On May 2, 3:40 pm, Robert Clark wrote:
...
> A Mach 6.5+ transport could make transatlantic and trans continental
> U.S. flights in less than an hour, compared to 6 hour flights now. The
> financial incentive will make it likely that a commercial transport
> would be produced within a few years of the first manned prototype > vehicle.
>
The reluctance to use airbreathing engines for part of the time to reach orbit is due in large part to the fact that jet engines are heavy compared to the thrust they can produce. See the list of thrust- to-weight ratios for some engines here:
Thrust-to-weight ratio.
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The thrust-to-weight ratio for turbojets might be only 5 to 6, where as for rocket engines such as the space shuttle main engines might be
73 or above. A big part of this poor thrust-to-weight ratio for jets is the complexity and weight of the compressors and turbines jet engines have to carry:
Jet engine.
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However, the thrust-to-weight ratio for ramjets because of their simplicity can be quite high:
Ramjet Performance Primer. "There are no physical limits to the minimum weight of a ramjet other than design and materials. The 1950's Marquardt RJ43-MA-7 had a thrust/ weight (T/W) ratio of about 40. With today's engineering and materials that could probably be brought up to 150-200 without too much effort. Such T/W ratios would make ramjet powered vehicles excellent accelerators."
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Airbreathing engines need compression of the air to create high thrust. Turbojets use compressors. Ramjets are able to get high compression from the high velocity of the incoming air alone, dispensing with the compressors and accompanying turbines. Then the suggestion is to replace the compressors/turbines in turbojets with other means to achieve this high compression. One method that has been tested is the ejector ramjet or rocket-based combined cycle engine, where rocket exhaust is used to accelerate air into the intake of a ramjet thus allowing the ramjet to operate even at zero speed. This method still needs to use onboard oxidizer, for the rocket, to operate. An ideal method would only use the burnable fuel to operate, as do ramjets and turbojets. For a turbojet/ramjet intended as the first phase of a SSTO vehicle that uses rockets at the end stage, what might work is to use the very high pressure turbopumps that high performance rocket engines such as the space shuttle main engines use. Since these high pressure turbopumps are needed to be carried along for the rocket phase anyway perhaps they can be used as well during the airbreathing portion of the trip. There are several ways this might be accomplished. The shuttle liquid hydrogen turbopumps can produce 500 bars of pressure of the liquid hydrogen with a through put of 73 kg/sec each. I'm imagining this high pressure liquid hydrogen be directed into the intake of the jet engine. You want to do this in a way to compress the air. One way might be that the turbopump outlet into the jet engine be in the form of an annular (ring) opening all around the inlet, some distance into the inlet. This would tend to compress the air together as the liquid comes out directed inward to the center. You also want the air to be forced back to the rear of the engine so the liquid hydrogen would need to be angled somewhat also backwards towards the rear. The liquid would tend to spread out however, and for a large intake say a meter across or more for the large supersonic turbojet inlets, it's not certain how far the liquid would go to penetrate into the middle portion of the air to achieve the high compression needed here as well, not just the outer air. You want most of the air to be compressed at least to the 20 bar range commonly seen with turbojets in order to achieve the high thrust achieved by the means of compressors. Then another possibility would be to use an analogue of the ejector ramjet compression method. This works by using supersonic exhaust from a rocket to force the air into the intake, thus being compressed as is the case with ramjets flying at supersonic speeds. Then what we could do with the turbopump's output, is to use the Bernoulli principle to convert the very high pressure into a supersonic velocity:
Bernoulli's principle. Incompressible flow equation.
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For a streamline at constant height, (1/2)(velocity)^2 + pressure/ density = constant. With pipelines leading out of the liquid hydrogen turbopumps of about 30 cm wide, a density of liquid hydrogen of 72 kg/ m^3, and mass flow rate of 73 kg/sec, I calculate the flow speed as 33 m/s. Then if we want to convert the pressure of 500 bar = 50,000,000 pascals to high velocity we would get a speed of 1180 m/s, about Mach
- Then this supersonic flow could be directed into the intakes to accelerate and thereby compress the air as is down with ejector ramjets. Still another possibility to get the air to flow at high speed to induce similar compression as with a ramjet might be to ionize the air and accelerate it by electromagnetic fields. The turbopumps use a turbine which is a key means by which electric power is generated. The SSME turbopumps operate at 70,000 horsepower while weighing only about
700 pounds. There is pretty high efficiency conversion of turbine mechanical power to electrical power. However, we would need a lightweight means of ionizing and electromagnetically accelerating the air. A couple of possibilities for the ionization might be by using a microwave generator or electrically charged wires running throughout the inner volume of the intakes. In any case some of the exhaust from the jet would have to be bled off to run the turbopump. This might seem to reduce the performance of the jet engine but actually quite a large proportion of the power generated in usual jet engines is used just to run the compressors:
What is a Gas Turbine Engine and How Does it Work? "The cycle that governs the operation of a gas turbine engine is referred to as the Brayton constant pressure cycle. The engine compressor typically requires about 2/3 (!) of the usable heat energy produced in the burner to turn at maximum speed; the remaining energy can then be used to produce thrust or mechanical power, or a combination of the two."
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To get an idea of the power we need, we'll use as a model the J58 engine which powered the SR-71 to Mach 3+. I haven't seen any numbers on the horsepower generated by the J58 but I'll estimated it from the
1 horsepower per 2.5 pounds thrust common for turbojets:
Turbojet. Thrust to power ratio.
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The J58 generated about 25,000 lbs thrust in usual turbojet mode, so a horsepower of 10,000 hp. Note though that fuel needed to run the J58 is much less than the 73 kg/sec liquid hydrogen put out by the shuttle turbopump. This page gives its fuel use in the usual turbojet mode as
0.9 lb/(lbf-h), i.e., .9 lbs/hour for each pound of thrust:
Pratt & Whitney J58. Specification of J58-P4.
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This is 22,500 lbs/hr of fuel at 25,000 lbs thrust, or 6.25 lbs/sec,
2.8 kg/sec. This is in jet fuel. Hydrogen would give higher thrust and indeed will use about half the fuel for the same thrust as shown in the attached diagram of turbojet/ramjet/scramjet Isp's. So this would be 1.4 kg/sec of hydrogen. This is 1/52nd the usual mass flow rate of the SSME turbopump of 73 kg/sec. The power used by a turbopump is proportional to the mass flow rate, so the power needed would be
70,000 hp/52 = 1,346 hp This about 1/7th the power output of the J58 engine. A problem though is whether this would supply sufficient compression for the high air inflow of the jet. We might need to flow more fuel through the turbopumps than is burned by the engines. But this would mean we are running the jet engine fuel rich. However, the Isp for jet engines is so high we could afford to run fuel rich and still have a significantly better Isp than rockets.
Bob Clark