# Would an ionocraft have better or worse performance in the upper atmosphere?

The ionocraft produces lift by accelerating ions in the air downward by the use of two meshes held at a large relative voltage difference.

With a cursory look at the physical principle, it seems like it could have advantages over other methods of propulsion in sub-orbital high altitude flight. It's not limited by having to take reaction mass on board, it doesn't have to deal with high drag because it can be functionally stationary, and higher altitude might not force it to scale up size like balloons.

Only problem is that the idea isn't practical. Wikipedia notes power requirements of 1 Watt per gram.

However, ions are more available in the higher atmosphere. Qualitatively, more ions for an ionocraft would seem to imply that you would get more force with less power input. The lift equation for an ionocraft is:

$$F = \frac{Id}{k}$$

$k$ is "ion mobility coefficient of air". I'm confused about the meaning of that so I can't answer this myself. Should this be lower or higher at very high altitudes? And considering the entire picture, might an ionocraft (which is non-viable at sea level) become viable if you flew it up to high altitudes first?

This paper from 1970 makes some progress to answering the question. It gives the following graph:

This gives the ion mobilities for different altitudes, and for both positive and negative charges. Considering that the units match as well, I'm going to identify this as $k$ in the equation with fairly good confidence.

The correlation is from applying physical principles to the atmosphere, so there is no expectation that this would be correct in real life. Actually, there are several confounding factors in real life, including a significant difference between day and night. Attempts at a real real measured curve are much more messy, and even has a global maximum. However, this global max is far above the 100 km mark, and up to that point, this exponential relationship looks like it could hold fairly well. For a straightforward order-of-magnitude estimation (which is what this question wants), this seems perfectly sufficient.

Now, to compare values, the above graph's value for sea-level can be roughly estimated by observation:

$$k|_{h=0} = 1.5 - 2.0 \frac{ cm^2 }{ V s} = 1.5 - 2.0 \times 10^{-4} \frac{ m^2 }{ V s}$$

Let's compare to the Wikipedia article on ionocraft:

k is the ion mobility coefficient of air, measured in dimension M−1 T2 I (Nominal value 2·10−4 m2 V−1 s−1).

$$k|_{h=0} = 2.0 \times 10^{-4} \frac{ m^2 }{ V s}$$

These numbers look to be in fairly good correspondence. This gives a little more credibility to the graph's numbers. If they are correct, we're looking at a change in the value from sea-level to higher altitudes of around:

$$\frac{ k|_{h=70 km} }{k|_{h=0}} \approx 2 \times 10^4$$

It is clear enough that the ionocraft equation would benefit from the difference in the k value. The real question is if a detriment to the other independent variables would also exist? Perhaps electrical arcing would happen at a lower voltage, which would further constrain the I and d tradeoffs. That's still unclear to me.

It's also unclear if a factor of 10,000 would be sufficient to move from non-viable to viable. Or if this would be sufficient to compensate for the cost of running wires from the ground to a high-altitude craft. You could still go higher. The global minimum looks closer to maybe 200 or 300 km in altitude. By pushing the 70 km to maybe 100 or 150 km you could certainly buy yourself several more orders of magnitude in k.

• I might be wrong here, but I have looked at the article referenced by AlanSE and, as he mentioned, the ion mobility increases with altitude (as expected I would add). However I don't understand how this helps the ionocraft as the force is inversly proportional to the ion mobility (F=Id/k), so if k increases the force would decrease, no? I know that drag would decrease as well but with the current efficiency of lifters I doubt that a ionocraft at higher altitudes would perform considerably better. – user4653 Jun 26 '14 at 10:30