sevenperforce

All those things looks weird to you because you never use them.. In fact that problem seems harder with ounce and cups than with ml or liters.. That is a piece of cake. Never use them? I use metric almost exclusively. There are a few exceptions, though, and baking is one of them. Consider the following (real) recipe: 2 cups (473 mL) all-purpose flour 1 1/3 cups (315 mL) white sugar 2/3 cup (159 mL) brown sugar 3/4 cup (177 mL) unsweetened cocoa powder 1 1/2 teaspoons (7 mL) baking soda 1 teaspoon (5 mL) salt 1 teaspoon (5 mL) espresso powder 1 cup (237 mL) milk 1/2 cup (118 mL) vegetable oil 1/2 cup (118 mL) mayonnaise 2 teaspoons (10 mL) vanilla extract 1 cup (237 mL) boiling water Serves 12 You only have measuring cups and measuring spoons; no graduated cylinders. No calculator, either. You need to adjust the amounts so that the cake serves 8 instead of serving 12. Assume that you know all Imperial and metric volume ratios by heart. Will it be easier to work in Imperial or in metric? Metric is easier to teach and easier to memorize, but it's not necessarily easier to use. If you have both of them memorized, Imperial is often much easier to work with. Millions of home cooks in the US convert alter volumes in recipes using metric volume measurements without calculators every single day? I doubt it.

Point taken, but then again, that WAS part of the original specification. And a reheat cycle is not particularly complicated; there would have to be some sort of pump or channel for controlled venting anyway.

I don't typically measure sugar in cubic inches. And one ounce of water by weight is also one ounce of water by volume. If I'm baking something, I'm more likely to be measuring things by volume anywhere between 3 mL and 1 L. Suppose you're making a recipe that serves 6 but you need to serve 9 instead, and the ingredients are all given in volumes between 5 mL and 1 L. Try doing that without a calculator.

Try baking without a scale, using volume measurements only for your ingredients.

Yes, the balloons would be huge. An appropriate design would probably do some kind of preheat cycle in order to warm up the hydrogen. The balloons would be cylindrical rather than spherical and would deploy along the outer skin of the booster, from top to bottom. I suggested three, but you could have a whole cocoon thing going on.

In a conventional rocket, the converging-diverging nozzle is used to force the high-pressure fluid inside the combustion chamber to exit all along the axial direction at the highest possible speed. But since you can't very well do that with a nuke, you've got to ride the shockwave instead.

Let's say a multistage, ground-launched solid-fueled rocket. How small can the terminal orbital insertion stage be?

You could go for a tripropellant kero-hydrolox booster. Yes, you'd need large balloons and a good deal of residual hydrogen. Recovery isn't a problem if you have an autonomous solar-powered high-altitude drone to tow it in.

You could get better momentum exchange from an orion-type device if you built a large indestructible tube and detonated the bomb inside the tube. The tube would fill up with plasma and shoot out the open end; the sum forces on the inside of the tube would push you in the opposite direction.

I bolded the problem part.

Rockets function based on equal and opposite forces. Fuel has to be burned inside a rocket and then expelled out at high speed; if fuel is ejected unburned and then burns in the exhaust stream, it does nothing for the rocket because it is independent and thus exerts no force. Since you can't very well blow up a nuke inside a combustion chamber, you can't get any benefit from the stuff that explodes in the opposite direction, like the blue part of the casing. Instead, you've got to depend on a shockwave to bounce off a pusher plate.

Well, hydrazine and peroxide are merrily hypergolic together, but with a very poor ISP. Combustion against a diverging nozzle via shockwave-induced compression of a supersonic flow is the only way I can think of to have a chance of stacking velocities. A supersonic flow has the advantage of not being able to have back-propagation.

This might be a stupid idea, but... Consider a basic hydrolox strap-on booster. At the end of its burn, it will still have some residual hydrogen in its tanks. If the booster had three really large cylindrical balloons collapsed and packed along its outer skin, could it use that residual hydrogen to rapidly inflate them, both stabilizing the booster and allowing it to float? A high-altitude drone could be used to recover and tow it to the launch facility, where it could land softly using the balloons as airbags.

Yeah, it all comes down to conversion. Do you need to convert on an order-of-magnitude scale, or do you need to convert on a single-digit-integer scale? If the former, use metric; if the latter, use imperial.

Poor example, the recipe is given in dimensionless physical constants! Well, dimensionless ratios are the gold standard for comparing different units of measure. I would argue that it's a little different. If you deal with measurements in a way that requires you to multiply and divide by simple integers on a regular basis, the Imperial system will usually be easier. If you deal with measurements in a way that requires you to move between orders of magnitude on a regular basis, the metric system will usually be easier. I prefer the metric system because I do the latter more often than I do the former. But I can recognize the utility of the Imperial system for the former practice. Well, no. All metric units are divisible by 2 or 5 or 10n, but that's it. You're screwed if you need to divide by any other prime. A meterstick marked in 10-cm increments can be divided into halves, fifths, or tenths; a yardstick marked in inches can be divided into halves, thirds, quarters, sixths, ninths, or twelfths. Granted, a meterstick divided into individual cm gives you a little more flexibility, but not much more.

All Imperial units are "built" by successive multiplication by primes. The pre-industrial British economy didn't have much reason to relate small units of length with small units of volume. They did, however, relate cubic inches to gallons; there are 3x7x11 = 231 cubic inches per gallon. So a 3" cube is 3x3x3/3x7x11 = 9/77 parts of a gallon. A gallon is 25 gills, so a 3" cube is 32 gills/gallon times 9/77 gallons, or 288/77 gills. That's the same as 3 57/77 gills, which is almost exactly 3 3/4 gills or 3 gills and 3 ounces, and I did that in a few seconds without a calculator. I can turn it around. Suppose a certain type of grain costs $3 per kilogram and masses 1.5 kilograms per liter, and your 5 liter bucket is half full. How much is the grain in your bucket worth? Kinda tricky in a pre-industrial society without a calculator. However, if you're working with comparable values but using pounds, shillings, pence, gallons, pints, and ounces, it's a good deal simpler.

I wonder if dinitrogen pentoxide salt could be dissolved into high-test hydrogen peroxide to increase both its monopropellant impulse and its oxidizer ratio. Thanks, I'll try to do that. As far as qualifications -- I've got a research degree in the hard sciences, but rocket engineering is just a hobby. ISP ultimately depends on chemical energy, yes, but it is much more directly sensitive to variables like chamber pressure. The larger your pressure drop, the better your ISP. I don't think the ~470 seconds is anywhere close to the thermodynamic maximum for these fuels; a tripropellant fluorine-LH2-lithium rocket can get upwards of 540 seconds. Injecting a very small amount of liquid hydrogen into a kerolox engine can boost the specific impulse from 330 seconds to 415 seconds because of how it changes the expansion rate and ratio of the propellant, not because the hydrogen adds significantly more chemical potential energy. The peak pressure of a subsonic choked flow is distributed in every direction and places tremendous stress on your combustion chamber; the peak pressure of a supersonic flow is limited to the flow axis and results in vastly-reduced stress loading. I see no reason why a second combustion cannot achieve extremely high efficiencies via uniaxial supersonic compression and stack velocities. I used the term "dual monopropellant combustion" because the two fuels are accelerated through monopropellant thrusters before being combusted together at supersonic speeds. If you can think of a better descriptor, I'd be interested! An afterburner suffers from low efficiency due to the inherently poor compression ratio of combining a supersonic gas flow (usually of oxidizer) with a subsonic aerosolized liquid flow (usually fuel). When both fuels are highly-tuned supersonic gas flows, stupidly high compression ratios can be achieved. Hydrazine will break down into pure diatomic nitrogen and diatomic oxygen when the chamber temperature is raised high enough. So although the fuel is toxic, the products are not. The design uses a supersonic combustor "chamber" for secondary combustion; one side is formed by the aerospike nozzle while the other side of the "chamber" is formed by the standing shockwave where the two supersonic propellant flows meet. Thus, a high compression ratio can be achieved. The hydrazine will flash completely to nitrogen and oxygen (and maybe a little ammonia) in its monoprop thrust chamber; the hydrogen and oxygen from H2O2 decomposition will burn quite merrily. At most you'll have some leftover unburned hydrogen in the exhaust. Picking a lower hydrazine combustion temperature, resulting in some ammonia in the flow, might actually be better. At the right ratios, you could get ammonia, oxygen, and hydrogen in and nothing but water and diatomic nitrogen out, causing a huge energy boost from the highly-energetic nitrogen-nitrogen reaction.

Besides, you can make the same sort of argument in reverse. A drink recipe calls for two parts vodka, three parts gin, and half a part of dry vermouth. You know that after shaking with ice, the volume will increase by one fifth. The martini glass can hold six ounces (177.441 mL) of fluid. Do you want to use Imperial measures (teaspoons, tablespoons, ounces) or metric measures (1 mL, 10 mL, 100 mL)?

Wonder what the theoretical maximum TWR for monoprop thrusters is, then.

As previously mentioned, Imperial has quite excellent logic; it's all based on factoring by prime numbers. Really useful in a pre-industrial or trans-industrial feudal/quasi-capitalist society where bargaining and bartering must be done without the aid of a calculator. Length: 2x2x3 inches per foot, 2x3x11 feet per chain, 2x5 chains per furlong, 2x2x2x3 furlongs per league. Area: 2x2x2x5 perches per rood, 2x2 roods per acre, 1 acre = 1 furlong x 1 chain. Volume: 5 ounces per gill, 2x2 gills per pint, 2 pints per quart, 2x2 quarts per gallon, 2 gallons per peck, 2x2 pecks per bushel. Weight: 2x2x2x2 ounces per pound, 2x7 pounds per stone, 2x2x2 stones per hundredweight, 2x2x5 hundredweight per ton. All the largest units are made up of so many prime factors that you can just divide and divide endlessly without having to worry about running into fractions and long division.

Well, dammit. How did I miss that? Vacuum exhaust velocity ends up being 3,273 m/s, for a specific impulse of 334 seconds. Not nearly so fantastic as formerly expected, but still quite viable. EDIT: Actually, on second thought, I'm not so sure. Chemical energy is not the limiting factor here; chemical rocket propellants have an insane amount of potential energy. After all, only a small amount of the potential energy of a chemical rocket's fuel actually ends up as the kinetic energy of the rocket itself. The limiting factor is the conversion of thermal energy into kinetic energy, and dynamic pressure plays a huge role in that. I don't think conservation of energy is the operative principle here, even if that seems like the easiest way to crunch the numbers. Kind of how the Oberth effect seems to violate conservation of energy at first glance, but in reality it doesn't.

I haven't been able to find much in the way of theoretical maximum-efficiency thrust-to-weight ratios for monopropellant thrusters, but if it they are anywhere in the 100:1 range (median for medium-efficiency bipropellant engines), then with the supersonic combustion stage of the burn increasing the flow momentum (and, correspondingly, the thrust) by 120%, we'd be looking at a sum T/W ratio of 220:1, which is...dizzying. At the proper ratio, this fuel combination has a density of 1.255 g/cc. If the Space Shuttle's payload bay were replaced with internal fuel tanks, the total volume would be about 565 cubic meters, containing 710 tonnes of fuel. Sans SSMEs, the Shuttle massed just 59 tonnes. With a 7-tonne aerospike engine of the dual-monocombustion design, the Shuttle Orbiter could launch on its own with a vehicle T/W ratio of 2 and an onboard dV of 11.3 km/s.

Supersonic combustion is a challenge, yes, but it's not like trying to design a scramjet. With a scramjet, you have very little control over most of what's going into the whole equation. With this design, you have total control over virtually all the variables. There's an important difference between chamber pressure and flow pressure. Chamber pressure of a monopropellant thruster is typically pretty low, simply because of the application it's used for, though this can be improved with full-flow precombustion turbopumping. Flow pressure, on the other hand, is going to be high because the higher density of the propellant results in a high fluid momentum. And yes, I'm definitely taking into account the fuel/propellant fractions, as you'll see from the maths that follow. Anyway, as promised: maths. I decided to go ahead and calculate the maximum possible vacuum Isp and then dial back from there; getting a feel for maximum possible performance is better than trying to be conservative and adjusting wildly as you go. These Wikipedia tables helpfully gave a vacuum exhaust velocity of 1.86 km/s for 100% hydrogen peroxide and a dizzying 4.462 km/s for H2/LOX at a 4.86 mass ratio. Astronautix cites a peak 239 s vacuum specific impulse for certain hydrazine thrusters. Of course these are higher than what would probably be achievable, but again, I'm trying to get a peak characteristic specific impulse for the fuel/combustion system. I wasn't able to find an exhaustive (pun almost intended) table relating exhaust velocity to mass ratio for H2/LOX, but picking the optimized 4.83 mass ratio from Wikipedia is probably going to provide the best performance in the end, so that's what I decided to go with. Given the molar masses of hydrogen and oxygen, an H2:LOX ratio of 1:4.83 can be achieved at a hydrazine:peroxide molar ratio of 1:1.21. One mole of hydrazine has a mass of 32 grams; its vacuum exhaust velocity of 2.345 km/s means it has a kinetic energy of 88 kJ/mol. One mole of peroxide has a mass of 34 grams; its vacuum exhaust velocity of 1.86 km/s yields a kinetic energy of 71 kJ for 1.21 moles. The total kinetic energy of the combined flow at this ratio will be 159 kJ per mole of hydrazine, corresponding to a flow velocity of 2.09 km/s. So far, so good. At this ratio, the fluid flow masses 73 grams per mole of hydrazine and contains 23.3 grams of H2/LOX at the optimal ratio. Combustion of those 23.3 grams at the vacuum exhaust velocity of 4.462 km/s adds 232 kJ to the fluid flow. Distributed within that 73 grams, this adds 2.521 km/s to the flow velocity, resulting in a net flow speed of 4.607 km/s and a specific impulse of 469.6 seconds. Of course, this is all peak performance. Using solely SL performance and capping the initial flow velocity at the flow speed of peroxide exhaust (e.g., if the excess velocity of the hydrazine is wasted entirely), the same math produces a lower-bound specific impulse of 379 seconds. But that's still not bad for high-density, room-temperature-liquid propellants. This design could very easily be adapted for air augmentation to compensate for this as well, and since the vacuum exhaust velocity is just 3.2 km/s short of orbital velocity, air augmentation will be possible at far higher speeds than would be realistic for conventional rockets. A spaceship with this rocket engine running at optimal specific impulse would only need a remaining propellant mass fraction of 44.8% for the vacuum orbital insertion burn.

I love bimodal NTRs like the Triton.

Good questions. As I understand the physics/chemistry, this is going to be a case of shockwave-induced supersonic ram combustion, which is almost impossibly difficult to achieve in scramjets (which must mix a supersonic airflow with a subsonic fuel flow), but will be comparatively straightforward here because both exhaust flows are supersonic. The difference in speed will result in a standing shockwave where they meet; careful shaping of this standing wave by adjustment of the thruster expansion ratios and alignment can be used to ensure complete combustion. The shape of the aerospike might need to be slightly suboptimal in order to ensure the proper thrust vector, but this will only bleed a few percent of vacuum ISP at most. I'm about 98% sure that an aerospike surface can be used as a combustion chamber in supersonic flow conditions. The flow pressure of the propellants serves to confine and direct the combustion. The monopropellants have different molar masses and speeds, meaning that their momentum can be configured to ensure proper combustion as well. But think of the children! You know, the ones who want to grow up to be astronauts. We figured out how to handle liquid hydrogen; high-test peroxide presents different challenges but no less surmountable ones. Interesting. I wonder if gimballing the thrusters to direct them further in or further down could compensate for this. It will have to be an extended aerospike regardless, in order to allow for combustion time, but the weight cost of the extended aerospike will be negligible compared to the dramatically higher T/W ratio. And I had promised you those maths, so as soon as I can get Excel up and running with the optimization equations, I'll post them. Anyone happen to have a handy hydrolox specific-impulse-vs-ratio table? The key here is that the standing wave between the two supersonic flows re-creates a new density/velocity maximum which exists within an already-moving reference frame, allowing exhaust velocity to stack. At least, that's how I've designed it; I have no way of knowing whether it will actually work. I've poked around looking for something like this and I've never found anything, so either it's an absolutely horrible idea which is prohibitively inefficient for reasons which currently escape me, or it's something that simply never occurred to anyone before. (edit): P.S. You can look at different scramjet designs for a better idea of how such nozzles end up being shaped. The converging/diverging nozzle is no longer optimal for supersonic flow. Scramjets don't work, of course, but this is different because both flows are supersonic because they're both already-expanded exhaust plumes.