The Impact Reaction Engine

The impact reaction engine was proposed by Donald Kingsbury, Clifford D. Simak, and Roger Arnold as early as 1979. It is a variant of continuous inverted aerobraking, using a 150 km long rail which releases oxygen as kinetic fuel and possibly adds hydrogen as on-board fuel.

Unfortunately it did not make it into the compiled lists of alternative ways to go to orbit available on the internet as it would have deserved. I can only speculate about the reasons for this. Maybe it was ignored because it was only mentioned as a possible extension of an orbital magnetic accellerator / decellerator (also often called "coil gun" or "mass driver").

Maybe the biggest shortcoming of this proposal is its self-imposed limitation to bridge only a delta-v gap of 4 km/s, i.e. half orbital speed. This limitation is probably imposed by the desire to use conventional rocket chamber technology, which would overheat at higher delta-v. Another point which is not discussed is that a small part of the reflected kinetic fuel will impact on the rail. As the authors point out, even small alignment problems of the rail in front of the braking space ship will result in destructive bumps. This may invalidate the authors claim of an arbitrary lightweight structure of the rail or it adds many short duration, high power corrective propulsion engines to the rail. In the end I believe a swarm of robotic space crafts would have a much lower net mass. And a swarm of robots can be stretched to become much longer than 150 km at almost no additional mass, so in combination with a more robust "rocket chamber" a delta-v of 8 km/s becomes possible. To be fair we should remember that around 1979 the robot-enabling technology of micro-electronics was much less developed than today. These days a video recorder did cost around 1000$, while today it is about ten times cheaper, has better quality, and is more reliable. So today a swarm of cheap robotic spacecrafts is much more realistic than it was 25 years ago.

Maybe this is the place for a short note comparing inverted aerobraking with alternative propulsion suggestions that don't use fuel, like the magnetic accellerator mentioned above or rotating cables (also sometimes called sky-hooks or rotovators). These methods don't have to use up fuel, but then they as well depend on the balance of mass going up to space and mass coming down to earth. Furthermore costs of operation do not only depend on fuel cost. Costs per flight also depend on the costs of building the launcher divided by its life time, plus costs of maintenance, e.g. bringing up replacement parts and paying the astronauts doing the repairs, life support for the astronaut, the ground crew supporting the astronaut etc. Everything built in low earth orbit has a limited life time, and sometimes a surprisingly short one. First tests with orbital cables did demonstrate that long and thin cables have a high probability to get destroyed within a few weeks(!) by micro-meteorites attracted by earths gravity well. Oscillations induced by irregularities in earths magnetic field can build up until the cable snaps. So the total mass of the structure to be built and maintained directly translates into launch costs. My current estimate is that the mass of the robotic swarm is about the mass of the kinetic fuel, which in turn is about the mass of the space ship. Try to beat this for a magnetic accelearator / decellerator including structural mass, magnetic coils, power supply, power storage systems etc.!

Another potential cost factor are damages due to launch mishaps. Especially regarding magnetic decellerators built in one piece I believe that the risks of a near miss when trying to fly into the decellerator is much larger for a solid structure than for a swarm of robots. While such a near miss will destroy many or even all segments of the solid decellerator in a domino-like chain reaction, a robotic swarm will be able to jump out of the way and out of the danger zone only milliseconds after a dangerous problem is detected. This is much safer for the robotic swarm and—which is even more important to everyone who values lifes more than money—gives the mislaunched space ship a much better chance of aborting safely.

And finally regarding rotating cables: due to the limits of material strength they can handle 2 km/s rather easily but they become more and more heavy for a bigger delta-v and run into real troubles above 4 km/s. Once a space ship is in orbit, it should be possible to use one cable to go to a higher orbit where the next cable is waiting, if you have plenty of time to wait for the right moments to change cable. But below orbital speed this is impossible, because the cable must be in orbit in the first place. Bridging the first 8 km/s is the hardest part, and rotating cables can't do this.

Here is the original description of the impact reaction engine from:

Donald Kingsbury, Clifford D. Simak, Roger Arnold: "The Moon Goddess and the Son", Analog Science Fiction Fact, December 1979, pp. 71-74.

[...] An alternative and more interesting solution to the large payload problem involves what we call an impact reaction engine. Let us perform a thought experiment.

Suppose we have a stream of perfectly elastic balls moving with circular velocity c in orbit around the Earth. Suppose we place a massive ship in this stream with velocity u relative to Earth. Further, suppose that this ship carries a perfectly elastic shield upon which the balls impact perpendicularly. The balls approach the shield with velocity (c-u) and after impact bounce off the shield with reversed velocity, minus (c-u). This bounce results in momentum changes and since rate of change of momentum is force we can calculate the force acting on our ship. The force in newtons is the mass in kg of the balls which bounce off the shield every second times 2(c-u) m/sec, and will accelerate the ship in the direction of the stream.

This is in principle the impact reaction engine. The mass flow against the shield is analogous to the flow of propellant into a rocket motor—with the exception that an impact reaction engine does not have to carry its propellant with it as does a rocketship. The velocity 2(c-u) is analogous to the rocket's exhaust velocity. The best rocket exhaust velocity we have today is the 4400 m/sec of the oxygen/hydrogen motor. If an impact engine, at rest relative to the Earth, entered a mass flow stream at an altitude of 275 km, its "exhaust velocity" would approach (depending upon the elesticity of the collision) 15,500 m/sec, 3.5 times as great as that from the Space Shuttle's motors! Of course, since (c-u) tends to zero as the impact engine approaches circular velocity, the efficiencyof this enginge declines drastically at high speeds, a flaw which we shall see can be overcome by marrying the impact engine with the rocket motor.

The impact reaction engine makes an amusing thought experiment, but can it be built? There are no basic physical reasons why it cannot, and there are economic reasons indicating that it could wisely be utilized in passenger and heavy freight transport. Once a moon colony is viable it will be supplying mass to the spaceport both to generate electricity an to balance the spaceports's momentum. If we choose to import plentiful lunar oxygen for this purpose we can not only remove part of its potential energy in the form of electricity by capture, but can also extract a large portion of the remaining energy by disposing of the oxygen to power an impact system.

A basic scheme consists of an oxygen feed pipe and a magnetic supension track laid parallel to the spaceport and perhaps far longer than 150 km. This need not be a massive structure since it would not have to take any great stresses. The accelerating impact ship exchanges momentum with the oxygen, not with the pipeline. Because of this fact, the impact ship [...] can be quite massive. It can be as massive as a present day commercial jet aircraft like the Boeing 727.

The oxygen intake of the ship rides along the suspension track only centimeters from the oxygen supply jets on the pipeline, which are pulsed for a few milliseconds prior to the passage of the ship. The track and pipe must be extremely straight because, at the speed of the ship, there is no possibility for it to follow bumps and irregularities. But that is why laser beams and active control systems where invented.

As the oxygen is scooped into the vehicle it is guided through tubes in such a way that its direction of flow is reversed through 180 degrees. As we have seen, the force applied by this impact is the product of the mass flow times twice the relative velocity between ship and pipeline. At any relative velocity above 2200 m/sec oxygen alone in such a reaction engine will do better than an oxygen/hydrogen rocket —and not be required to carry its own reaction mass.

Some heating through compression and turbulence will occur and there will be boundary layser friction. But the object of the game is game is to keep as much of the oxygen's energy as possible in kinetic form. That requires that its speed be maintained while its direction is changing. We can get a worst case estimate of the heating problem by assuming that the oxygen is completely stopped by the impact and then expanded through a rocket nozzle.

Cold oxygen impacting at half circular velocity and bourhgt to a dead stop will only rise in temperature to 4500°K, about five or six hundred degrees hotter than the normal operating range of an oxygen/hydrogen rocket chamber. At these temperatures the dissociation of oxygen into monatomic oxygen is soaking up a great deal of energy. Since we will not be stopping the oxygen, we will not have to deal with such extremes except at very local boundary regions where we can use dynamic insulation with hydrogen to keep the flow surface cool.

As the relative speed of ship and pipeline falls, so does the performance of the impact engine. The declining thrust can be compensated by adding ship supplied hydrogen to the reaction, the hydrogen doing double duty as a coolant. By the time the ship has stopped we will be using the standard 6 to 1 oxygen/hydrogen mix ration and will have dropped down to an exhaust velocity of 4400 m/sec.

The performance of such a ship makes it worth inverstigating seriously. If we could build a hybrid rocket-impact vehicle that reaches orbital altitude and half circular velocity by means of oxygen/hydrogen rockets, and then achieves the second half of its velocity through impact acceleration it will go into orbit starting with a gross-lift-off-mass only 3.5 times its final mass—an easy design criterion for an oxygen/hydrogen vehicle to meet.

For those who want to do some back-of the envelope calculations themselves, the formula to compute the mass m needed to change the velocity of a ship of mass M from u0 to uf is:

m = (1/2)M[ln(c-u0)-ln(c-uf)]      (4)

where c is the velocity of the oxygen supply pipeline and ln is the natural logarithm. If we carry hydrogen and burn it with the impacting oxygen, the equation is slightly more complicated and does not give an infinite m when uf = c!

FIGURE 3. In this schematic diagram of the impact reaction engine (imp), the ship approaches backwards, with velocity (u), the forward end of the orbiting pipeline and magnetic guide track (p) which overtakes it at circular velocity (c). Oxygen at (0) cannot escape because the valves are closed. Oxygen at (1), just prior to the ship's arrival , escapes through rapidly opened valves, where it is captured by the ship's scoops at (2) and swiveled through pipes (3) where it is ejected at (4). After the ship passes, the valves at (5) close. The impact reaction engine exerts a force equal to the mass flow through the engine times twice the difference between velocities c and u. Injected hydrogen, carried by the ship, can be used to cool the engine, simultaneously burning with the oxygen to increase the thrust. The oxygen is imported from the moon. The pipeline itself need not be very massive because the ship and pipeline do not exchange momentum while the ship is being accelerated.