# Electrical Propulsion Thrust

Is there an ultimate limit to the thrust outputs of electric propulsion thrusters?

Although they work best providing low amounts of thrust for long periods of time, could improvements in technology allow their thrust to compete with that of modern chemical rockets, or is it just their nature to have a low thrust output (despite a high specific impulse)?

• That's an interesting question. I think you should narrow it down to rockets used in space for two reasons; 1) you have vacuum or very low pressure, and 2) the ridiculously large amount of thrust needed to get off the Earth is too far out of reach to even consider - we're talking at least many billions of DC Amperes of current for that.
– uhoh
Jan 8 '17 at 16:16

## 3 Answers

Thrust isn't the bottle neck. Rather thrust to mass. In other words, acceleration.

A 10 kilowatt Hall thruster exerts about half a newton. Half a newton is about a tenth of a pound or a little more than an ounce.

If the power source, Hall Thruster and payload have a total mass of 500 kilograms, an ounce of force doesn't give much acceleration. About $1 millimeter/second^2$.

Can you get low mass power sources that provide enough juice? Possibly.

Very thin solar panels might do it. But deploying solar panels thinner than Saran Wrap® might be difficult. There would also need to be supporting structure as well as gimbals to point the array.

How about a nuclear power source? There is a need to dump waste heat. Here on earth, nuclear power plants often are located near a river and water carries away waste heat. This is a lot harder in space — vacuum is a great insulator. You would likely need many square meters of radiator surface to dump the heat. Again, the need for a lot of area but little mass mandates thin, fragile structures.

Ratio of mass to power is sometimes called Alpha. I talk about this more in my blog post The Need For a Better Alpha. Another related article is Xenon

In principle, ion thrusters can be scaled to very large thrusts, but their thrust per watt of input power is inherently low. This means that the power supply for any electrical thruster is going to be very heavy, so the thrust-to-weight ratio is always going to be low. This holds for solar, radiothermal, and even nuclear reactor supplies; it's possible that future power plant technology could shift this balance.

Spacecraft solar panels are very lightweight and efficient -- they deliver on the order of 100 watts per kilogram of panel at Earth's distance from the sun, but the delivered power rapidly decreases as you get farther from the sun.

RTGs produce only 2-5 watts per kilogram, and the few nuclear fission plants that have been used in spacecraft delivered no more than about 15 watts per kilogram.

TL;DR: If you want more thrust, you can either get more energy or just reduce the propellant efficiency.

Long version: You can create electric propulsion for any range of thrust/Isp (propellant efficiency).

It basically boils down to the impulse formula and the kinetic energy formula.

All types of electric propulsion turn electric energy into kinetic energy. The amount of electric energy depends on your power source.

If you have an amount of energy X you can turn it into kinetic energy by $E= 0.5mv^2$. But, the amount of thrust you generate depends on the impulse formula: $I = mv$. There is your problem: to get more thrust you can increase either mass expelled per second or the speed at which you expel that mass. But increasing speed of propellant requires an exponential increase in energy ($v^2$ remember) while an increase in mass requires just a linear increase in energy.

This boils down to a simple formula: If you have a fixed amount of energy available you basically can trade between propellant efficiency and amount of thrust generated: halving your exhaust velocity means generating four times the thrust.

Now, since a rocket has to carry all the propellant with it from the start, you normally want it to be as propellant-efficient as possible (basically in space, mass is a far more valuable thing than time). This is why electric propulsion normally trades thrust for as high an Isp as possible.

Now if you find a way to generate more energy for the same mass…than you can keep your high-Isp electric propulsion engine and increase the thrust for the same amount. (Or increase your Isp a tiny bit more.)