# Supersonic in ground effect

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## Contents

### Mars to Luna Transport

The cost of lifting items from Mars surface to orbit should be considerably less than the cost of lifting them from Earth. This is due to the fact that since Mars' gravity is lower, the energy required to reach orbit is lower. When expressed in terms of velocity change required to reach orbit (deltaV) the values are:

Reaching orbit
DeltaV to orbit (m/s) Exhaust velocity (m/s) Mass ratio Mo/mf
Earth 10 000 3400 19
Mars 3800 3400 3
Moon 1800 3400 1,7

DeltaV = Ve*ln(Mo/Mf) or M0/mf=e(DeltaV/ve)

With reusable rockets using liquid methane and liquid oxygen, the propellant must mass 19 times the mass of the rocket and payload to lift off from Earth. This goes down to 3 for Mars and 1,7 for the moon. This might favor some kind of transportation system between the Moon and Mars, rather than between the Earth and Mars.

## Landing at supersonic speeds

However, landing on Mars, compared to landing on Earth or landing on Luna are significantly different problems. Landing on Earth requires very little energy as the thick atmosphere an be used to slow down the ship. Landing on the moon, as there is no atmosphere, is exactly like taking off from the moon. Landing on Mars is a special problem, with just enough atmosphere to help slow down a vehicle, but not quite enough. In fact, the landing velocities of a martian shuttle depending only on aerodynamic breaking would be supersonic. In most cases, this means a crash. Landing on Mars the same way we land on the moon, with propulsive landing, requires a lot of fuel. However, it might be possible to land at very high velocities if supersonic ground effect and corresponding lifting forces could be known, since there is some atmosphere on Mars.

Supersonic ground effects at landing is very likely to be a significant problem. However, if it can be solved, this might result in an economy for a Mars surface to Mars orbit shuttle. Some elements of the problem can be found in the following list:

• Donald Campbell was killed on the 4th of January, 1967 when the "Bluebird K7" racing boat flipped over and disintegrated at a speed greater than 300 mph. [1] The problem seems to have been longitudinal instability when high ground effect lifting forces acted on a center of lift that shifted rapidly with changing attitude. This sort of problem is made more difficult by the need to consider the reflection of shock waves from supersonic flight in the ground effect. Such problems were handled successfully when the "Thrust SSC" broke the speed of sound on land on the 15th of October 1997, setting of the world's land speed record. [2]
• An ordinary wind tunnel by itself is insufficient for testing craft in supersonic ground effect conditions. A moving belt of caterpillar like treads on the bottom of the wind tunnel moving as fast as the gas in the wind tunnel could simulate the runway rushing past during landing. Having a belt of treads that are broad enough and move fast enough for the simulation would be expensive, but not as expensive as doing the testing on Mars. A low pressure wind tunnel, operating at 600 Pa (0.1 psi) of carbon dioxide would be needed for a simulation.
• An alternate wind tunnel design would be a torus (donut) or shaped wind tunnel, made with a one kilometer radius. It should contain a ring in a track along the wall closest to the center of the torus. This ring would be electrically accelerated to 450 meters per second and supported in its track by a film of high-pressure carbon dioxide. Model aircraft could be supported in such a wind tunnel by this ring and experience the effects of supersonic ground effect. The radial acceleration needed to hold the models in circular motion would be 20.7 gravities. The portion of the ring not supporting the models would be weighted to balance loading radially with respect to the center of the torus. Gas added to the wind tunnel by the carbon dioxide bearings would be removed by vacuum pumps.
• Landing at a speed in the neighborhood of 1000 mph (450 meters per second or mach 1.9 on Mars) might seem more difficult than the feat accomplished by "Thrust SSC," but moving through only 150th of the gas pressure (100th of the density) more than compensates for the increased speed. Maintaining lift and orientation stability are problems for which we have aeronautical engineers, computational fluid dynamics, and wind tunnels.

## Criticism

• The vehicle would need to slow down after the landing to eventually stop. This would require systems capable of dissipating gigantic amounts of heat in the landing gear.
• The landing field would need to be extremely long. The cost of this landing infrastructure might cancel out the gains in propellant savings.
• The suggested wind tunnel would be extremely costly and difficult to operate. Creating a vacuum in a km long structure is difficult. However, this might be just the thing for the Boring Company.
• Supersonic retro propulsion may solve the landing problem, allowing for a Mars landing with large payloads and low propellant requirements.

## references

1. Bluebird K7 article at Wikipedia