I read that with our current ion propulsion technology it is possible we could send a craft moving the maximum of 100km per second, or around 62 miles. However we seem to be limited by how strong of a power generator we are able to put aboard the craft.. Is it possible that with enough power we could accelerate a spacecraft beyond this 100km per second limit? What is the maximum speed we could send a craft moving in space at with our current ion engine technology?
Asked
Active
Viewed 1.2k times
5
-
7(0.999999...)c. – Erik Jun 30 '17 at 01:01
-
@Erik Not without fantasy engineering. – Russell Borogove Jun 30 '17 at 01:08
-
But it is possible with current technology. – Erik Jun 30 '17 at 01:09
-
5@Erik It's really not -- see my answer. – Russell Borogove Jun 30 '17 at 01:13
-
So it was just a comment, not a serious answer. Having said that, the OP never restricted the answer to a single stage launch, nor did they say how big the spacecraft is. Your engine lifetime point is a good one however, but in the end, it just more dry mass on a very big vehicle. – Erik Jun 30 '17 at 01:16
-
Also, to your point, the T. equation doesn't account for relativistic effects -- which makes it even more difficult. – Erik Jun 30 '17 at 01:17
-
You run out of Xenon on the planet long before you need to worry about relativistic speeds. – Russell Borogove Jun 30 '17 at 01:24
-
Why are limited to Xenon on the planet? – Erik Jun 30 '17 at 01:33
-
1Let us continue this discussion in chat. – Russell Borogove Jun 30 '17 at 01:45
-
Let me ask, if we send a probe into vicinity of Kuiper Belt, then lose the 4.7km/s or so of orbital speed and let it drop like a rock into the Sun, what will its speed be before it's incinerated? – SF. Jun 30 '17 at 10:16
-
...100km/s is the escape speed of solar system from a 38 solar radii altitude above Sun. Probes can definitely survive that. So yeah, lob the probe into Kuiper belt, arrest the orbital speed, give a bit of a kick towards the Sun (otherwise the beginning will take ages) and let it take the plunge. You'll get ~600km/s before it impacts the surface. – SF. Jun 30 '17 at 10:35
2 Answers
20
The limit isn't due to power, but to engine lifetime and fuel limits.
Ion engines produce very little thrust, so in order to reach speeds of 100km/s they must accelerate continuously for months or years. The Dawn spacecraft, for example, was built with three redundant ion thrusters to extend its lifetime, and got nowhere near 100km/s; it carried enough propellant to change its speed by about 10km/s, and took 15000 hours (~1.7 years) of continuous thrust to change its speed by 4.3km/s.
To achieve a ∆v of 100km/s with an ion engine like those on Dawn (with a specific impulse of 3100 s (exhaust velocity of 30400 m/s)) we turn to the Tsiolkovsky rocket equation:
$$\Delta v = v_\text{e} \ln \frac {m_0} {m_f}$$
Where $v_\text{e}$ is the rocket exhaust velocity and ${m_0}$ and ${m_f}$ are the mass of the craft full of fuel and empty respectively.
$$100000 = 30400 \ln \frac {m_0} {m_f} \Rightarrow 3.29 = \ln \frac {m_0} {m_f} \Rightarrow \frac {m_0} {m_f} = e^{3.29} = 26.8$$
So an ion-thruster spacecraft intending to reach 100km/s must carry 26 times its dry mass in xenon propellant. This is an extremely high mass ratio, not generally achievable in a single-stage spacecraft. A two- or three-stage spacecraft could do it with reasonable mass ratios.
Ion engines are already very power-hungry, and need to be paired with a lot of mass in solar panels or RTGs. More powerful thrusters could increase the exhaust velocity by a small amount, driving down the mass ratio, but at the cost of greatly increasing the dry mass with the larger power supply.
Note that I'm referring to a change in speed or ∆v throughout this answer, rather than a maximum speed. This is because the speed of objects in space must be described relative to a particular reference point, and speed limits don't work the way they do for Earth-bound vehicles.
Russell Borogove
- 168,364
- 13
- 593
- 699
-
1It's a bit of a nitpick, but shouldn't that be $\Rightarrow$ (
\Rightarrow) rather than $\rightarrow$ (\rightarrow)? The first time I read this, I read $\rightarrow$ as $\to$ (the "goes to" operator; in LaTeX,\to). – user Jun 30 '17 at 07:58 -
@MichaelKjörling Thank you -- it looked wrong to me but I wasn't sure if there was a formal convention.
\rightarrowwas the first thing I tried that looked vaguely useful. – Russell Borogove Jun 30 '17 at 14:19 -
I don't know if it's formally correct, but it is what I learned back in school. – user Jun 30 '17 at 17:55
5
You have it correct, but you are looking at a very narrow range of ISP.
The BepiColombo mission to mercury uses an ion thruster with a ISP of 4,200 seconds(41,202 M/s). The same formula yields a mass ratio of 11.325.
The NEXIS ion thruster can achieve 8000 seconds (78,200 m/s)
The European DS4G innovative thruster manages 19,300 seconds (188,200 m/s) exceeding the 100 km/sec from the above question.
Lithium fed GIT (gridded ion thrusters) have demonstrated 50,000 - 80,000 seconds of ISP(490 km/s to 780 km/sec).
The problem is not so much mass ratio but power applied to the thruster and electrode erosion. The DS4G is the first thruster to have concentrated power in a small form, what is needed a nuclear reactor delivering 100 of KW's or maybe Mw of power.
With Megawatts of power it is possible to have Ion thrusters exceeding 100,000 seconds of ISP (over 1,000 km/sec).
