Landing in Lava
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Down To Rock
Most of the potent engines have exhausts measured in thousands of degrees. What about landing? We don't want our ships to touch down on a new planet only to immediately sink out of sight in a self-created sea of lava.
(We will ignore that unpleasant little man in the front row who is asking loudly: why don't we keep the rocket in orbit and land with the small shuttle we carried along?)
As a wild guess, the exhaust temperature is approximately 100 K * Ve2. So an exhaust velocity of 20,000 m/s is on the order of 40,000 K.
The particle energy(approximately the temperature inside the engine) is
Ae = (0.5 * Am * Av2) / B
- Ae = particle energy (Kelvin)
- Am = mass of particle (g) (1.6733e-24 grams for monatomic hydrogen)
- Av = exhaust velocity (cm/s)
- B = Boltzmann's constant: 1.38e-16 (erg K-1)
But more to the point is total plume energy.
Fp = (F * Ve) / 2
- Fp = thrust power (watts)
- F = thrust (newtons)
- Ve = exhaust velocity (m/s)
(Note that exhaust velocity is in two different units in the two equations)
 Exhaust power. Say we have a gas core rocket with an exhaust velocity of 50,000 m/s and 1,000,000 newtons of thrust. We've got 25,000,000,000 watts on our hands (25 gigawatts). Say that the exhaust is concentrated mainly in a 10 meter diameter circle on the final descent. The area is about 80 square meters, for a heat flux of roughly 300 megawatts per square meter. Which will vaporize the surface layer of about anything. The question becomes: how deep?
 Heat radiation. We're talking about very high temperatures here, so maybe the surface might radiate heat away faster than the exhaust deposits it? If nothing else, it will give a rough upper limit to the temperatures involved. The 300 MW/m2 flux correspond roughly to black-body radiation at 8500 K. So the temperatures may well be of that order of magnitude.
 Heat Conduction. Let's say the surface gets really hot. How fast is the heat conducted below the surface? Many rocks seem to have conductivities on the order of 2 W/m-K or so. At that rate, the temperature gradient would have to be incredibly high to balance the influx; 150 MK/m. I suspect that indicates that the surface would probably ablate to vapour and escape, with only the thinnest layer liquid at any given time. Maybe a micrometre or so on average.
 Quantity vaporized. As a rough guideline, many rocks at normal temperatures have heat capacities of about 1 kJ/kg-K. Extrapolating wildly, I could assume that they don't vary by too much at higher temperatures. If their temperature is raised on the order of 7000 K, then they will carry off something like 7 MJ/kg. Now, we can probably assume a density of about 3000 kg/m3, so that's 21 GJ/m3. If the final part of the landing takes about 20 seconds, that's up to about 23 m3 of rock. Dividing by the assumed area, we get a very shallow crater about 30 cm deep (about a foot).
So, based on the above figures I'd guess that a plume of exhaust like that would erode the surface, breaking it down into vapour or even decomposing it, with the resulting gases dissipating rapidly. With heat conduction so low compared to the incoming energy, there simply won't be enough time for a pool of lava to form. Any liquid would be blasted outward by superhot gases, vaporizing and then recondensing along the way.
My guess is that you'd get a broad but shallow crater, surrounded for quite some distance by ash condensed from the escaping gases and of course any debris that might have been carried along for the ride.
Timothy's masterful analysis does have some alarming consequences. Considering that we might be using a gas core atomic rocket, this means when it lands it becomes a lean, mean, fallout machine.
The poor man's way of landing on a planet with an atmosphere is by utilizing aerobraking. Pretty much all of NASA's manned rockets use this method. What you do is equip your spacecraft with a streamlined heat shield, and use air friction to eliminate your deltaV. Hopefully you can reduce the deltaV to zero before you run out of either heat shield (i.e., "burning up in re-entry") or altitude (i.e., "auger in").
The advantage is that it allows landing without requiring a powerful engine (which is a problem with tiny landing boats or inhabitants with strict laws about nuclear radiation). The disadvantage is there is a limit to the deltaV that can be shed, your trajectory has to be incredibly on course, and only very few planets and moons in our solar system have atmosphere. Not to mention the fact that most heat shields have to be replaced after each use, which was one of the major drawbacks of the Space Shuttle.
The deltaV limit is due to a couple of factors. The faster you shed deltaV, the more heat the heat shield will have to cope with, and there is a limit to the heat shield's ability to cope. There is also a limit to the amount of atmosphere you can pass through with a given trajectory, but it is possible to plot clever paths that loop back and pass through the atmosphere repeatably.
There is some current research into magneto-hydrodynamic force fields as heat shields. You can read more about it here.
Your trajectory has to be dead on course. If you are too steep, the generated heat will cause heat shield failure. If you are too shallow, you will ricochet off the atmosphere on a one way trip into the big dark.
Terrestrial planets with atmospheres include Venus, Earth, Mars, Titan, and maybe Pluto. All the gas giants have atmospheres, so much in fact that the pressure will eventually implode your ship. As a side note, aerobraking can be used with gas giants in order to change one's trajectory instead of landing. This was done in the movie 2010, The Year We Make Contact, where they used a ballute as a heat shield.
...From the outside there was no evidence of damage or repair. Part of the heat shield hung below the cutter's nose like a great shovel blade, exposing the control room blister, windows, and the snout of the cutter's main armament: a laser cannon...
...The starboard air lock had been reconnected to the embassy ship. They left by the port side. Lenin's boat crew had already rigged lines from the auxiliary vessel to the cutter. The boat was almost a twin for MacArthur's cutter, a flat-topped lifting body with a shovel-blade reentry shield hanging below the nose...
The ship was now rocking noticeably, like a small boat in a choppy sea. Was that normal? wondered Floyd. He was glad that he had Zenia to worry about; it took his mind away from his own fears. Just for a moment, before he managed to expel the thought, he had a vision of the walls suddenly glowing cherry red, and caving in upon him. Like the nightmare fantasy of Edgar Allan Poe's 'The Pit and the Pendulum', which he'd forgotten for thirty years.
But that would never happen. If the heat shield failed, the ship would crumble instantly, hammered flat by a solid wall of gas. There would be no pain; his nervous system would not have time to react before it ceased to exist. He had experienced more consoling thoughts, but this one was not to be despised.
As a side note, there is a good reason for having either three landing legs/fins or adjustable landing legs. Have you ever had to sit on a stool or chair with four legs, and one of the legs was shorter than the other? You sort of rock back and forth. This is annoying for a seated person, but can be disastrous for a sixty meter tall rocketship. In Andre Norton's space novels, the height of a pilot's skill was to make a "perfect three-fin landing".
The reason for the rocking is that three points automatically determine a plane, but four or more points are not guaranteed to. If you have four or more, the landing jacks had better be adjustable, or you will only be able to land on a perfectly flat surface. Don't even think about a landing on a random spot on the rocky planes of Luna.
Of course there is an argument for four or more landing legs. Imagine you are looking at the rocket from overhead. Draw dotted lines from the foot pad of each leg to the adjacent pads. With three legs you'll have a triangle. The key point is that if from your overhead view the rocket's center of gravity moves outside of the triangle, the rocket will topple over and crash.
This can happen if you have the misfortune to be landing on a slope, and a single pad touches down first on the up slope section. As the other two pads lower, the already landed pad will force the rocket off vertical until it topples. The rocket can also tip a bit if it is moving a bit sideways as it comes down. The two pads bracketing the sideways direction can dig in and stop while the nose of the rocket is still moving, causing a tip.
The advantage of four pads is that now you have the dotted lines forming a square. This increases the distance the center of gravity has to move in order to topple, which increases your safely margin.
If you go with more than three landing pads, just make the landing legs adjustable in length to deal with the "rocking stool" problem.
Mike Williams points out the extra mass problem of four landing pads:
A possibly significant advantage of three landing jacks is that they all get approximately evenly loaded when you land on an uneven surface. With four jacks you either have to build them strong enough that the heavily loaded jacks can take the strain, or add some sort of compensating mechanism (which would require extra mass).
If the feet are distance D from the centre, then with 4 feet the rocket can be stable with the center of gravity up to sin(45)*D from the centre. For a ship with 3 feet, to achieve the same stability, you'd need to extend the feet to be 1.414*D from the centre. It may well be that three such extensions require less mass than adding a fourth leg.
There are probably swings and roundabouts, with one system being slightly superior than the other depending on other factors of the design, such as the mass of the feet (which still mass the same when you increase the length of three legs, but if you have four legs you need to budget for a whole extra foot).
But if safety is primary, Bernard Peek notes that current European safety legislation requires office chairs to have five castors so that losing one is not a catastrophic failure.
Sean Willard brought to my attention an important mathematical proof. It has been proven that if:
- you have a four legged structure
- all the legs are exactly the same length
- the ground is a continuous surface with a local slope of no more than fifteen degrees
- you rotate the structure around the plane of the feet
Please note that the non-rocking position is not guaranteed to be level. If you want the intricate details, you will find them in this paper.
Sean goes on to say:
One could therefore devise a system comprising high-resolution landing radar or lidar (perhaps four antennae, one on each leg), computer, and attitude jets, to automatically rotate the ship as it lands to the optimum orientation. It would be quite difficult for a human helmsman, but maybe not fiendishly so, given the right instrumentation.
Recovering from a Topple
However, what if you do have a catastrophic failure and your rocket topples over? If you are at a civilized spaceport, as you float in the burn-recovery medical tank, you can console yourself with the thought that the port will probably have the equipment required to restore your ship to an upright position. Provided, of course, that the ship didn't break its spine and that you or your insurance can cover the cost.
If your ship is a deep space explorer on an uncharted planet, and you have no communication system with which to yell for help, then you have a problem.
If the ship isn't too terribly huge, Isaac Kuo suggests that it might be possible to construct a sort of gigantic A-frame and raise the ship with cables. Isaac suggests attaching cables to the ship's nose and hoisting it vertical. The ship's landing jacks are repaired, if necessary, then the ship is lowered to stand on its own three feet.
He was right, the digging was recent and it was not yet finished, for only half of the soil had been cleared away from around the fins of the ship. The cruiser had been buried after it had been landed, partly to help conceal it, partly to keep it steady in a proper position for a take-off where there was no cradle to hold it. If a storm here had battered it off fin level, with no port cranes to right it, the ship would be useless scrap until it rusted away.
Eric Tolle points out that care must be taken not to drag the ship's tail. He makes the brilliant suggestion that studying the engineering associated with Egyptian Obelisks would provide answers! In many ways it is the same problem.
Back in 1586 engineers lowered, moved, and erected the Vatican Obelisk (because it wasn't in the aesthetically perfect spot). The Obelisk is about 25 meters tall and weighs 330 tons. This isn't much smaller than the Polaris I worked out in the example. That was about 43 meters tall and massed 378 metric tons.
The Obelisk required about 140 horses and a year of work, but I'm sure things will go quicker with modern machinery and engineering (however, extra time will be required if the natives are shooting at you). The girders for the A-frame could be a standard feature with wilderness spacecraft, perhaps stored in the ship's core and extracted from the nose. Storing the girders as removable parts of the hull may make it easier to access, but they might be damaged in the initial topple.
Isaac says that avoiding tail dragging can be done by anchoring the tail with cables. But a better solution might be raising the ship by cables attached to the midpoint, instead of the nose. The ship is raised entirely free of the ground, then a cable attached to the tail is pulled to pivot the ship into proper nose-upward orientation. You might be able to get away with an A-frame only half the height of the ship.
Garon Whited points out some of the trade-offs:
There are substantial trade-offs, however, depending on which method you use. Midpoint lifting requires an A-frame to support the entire weight of the ship in whatever gravity you happen to be. Lifting the ship by the nose requires longer, but less sturdy members for the A-frame. Shorter, more sturdy members are more likely to survive the initial crash, but may very well mass more than the longer ones. Longer members may be "recycled" into shorter members if they are damaged. Shorter members may be replaced by native materials -- trees, stone blocks, etc -- provided such are of sufficient strength.
It all boils down to your ship design. How much emergency gear can you carry? Is it better to stock up on ship repair materials to maximize the chance of getting off that space-rock, or on survival equipment to stay alive until rescue comes? Which then brings us back to the question of how far out your ship is meant to go...
If that fails, Eric suggest rolling the ship into a nearby lake or ocean and hoping that the ship floats with the nose uppermost. He notes that this will probably terminate the ship's warranty with extreme prejudice. One can hope that the heavy nuclear propulsion system will make the ship tail-heavy. However, Isaac points out that the huge propellant tank will tend to make the ship float sideways, with the propulsion system providing little or no tipping, much like the outboard motor on a speedboat.
In Heinlein's Time For The Stars, the torchship Lewis & Clark avoids both the "uneven landing site" problem and the "vaporizing the landing site" problem by the simple expedient of only landing in oceans. This is also true of the landing shuttles carried by starships in Jerry Pournelle's CoDominion universe. Alas, this won't work very well for a non-interstellar spacecraft, as the only planet in the solar system with an ocean is Terra (with the possible exception of a methane ocean on Titan. Some of Jupiter's moons may have oceans of water, but these are covered by many miles of ice.)
While landed, for extra safety, keep the reaction wheels clutched and powered up. This will help keep the ship from toppling.
At a spaceport, moving a landed ship to another site is tricky. The spacecraft's lateral jacks are extended so the tail of the ship is lifted off the landing apron. A crawler is then backed under the spacecraft, and the ship is lowered onto it. The "bottom handler" runs the crawler. The "top handler" rides in the control room of the spacecraft. Under each fin of the spacecraft is a hydraulic mercury capsule. The top handler keeps an unblinking eye on a bubble level gauge, and uses a joystick to control the mercury capsules. If the spacecraft starts to tip, the appropriate mercury capsules are pressurized to counteract the tip.
The spaceport will also offer the services of a "weightmaster". Each fin of the spacecraft rests on a scale (while the exhaust bell points at a splash baffle or thrust diverter). The weightmaster reads the scales, totals the weight, and advises the captain. If the mass is too much over or below the mass the calculations are based on, mass will have to be removed or added.
This is one of the reasons why spaceports charge berthing fees.
Spaceports are also likely to have extensive medical facilities with special equipment for treating burn victims (survivors of crashed chemically fueled rockets) or radiation exposure victims (survivors of crashed nuclear fueled rockets), or both. If the spaceport services starships from alien ecosystems, there will be quarantine facilities as well.
In a setting with interstellar ships, spaceports will be an economically valuable source of off-planet trade goods. As such they will probably be considered extraterritorial, like a foreign embassy, and not subject to local laws. Local governments will be anxious to avoid annoying the starship crew, which would endanger off-world trade. If the spaceport is not considered extraterritorial, the interiors of the spacecraft will. They are part of the planet the spacecraft is registered at.
Having said that, there will be large custom departments carefully scrutinizing all incoming and out going cargo. And maybe a deportment department to kick "undesirable aliens" off world.
However, there will spring up a "star-town", i.e., a thick border around the starport composed of bars, tourist traps, restaurants, casinos and bordellos meant to painlessly separate starship crew members from their flight pay. Plus a few pawn shops where crew members can get extra cash by hocking their equipment, personal items, and or alien curios they acquired during their travels. Not to mention smugglers and black marketeers, who are buying and selling contraband goods and illegal transport services. Not to mention fugitives attempting to escape.
They went to the address the driver had given them, in Old Town under the original bubble. I gathered that it was the sort of jungle every port has had since the Phoenicians sailed through the shoulder of Africa, a place of released transportees, prostitutes, monkey-pushers (drug dealers), rangees, and other dregs -- a neighborhood where policemen travel only in pairs.
Michael Andre-Driussi points out that the location of Star-town will depend upon how often spacecraft crash and how radioactive their exhaust is. Maybe Star-town will be at some distance from the actual landing site. Or it might be milder: with Star-town encircling the landing site, but with the low-rent district downwind in the footprint of the fallout zone. He also points out that the same factors will determine how far the spaceport itself is from any cities or other populated areas. Lots of crashes or landing pads that glow in the dark mean a spaceport in the middle of the desert or other barren wasteland. In that case, Star-town will be located approximately halfway between the starport and the nearest city, with regular mass-transit service to the port.
Radioactive fallout is typically in a long skinny plume pointing in the wind direction. So, for instance, if the wind generally blows to the south-east, the prime Star-Town locations would be north-west of the launch site, the upscale locations would be north and west, the average locations would be north-east and south-west, the ghetto would be at east and south, and the real bad part of town would be south-east.
Of course if the planet has an oppressive government and is full of people eager to flee, the spaceport is likely to be surrounded by the futuristic equivalent of the Berlin Wall, complete with barbed-wire, machine gun nests, spotlights, and ferocious guard dogs.
A more realistic situation will be with the starport only offering surface to orbit transportation, instead of landing dozens of flying Chernobyls every day.
When a ship is landed, and still manned, the central control is generally shifted from the control or flight deck to another part of the ship, called a quarterdeck. In a merchant spacecraft, this will probably be somewhere in the cargo hold. The watch officer and their staff will be found in the quarterdeck.
In "wet navy" ships, the quarterdeck is merely the area just inboard of the crew hatch, where visitors are received aboard.
Remember that the ship has to be balanced around the axis of thrust or it will tumble. Cargo will have to be stowed in a balanced manner, and logged in a mass distribution schedule (sometimes called a "Center-of-mass and moment-of-inertia chart).
They were in a conical room. Above them the pilot lay in his acceleration rest. Beside them, feet in and head out, were acceleration couches for passengers. "Get in the bunks!" shouted the pilot. "Strap down."
Ten boys jostled one another to reach the couches. One hesitated. "Uh, oh, Mister!" he called out.
"Yes? Get in your couch."
"I've changed my mind. I'm not going."
The pilot used language decidedly not officerlike and turned to his control board. 'Tower! Remove passenger from number nineteen." He listened, then said, "Too late to change the flight plan. Send up mass." He shouted to the waiting boy, "What do you weigh?"
"Uh, a hundred thirty-two pounds, sir."
"One hundred and thirty-two pounds and make it fast!" He turned back to the youngster. "You better get off this base fast, for if I have to skip my take-off I'll wring your neck."
The elevator climbed into place presently and three cadets poured across. Two were carrying sandbags, one had five lead weights. They strapped the sandbags to the' vacant couch, and clamped the weights to its sides. "One thirty-two mass," announced one of the cadets.
"Get going," snapped the pilot and turned back to the board.
Matt pulled himself along, last in line, and found the scooter loaded. He could not find a place; the passenger racks were filled with space-suited cadets, busy strapping down.
The cadet pilot beckoned to him. Matt picked his way forward and touched helmets. "Mister," said the oldster, "can you read instruments?"
Guessing that he referred only to the simple instrument panel of a scooter, Matt answered, "Yes, sir."
"Then get in the co-pilot's chair. What's your mass?"
"Two eighty-seven, sir," Matt answered, giving the combined mass, in pounds, of himself and his suit with all its equipment. Matt strapped down, then looked around, trying to locate Tex and Oscar. He was feeling very important, even though a scooter requires a co-pilot about as much as a hog needs a spare tail.
The oldster entered Mart's mass on his center-of-gravity and moment-of-inertia chart, stared at it thoughtfully and said to Matt, "Tell Gee-three to swap places with Bee-two."
Matt switched on his walky-talky and gave the order. There was a scramble while a heavy-set youngster changed seats with a smaller cadet. The pilot gave a high sign to the cadet manning the hangar pocket; the scooter and its launching cradle swung out of the pocket, pushed by power-driven lazy tongs.
A scooter is a passenger rocket reduced to its simplest terms and has been described as a hat rack with an outboard motor. It operates only in empty space and does not have to be streamlined.
The rocket motor is unenclosed. Around it is a tier of light metal supports, the passenger rack. There is no "ship" in the sense of a hull, airtight compartments, etc. The passengers just belt themselves to the rack and let the rocket motor scoot them along.
Shortly after blast-off from a spaceport, the spacecraft can call the tower to request range, bearing and separation rate, and flight plan deviations. This is not only to check if the spacecraft is on track, but also to used to double check the performance of the spacecraft's own instruments against the land based ones. This is usually the co-pilot's job.
In Isaac Asimov's The Currents Of Space, the ships are equipped with a science fictional "diamagnetic field", which allows the ships to float out to the launch pad. Diamagnetism is when a substance is repelled by both poles of a magnet, but it is unclear if such levitation is possible by the laws of physics.
The ship rolled out of the hangar like an air-borne whale, moving slowly, its diamagnetized hull clearing the smooth-packed clay of the field by three inches.
Terens watched Genro handling the controls with finger-tip precision. The ship was a live thing under his touch. The small replica of the field that was upon the visiplate shifted and changed with each tiny motion of every contact.
The ship came to a halt, pinpointed at the lip of a take-off pit. The diamagnetic field strengthened progressively towards the ship's prow and it began tipping upward. Terens was mercifully unaware of this as the pilot room turned on its universal gimbals to meet the shifting gravity. Majestically, the ship's rear flanges fitted into the appropriate grooves of the pit. It stood upright, pointing to the sky.
The duralite cover of the take-off pit slipped into its recess, revealing the neutralized lining, a hundred yards deep, that received the first energy thrusts of the hyperatomic motors.