Gdddk

I am wondering if any space agency has ever considered using a grinding machine as a propulsion system for an interplanetary spacecraft. This system would not be used to lift the spacecraft off of a planet's surface, but rather used solely as an interplanetary/interstellar propulsion system.

The working principle is a simple one (see picture below). This grinding machine would be located at the stern of the spacecraft. Metal shavings flying off of the grinding wheel of this grinding machine would produce a propelling force for the spacecraft via Newton's Third Law of Motion. The amount of propulsion produced at any one time would be achieved by increasing/decreasing the rotational speed of the grinding wheel.

The electrical source for the electric motor of the grinding machine could be a small nuclear power plant on board the spacecraft. The 'fuel' source could be long steel rods or large rocks. A source of rocks could be obtained by mining an asteroid field or a small moon. Lastly, I think that diamond grinding wheels would probably be the most ideal to use due to their durability and longevity.

Would a grinding machine be a simple and workable propulsion system for an interplanetary spacecraft?

I don't know if it has ever been considered by anyone.

In my view, this is not a good idea for at least the following reasons:

1. It is equivalent to mechanically throwing things retrograde. See this video for an overly simple example. This is obviously not a good way for propulsion, as the specific impulse is very low. Let's talk just about the impulse $$p=mv$$ here, where $m$ is the "reaction mass", i.e. the mass of the material that's being ground, the object being throw backwards, or chemical propellant. $v$ is the velocity of the reaction mass relative to the spacecraft. The velocity $v$ of the sparks is in the order of a few m/s (same velocity as the edge of the grinding wheel. With chemical propellants, it is a few km/s. So, for the same amount $m$ of reaction mass that you carry, classical propulsion gives you a factor of about 1000 more impulse than grinding.


2. The produced momentum is kind of stochastic. As can be seen in your graphic, the sparks form a cone instead of a straight line. While the upward and the downward motions statistically cancel each other, their vertical components are a waste. While admittedly this also applies to chemical rocket engines (and ion thrusters?), just throwing some stuff overboard would be more efficient in this respect.

Still, I like this question for thinking out of the box. On a side note, reading the title reminded me of this passage of J.D. Clark's book "Ignition!":

F.A. Tsander in Moscow [...] had suggested that an astronaut might stretch his fuel supply by imitating Phileas Fogg. When a fuel tank was emptied, the astronaut could simply grind it up and add the powdered aluminum thus obtaining to the remaining fuel, whose heating value would be correspondingly enhanced!

I think this was actually tried, but found not to work well because the Aluminium particles take too long to combust, i.e. they continue to burn after they have left the combustion chamber. (Some?) Solid rocket propellants are based on Aluminium, though, but that's different.

Good for you, for thinking outside the box! Fearlessly pursuing new ideas is where any new breakthrough comes from.

But rocket exhaust moves at thousands of meters per second -- supersonic speeds. Recalling the formula relating acceleration to velocity for circular motion, a=v^2/r. So, given a velocity of 3,000 meters per second and a wheel radius of, say, 1 meter, the acceleration at the rim would be roughly 9,000,000 m/s^2, or 900,000 times Earth gravity. And angular velocity, v=Rw, or 9,000,000 radians per second. I think you would have trouble spinning the wheel up to that kind of speed, and I think you would have trouble finding a wheel material that wouldn't fly apart.

Propulsion comes from acceleration of a reaction mass.

In this case the grinding wheel serves two purposes:

1. separate small bits of the workpiece from bulk at a slow and roughly uniform rate


2. accelerate those bits by mechanical friction, in a similar way that a tennis ball launcher uses a matched pair of counter-propagating spinning wheels to shoot a box full of tennis balls one at at time in a controlled direction and speed.

As @Muze points out using a matched pair of counter-propagating spinning wheels would be important in spaceflight as well.

Step 1: requires a large amount of work and there's no reason to do that in space. You can produce the particle on the ground, so your propellant "tank" would be a feed system dispensing pellets or powder. They could be suspended in a fluid for easier feed and to avoid electrostatic clumping.

If you have to produce it in space, for example if you are reusing your lower stage as a reaction mass Horace style (Monty Python reference), then you can grind or otherwise form at a lower speed first with a separate wheel. Particles could be remelted in order to make them spherical, and then size-sorted for the following step.

Step 2: would conceptually be accomplished with a mechanism similar to that of a tennis ball launcher. Two counter-propagating wheels with the particle feed introduced in the small gap between the two wheels' surfaces. The particles would have to be monodipserse, meaning all of a fairly uniform size, and slightly smaller than the gap for good friction. Either the particles or the wheels would have to be elastically compressible enough so that there's a good grip for acceleration, and yet the surfaces should not be readily damaged during the process.

You could also very slightly incline the wheels such that if you had a sorted range of particle sizes they can all be introduced at the appropriate gap width.

However, as @Greg points out getting your wheels to spin at mach 10 or faster (for a (mass-)specific impulse or Isp of say 300 or so) is a real materials problem.

One possibility for propellant would be a maximal concentration (essentially HCP) liquid suspension of latex or polymer spheres which can be obtained highly monodisperse with sufficient money. If you don't have a lot of room for propellant, then perhaps metallic or metal oxide or nitride nanospheres can be produced by pyrolysis.

Horiba Scientific

GIF from Tennis ball machine DIY - part 1 a better view of a similar mechanism can be seen in Tennis Tutor Ball Machine mechanics in operation.

The main engineering challenge in implementing your proposal is that in order to be competitive with a chemical rocket engine, the grinding wheel must rotate at an extremely high velocity. A typical chemical rocket might have a specific impulse between about 250 and 450 seconds; therefore, the exhaust velocity is about 2500-4500 m/s. In a competitive propulsion system, the edge of the wheel must move at least this fast.

So the real question is: can we build a grinding wheel strong enough to rotate at this velocity without exploding?

For now, the answer is no. The tensile stress at the edge of the wheel is $rho r^2 omega^2 = rho v^2$, where $rho$ is the density, $r$ is the radius, $omega$ is the angular velocity, and $v$ is the velocity. Thus, the velocity at which the edge rotates is limited to $v < sqrtTS / rho$, where $TS$ is the ultimate tensile strength of the material the grinding wheel is composed of. Of all materials that we currently know how to produce at macroscopic scales, carbon fiber has the highest ultimate tensile strength per unit mass at about 4000 kN-m/kg. This gives a maximum velocity of 2000 m/s. This is less than the exhaust velocity of even a simple, relatively inefficient chemical rocket.

However, suppose that someone invents a way of mass-producing carbon nanotubes with an ultimate tensile strength of 60 GPa and a density of 1 g/cm$^3$. Then we could theoretically achieve an exhaust velocity of over 7500 m/s, which is excellent. In this scenario, your grinding wheel actually starts to look like a really good idea.