Ask anybody taking airplane piloting lessons and they'll tell you that taking off is easy, the incredibly hard part landing. At least landing safely.
Naturally this is an order of magnitude harder when doing a tailsitting rocket (Vertical takeoff, vertical landing or VTVL) landing, which is basically a controlled crash. Try playing a few games of Lunar Lander to get a feel for it.
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)
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.
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:
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:
While landed, for extra safety, keep the control moment gyroscope clutched and powered up. This will help keep the ship from toppling.
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.
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:
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.
The "uneven landing site" problem is so daunting that it is tempting for a science fiction author to invent incredibly high tech solutions that are unobtanium at best and technobabble at worse. Much like David Drake did in his classic series of novels about Hammer's Slammers. Mr. Drake noted the many problems of using caterpillar tracks for armored fighting vehicles. His solution was to make the tanks into hovercraft, using ducted fans so that they could float over irregular ground. All you need to make it work is to equip each tank with a fusion power source capable of supplying the electricity needs of California. Mr. Drake did analyze and accommodate the logical consequences of the tanks possessing so much electrical generation capacity, so this is a case of an author doing the job right.
I will note in passing the jaw-dropping stupidity of the landing legs on the starship Voyager. Not only would they not work, Star Trek starships as a general rule never have a need to land anyway. Shuttlecraft and transporters are a much more efficient solution. The Voyager is not designed to land, it probably cannot support its own structure without technobabble force fields reinforcing the internal girders, the same goes for the ludicrously tiny landing gear, seven hundred thousand metric tons concentrated on those tiny foot pads will poke holes in solid bedrock, once landed the Voyager is suddenly vulnerable to all ground-based hazards, the list goes on and on. About the only reason for landing is to make flashy eye-candy images for the audience in a desperate attempt to prop up the TV ratings.
The standard science fiction gag is to support the spacecraft on the ground using technobabble "force fields" or "pressor/repulsor beams". These are fields or beams of as-yet undiscovered energy that are perfectly adjustable, capable of allowing for any ground level irregularities. They are also also somehow much stronger than steel girders or anything else composed of matter. Their main drawback is that they consume energy, and steel girders do not vanish if the energy becomes exhausted.
However, from the standpoint of basic physics it would imply that any hapless person who walked through one of the beams would be flattened into a thin layer of bloody goo under a crushing force of N where N is equal to the weight of the spacecraft divided by the number of landing leg beams.
In Isaac Asimov's The Currents Of Space, the ships are equipped with an unobtanium "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.
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.)