Will an array of multiple ion engines still be more efficient than a single chemical engine?

Question

I was just thinking the other day and got this idea out of my head. I'm not an aerospace expert or anything even close to it, so please understand even if this turns out to be a really basic question:

Provided that the power issue can be solved, would an array of multiple ion engines (or a scaled up version of one engine for that matter) that has the same amount of thrust with that of a traditional chemical engine, still be more efficient than the chemical engine?

I am well aware that given the T-W ratio of the ion engines, it would still make it impossible for them to be used as first stage engines no matter how many you strap them together, but what about for the space stations or reusable interplanetary vehicles?

Answer 1

While this seems like a good idea at first, you very quickly run into the main problem with ion engines: their tiny thrust.

Let's compare a typical ion engine from the Dawn mission and an upper stage commonly used for interplanetary injections, the Centaur Upper Stage with its RL10 Hydrogen-Oxygen engine.

Ion Engine

• Thrust: 90 mN
• Mass: 8.2 kg

RL10 C-1

• Thrust: 102 kN
• Mass: 190 kg

We can see that the RL10 generates on the order of 1 million times more thrust for around only 20 times more mass. This means that we're going to need some 8 million kg of ion thrusters to produce the same thrust – equivalent to about 2.5 fully fueled Saturn V's.

It gets even worse when we consider the fact that this massive array of thrusters will require a similarly enormous amount of extra plumbing and structural support for it to run. Not to mention the difficulties in trying to squeeze a million engines onto the mounting plate at the base of the stage.

This will clearly negate any benefit we gain from using a higher-efficiency engine.

Of course, there will be a break-even point. A very quick-and-dirty approximation says that if we modified a Centaur Upper Stage to give it ion engines and filled the tanks with xenon (this obviously wouldn't actually work), an array of ~500 ion thrusters would give a 1000 kg payload about the same delta-v as a single RL10, albeit at a much lower thrust.

So any useful benefit to be gained by using ion thrusters will involve far, far fewer than this break-even point which is what we see on existing spacecraft. For example, Hayabusa2 has four ion engines on a gimbal mount, three of which can be run simultaneously.

Answer 2

Why is an ion engine more efficient than a chemical engine? The exhaust velocity is much higher.

If the power issue can be solved and each ion engine of the bundle has the same high exhaust velocity, the bundle is still more efficient than a single chemical engine.

But what about weight? To provide more power will increase the weight of the vehicle as well as the additional ion engines. To compensate the increased weight more ion fuel is necessary. To store more fuel a larger and heavier tank is needed.

So if there is enough time for slow acceleration with a single ion engine over years the total costs are lower than for the bundle of engines delivering the same delta-v in months. You will need a larger first and second chemical stage to lift that vehicle into orbit where the ion engines may take over.

Answer 3

Thrust is the wrong measurement to use for this comparison, as is thrust to weight. What matters is the Specific Impluse $I_{\text{sp}}$, which is a measure of the ability to change momentum per unit of propellent.

The RL10C has a specific impulse of 450s, while the Dawn engine is over 3,000, in other words, the Dawn engine can do over over 6 times more work per unit of propellant though its lower thrust means it will take longer to do it, but unless you are trying to escape a gravity well, there is no hurry. One source of the difference is the fact that a chemical motor includes its power source in the mass of its propellant through oxidation, while for an ion motor the power comes from an fission - reactor or solar panels etc. Now the weight of the engine itself starts to make a big difference. To use Jacks example, the 200Kg RL10C with 799Kg of fuel and 1 kilo of payload would produce a $\Delta v$ of:

$\displaystyle \Delta v=v_{\text{e}}\ln {\frac {m_{0}}{m_{f}}}$

Where

${\displaystyle v_{\text{e}}=I_{\text{sp}}\cdot g_{0}}$

$\displaystyle \Delta v=450 \times 9.8 \times \ln {\frac {(200+799+1)}{(200+1)}}$ $ = 7075ms^{-1}$

The 8.3Kg Dawn engine and 2.5Kg of propellant with the same payload would get you

$\displaystyle \Delta v=3000 \times 9.8\ln {\frac {(8.3+2.5+1)}{(8.3+1)}}$ $ = 6999ms^{-1}$

but would be much cheaper to get 11.8 kilos to LEO so that you can accelerate a 1kg payload to 7,000 m/s then getting 1000kgs to LEO to accelerate the same payload to the same speed.

Adding more engines does not change the Specific Impluse, it just increases the fuel flow (ie it increases the thrust), but since you are now moving the weight of the additional engines, it reduces your final $\Delta v$, as rocket scientists love to say, you get there faster but not as fast, (you reach a lower velocity but you reach it sooner). Engines which produce thrust in excess of their own mass can be combined to use that excess thrust to accelerate out of a gravity well, however, ion engines do not have any excess thrust so combining them has limited benefits.

Doing this with two chemical engines would give: $\displaystyle \Delta v=450 \times 9.8 \times \ln {\frac {(200+200+799+1)}{(200+200+1)}}$ $ = 4833ms^{-1}$

Two ion engines would give you:

$\displaystyle \Delta v=3000 \times 9.8\ln {\frac {(8.3+8.3+2.5+1)}{(8.3+8.3+1)}}$ $ = 3904ms^{-1}$