This question goes to a very basic non-understanding of mine that I have had in the back of my mind for ages – I just read the following here:
ion thrusters are capable of propelling a spacecraft up to 90,000
meters per second (over 200,000 miles per hour (mph). To put that into
perspective, the space shuttle is capable of a top speed of around
18,000 mph. The tradeoff for this high top speed is low thrust (or low
acceleration). Thrust is the force that the thruster applies to the
spacecraft. Modern ion thrusters can deliver up to 0.5 Newtons (0.1
pounds) of thrust, which is equivalent to the force you would feel by
holding nine U.S. quarters in your hand.
So when it hits the top speed what is the bottle neck? The logical thing to me is that it takes more and more electricity to maintain the 0.1 pounds of thrust, but if this is the case, does this not violate the premise that you cannot tell how fast you are going without something to compare to? In other words, if I turn the engine on and then off again repeatedly, should I expect different results from one time to the next?
I know I'm confused about something very basic here – that's why I'm asking..
Best Answer
The answer to this question is no.
The bottleneck is that the vehicle runs out of propellant. The problem is described by the rocket equation, $$\frac {\Delta v}{v_e} = \ln\frac{m_{\text{initial}}}{m_{\text{final}}}$$
Where
$m_{\text{final}}$ is the final mass of the rocket, the masses of the structures that previously held the propellant, the engines, the power plants, the structure of the rocket itself, and finally, the payload;
$m_{\text{initial}}$ is the initial mass of the rocket, the final mass plus the mass of the propellant;
$v_e$ is the velocity of the exhaust relative to the vehicle; and
$\Delta v$ is the change in velocity that results from using the propellant.
Note the logarithm on the left hand side of the rocket equation. Adding more propellant has an ever decreasing effect on the change in the rocket's velocity. Another way to look at the rocket equation is to look at the proportion of the initial mass that is propellant:
$$\frac{m_{\text{propellant}}}{m_{\text{initial}}} = 1 - \exp\left(-\frac{\Delta v}{v_e}\right)$$
This means that attaining a $\Delta v$ equal to twice the exhaust velocity requires that 86.5% of the initial mass be propellant. This is quite doable. On the other hand, attaining three times the exhaust velocity requires that 95% of the initial mass be propellant. This is almost possible from an engineering perspective. Anything beyond that is not. Single stage rockets have an upper limit on the change in velocity that is somewhere between two to three times the exhaust velocity.
There are ways to overcome the tyranny of the rocket equation. One approach is to use a multi-stage rocket. The math described above pertains to single stage rockets. A single stage rocket using traditional chemical-based techniques cannot achieve orbital velocity from the Earth's surface thanks to that limit of two to three times exhaust velocity. The rocket equation changes a bit for multi-stage rockets. Another approach is to use a better kind of propellant, one with a higher exhaust velocity. That's what makes ion engines so appealing.