circulates through the walls of the combustion chamber keeping it cool. This also heats the fuel aiding in the combustion process. Regenerativly cooled rocket engines are the lightest, most efficient, and the most expensive. Regenerative cooling is also restricted to liquid fueled engines whose fuel is suitable for cooling. Robert Goddard's engines were regenerativly cooled, as were the German V2's and the Saturn Moon rockets.
The shape of the rocket nozzle hasn't really changed since Carl Laval designed the convergent divergent steam turbine nozzle back in the 1880's. It is such a simple device that there is not a lot of room for improvement. For comparison we will consider the progress made in liquid hydrogen / liquid oxygen rocket engines. Although hydrogen was proposed as a rocket propellant by Tsiolkovsky in the 1920's, the technology to produce large quantities of liquid hydrogen for rocket testing did not exist until 1946. In 1947 Ohio State University began firing the first LOX/LH2 engines. One model was regenerativly cooled with a chamber pressure of 310 PSI and a sea level ISP of 335. Fifty four years later the Space Shuttle Main Engines are considered the highest level technology rocket engines ever produced, and are the most expensive. Operating at an incredible chamber pressure of 3000 PSI, they achieve a sea level ISP of 363, an improvement of just 8%. In space ratings, the Pratt & Whitney RL-10 rocket engine developed in 1962, with a chamber pressure of 353 PSI achieved a vacuum ISP of 433. The SSME has a vacuum ISP of 455, which is a 5% improvement in thirty nine years. So there have not been large improvements in rocket engine efficiency despite the intense efforts and great expense of our current rocket researchers, and it is unlikely that any great improvements are soon to be seen.
But are these minuscule improvements worth the effort? The basic rocket equation; Delta V = ISP * G * ln(initial weight/final weight), in plain English this indicates that the benefit of a more efficient rocket engine is directly related to it's cost. So, If one engine costs twice as much as another engine for each pound of thrust, then the more expensive engine must produce twice the ISP just to be equal to the cost performance of the cheaper engine. With short burn duration and low costs indicated for lower stages of a rocket, refractive engines have a great cost advantage, while regenerativly cooled engines are indicated for upper stages.
There is one area where high technology regenerativly cooled engines have an overwhelming advantage. Manned spaceflight. If you're riding in the nose of a rocket, you want a thoroughly tested, certified, and very reliable engine under your tail. The long life span, controllability, and extensive testing of regenerativly cooled rocket engines develops that level of confidence. The huge investment such engines require favors a reusable launch vehicle design.