Date: 5 Jul 87 00:07:09 GMT From: ssc-vax!eder@beaver.cs.washington.edu (Dani Eder) Subject: Re: Launch Vehicle Size In article <452@telesoft.UUCP>, roger@telesoft.UUCP (Roger Arnold @prodigal) writes: > > A typical value today is 2500 lbs total for this set of hardware. > > Typical? I'll take your word for it. But hardly representative of > what ought to be feasible. Otherwise, your own plans for a small > demonstration model catapult fired launch system are infeasible. That is correct. Perhaps I should restate that more clearly: A typical value for a rocket that flies today, with 1 year old electrical systems, is 2500 lb. For example, the computer on the IUS built by Boeing is smart enough to control a Titan launch vehicle. The computer is an 8-bit processor with 48k of ram (= about an Apple II). It weighs 40 lb, not counting batteries. There are two of them on the IUS. Of course, the IUS was designed in 1973. For a new rocket, we can do much better with today's electrical equipment. But, at any given time, there will still be a constant weight component to a rocket design. > excludes fiber based composites. There is no optimal shape for a > tank made from a fiber based composite, so long as the fibers are > laid up in a manner that places them all under equal stress in the > loaded, pressurized tank. But there is a minimum gage. Let us take the case of very good carbon fiber/epoxy with a tensile stength of 400 ksi. We design to 300 ksi to allow some factor of safety. Available materials are 7/1000 inch thick per ply of fibers. Assume the internal tank pressure is 10 psi. Since stress=pD/2t for a cylindrical thin shell, we can calculate the D that corresponds to 1 ply of composite. It is (stress/p)*2t=d=(300,000/10)*2*0.007=420 inches. Thus, any tank smaller than this would waste some of the strength inherent in 1 ply of composite. In a realisitic design there would be at least 2 plies oriented,say at +-20 degrees from horizontal, to give longitudinal strength, so this is even worse. In response to the engine inlet pressure issue, the trade is usually tank weight vs engine pump weight, the lower the inlet pressure, the bigger the low pressure pump inlet has to be to avoid sucking vacuum (cavitation). Cavitation is death to rocket engines, because they are not normally designed for (1) the vibrations on the pump blades (2) the vibrations caused inside the combustion chamber when you burp gas rather than fluid and (3) the loss in wall cooling of bubbles in the coolant lin. All of these have caused engines to fail in the past. Solving these types of problems keeps propulsion engineers employed. Of course, you could design your engine to survive these problems, but then it weighs twice as much. > For a given chamber pressure, the nozzle > area required is directly proportional to the mass being lifted. A > certain nozzle area can only supply lift for a certain mass, which > translates to a certain height of rocket. You can't make a rocket > arbitrarily tall; to make it bigger, you have to make it wider. This is incorrect. The nozzle area = throat area x expansion ratio of the nozzle. Most of the thrust in a rocket arises from the thrust imbalance between the throat and a corresponding area on the top of the engine. In a converging-diverging nozzle, the flow becomes supersonic, and thus is effectively zero pressure as seen from inside the combustion chamber. For example, in the SSME, the chamber pressure is 3000 psi. The liftoff mass is 4,500,000 lb. Hence, only 1500 square inches, or 10.42 square feet of throat area is required for liftoff. The actual SSME nozzles have an expansion ratio of 77:1. This expansion against the nozzle walls has an upward component, which provides thrust in addition to the throat component. I belive in this case it adds 40% more thrust. The solid rocket boosters, on the other hand, have an expansion ratio of only 10-15:1 (I'm at home and don't have my refernce books handy). This is because they work at 700 psi pressure. In both cases the expansion is limited by when the gas reaches 15 psi in the nozzle (= sea level pressure). The sea-level back pressure in the SSME nozzle causes it to lose 23% of vacuum thrust. > But there is one area that you didn't mention where skinny tanks > (and small vehicles) eat it: tank insulation efficiency. I don't > know how much of a problem that really turns out to be. It is non-trivial. A typical value is 0.2 inches of cork insulation required on the forward part of a rocket to protect it from aerodynamic heating. Propellant boiloff is generally not a problem, since you are using it very quickly. The main reason to insulate a cryogenic tank is to prevent ice (water, CO2, even air) buildup on the ground. > For the sake of argument, let's accept your implication that a system > sized for 10,000 lb. of payload would be only 55% as efficient, in > terms of fuel consumed per pound of payload, as one sized for 100,000 > pounds. That represents a cost penalty of something like $2.00 to > $3.00 per pound. If the high launch rate, the steady production of > vehicles, and the confidence attained from an extensive track record > enabled the small system to achieve operational costs as low as 10 > times its fuel costs, then it would be more than twice as economical > as a larger system whose operational costs were 50 times its fuel > costs. (For comparison, I think that operation costs for airlines run > about 3 times their fuel costs, while for the Shuttle, they're on the > order of 500 times, or more, depending on how one does the accounting). In the aerospace industry, we experience a production 'learning curve' as the quantity of production goes up. Typically the reduction is 15% in unit cost per doubling of cumulative production. So if we have 10 times as many units made, we would expect the unit cost to be 58.3% as much. Since 1.82 times as much vehicle dry weight would be required, the total cost would be 1.06 higher for the small rocket IF costs were proportional to dry weight. In practice, much of the cost of a rocket is in the fixed weight items, rather than in the tanks and other structure, so the cost/lb of dry weight goes up for small rockets. Another way of looking at this, is that, roughly, we use up the same number of pounds of engines and tanks in 10 10,000 lb launches as we do in 1 100,000 lb launch, but in the former case we use up 10 times as many sets of electrical equipment. The key measure in determining space launch cost is the number of pounds of hardware thrown away per pound of payload delivered to orbit. In an expendable rocket it is about 2 lb hardware/lb payload. In the shuttle, it was not much lower. We threw away 1 lb of external tank per pound of payload. Allowing for reuseable element comsumption at weight/life, we use up 15,000 lb of SRBs and 3000 lb of orbiter per flight, giving a total of 84,000 lb/50,000 lb payload= 1.68 lb/lb. For the advanced launch system we are about to start work on, the figure will be 0.56 lb hardware/lb payload. I agree that propellant is cheap. My dream is a launch system where I have to worry about propellant cost. Even on the ALS, it only is 1% of the total costs.

From: jtkare@ibm.net (Jordin Kare) Newsgroups: sci.space.tech Subject: Re: Do small engines have higher T/W ratios? (was mini-engines, candles) Date: Fri, 03 Dec 1999 18:35:06 -0800 In article <38471859.3F8B9EB3@primary.net>, jimdavis2@primary.net wrote: > Andrew and Henry's discussion got me to think about whether small > engines can be demonstrated analytically to have a higher thrust to > weight (T/W) ratio. > > Thrust chamber weight scales with size squared, thickness, and material > density > > W = k2 * g * t * r2 * rho > > where > > W = thrust chamber weight > g = acceleration of gravity > t = chamber thickness > rho = material density > k2 = constant of proportionality This assumes a constant engine shape. Engine shape may vary with size, especially if constrained by required combustion chamber length for complete combustion. > > This indicates that T/W ratio is directly proportional to material > strength to weight > (s / rho) ratio (well, duh!) and inversely proportional to engine size. > Now I realize there is more to the engine than the thrust chamber but I > wonder whether this crude analysis holds any water in the real world. When we did the Mockingbird minimum-scale SSTO design at LLNL, Rod Hyde went through a bunch of scaling relationships, with results similar to yours. Note that T/W proportional to 1/r means T/W proportional to 1/(sqrt(thrust)) so it's not as fast a gain as it might seem. In practice, as I note above, there are some factors which limit the scaling of the chamber so the advantage of small engines is reduced. A larger factor in the "real world" is that turbopumps scale badly to small sizes, so T/W for turbopump-fed engines, including the pumps, tends to improve for larger sizes. Overall, historical data gives better T/W for large engines. Mockingbird got around the turbopump problem by using reciprocating pumps, whose specific mass *improves* at smaller sizes, with a crossover relative to turbopumps somewhere in the general ballpark of 20,000 N (~4000 lbf) thrust (highly implementation and technology dependent). Mockingbird baseline engine design was regen-cooled peroxide/kerosene with a pump+chamber mass (8 chambers) of 13.3 kg and a vacuum thrust of 3.2 kN per chamber (25.6 kN total) for a T/W of 188. (Sea level thrust was 2.5 kN per chamber, 20 kN total, T/W 147) Jordin Kare

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