Propellant is the crap you chuck out the exhaust pipe to make rocket thrust. It's Newton's Law of Action and Reaction, savvy? Fuel is what you burn to get the energy to chuck crap out the exhaust pipe. As I told you before they ain't the same. And any show-oaf who asks me "what about reactionless drives" is gonna get an instant RocketCat Atomic Wedgie.

Say the good ship Polaris has a mass of 181,000 kilograms (181 metric tons). It has super powerful Nuclear Salt Water Rockets with an exhaust velocity of 182,000 meters per second (because it is using 22% enriched uranium) and a remass flow of 71 kilograms per second. If the Polaris is floating in space with a speed of zero, how fast will it be moving if it burns its engine for ten seconds?

In ten seconds it will spit out 71 × 10 = 710 kilograms of reaction mass.

The exhaust velocity is 182,000 m/s, so the momentum of the action is 182,000 × 710 = 129,220,000 kg⋅m/s

The Polaris gets an equal but opposite reaction of 129,220,000 kg⋅m/s. The mass of the Polaris is 181,000 kg. So the velocity is 129,220,000 / 181,000 = 714 m/s, which is about 1,597 miles per hour (in the opposite direction the remass is traveling). Not bad for a ten-second burn.

• 

(ed note: Long and Rioz are Scavengers: citizens of Mars whose job is to intercept cast-off propellant tanks, brand them, and send them to Deimos. They are listening to a broadcast from Terra. It is a propaganda piece from a nastly little politician named "Hilder" {Asimov's thinly disguised stand in for you-know-who}. Hilder is making a fake controversy about Mars wasting water as rocket propellant, which is nonsense. But Hilder needs an issue if he is going to be elected as global co-ordinator)

      Rioz took a hesitant step forward. Space was clear, so to hell with sitting and looking at a blank, green, pipless line. He said, “What's the Grounder been talking about?”
     “History of space travel mostly. Old stuff, but he's doing it well. He's giving the whole works—color cartoons, trick photography, stills from old films, everything.”

     As if to illustrate Long's remarks, the bearded figure faded out of view, and a cross-sectional view of a spaceship flitted onto the screen. Hilder's voice continued, pointing out features of interest that appeared in schematic color. The communications system of the ship outlined itself in red as he talked about it, the storerooms, the proton micropile drive, the cybernetic circuits…
     Then Hilder was back on the screen. “But this is only the travel-head of the ship. What moves it? What gets it off the Earth?”
     Everyone knew what moved a spaceship, but Hilder's voice was like a drug. He made spaceship propulsion sound like the secret of the ages, like an ultimate revelation. Even Rioz felt a slight tingling of suspense, though he had spent the greater part of his life aboard ship.
     Hilder went on. ”Scientists call it different names. They call it the Law of Action and Reaction. Sometimes they call it Newton's Third Law. Sometimes they call it Conservation of Momentum. But we don't have to call it any name. We can just use our common sense. When we swim, we push water backward and move forward ourselves. When we walk, we push back against the ground and move forward. When we fly a gyro-flivver, we push air backward and move forward.
     “Nothing can move forward unless something else moves backward. It's the old principle of ‘You can't get something for nothing.'
     “Now imagine a spaceship that weighs a hundred thousand tons lifting off Earth. To do that, something else must be moved downward. Since a spaceship is extremely heavy, a great deal of material must be moved downwards. So much material, in fact, that there is no place to keep it all aboard ship. A special compartment must be built behind the ship to hold it.”
     Again Hilder faded out and the ship returned. It shrank and a truncated cone appeared behind it. In bright yellow, words appeared within it: MATERIAL TO BE THROWN AWAY.
     “But now,” said Hilder, “the total weight of the ship is much greater. You need still more propulsion and still more.”
     The ship shrank enormously to add on another larger shell and still another immense one. The ship proper, the travel-head, was a little dot on the screen, a glowing red dot.

(ed note: i.e., The Tyranny of the Rocket Equation)

     Rioz said, “Hell, this is kindergarten stuff.”
     “Not to the people he's speaking to, Mario,” replied Long “Earth isn't Mars. There must be billions of Earth people who've never even seen a spaceship; don't know the first thing about it.”

     Hilder was saying, “When the material inside the biggest shell is used up, the shell is detached. It's thrown away, too.”
     The outermost shell came loose, wobbled about the screen.
     “Then the second one goes,” said Hilder, “and then, if the trip is a long one, the last is ejected.”
     The ship was just a red dot now, with three shells shifting and moving, lost in space.
     Hilder said, “These shells represent a hundred thousand tons of tungsten, magnesium, aluminum, and steel. They are gone forever from Earth. Mars is ringed by Scavengers, waiting along the routes of space travel, waiting for the cast-off shells, netting and branding them, saving them for Mars. Not one cent of payment reaches Earth for them. They are salvage. They belong to the ship that finds them.”

     Rioz said, “We risk our investment and our lives. If we don't pick them up, no one gets them. What loss is that to Earth?”
     “Look,” said Long, “he's been talking about nothing but the drain that Mars, Venus, and the Moon put on Earth. This is just another item of loss.”
     “They'll get their return. We're mining more iron every year.”
     “And most of it goes right back into Mars. If you can believe his figures, Earth has invested two hundred billion dollars in Mars and received back about five billion dollars' worth of iron. It's put five hundred billion dollars into the Moon and gotten back a little over twenty-five billion dollars of magnesium, titanium, and assorted light metals. It's put fifty billion dollars into Venus and gotten back nothing. And that's what the taxpayers of Earth are really interested in—tax money out; nothing in”.

     The screen was filled, as he spoke, with diagrams of the Scavengers on the route to Mars; little, grinning caricatures of ships, reaching out wiry, tenuous arms that groped for the tumbling, empty shells, seizing and snaking them in, branding them MARS PROPERTY in glowing letters, then scaling them down to Phobos.
     Then it was Hilder again. ”They tell us eventually they will return it all to us. Eventually! Once they are a going concern! We don't know when that will be. A century from now? A thousand years? A million? 'Eventually.' Let's take them at their word. Someday they will give us back all our metals. Someday they will grow their own food, use their own power, live their own lives.
     “But one thing they can never return. Not in a hundred million years. Water!
     “Mars has only a trickle of water because it is too small. Venus has no water at all because it is too hot. The Moon has none because it is too hot and too small. So Earth must supply not only drinking water and washing water for the Spacers, water to run their industries, water for the hydroponic factories they claim to be setting up—but even water to throw away by the millions of tons.
     “What is the propulsive force that spaceships use? What is it they throw out behind so that they can accelerate forward? Once it was the gasses generated from explosives. That was very expensive. Then the proton micropile was invented—a cheap power source that could heat up any liquid until it was a gas under tremendous pressure. What is the cheapest and most plentiful liquid available? Why, water, of course.
     “Each spaceship leaves Earth carrying nearly a million tons—not pounds, tons—of water, for the sole purpose of driving it into space so that it may speed up or slow down.
     “Our ancestors burned the oil of Earth madly and wilfully. They destroyed its coal recklessly. We despise and condemn, them for that, but at least they had this excuse—they thought that when the need arose, substitutes would be found. And they were right. We have our plankton farms and our proton micro-piles.
     “But there is no substitute for water. None! There never can be. And when our descendants view the desert we will have made of Earth, what excuse will they find for us? When the droughts come and grow—.”

     Long leaned forward and turned off the set. He said, “That bothers me. The damn fool is deliberately—”

• 

(ed note: Keven, Glenda, and Jacob have been stranded on a tiny asteroid orbiting Ceres by the Bad Guys. They are in a mostly stripped base, trying to figure out how to get down to Ceres using only what is available)

     Kevin prowled through the corridors of their prison. There has to be some way, he told himself. Ceres mocked him from below, less than three hundred kilometers down. It hung huge in the night sky.
     Three hundred kilometers down, and we're moving about half a kilometer a second relative to Ceres, Kevin thought. That's not very much velocity. Under a thousand miles an hour. It doesn't take much energy to get to that speed. How much gasoline does it take to accelerate a car on Earth up to a hundred miles an hour—a gallon or so? We only need ten times that, not even that much.
     There's plenty of hydrogen and oxygen. Marvelous rocket fuels if we only had a rocket. More than enough to get us down, except that the temperature of hydrogen burning in oxygen is a lot hotter than anything we have to contain in it—
     No. That's not right. The fuel cells do it. But they do it by slowing down the reaction, and they can't be turned into rocket engines.
     He remembered the early German Rocket Society experiments described by Willy Ley. The Berliners had blown up more rockets than they flew, and they were only using gasoline, not hydrogen. Liquid-fuel rockets need big hairy pumps, and Kevin didn't have any pumps.
     What did he have? Fuel cells, plenty of them, and so what? An electric-powered rocket was theoretically possible, but Kevin didn't have the faintest idea of how to build one, even if there was enough equipment around to do it with. He wasn't sure anyone had ever built one—certainly he couldn't.
     Back to first principles, he thought. The only way to change velocity in space is with a rocket. What is a rocket? A machine for throwing mass overboard. The faster the mass thrown away goes in one direction, the faster the rocket will go in the other, and the less you have to throw. All rockets are no more than a means of spewing out mass in a narrow direction. A rocket could consist of a man sitting in a bucket and throwing rocks backward.
     That might get a few feet per second velocity change, but so what? There simply wasn't enough power in human muscles—even if he did have a lot of rocks. Was there any other way to throw them? Not fast; and unless the thrown-away mass had a high velocity, the rocket wouldn't be any use. He went on through the tunnels, looking at each piece of equipment he found, trying to think of how it might be used.
     You can throw anything overboard to make a rocket. Hydrogen, for example. That's all Wayfarer's engines did, heat up hydrogen and let it go out through the rocket nozzle. We have hydrogen under pressure— Not enough. Nowhere near enough hydrogen and nowhere near enough pressure, not to get velocity changes of hundreds of miles an hour. Ditto for oxygen. Gas under compression just can't furnish enough energy. What would? Chemical energy; burning hydrogen in oxygen would do it, but it gave off too much; there was nothing to contain that reaction except the fuel cells and they did it by slowing the reaction way down and—
     And I'm back where I started, Kevin thought. Plenty of energy in the fuel cells if I could find a way to use it. Could I heat a gas with electricity? Certainly, only how—
     His eye fell on the hot-water tank in the crew quarters. An electric hot-water tank. There was a pressure gauge: forty pounds per square inch. Forty p.s.i.—He looked at the tank as if seeing it for the first time, then went running back to the others.
     "Glenda, Jacob, I've got it."

---

     "Sure it works." Kevin grinned. "Steam at forty p.s.i. will come out fast. About a kilometer a second."
     "I believe you," Glenda said. "But it sounds silly. Steam rockets?"
     Kevin shrugged. "It is silly. There are a lot more efficient systems. But this will work—"
     "In a low g field," Jacob said. "You will not have much thrust. Of course you won't need much."
     "I'm sure it works," Kevin said. "Now all we have to do is build it." He made himself sound confident; he knew how much room for error there was in his figures. "Look, it takes nine hundred and eighty calories to turn a gram of water into steam. We heat that steam up another thirty or forty degrees and let it out. The energy is moving molecules. We know the molecular weight of water, so we can figure the number of molecules in a gram and—"

---

     They disconnected the hot-water tank and drilled holes in it. Several turns of heating wire went through the holes, then they sealed them in epoxy. At one end of the tank they drilled a large hole and threaded a pipe into it, threaded a large valve onto the pipe, and welded a makeshift rocket nozzle beyond that.
     When it was done they tethered the tank and filled it with water, then connected a fuel cell to the heating leads. "Here goes," Kevin said. He threw the switch to start the heaters.
     Slowly the water inside heated, then began to boil. The pressure shown on the gauge began to rise. In half an hour they had forty-five pounds of pressure. "All right, let's try it," Kevin said.
     Glenda turned the valve to let out steam. A jet of steam and water shot out across the surface of the moonlet. Ice crystals formed in space and slowly settled to the rocket surface. The jet reached far away from them, well off the moonlet itself. The tank pulled against its tether lines, stretching the rope.
     "It works!" Kevin shouted. "Damn it, we're going to make it!" He shut off the electricity. "Let's get her finished."

---

• 

• 

     It didn't look like a spaceship. It didn't even resemble a scooter, crude as those were. It looked like a hot-water tank with fuel cells bolted onto it. For controls it had vanes set crosswise in the exhaust stream, spring-loaded to center, with two tillers, one for each vane; a valve to control steam flow; and switches to connect the fuel cells to the heaters. Nothing else.
     The tank itself was fuzzy: They'd sprayed it with Styrofoam, building it up in layers until they had nearly a foot of insulation. There were straps on opposite sides of the tank to hold two passengers on.
     The tank held nearly a hundred gallons of water. Kevin calculated that they had more than enough energy to boil it all in their two fuel cells, and they would only need sixty gallons to get to Ceres. The number was so small that he ran it four times, but it was correct.
     The strangest part was the stability system: a pair of wheels taken from a mining cart and set up in front of the water tank. Electric motors rotated the wheels in opposite directions.

---

     The total mass of Galahad with full water tank was just under 550 kilograms.

---

     It took only a gentle effort to push the steam rocket away from the moonlet, but the cartwheel-gyros resisted any effort to turn it. Finally they got it oriented properly in space. Then they climbed aboard.
     "Full head of steam," Kevin said. "Almost fifty pounds. Ready?"
     "Ready—"
     He twisted the steam valve. At first both steam and water were expelled from the tank, but as they began to accelerate, the water settled and the exhaust valve let out only steam. C-2 dropped away. They missed it. It was a prison, but a safe one; now they had only their makeshift steam rocket.
     Galahad showed a tendency to tumble, but with the gyros resisting, they were able to control it with the steering vanes. A plume of steam shot from the tank, rapidly crystallizing into ice fog that engulfed them.
     "Damn. That's going to make it hard to see," Kevin said. "Nothing we can do about it." He peered down toward Ceres. It didn't seem any closer. Jacob's farewell faded in their headsets.
     Norsedal's calculations had shown that twenty minutes' thrust should be enough to cancel all their orbital velocity. It would use up just about half their fuel. Once Galahad was stopped dead in orbit above Ceres, they would fall toward the asteroid, and they would have half their steam left to counteract that.
     The trouble was that Jacob couldn't calculate how high above Ceres they would be when the twenty minutes were finished. As they lost velocity, they would lose altitude, and their orbit would no longer be a smooth circle, but an ellipse intersecting Ceres—somewhere. At the end of twenty minutes Kevin cut the power off. He was pleased that they still had thirty pounds of steam pressure.

---

     "Yes, but that's what the numbers say."
     "All right."
     And a year ago I was working equations in school, Kevin thought. Numbers to crunch and write down for examinations. Now they're something to stake your life on.

• 

• 

(ed note: In the future people use handwavium paragravity to terraform asteroids. They also use them as torchships. Some royal morons want to move an inhabited asteroid from one cluster to another, an action that will spark a localized war. Our heroes Captain Dhan Gopal Radhakrishnan and Engineer Knud Axel Syrup arrive in the Mercury Girl, and are captured by the royal morons. All radios have been confiscated, so no warning can be broadcast. But our heroes figure out how to make a makeshift rocket out of local materials in order to travel to another asteroid to spread the alarm. They are forced to use only locally available materials.)

      The first beer-powered spaceship in history rested beneath a derrick by the main cargo hatch.

     It was not as impressive as Herr Syrup could have wished. Using a small traveling lift for the heavy work, he had joined four ten-ton casks of Nashornbräu end to end with a light framework. The taps had been removed from the kegs and their bungholes plugged, simple electrically-controlled Venturi valves in the plumb center being substituted. Jutting an orthogonal axes from each barrel there were also L-shaped exhaust pipes, by which it was hoped to control rotation and sideways motion. Various wires and shafts, their points of entry sealed with gunk, plunged into the barrels, ending in electric beaters (to agitate the beer. Much like shaking up a bottle of beer before opening the lid). A set of relays was intended to release each container as it was exhausted. The power for all this— it did not amount to much—came from a system of heavy-duty EXW batteries at the front end.
     Ahead of those batteries was fastened a box, some two meters square and three meters long. Sheets of plastic were set in its black-painted sides by way of windows. The torso and helmet of a spacesuit jutted from the roof, removably fastened in a screw-threaded hatch cover which could be turned around. Beside it was a small stovepipe valve holding two self-closing elastic diaphragms through which tools could be pushed without undue air loss. The box had been put together out of cardboard beer cases, bolted to a light metal frame and carefully sized and gunked.
     "You see,’’ Herr Syrup had explained grandly, "in dis situation, vat do ve need to go to New Vinshester? Not an atomic motor, for sure, because dere is almost neglishible gravity to overcome. Not a nice streamlined shape, because ve have no air hereabouts. Not great structural strengt’, for dere is no strain odder dan a very easy acceleration; so beer cardboard is strong enough for two, free men to sit on a box of it under Eart’ gravity. Not a fancy t’ermostatic system for so short a hop, for de sun is far avay, our own bodies make heat and losing dat heat by radiation is a slow process. If it does get too hot inside, ve can let a little vater evaporate into space though de stovepipe valve to cool us; if ve get shilly, ve can tap a little heat though a coil off de batteries.
     "All ve need is air. Not even mush air, since I is sitting most of de time and you ban a Martian. A pair of oxygen cylinders should make more dan enough; ja, and ve vill need a chemical, carbon-dioxide absorber, and some desiccating stuffs so you do not get a vater vapor drunk. For comfort ve vill take along a few bottles beer and some pretzels to nibble on.
     "As for de minimal boat itself, I have tested de exhaust velocity of hot, agitated beer against vacuum, and it is enough to accelerate us to a few hundred kilometers per hour, maybe t'ree hundred, if ve use a high enough mass ratio. And ve vill need a few simple navigating instruments, an ephemeris, slide rule, and so on. As a precaution, I install my bicycle in de cabin, hooked to a simple homemade g’enerator, yust a little electric motor yuggled around to be run in reverse, vit’ a rectifier. Dat vay, if de batteries get too veak ve can resharshe dem. And also a small, primitive oscillator ve can make, short range, ja, but able to run a gamut of freqvencies vit’ out exhausting de batteries, so ve can send an SOS ven ve ban qvite close to New Vinshester. Dey hear it and send a spaceship out to pick us up, and dat is dat.”

---

     The execution of this theory had been somewhat more difficult, but Herr Syrup’s ears aboard the Mercury Girl had made him a highly skilled improviser and jackleg inventor. Now, tired, greasy, and content, he smoked a well-earned pipe as he stood admiring his creation. Partly, he waited for the electric coils which surrounded the boat and tapped the ship’s power lines, to heat the beer sufficiently; but that was very nearly complete, to the point of unsafeness. And partly he waited for the ship to reach that orbital point which would give his boat full tangential velocity toward the goal; that would be in a couple of hours.
     Er … are you sure we had better not test it first?” asked Sarmishkidu uneasily.
     "No, I t’ink not,” said Herr Syrup. "First, it vould take too long to fix up an extra barrel. Ve been up here a veek or more vit’out a vord to Grendel. If O’Toole gets suspicious and looks t’ rough a telescope and sees us scooting around, right avay he sends up a lifeboat full of soldiers; vich is a second reason for not making a test flight.”
     "But, well, that is, suppose something goes wrong?”
     "Den de spacesuit keeps me alive for several hours and you can stand vacuum about de same lengt’ of time. Emily vill be vatching us t’rough de ship’s telescope, so she can let McConnell out and he can come rescue us.”
     "And what if he can’t find us? Or if we have an accident out of telescopic range from here? Space is a large volume.”
     “I prefer you vould not mention dat possibility,” said Herr Syrup with a touch of hauteur.

• 

• 

5 milligee (0.05 m/s²) : General rule practical minimum for ion drive, laser sail or other low thrust / long duration drive. Otherwise the poor spacecraft will take years to change orbits. Unfortunately pure solar sails are lucky to do 3 milligees.

0.6 gee (5.88 m/s²) : General rule average for high thrust / short duration drive. Useful for Hohmann transfer orbits, or crossing the Van Allen radiation belts before they fry the astronauts.

3.0 gee (29.43 m/s²) : General rule minimum to lift off from Terra's surface into LEO.

Ken Burnside: Ignoring the ground to orbit issue for the moment, I see list consensus has found three thrust regimes.

     EKLUNDIAN — thrusts are greater than solar gravitation, but not by much. Isps (specific impulse) are low enough that conserving delta v is the paramount concern. Travel time is known more or less in advance, and everyone has launch windows to observe.

     HEINLEINIAN — thrusts are so significantly greater than local gravitation that orbital mechanics is meaningless. Isps are high enough in concert with these thrusts that Heinlein style "burn-flip-burn" moves are the norm; travel time reduction becomes the paramount concern.

     THE FUZZY MIDDLE — thrusts are higher than local gravitation, but usually within an order of magnitude of it. When local gravitation as a function of range exceeds some percentage of thrust, it turns things into an Eklundian model. Isps are low enough that total delta v doesn't permit Heinlein-style brachistochrone orbits.

     Now the questions:

     1) Have I categorized this properly? Or is there a category I'm missing? Does category three need a better name, or further subdivision?
     2) At what percentage of thrust does local gravitation force Eklundian style "slow spiral orbits"?
     3) At what range of ISps do we get to "It's better to just burn more gas to save time" assuming point 2 is met?

---

• 

• 

RICK ROBINSON'S RESPONSE:

Ken Burnside:
     Ignoring the ground to orbit issue for the moment, I see list consensus has found three thrust regimes.
     EKLUNDIAN — thrusts are greater than solar gravitation, but not by much. Isps are low enough that conserving delta v is the paramount concern. Travel time is known more or less in advance, and everyone has launch windows to observe.

Thrust hardly really matters in the limited Isp regime, so long as it is an appreciable fraction of a milligee — it can probably even be less than solar gravitation, so long as it isn't too much less.

Thrust above about 0.1 g allows more efficient planetary departures, saving a few km/s, but this is nearly irrelevant to interplanetary transfer orbits, so the Eklundian conditions apply.

Ken Burnside:
     HEINLEINIAN — thrusts are so significantly greater than local gravitation that orbital mechanics is meaningless. ISps are high enough in concert with these thrusts that Heinlein style "burn-flip-burn" moves are the norm; travel time reduction becomes the paramount concern.

I don't like the term Heinleinian, because Heinlein also (and more often) described Eklundian or fuzzy-middle travel. Call it torchship, or torchlike.

Note that acceleration of about 5-10 milligees is enough for torchlike performance, if you have the delta v. You'll still have to spiral out from planets, but once clear of them, 10 milligees gives you 8.5 km/s per day, solar escape speed in a week (with displacement in the frame of reference less than 0.1 AU).

Ken Burnside:
     THE FUZZY MIDDLE — thrusts are higher than local gravitation, but usually within an order of magnitude of it. When local gravitation as a function of range exceeds some percentage of thrust, it turns things into an Eklundian model. ISps are low enough that total delta v doesn't permit Heinlein-style brachistochrone orbits.

Yes.

Note also a relationship between the inner and outer Solar System (roughly, inside and outside Jupiter). Ships that are Eklundian in the inner system can barely reach the outer system at all. Ships that are fuzzy-middle in the inner system behave nearly like torchships in the outer system — they have to coast most of the way, but nearly in a straight line.

Ken Burnside:
Now the questions:
1) Have I categorized this properly? Or is there a category I'm missing? Does category three need a better name, or further subdivision?

No, these sound about right. I'd call the fuzzy middle "transitional."

My impressionistic description. The Solar System is a vast, slowly revolving whirlpool. Eklund ships are galleys caught in it; by hard rowing they can shift themselves inward or outward to visit the whirlpool's floating, revolving islands.

Torchships are hydrofoils that zip from island to island, so fast they can effectively ignore the motion of the whirlpool, except for the movement of their destination.

In the transition are steamboats, which are able to cut steeply across the vortex, but cannot ignore it.

Ken Burnside:
2) At what percentage of thrust does local gravitation force Eklundian style "slow spiral orbits"?

Less than perhaps 5-10 milligees.

In terms of whether you have to spiral out from individual planets, or can make the more efficient slingshot burn from low orbit, I would say that the threshold is about 0.1 g.

Ken Burnside:
3) At what range of Isps do we get to "It's better to just burn more gas to save time" assuming point 2 is met?

I am going to swag this as a ship delta v of about 50-100 km/s — assuming roughly a 65 percent fuel fraction, your exhaust velocity is the same, so Isp about 5000-10,000 seconds. For fast commercial travel you probably want a lower fuel fraction, so you need a drive with upwards of 10,000 seconds of Isp.

Ken Burnside:
Ignore specifics of rockets - we've seen enough arguments over people's favorite propulsion systems for the last 5 weeks. :) I'm just looking to establish the categories for now, so we can use them to organize discussions in the future.

Keeping it general, chemfuel is strictly Eklundian in spite of its high thrust.

Nuclear-thermal (even Orion) is largely Eklundian, struggling to get ship delta v above 20 km/s or so. The advantage over chemfuel is that it does Hohmann and near-Hohmann orbits with a considerably lower fuel fraction, allowing perhaps 2x to 5x the payload.

Nuclear-electric drives like VASIMR live in the transition zone — they have supra-Eklund delta v, but sluggish acceleration around 1 milligee. In practice, commercial ships at least may still live in Eklundian space, using the higher specific impulse to further reduce fuel fraction, allowing more cargo, rather than for higher speed.

The threshold of torchlike performance is roughly Isp of 10,000 seconds combined with thrust around 5 milligees. For a 1000-ton ship this requires 2.5 gigawatts of thrust power. If the drive engine itself is 250 tons, that requires a drive power density of 10 kw/kg, comparable to a jet engine.

So, very roughly 1 gigawatt (GW, 10⁹W) thrust power for a moderate size ship marks the minimum torchship threshold. But "classical" torchships are about 1000x more powerful, approaching the terawatt (TW, 10¹²W) range, allowing acceleration near 1 g or exhaust velocity near 1000 km/s.

Since almost all rockets are giant propellant tanks with an engine on the bottom and the pilot's chair at the top, most of the rocket is propellant. A titanic metal foil balloon with tiny rocket bits stuck on with vacuum tape.

"Mass Ratio" is just a fancy way to measure how much mass is the propellant and how much is the rest of the blasted rocket.

Propellant is the crap you chuck out the exhaust pipe to make rocket thrust. Fuel is what you burn to get the energy to chuck propellant out the exhaust pipe. As I told you before they ain't the same.

If the Star Spear carries 70 metric tons of propellant, and the rocket masses 40 metric tons with dry tanks, its mass ratio is (70 / 40) + 1 = 2.75. This means that for every ton of rocket and payload there is 2.75 tons of propellant. Alternatively, if the Star Spear masses 110 metric tons full of propellant and 40 metric tons empty, the mass ratio is still 110 / 40 = 2.75. Note that mass ratios are generally always much higher than 1.0.

The Star Spear's propellant fraction is 1 - (1 / 2.75) = 0.63 or 63%

This section is intended to address some gaps in available information about spacecraft design in the Plausible Mid-Future (PMF), with an eye towards space warfare. It is not a summary of such information, most of which can be found at Atomic Rockets.

The largest gap in current practice comes in the preliminary design phase. A normal method used is to specify the fully-loaded mass of a vessel, and then work out the amounts required for remass (propellant), tanks, engine, and so on, and then figure out the payload (habitat, weapons, sensors, cargo, and so on) from there.

While there are times this is appropriate engineering practice (notably if you’re launching the spacecraft from Earth and have a fixed launch mass), in the majority of cases the payload mass should be the starting point. The following equation can be used for such calculations:

M = R * ( M_pl / (1 - (P_f * (R-1)) - (Pi * R)) )

• M = mass of rocket with full propellant tanks, the Wet Mass (kg)
• R = mass ratio (dimensionless number)
• M_pl = Payload Mass (kg)
• P_f = propellant fraction, that is, percent of total rocket mass M that is propellant: 1.0 = 100% , 0.25 = 25%, etc.
• P_i = inert fraction, that is, percent of total rocket mass M that is Inert Mass: 1.0 = 100% , 0.25 = 25%, etc.

(ed note: P_f is actually any mass that "scales" with the propellant mass, such as the mass of the tank. "Scale" means if the propellant mass is increased, the tank mass will also increase since you need more tankage to hold more propellant.

P_i is actually any mass that "scales" with the size of the spacecraft, such as such as engines or structure.

M_pl is actually any mass that is of fixed mass (does not scale) regardless of size of spacecraft, such as habitats, weapons, or sensors.)

To find the engine's exhaust velocity, look it up in the table. Now you can skip the rest of this section.

If you ony have the engine's specific impulse, mulitiply it by 9.81 to get exhaust velocity. You can do multiplication, can't you?

Rocket scientists like to use specific impulse instead of exhaust velocity because then they can use any other units they want for the rest of the equations. I know you are not a rocket scientist or you would have hurt yourself laughing by now reading this site. Therefore I'm giving you all the equations with fixed units, because otherwise it is just one more thing that will cause math mistakes.

Oh, and the use of 9.81 m/s² in the equation does NOT mean that the exhaust velocity changes under a different gravity.

It is because those idiot scientists back at the dawn of history mistakenly thought it would be a splendid idea to use the term "pound" as both a unit of force and a unit of mass. Morons. It has been causing confusion ever since.

If you must know, technical reason is that specific impulse in seconds is really "pounds-force seconds per pound-mass" which has the same dimensionality as N·s/kg. Don't worry about it, just use 9.81 m/s² and everything will be fine.

MaturinTheTurtle

When a physicist tells you something is "specific" he means that quantity is per something else. Specific impulse is impulse per unit weight of propellant.

Impulse, in a rocketry context, is thrust applied over time. One newton of thrust (metric system) applied for one second results in one newton-second of impulse.

The importance of impulse in rocketry should be pretty obvious: thrust alone is not a meaningful quantity if you're talking about get-up-and-go. Thrust tells you how hard an engine can push, but it's not until that engine pushes for some time that you get anywhere.

But how long an engine can push for depends on how much propellant you have. If you have infinite propellant then you can keep any engine going for infinite time; that's obvious. But if you have a finite amount of propellant, then how long can you make an engine go? Well, that depends on the engine.

Which is where specific impulse comes in. Specific impulse is how much impulse — thrust over time — you get out of a given weight of propellant. If you have a thousand pounds of propellant and that results in your engine giving you a kilonewton of thrust for three seconds, then your engine has a specific impulse of 3000 newton-seconds per thousand pounds, or 3 newton-seconds per pound.

Except these days people tend to measure everything in the metric system, which results in a bit of confusion. See, both thrust and weight, in the metric system, are measured in newtons or multiples thereof. So you end up quantifying specific impulse in units of newton-seconds per newton, and then people cancel out the newtons … even though they really shouldn't, because they're different kinds of newtons. Specific impulse really has units of newton (thrust)-seconds per newton (weight), but it's become traditional to just drop the newtons and call it seconds instead.

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DrScrubbington

TL;DR, specific impulse is how long an engine can hover for, while carrying its own fuel and neglecting the mass of the engine.

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MaturinTheTurtle

People keep saying that, but it's not right. Thrust is constant under given conditions but weight falls continuously, so your "the engine is hovering" thing is only true for a single instant. After that, it's accelerating steadily upward at an increasing rate (the third derivative of altitude is positive).

If you want to explain it succinctly to somebody, say that specific impulse is the amount of time it takes for a given engine to burn a weight of propellant equal to its thrust. Then tell them what it really means — thrust time per unit weight of propellant — once they point out to you that that succinct explanation is useless.

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Dimensional analysis: a newton is a unit of weight or force (same thing, different points of view). Weight and force are both mass accelerated, so a newton is mass times acceleration. Integrate that over time and you have mass times acceleration times time … but acceleration is length per unit time per unit time. So that become mass-length-per-time, which is how you quantify impulse. (You will recognize these as the units of momentum; impulse and momentum are two sides of the same coin. Momentum is mass moving with a certain velocity, and impulse is thrust applied for a given time. Tomayto, tomahto.)

But if you then divide that out by mass, you end up with mass-length-per-time-per-mass, and the masses cancel leaving you just with length-per-time. That looks like a velocity, which turns out to be a very inconvenient way to quantify the specific impulse of a motor.

If you multiply the specific impulse of a motor times the conversion factor between units of weight and units of mass (which in the metric system is 9.80665 m/s/s exactly by definition; it is NOT local g) you get a quantity called the "effective exhaust velocity" which shows up in a few equations, but in practice nobody uses that quantity. Everybody just writes "Isp g₀" instead.

(ed note: engineer Rob Davidoff gently points out that I don't know what I am talking about. It is possible to use low molecular weight propellant, at least a little bit)

It's worth noting you can actually "spice up" the propellants with low mass exhaust products. This is how a lot of tripropellant chemical works, by adding hydrogen as much to have lower average molecular mass in the exhaust as to actually burn it for its energy release.

It's also among two or three reasons why you see a lot of hydrolox engines run fuel-rich, so there's unburnt excess H₂ in the exhaust.

All those cute starship spec sheets you see with moronic entries like "range" or "maximum distance" betray a dire lack of spaceflight knowledge. Spacecraft ain't automobiles, if they run out of gas they don't drift to a halt. Delta-V is the key.

Konstantin Tsiolkovsky is The Man and don't you forget it! Every single time you design a rocket, you will be using his brilliant delta-V equation. It is the sine qua non of rocketry, without it this entire freaking website would not exist. If you are a serious rocket geek, you should have Tsiolkovsky's portrait hanging on your wall and the rocket equation on your T-shirt.

I love the smell of delta-V in the morning. Smelled like ... trajectory.

Suppose that the Polaris has a 1^st generation Gaseous Core Fission drive. Exhaust velocity of 35,000 m/s (see table in engine list).

Let's try a mass ratio of 2 (50% propellant). 35,000 * ln[2] = 24,260 m/s. Not good enough, we need 39,528 m/s.

Let's try a mass ratio of 3.1 (68% propellant). 35,000 * ln[3.1] = 39,600 m/s. That'll do.

• 

      Tyranny is a human trait that we sometimes project onto Nature. This projection is a form of rationalization, perhaps a means to cope with matters that we cannot control. Such is the case when we invent machines to free us from the bounds of Earth, affecting our escape into space. If we want to expand into the solar system, this tyranny must somehow be deposed.

     Rockets are momentum machines. They spew gas out of a nozzle at high velocity causing the nozzle and the rocket attached to it to move in the opposite direction. Isaac Newton correctly defined the mathematics for this exchange of momentum in 1687. Conservation of momentum applied to a rocket was first done by Russian visionary and scientist Konstantin Tsiolkovsky in 1903. All our rockets are governed by Tsiolkovsky’s rocket equation.
     The rocket equation contains three variables. Given any two of these, the third becomes cast in stone. Hope, wishing, or tantrums cannot alter this result. Although a momentum balance, these variables can be cast as energies. They are the energy expenditure against gravity (often called delta V or the change in rocket velocity), the energy available in your rocket propellant (often called exhaust velocity or specific impulse), and the propellant mass fraction (how much propellant you need compared to the total rocket mass).

     The energy expenditure against gravity is specified by where you want to go. For human exploration, there are only a handful places we can realistically consider at this time. The most likely candidates are: from the surface of Earth to Earth orbit, Earth orbit to surface of the Moon, Earth orbit to surface of Mars, Earth orbit to cis-lunar space (the region between the Earth and the Moon, including a variety of locations such as Lagrange points, geostationary orbit, and more). Of course there are permutations to these routes but they are the most likely ones considering our current state of technology.
     In planning an expedition into space, we first must select where we want to go. The energy expenditure against gravity is then specified by the starting and ending points of our journey. As humans, we are powerless to change this number. We simply have to accept its consequences. I like to think of this as the travel cost.

     Next we need to choose the type of rocket propellant, thus specifying the available energy. Currently, all our human rated rocket engines use chemical reactions (combustion of a fuel and oxidizer) to produce the energy. There are limits to the quantity of energy that can be extracted from chemistry and thus bounds placed outside of human control on the energy we can pack into a rocket. Some of the most energetic chemical reactions known are chosen for rocket propulsion (e.g. like hydrogen-oxygen combustion) and thus, the second variable is now specified. Again, we simply have to accept the limit to what chemistry can offer (unless we choose other energy sources, such as nuclear). I like to think of this selection as what you have to pay for the travel cost.

     With these two variables set, the rocket mass fraction is now dictated by the rocket equation. We must build our rocket within this mass fraction or it will not reach its destination. This also applies to existing rockets when new uses are contemplated. There is very little we can do to alter this result. With some clever engineering we might be able to shave a few percentage points off the fraction, but the basic result is set by the gravitational environment of our solar system (choice of where we want to go) and the chemistry of the energetic bonds of our selected chemical components (choice of propellant).
     It is constructive to put a few numbers together to illustrate the grip that simple momentum balance places upon our rockets. Here the approximate cost in energy has been given in terms of velocity (kilometers per second, km/s), a common ploy engineers use to simplify the discussion. These numbers assume ideal conditions such as no losses for atmospheric drag or combustion but are close enough for the sake of this illustration.

Destination	Energy Cost (km/s)
Surface of Earth to Earth orbit	8
Earth orbit to cis-lunar locations: Lagrange points	3.5
Earth orbit to cis-lunar locations: Low Lunar orbit	4.1
Earth orbit to near-Earth asteroids	> 4
Earth orbit to surface Moon	6
Earth orbit to surface Mars	8

     From this simple table, a few conclusions can be drawn. Travelling from the surface of Earth to Earth orbit is one of the most energy intensive steps of going anywhere else. This first step, about 400 kilometers away from Earth, requires half of the total energy needed to go to the surface of Mars ("halfway to anywhere"). Destinations between the Earth and the Moon are only a fraction of that required to simply get into Earth orbit. The cost of this first step is due to the magnitude of Earth’s gravity. And physics dictates that paying a penny less than the full cost will result in Earth repossessing your spacecraft in a not so gentle way. The giant leap for mankind is not the first step on the Moon, but in attaining Earth orbit.

     Listed next are the major categories for our chemical rocket propellants and their energy content used for payment of the gravitational cost of travel. These are selected from propellants with an operational history in manned spacecraft. “Hypergols” are contact-ignited propellants, used in the Lunar Module ascent stage to simplify the engine design and methane-oxygen has not been used in space to date, but is under consideration for future human missions to the Moon and Mars. The first law of thermodynamics was used to convert the energy of combustion into an equivalent exhaust velocity so that these units of payment are consistent with the costs shown above.

Propellant	Payment Energy (km/s)
Solid Rocket	3.0
Kerosene-Oxygen	3.1
Hypergols	3.2
Earth orbit to near-Earth asteroids:	3.4
Methane-Oxygen	4.5

     Hydrogen-oxygen is the most energetic chemical reaction known for use in a human rated rocket. Chemistry is unable to give us any more. In the 1970’s, an experimental nuclear thermal rocket engine gave an energy equivalent of 8.3 km/s. This engine used a nuclear reactor as the source of energy and hydrogen as the propellant.
     Since the giant leap for mankind is the first step off of Earth, our illustration of the rocket equation uses earth orbit as the destination with the cost of 8 kilometers per second. To pay for this cost, each of the chemical propellants above are used with the rocket equation which results in the following mass fractions (given as percent of the total rocket mass):

Propellant	Rocket Percent Propellant for Earth Orbit
Solid Rocket	96%
Kerosene-Oxygen	94%
Hypergols	93%
Methane-Oxygen	90%
Hydrogen-Oxygen	83%

     These are ideal numbers free from losses due to atmospheric drag, incomplete combustion, and other factors that reduce the efficiencies of a rocket. Such losses make these numbers even worse (moving the mass fraction closer to a rocket being 100% propellant). However, clever engineering constructs such as rocket staging, multiple kinds of propellants (1st stage solids or kerosene, upper stages hydrogen), and gravitational lean (converts radial velocity into tangential) can help compensate. When making a rocket that is near 90% propellant (which means it is only 10% rocket), small gains through engineering are literally worth more than their equivalent weight in gold.

     Real mass fractions from real rockets include the effect of many engineering details. However, these machines at root are the result of the simple application of Tsiolkovsky’s rocket equation. The ideal results presented here are not far removed from actual rockets. The Saturn V rocket on the launch pad was 85% propellant by mass. It had three stages; the first using kerosene-oxygen and the second and third stages using hydrogen-oxygen. The Space Shuttle was also 85% propellant by mass, using a blend of solids and hydrogen-oxygen for the first stage and hydrogen-oxygen for second. The Soyuz rocket is 91% propellant by mass and uses kerosene-oxygen in all of its three stages. There is an advantage to using hydrogen-oxygen as a high performance propellant; however, it is technically more complex. Kerosene offers less performance but gives a simpler, robust, and easier to fabricate rocket. These numbers represent the best that our engineering can do when working against Earth’s gravity and the energy from chemical bonds.

     What are the engineering implications of fabricating a rocket that is 85% propellant and 15% rocket? The rocket must have engines, tanks, and plumbing. It needs a structure, a backbone to support all this and it must survive the highly dynamic environment of launch (there is fire, shake, and force at work.) The rocket must be able to fly in the atmosphere as well as the vacuum of space. Wings are of no use in space; small rocket thrusters are used to control attitude. Then there are people with their pinky flesh and their required life support machinery. Life support equipment is complex, problematic, and heavy. You can’t roll down the windows if the cabin gets a bit stale. If you want to return to Earth (and most crews do), there has to be structure to protect the crew through a fiery entry and then provide a soft landing. Wings are heavy but allow soft landings at well equipped airfields. Parachutes are light, giving a big splash finale. The Soyuz goes thump, roll, roll, roll; aptly described by one of my colleagues as a series of explosions followed by a car wreck. And finally, you want to bring some payload – equipment with which to do something other than just be in space. “Because it is there” (or possibly because it is not there, depending on your definition of a vacuum) is fitting for the first time but subsequent missions need a stronger justification. Missions into space to do meaningful exploration require bringing significant payload.

     Real payload fractions from real rockets are rather disappointing. The Saturn V payload to Earth orbit was about 4% of its total mass at liftoff. The Space Shuttle was only about 1%. Both the Saturn V and Space Shuttle placed about 120 metric tons into Earth orbit. However, the reusable part of the Space Shuttle was 100 metric tons, so its deliverable payload was reduced to about 20 tons.
     It is instructive to compare rocket mass fractions to those of other everyday Earth vehicles. Here, the approximate numbers for propellant (or fuel when air is used as the oxidizer) are given to illustrate the general categories of mass fractions:

Vehicle	Percent Propellant (fuel)
Large Ship	3%
Pickup Truck	3%
Car	4%
Locomotive	7%
Fighter Jet	30%
Cargo Jet	40%
Rocket	85%

     The percent propellant has huge implications on the ease of fabrication and robustness in achieving the engineering design (and cost). If a vehicle is less than 10% propellant, it is typically made from billets of steel. Changes to its structure are readily done without engineering analysis; you simple weld on another hunk of steel to reinforce the frame according to what your intuition might say. I can easily overload my ¾ ton pickup by a factor of two. It might be moving slowly but it is hauling the load.

     Once the vehicles become airborne, the engineering becomes more serious. Light weight structures made of aluminum, magnesium, titanium, epoxy-graphite composites are the norm. To alter the structure takes significant engineering; one does not simply weld on another chunk to your airframe if you want to live (or drill a hole through some convenient section). These vehicles cannot operate far from their designed limits; overloading an airplane by a factor of two results in disaster. Even though these vehicles are 30 to 40% propellant (60 to 70% structure and payload), there is room for engineering to comfortably operate thus there is a robust, safe, and cost effective aviation industry.

     Rockets at 85% propellant and 15% structure and payload are on the extreme edge of our engineering ability to even fabricate (and to pay for!). They require constant engineering to keep flying. The seemingly smallest modifications require monumental analysis and testing of prototypes in vacuum chambers, shaker tables, and sometimes test launches in desert regions. Typical margins in structural design are 40%. Often, testing and analysis are only taken to 10% above the designed limit. For a Space Shuttle launch, 3 g’s are the designed limit of acceleration. The stack has been certified (meaning tested to the point that we know it will keep working) to 3.3 g’s. This operation has a 10% envelope for error. Imagine driving your car at 60 mph and then drifting to 66 mph, only to have your car self-destruct. This is life riding rockets, compliments of the rocket equation.
     Here are a few other interesting examples from container engineering to further illustrate the extreme nature of rocket design:

Other Containers	Percent Useful Contents
Soda Can	94%
Shuttle External Tank	96%
Molotov Cocktail	52%

     The common soda can, a marvel of mass production, is 94% soda and 6% can by mass. Compare that to the external tank for the Space Shuttle at 96% propellant and thus, 4% structure. The external tank, big enough inside to hold a barn dance, contains cryogenic fluids at 20 degrees above absolute zero (0 Kelvin), pressurized to 60 pounds per square inch, (for a tank this size, such pressure represents a huge amount of stored energy) and can withstand 3gs while pumping out propellant at 1.5 metric tons per second. The level of engineering knowledge behind such a device in our time is every bit as amazing and cutting-edge as the construction of the pyramids was for their time.
     A veteran astronaut who has been to the Moon once told me, “Sitting on top of a rocket is like sitting on top of a Molotov cocktail”. I took his comment to heart by first weighing a bottle of wine, emptying the bottle, and weighing it again. Simple engineering analysis allowed me to estimate and compensate for the density difference between wine and gasoline (which, for this particular vintage, I am sure was not much different). A Molotov cocktail was measured to be 52% propellant. So sitting on top of a rocket is more dangerous than sitting on a bottle of gasoline!

     Another less recognized side effect of the rocket equation is the sensitivity of completing the rocket burn to obtaining your goal. To illustrate this, I will use some numbers from my Shuttle flight, STS 126 in November 2008. Our target velocity at main engine cut off was 7824 m/s (25819 ft/s). If our engines shut down at 7806 m/s (25760 ft/s), only 18 m/s (59 ft/s) shy of the target value, we would make an orbit but not our designated target orbit. We would not be able to rendezvous with space station and would lose our mission objective. Like being two pennies short of a ten dollar purchase, this is only 0.2% less than the price of admission into space. In this case, we do have some options. We could burn our orbital maneuvering propellant and make up this difference. If we were 3% shy of our target, 7596 (25067 ft/s) we would not have sufficient orbital maneuvering propellant and we would not make any orbit. We would be forced into a trans-Atlantic abort, falling back to Earth and landing in Spain. This final 3% of our required velocity comes during the last 8 seconds of our burn. For astronauts and bull riders, 8 seconds is a long time.

     If the radius of our planet were larger, there could be a point at which an Earth escaping rocket could not be built. Let us assume that building a rocket at 96% propellant (4% rocket), currently the limit for just the Shuttle External Tank, is the practical limit for launch vehicle engineering. Let us also choose hydrogen-oxygen, the most energetic chemical propellant known and currently capable of use in a human rated rocket engine. By plugging these numbers into the rocket equation, we can transform the calculated escape velocity into its equivalent planetary radius. That radius would be about 9680 kilometers (Earth is 6670 km). If our planet was 50% larger in diameter, we would not be able to venture into space, at least using rockets for transport.

     Revolting against tyranny is a recurring human trait and perhaps we will figure some way to depose the rocket equation and venture away from our planet in a significant way. I am referring to exploration with continuous human presence with the first step like Antarctic-type bases (which support several thousand people) and eventually leading to colonization, a template comparable to the expansion of western civilization across the globe during the 17th and 18th centuries. To call yourself a sea-faring nation in that time meant that you could set sail on a variety of missions in a number of different types of vessels to a myriad of destinations whenever you wanted. We have a long way to go before anyone can claim to be a space-faring nation.
     The giant leap for mankind is not the first step on the Moon but attaining Earth orbit. If we want to break the tyranny of the rocket equation, new paradigms of operating and new technology will be needed. If we keep to our rockets, they must become as routine, safe, and affordable as airplanes. One of the most rudimentary and basic skills to master is to learn how to use raw materials from sources outside the Earth. Our nearest planetary neighbor, the Moon is close, useful, and interesting. Extracting and producing useful products from the raw materials of the Moon would relieve us from the need to drag everything required in space from the bottom of Earth’s deep gravity well, significantly altering the consequences of the rocket equation more in our favor. The discovery of some new physical principle could break the tyranny and allow Earth escape outside the governance of the rocket paradigm.
     The need for new places to live and resources to use will eventually beckon humanity off this planet. Having access to space removes the lid from the Petri dish of Earth. And we all know what eventually happens if the lid is not removed.

(ed note: In the AppleTV series For All Mankind, episode 14 features the space shuttle Pathfinder. In this alternate-history, the shuttle is not launched via a huge external tank and two strap on solid rocket boosters. No, this alternate shuttle lifts off from the back of a C-5 Galaxy aircraft. This was considered back in the 1980s but was dropped.

Gabriel 'GAB' Fonseca {science advisor for The Sojourn} did some math on that and came to some suprising conclusions.)

My friends and I did some math on For All Mankind's Pathfinder shuttle and came to the conclusion that, to be able to reach orbit from an airlaunch, have the propellant fit inside its hull, and be light enough for a C-5 Galaxy to lift it, it needs to have a Liquid Core Nuclear Thermal Rocket engine (this is quite a bit more advanced than the standard solid core NTR such as NERVA).

From an airplane launch, let us assume you need around 8.8 km/s of ΔV. A NERVA engine has an Exhaust Velocity of about 8.25 km/s. Using Tsiolkovsky's rearranged to find the mass ratio, we get that:

e^(8.8/8.25) ≈ 2.9

Let us assume Pathfinder weights more-or-less the same as the Shuttle Orbiter ~80 Tons, and has a payload capacity of ~20 Tons. It thus has 80 + 20 tons = 100 Tons at launch, sans propellant (i.e., dry mass).

A mass ratio of 2.9 makes it so it has a wet mass of 290 tons (100 * 2.9 = 290). Wet mass of 290 t - 100 t of combined payload and vehicle means it has 190 t of propellant, usually Liquid Hydrogen (LH₂). LH₂ has a density of 0.072 tons per m³, so 190 tons of LH₂ would take up a volume of 2639 m³.

That's… a lot. For comparison:

The Space Shuttle cargo bay is 18.3 meters long and has a diameter of 4.57 meters. Assume it is a cylinder. It'd have a volume of ~300 m³. Pathfinder's wings may be THICCC (with 3 Cs), but they most certainly do NOT total 8.79666… times the volume of the cargo bay.

Let us assume instead that the NTR is running on water (H₂O). A solid-core NTR operating at 3200 K running on water has an Exhaust velocity of 4.042 km/s (which has a better density, but at the cost of a worse exhaust velocity).

e^(8.8/4.042) ≈ 8.82

That translates to a total of 782 tons of water, taking up… 782 m³. That's still too much.

A liquid-core NTR running on water has, instead, an exhaust velocity of 10.3 km/s (see the LARS engine). Let us assume 10 km/s for error margins.

e^(8.8/10) ≈ 2.41

That translates to 141 tons of water, for a total vehicle launch mass of 241 tons.

A C-5M Comet has a maximum takeoff weight of 417.3 tons. It weighs 172.4 tons. So it can take off with our Liquid NTR Pathfinder, but with only a measly 3.94 tons of jet fuel. Presumably the Pathfinder carrier variant is of the C-5 is lighter.

Thus we conclude that uh… some liberties were taken. Then again, who knows? Maybe they have all the data and they'll release it to us at some point.

Maybe Pathfinder is just much lighter than the Shuttle.

The current figure for the VASIMR's thrust power is 5.8 megawatts (5,800,000 watts). If its exhaust velocity is set to 294,000 m/s (specific impulse of 30,000 seconds), what would the thrust be?

F = (F_p * 2) / V_e
F = (5,800,000 * 2) / 294,000
F = 11,600,000 / 294,000
F = 40 Newtons

What if you set the thrust to 400 Newtons, what would the exhaust velocity be? Remember for a given engine the thrust power is a constant, it is still 5,800,000 watts

V_e = (F_p * 2) / F
V_e = (5,800,000 * 2) / 400
V_e = 11,600,000 / 400
V_e = 29,000 m/s

Rick Robinson:

Those performance stats (for the Project Daedalus) are certainly torchlike, and in fact an exhaust velocity of 10,000 km/s is wasteful for nearly all Solar System travel — on most routes you just don't have time to reach more than a few hundred km/s.

Using STL starship technology on interplanetary routes is like using a jet plane to get around town.

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Jean Remy:

There's no such thing as going somewhere "too fast". At least in terms of military strategy you'll want the ability to get somewhere faster than anyone else can, and damn the price at the pump. It is more costly to arrive at a battle late (and for want of a horse)

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Rick Robinson:

Oh, I have nothing against speed! A better way to put it is that STL starships are geared all wrong for insystem travel, like driving city streets in 5th gear.

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Luke Campbell:

Consider a 1,000 ton spacecraft with a 10,000 km/s exhaust velocity and an acceleration of 0.722 m/s/s. For a 1 AU trip at constant acceleration, flipping at the midpoint, it will take 10.5 days and consume 66 tons of propellant/fuel.

Now let's add extra mass into the exhaust stream, so that the spacecraft uses propellant at 16 times the rate but expells it at 1/4 the exhaust velocity (thus keeping the same power). This brings the acceleration up to 2.89 m/s/s. We will accelerate for 1/10 the distance, drift for 8/10 the distance, and then decelerate for 1/10 the distance. The trip now takes 7 days and uses 240 tons of propellant, of which only 14 tons is fuel.

Bulk inert (non-fuel) propellant is probably cheap (water or hydrogen). Fuel is probably expensive (He-3 and D). The second option gets you there faster and cheaper.

(ed note: see the mathematical details of Luke Campbell's example below)

In Rick's analogy, high exhaust velocity, low thrust, low propellant flow corresponds to high gear. Low exhaust velocity, high thrust, high propellant flow is low gear. In this case, a lower gear than the default "interstellar" Daedelus thrust parameters is preferable.

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Rick Robinson:

'Gearing' is highly desirable even if the drive won't produce surface lift thrust from any significant body. Each deep space mission also has its own optimum balance of acceleration and delta v, favoring an adjustable drive.

(ed note: given the mission delta V, the optimal exhaust velocity is Δ_v * 0.72.)

Luke Campbell: Consider a 1,000 ton spacecraft with a 10,000 km/s exhaust velocity and an acceleration of 0.722 m/s/s.

GIVEN:
M (spacecraft wet mass) = 1×10⁶ kg (1,000 tons)
V_e (exhaust velocity) = 1×10⁷ m/s (10,000 km/s)
A (instantaneous acceleration) 0.722 m/s²

IMPLIED:
Isp (specific impulse) = Ve / g₀ = 1×10⁶ sec
F (thrust) = F = M * A = 722,000 N
F_p (thrust power) = (F * V_e ) / 2 = 3.61×10¹² watts (3.61 terawatts)
mDot (propellant mass flow) = F / V_e = 0.0722 kg/s
mDot_f (fusion fuel mass flow) = mDot = 0.0722 kg/s (because with pure fusion engines the fuel is also the mass)

Luke Campbell: For a 1 AU trip at constant acceleration, flipping at the midpoint, it will take 10.5 days and consume 66 tons of propellant/fuel.

GIVEN:
D (trip distance) = 1.496×10¹¹ m (1 AU)
Trajectory = Brachistochrone (constant acceleration flipping at endpoint)

IMPLIED:
T (transit time) = 2 * sqrt[ D/A ] = 910,389 seconds (10.5 days)
T_b (duration of burn) = T (because brachistochrone) = 910,389 seconds
M_pb (mass of propellant burnt in current burn) = mDot * T_b = 65,500 kg (66 tons)

Luke Campbell: Now let's add extra mass into the exhaust stream (implying that above is specifying a pure fusion ship), so that the spacecraft uses propellant at 16 times the rate but expells it at 1/4 the exhaust velocity. This brings the acceleration up to 2.89 m/s/s.

GIVEN:
V_eg (gearshifted exhaust velocity) = V_e / 4 = 2,500,000 m/s

IMPLIED:
F_g (gearshifted thrust) = (F_p * 2) / V_eg = 2,888,000 N (1/4 exhaust velocity, note F_p is still 3.61×10¹² watts!)
mDot_g (gearshifted propellant mass flow) = F_g / V_eg = 1.1552 kg/s (propellant at 16 times the rate)
A_g (gearshifted acceleration) = F_g / M = 2.89 m/s²

Luke Campbell: We will accelerate for 1/10 the distance, drift for 8/10 the distance, and then decelerate for 1/10 the distance. The trip now takes 7 days and uses 240 tons of propellant, of which only 14 tons is fuel.

GIVEN:
D_0.1 = D * 0.1 = 1.5×10¹⁰ m (1/10 the distance)
D_0.8 = D * 0.8 = 1.2×10¹¹ m (8/10 the distance)

IMPLIED:
T_a0.1 (time to accelerate 1/10 distance) = sqrt[(D_0.1 * 2) / A_g] = 101,885 seconds (1.2 days)
T_d0.1 (time to deccelerate 1/10 distance) = T_a0.1 = 101,885 seconds (1.2 days, takes just as long to slow down to stop as to speed up)
M_pba0.1 (mass of propellant burnt accelerating 1/10 distance) = mDot_g * T_0.1 = 120,000 kg (120 tons)
M_pbd0.1 (mass of propellant burnt decelerating 1/10 distance) = M_pba0.1 = 120,000 kg (120 tons)
R_0.8 (rate of speed during drift) = A_g * T_a0.1 = 294,000 m/s (ship speed at end of acceleration period)
T_0.8 (duration of drift) = D_0.8 / R_0.8 = 408,000 seconds (4.7 days)
T_g (Total gearshifted time) = T_a0.1 + T_0.8 + T_d0.1 = 611,770 seconds (7 days)
M_pbg (total mass gearshifted propellant burnt) = M_pba0.1 + M_pbd0.1 = 240,000 kg (240 tons)
M_fbg (total mass fuel burnt) = mDot_f * (T_a0.1 + T_d0.1) = 14,000 kg (14 tons)

• 

Sometimes "normal" Over Drive is not enough. Almost any piece of Applied Phlebotinum can be made to work a little harder, at the cost of an increased risk (or certainty) that it will eventually explode. A Necessary Drawback to show why it shouldn't be used this way very often.

Your chief engineer will technobabble some stuff about "bypassing the safety protocols", but this will not require laying new cables or replacing clock chips — it just requires a few pokes at the control console. This is often achieved by applying more power.

It's even possible to do it by accident: give a computer a sufficiently hard math problem, and it will grind out an answer just before it overheats and expires from the effort. Also, being overclocked causes a system to work at increased efficiency and then stop dead.

This does have some base in reality. In Real Life, an overclocked computer will run faster, although noticeably hotter (so the hardware can very well literally melt from overheating. More modern VLSIs are likely to have safeguards against overheating, but this isn't the case with standalone circuit components like power capacitors), and will have an increased chance of making (typically small) mathematical errors. Pushed too far, though, clocked hardware components will exert a rapidly increasing level of general malfunction (if not outright refuse to work thanks to safeguards). And even small computational errors in critical parts of software will eventually cause it to crash. A normally-clocked system can overheat and crash from high load (and thus increased heat output), too, if it has inadequate cooling.

In general, overclocked phlebotinum will last exactly long enough to solve your problem, exploding right after you've shot the big gun. Alternatively, it may solve or delay your immediate problem, then break down, leaving you stranded in space with a seized engine.

Overclocking an Energy Weapon (sometimes called "hotshotting") is a good way to create the equivalent of a One Bullet Left scenario: "I can boost the power of your weapon, but it'll only last long enough to give you one shot."

The idea probably comes from the notion of red-lining a car engine, which will give you extra speed, but puts so much strain on the engine and produces so much heat that its weaker parts are liable to break. But in Science Fiction, this ability is available to just about everything, without making massive time-consuming modifications to the equipment. (Go ahead, try to make your tablesaw run faster.)

One popular use of Explosive Overclocking is as a subversion of Tim Taylor Technology.

It may also cause Explosive Instrumentation, although enemy attack or Percussive Maintenance will usually do the same thing. Especially if your vessel is not properly grounded. It's usually safer to Reverse Polarities, but that wouldn't result in a pretty fireball from your automatic Self-Destruct Mechanism, would it? Especially with No Plans, No Prototype, No Backup.

Applied to The Hero himself, Heroic RRoD may be an organic counterpart to this trope (usually due to excessive use of a Dangerous Forbidden Technique or Super Mode).

Compare Overclocking Attack (you do this because you want something to explode), Forbidden Chekhov's Gun, Flawed Prototype (which usually can be overclocked to match a "perfect" model), Cast from Hit Points (instead of a chance of complete self-destruction there is a guarantee of partial self-destruction), Pent-Up Power Peril (when your power builds up in your body by itself and will overclock your body if you don't use it regularly), Awesomeness Is Volatile, and Deadly Upgrade. An organic equivalent is Uninhibited Muscle Power.

Not to be confused with Ramping Slo-mo in explosive action scenes.

(ed note: see TV Trope page for list of examples)

While they were waiting for the Captain to arrive with tackle from the ship to haul them out, Mercer and Davies began a close examination of their surroundings. They were in a circular room of roughly five yards diameter which had been hollowed out of the original rock outcropping, then covered by a thin, plastic shell treated to simulate rock on the outside.

In the centre of the room stood a tall, enigmatic piece of apparatus which they had narrowly missed in falling. Several of the heavy power lines about which Mercer had been so curious sprouted from the floor and disappeared into this imposing mechanism—which Mercer, after much peering and nosing around it, had guessed to be some form of communicator. Pointing to a silvery rod near its top he said that this was probably the antenna. However, as the rod was totally enclosed by a sphere of copper mesh it was obvious that the signal produced could not go out into the normal either. Also, the equipment was apparently activated by an impulse which should reach it via the metal bird’s-nest they had seen just before their fall.

"… Another thing which puzzles me,” Mercer said as they stared at the device, “is the amount of power the thing uses. It must operate for a split second at tremendous overload, then burn out—those power lines go right into it without fuses or safety cut-offs of any kind.”

• 

(ed note: The valiant warfleet of the Galactic Patrol has utterly destroyed the grand base of the dastardly Boskonians. Now the Patrol lightheartedly move to mop up the eighteen relatively tiny outlying Boskone orbital fortresses. The patrol thinks this will be a pushover.)

      While von Hohendorff and Kinnison had been talking, Haynes had issued orders and the Grand Fleet, divided roughly and with difficulty into eighteen parts, went raggedly outward to surround the eighteen outlying fortresses. But, and surprisingly enough to the Patrol forces, the reduction of those hulking monsters was to prove no easy task.
     The Boskonians had witnessed the destruction of Helmuth's Grand Base. Their master plates were dead. Try as they would, they could get in touch with no one with authority to give them orders, with no one to whom they could report their present plight. Nor could they escape: the slowest mauler in the Patrol Fleet could have caught any one of them in five minutes.
     To surrender was not even thought of—better far to die a clean death in the blazing holocaust of space-battle than to be thrown ignominiously into the lethal chambers of the Patrol.
     There was not, there could not be, any question of pardon or of sentence to any mere imprisonment, for the strife between Civilization and Boskonia in no respect resembled the wars between two fundamentally similar and friendly nations which small, green Terra knew so frequently of old. It was a galaxy-wide struggle for survival between two diametrically opposed, mutually exclusive, and absolutely incompatible cultures; a duel to the death in which quarter was neither asked nor given; a conflict which, except for the single instance which Kinnison himself had engineered, was and of stern necessity had to be one of ruthless, complete, and utter extinction.
     Die, then, the pirates must; and, although adherents to a scheme of existence monstrous indeed to our way of thinking, they were in no sense cowards. Not like cornered rats did they conduct themselves, but fought like what they were; courageous beings hopelessly outnumbered and outpowered, unable either to escape or to choose the field of operations, grimly resolved that in their passing they would take full toll of the minions of that detested and despised Galactic Civilization. Therefore, in suicidal glee, Boskonian engineers rigged up a fantastically potent weapon of offense, tuned in their defensive screens, and hung poised in space, awaiting calmly the massed attack so sure to come.

     Up flashed the heavy cruisers of the Patrol, serenely confident. Although of little offensive strength, these vessels mounted tractors and pressors of prodigious power, as well as defensive screens which—theoretically—no projector-driven beam of force could puncture.
     They had engaged mauler after mauler of Boskonia's mightiest, and never yet had one of those screens gone down. Theirs the task of immobilizing the opponent; since, as is of course well known, it is under any ordinary conditions impossible to wreak any hurt upon an object which is both inertialess and at liberty to move in space. It simply darts away from the touch of the harmful agent, whether it be immaterial beam or material substance.
     Formerly the attachment of two or three tractors was all that was necessary to insure immobility, and thus vulnerability; but with the Velantian development of a shear-plane to cut tractor beams, a new technique became necessary. This was englobement, in which a dozen or more vessels surrounded the proposed victim in space and held it motionless at the center of a sphere by means of pressors, which could not be cut or evaded. Serene, then, and confident, the heavy cruisers rushed out to englobe the Boskonian fortress.

     Flash! Flash! Flash! Three points of light, as unbearably brilliant as atomic vortices, sprang into being upon the fortress' side. Three needle-rays of inconceivable energy lashed out, hurtling through the cruisers' outer screens as though they had been so much inactive webbing.
     Through the second and through the first. Through the wall-shield, even that ultra-powerful field scarcely flashing as it went down. Through the armor, violating the prime tenet then held and which has just been referred to, that no object free in space can be damaged—in this case, so unthinkably vehement was the thrust, the few atoms of substance in the space surrounding the doomed cruisers afforded resistance enough. Through the ship itself, a ravening cylinder of annihilation.
     For perhaps a second—certainly no longer—those incredible, those undreamed-of beams persisted before winking out into blackness; but that second had been long enough.
     Three riddled hulks lay dead in space, and as the three original projectors went black three more flared out.
     Then three more. Nine of the mightiest of Civilization's ships of war were riddled before the others could hurl themselves backward out of range!

     Most of the officers of the flagship were stunned into temporary inactivity by that shocking development, but two reacted almost instantly.
     "Thorndyke!" the admiral snapped. "What did they do, and how?"
     And Kinnison, not speaking at all, leaped to a certain panel, to read for himself the analysis of those incredible beams of force.
     "They made super-needle-rays out of their main projectors," Master Technician LaVerne Thorndyke reported, crisply. "They must have shorted everything they've got onto them to burn them out that fast."
     "Those beams were hot—plenty hot," Kinnison corroborated the findings.
     "These recorders go to five billion and have a factor of safety of ten. Even that wasn't anywhere nearly enough—everything in the recorder circuits blew."

     "But how could they handle them..." von Hohendorff began to ask.
     "They didn't—they pointed them and died," Thorndyke explained, grimly.
     "They traded one projector and its crew for one cruiser and its crew—a good trade from their viewpoint."
     "There will be no more such trades," Haynes declared.

---

     "We are equipped to energize simultaneously eight of the new, replaceable-unit primary projectors," the C.F.O. stated, crisply. "There are twenty-one vessels englobing us, and no others within detection. With a discharge period of point six zero and a switching interval of point zero nine, the entire action should occupy one point nine eight seconds."
     The underlying principle of the destructive beam produced by overloading a regulation projector had, it is true, been discovered by a Boskonian technician. Insofar as Boskonia was concerned, however, the secret had died with its inventor; since the pirates had at that time no headquarters in the First Galaxy. And the Patrol had had months of time in which to perfect it, for that work was begun before the last of Helmuth's guardian fortresses had been destroyed.
     The projector was not now fatal to its crew, since they were protected from the lethal back-radiation, not only by shields of force, but also by foot after impenetrable foot of lead, osmium, carbon, cadmium, and paraffin. The refractories were of neo-carballoy, backed and permeated by MKR fields; the radiators were constructed of the most ultimately resistant materials known to the science of the age. But even so the unit had a useful life of but little over half a second, so frightful was the overload at which it was used. Like a rifle cartridge, it was good for only one shot. Then it was thrown away, to be replaced by a new unit.
     Those problems were relatively simple of solution. Switching those enormous energies was the great stumbling block. The old Kimmerling block-dispersion circuit-breaker was prone to arc-over under loads much in excess of a hundred billion KVA, hence could not even be considered in this new application. However, the Patrol force finally succeeded in working out a combination of the immersed-antenna and the semipermeable-condenser types, which they called the Thorndyke heavy-duty switch. It was cumbersome, of course—any device to interrupt voltages and amperages of the really astronomical magnitudes in question could not at that time be small—but it was positive, fast-acting, and reliable.

     At Kinnison's word of command eight of those indescribable primary beams lashed out; stilettoes of irresistibly penetrant energy which not even a Q-type helix could withstand. Through screens, through wall-shields, and through metal they hurtled in a space of time almost too brief to be measured. Then, before each beam expired, it was swung a little, so that the victim was literally split apart or carved into sections. Performance exceeded by far that of the hastily-improvised weapon which had so easily destroyed the heavy cruisers of the Patrol; in fact, it checked almost exactly with the theoretical figure of the designers.
     As the first eight beams winked out eight more came into being, then five more; and meanwhile the mighty secondaries were sweeping the heavens with full-aperture cones of destruction. Metal meant no more to those rays than did organic material; everything solid or liquid whiffed into vapor and disappeared. The Dauntless lay alone in the sky of that new world.

Payload is the load that the spacecraft owner is being paid to haul. Yeah, kind of like the cargo. Except the blasted cargo can be a crew of astronauts, a warship's weapon turrets, a pre-fab lunar colony, the spacecraft's built-in crew quarters, or anything else that is not propellant or ship structure.

With the Polaris, our payload is Tom Corbett and his buddies, the Polaris habitat module, the life-support system, the avionics, the command deck, the astrogation deck, the engineering deck, the space boats, and the atomic missile armaments.

• 

(ed note: The good ship Johannes Kepler is about midway on a 92 day journey to Mars colony when a meteor punctures the ship. Unfortunately the idiot captain was holding a meeting of all the officers in the control room, so they are all dead now. The only officer left is Lieutenant Donald Chase, who is actually the ship's medic. However, by the chain of command he is officially the captain.

They struggle through a variety of disasters, most recent of which was a solar proton storm. Now they have to somehow contact Mars Central because they are off-course, the astrogator is in the morgue, and a passenger named Ugalde who is a mathematician is not quite up to calculating a correction. Eventually they make radio contact with Mars through the solar interference by using morse code.)

      It took time, a lot of time, because the communication was so complex. Don typed a message into the computer, explaining what had happened, and this was recorded on tape as a series of dots and dashes. Another tape was prepared of up-to-date stellar observations which were recorded along with the earlier data. The computer on Mars would process these and determine the course corrections that would be needed. Time passed, and with each second they moved further from their proper course.
     They waited again and, instead of the course corrections, they received a request for the amount of reaction mass that remained in their tanks. This was sent back as quickly as possible and there were minutes of silence as they waited for the answer, for the corrections that would get them back into the proper orbit for Mars. The message finally came.
     ‘Hello Big Joe,’ the voice rasped and, although the man speaking tried to sound happy, there was an undertone of worry in his voice. ‘We are not saying that this is the final answer, the figures are being re-run, and something will be done. But the truth is … well … you have been in an incorrect orbit for too long a time. It appears that, with the reaction mass you have remaining … there is not enough to make a course correction for Mars. Your ship is on an unchangeable orbit into outer space.’

---

     ‘What is this reaction mass that Mars Central is so worried about?’ he asked. ‘I hate to act stupid, but medical studies leave little time for reading about anything else. I thought this ship was powered by atomic engines?’
     ‘It is, sir, but we still need reaction mass. A rocket moves not by pushing against anything, but by throwing something away. Whatever is thrown away is called reaction mass. In chemical rockets it is burning gas. The gas goes in one direction, the rocket goes in the other. The more you throw away, the more reaction you get and the faster you go. You also get more reaction by throwing something away faster. That is what we do. Our reaction mass is made up of finely divided particles of silicon. It’s made from steel plant slag, vaporized in a vacuum, so the particles are microscopic. These particles are accelerated by the engines to an incredible speed. That’s what gives us our push.’ (nowadays we know that liquid hydrogen is a superior reaction mass to finely-divided silicon)
     Don nodded. ‘Seems simple enough — at least in theory. So, although we have unlimited power from the atomic engines, we don’t have enough reaction mass for the course change required?’
     ‘Right, sir. Normally we carry more than enough mass for our needs, because the course corrections are made as early as possible. The more the ship gets away from the right orbit, the more mass is needed to get us back. We’ve waited a little too long this time.’

---

     Don refused to give in to the feeling of gloom that swept the control-room.
     ‘Can’t we use something else for reaction mass?’ he asked.
     Kurikka shook his head. ‘I’m afraid not. Nothing is small enough to get through the injectors. And the engines are designed to run with this kind of reaction mass only.’ He turned away and, for the very first time, Don saw that the rock-like chief petty officer was feeling defeat. ‘I’m afraid there is nothing we can do.’
     ‘We can’t give up!’ Don insisted. ‘If we can’t change the orbit to the correct one, we can certainly alter it as much as possible, get it closer to the correct one.’
     ‘Maybe we can, Captain, but it won’t help. With all our mass used to change course we won’t have enough for deceleration.’
     ‘Well at least we’ll be closer to Mars. There must be other ships there that can match orbits with us and take everyone off. Let’s ask Mars Central about it.’

---

     The answer was infuriatingly slow in coming, and not very hopeful.
     ‘We are running all the possibilities through the computer here, but there is nothing positive yet. There are no deepspacers here who can aid you, and the surface to satellite ferries don’t have the range to reach you, even with your correct orbit. Don’t give up hope, we are still working on the problem.’
     ‘Great lot of good that does us,’ Sparks muttered. ‘You’re not in our shoes.’

---

     ‘I am afraid I must disagree with Chief Kurikka and say that his last statement is wrong,’ Ugalde said. He had been standing in a daze of concentration for a long time, and did not realize that the Chief’s ‘last’ statement had been spoken almost fifteen minutes earlier. ‘There is something we can do. I have examined the situation from all sides and, if you will permit me to point out, you are looking at only part of the problem. This is because you have stated the question wrong.’ He began to pace back and forth.
     ‘The problem is to alter our orbit to the correct one, not to find more mass. Stated this way the problem becomes clear and the answer is obvious.’
     ‘Not to me,’ Kurikka said, speaking for all of them.
     Ugalde smiled. ‘If we cannot get more reaction mass, then we must get less mass for our present quantity of reaction mass to work against.’
     Don smiled back. ‘Of course! That’s it! We will just have to lighten ship.’

---

     ‘It is important that everything that is jettisoned be weighed first,’ Ugalde warned. ‘This will be needed in the computations. And the faster it is done the better our chances will be ! ’
     ‘We start right now,’ Don said, pulling over a notepad and electric stylo. ‘I want to list everything that is not essential to the operation of the ship and the lives of everyone aboard. Suggestions?’
     ‘The passengers’ luggage of course,’ Ugalde said. ‘They should keep what they are wearing and the rest will be discarded.’
     The purser moaned. ‘I can see the lawsuits already.’
     ‘I’m sure that the company is insured,’ Don said, making a note. ‘Their luggage or their lives — that is really not much of a choice. They can keep their valuables and personal items, but anything that can be replaced has to go. You’d better have them all assembled in the main dining-hall in fifteen minutes. I’ll come up and tell them myself.’
     Jonquet nodded and left. Don turned to the others.
     ‘The dining—tables, chairs, dishes, most of the kitchen equipment,’ Kurikka said, counting oif the items on his fingers. ‘All the frozen meat and refrigerated food. We can live off the dehydrated emergency rations which use recycled water.’
     ‘Good thinking. Who’s next?’
     Once they began to concentrate on it, it was amazing the number of items that they found. Carpets and decorations and banisters on the stairs, furniture, fittings and spare parts. The list grew and Don checked off the items. There was one obvious — and heavy — item missing. ‘The cargo,’ he said, ‘what about that?’
     Kurikka shook his head. ‘I only wish we could. There is heavy machinery, bales of clothing, a lot of items that we could do without. But all the cargo is container loaded for the most part, and sealed into place against the G stresses. The shuttle rockets have the special extensible power sockets to reach down past the containers to free them, but we don’t have the equipment. I suppose we could jury-rig something to get the containers out, but it would take a couple of days at least.’
     ‘Which is far too long for us. The cargo stays — but everything else that can go, goes! ’

Everything old is new again. AFAIK there ain't a smartphone app for this, and doing it longhand is a drag. So check out this 1900's tech called a Nomogram. Sneer at it if you like, it actually has some advantages over spreadsheets and online calculators. Consider it to be steampunk, because it is. I'm sure Robert Heinlein used nomograms.

Here's the deal: a slide rule is like a pocket calculator or the calculator app on your smartphone. It can do any calculation. But if there is a particular equation you use at work all the time, wouldn't it be nice if the calculator made it easier to do that equation?

Which leads us to nomograms. They are a pattern of scales printed on paper. They can only do one specific equation. They cannot calculate any other. But the advantage is it can solve it almost as fast as you can slap a ruler on the diagram.

In other words they are optimized to solve that equation. So if this is an equation you are constantly solving in the course of your work, just think of the time savings.

"So what?" I hear you scoff. "A simple web app can be optimized as well". Ah, but there is more.

Unlike a calculator or a web app, a nomogram can visualize a range of options. You lay the straight edge to solve the equation. But now you can pic one of the equation variables as a fixed value, and pivot the straight edge on that value (like you nailed a pin into that value and rotated the rule around it). You can then look at how the other variables change, and can then select the best set of values as the solution.

The General Electric Space Propulsion Calculator was manufactured by the GE Flight propulsion Laboratory. Front side calculates Thrust, Thrust Power, Propellant Mass Flow, Specific Impulse, and Exhaust Velocity. The flip side calculates Escape velocity, Orbital velocity, Period of revolution, and Gravitational pull for the major planets and moons of the solar system. Images are from the Calculating Blog.

• 

• 

• 

• 

• 

This engine is labeled an "isotopic motor", but nowadays is called a fission sail. Radioactive material has its radiation absorbed on all sides except in the desired thrust direction. Great specific impulse, but the thrust is microscopic.

• 

As near as I can figure, the spherical object labeled "reactor" is actually a type Radioisotope Thermoelectric Generator. I say this because the section labeled "5" appears to be a thermocouple. The spacecraft appears to be a generalized Nuclear-Electric rocket. The unspecified engine would be some kind of electrical propulsion, like ion or plasma.

• 

This uses a magnetohydrodynamic (MHD) generator to harvest electricity from the uranium-hydrogen plasma. The fissioning uranium ionizes the hydrogen. The ionized stream can conduct electricity. It is shot through a magnetic field (created by a solenoid), where it induces an electrical current in the side plates. The stream then enters the "divider" where the uranium is separated from the hydrogen. The unspent uranium is sent back to the reaction chamber. The hydrogen is sent to some kind of Electromagnetic accelerator which is powered by the electricity from the MHD generator.

I have no idea if this will acually work, or if it was discredited decades ago. Up until now I had only seen MHD harvesting of electricity associated with nuclear fusion reactions, not nuclear fission.

The "reactor" is actually the reaction chamber (12). The "motor" is the Electromagnetic accelerator. "Working mass" is another name for "reaction mass", "working fluid", or "propellant". The shadow shield is up near the nose, though generally it is more efficient to put it right on top of the reactor. The "vernier motor" is an attitude jet.

• 

Looks like every NERVA diagram I've ever seen. A nuclear reactor where the coolant flows directly to the exhaust.

• 

Uranium is just spraying into the reaction chamber along with the propellant. Easiest to engineer, but lots of expensive un-burnt uranium escapes out the exhaust. This angers the owner's accountants and the picketing anti-nuclear activists.

• 

Uranium is injected tanjentally, to make a spiral flow around the long axis. Hopefully this forces the uranium to loiter in the reaction chamber longer, reducing the amount of un-burnt uranium that escapes.

• 

I have never seen this one before.

By doing some research I stumbled over a paper on Russian gas-core design. There is a "recirculation intake" just before the exhaust nozzle that tries to catch the uranium before it escapes. The uranium is liquifed then pumped back to the top of the reaction chamber. Frankly I do not understand why the hot fissioning uranium does not instantly vaporize the intake scoop.

But that is not this design. In this one, the fissioning uranium is jetted in the contrary direction to the hydrogen propellant. It is captured at the top, the hydrogen is filtered out, and sent back to the bottom to be injected again. The author calls it a "coaxial gas reactor", but this is not the same thing as the coaxial-flow NTR.

• 

The uranium is liquid, and the reaction chamber is spun on the long axis to keep the uranium in the chamber by centrifugal force. Note the tiny arrow indicating the spin, it's a dead giveaway.

Fourth rocket engine (Fig. IV) works in a peculiar thermo-mechanical cycle. Part of the energy of the reactor is used to drive the pump, which feeds into the reactor core liquid working medium, where it vaporizes and heated at high pressure.

The resulting hot gas is pumped into a separate high-pressure chamber, which, through valve 11 communicates with tube shocks. At the other end of the shock tube we find structed diffuser serves to concentrate the energy of the shock wave, and the valve 12, connecting tube with a nozzle rocket. Duty cycle engine is as follows: pump 5 takes the working fluid from the reservoir and high-pressure pumps it through a reactor, where it evaporates and is heated to about 2500° C — and then injected into the high-pressure chamber. Shock tube at this point is still filled with gas of low pressure left over from the previous cycle. Then the valve 11 to quickly open, compressed gas, bursting into the pipe instantaneously compresses and heats the gas in the tube, causing the appearance in it of a strong shock wave.

The highest compression is achieved in the lower stream of the diffuser. Then, valve 11 closes and valve 12 opens and gas at high speed coming out of the nozzle. When the temperature of exhaust gas will decrease by 3-4 times compared with the maximum temperature reached in the shock tube, valve 12 closes and valve 13 opens, and by a pump 5 remains a shock tube fed into a radiator where it cools. This cycle is continuously repeated, creating "clusters" of high-temperature gas flowing from a nozzle at high speed.