Amount of nuclear power need to propel a shuttle at the speed of light

[Rob Benham]

Hi, haven't posted the forum before and would normally read in for a week or two before posting, but then I saw this thread.

In a sci-fi tale some bright folk accelerate a sizable vessel in space in a way that keeps them stuck to the floor. They need to contain their direction and maximum speed. These advanced people do what in aviation is called a barrel roll. After all, there is plenty of room, but of course a constant force would be needed to take the place of wings in the atmosphere.

The question is, what would it take to accelerate a vessel the mass of the Queen Mary at 1G?

These calculations are reduced to a few mumbled statements by the protagonist, but are based on these notes from a flying forum. Are they even in the right ballpark?

Let's use the first second after power is applied (from t0 to t1):
mass of ship (m) = 81961 tonnes = 81.961 x 10^6 kg
velocity at t0 = 0 m/s
acceleration: 9,81 m/s²
velocity at t1 (v) = 9.81 x 1 = 9.81 m/s (~ 35 km/h or 19 knots)
Kinetic energy of ship at t1 = ½ m v² = ½ (81961x10^3)(9.81)² = 3.94x10^9 Joules.
The energy was transferred over 1 second, so we can just say that the Power required is 3.94x10^9 Joules/second = 3.94 Gigawatts (GW).

Calculations based on the UK's power consumption figures from 2006, show the UK was using about 39.75 GW (average rate) in that year. In other words, accelerating a vessel the mass of the Queen Mary at 1G, would take about 10% of the UK's 2006 power consumption. Happily their energy comes free of charge, if you'll excuse the pun.

 

[Ryan_m_b]

Welcome to the forums Rob. Unfortunately there's a flaw in your calculations: it assumes perfect transfer of energy-to-momentum. Realistically no system is that efficient.

 

[Rob Benham]

Thanks for your welcome and reply. It doesn't matter too much as long as it's not total nonsense. Indeed, I carelessly used the displacement instead of true mass, and am given to understand this can vary from near 1:1 up to some significant ratio between the two weights/masses. I have no idea why this varies between vessels.

To get on-thread, I'll just mention I have long wondered what the theoretical maximum relative-velocity might be between our planet and some rogue body heading towards us from a (very) distant location. I have always understood it can not exceed the speed of light, but I'm not totally clear why no one seems concerned about something approaching at near to that figure. I assume most speculation about Earth impact is based on orbiting detritus of one sort or another.

In the former scenario, is extremely high relative velocity limited by the expansion of the universe or relativistic modification - or perhaps both?

 

[Nugatory]

I have always understood it can not exceed the speed of light, but I'm not totally clear why no one seems concerned about something approaching at near to that figure. I assume most speculation about Earth impact is based on orbiting detritus of one sort or another

It's mostly that there is a lot of solar system junk moving at a few tens of kilometers a second, so we worry more about it. Googling for "earth impact crater" or "Barringer crater" or "Chixculub" will find plenty of scary stories of both the "this has happened" and the "this could happen again" variety.

By comparison, massive objects moving at relativistic velocity haven't yet been observed anywhere near us - and a good thing too. A baseball moving at 99% of the speed of light would do far more damage than the meteor that blasted out Barringer crater in Arizona, and that was a lump of solid iron 50 meters across moving at many kilometers a second.

You can amuse yourself calculating what percentage of the speed of light a baseball would have to be traveling for its impact to blow the entire planet apart - there aren't as many nines after the decimal point as you'd expect.

[Edit: Dammit! They just called boarding for my plane, and I'm not sure I got the Barringer crater impact math right. If someone were to check the calculation, see if "far more damge" is in fact right, I'd be grateful. If not, I'll back in a few hours]

[Edit: Assuming 5x10¹⁶ Joules or 10 MT released in the Barringer impact, a 100 gram mass moving at 99% of the speed of light is indeed about right]

 

[Rob Benham]

Thanks for the reply.


We too are rushing for a tans-Atlantic. I will return, though my timescales are uncertain.

 

[Drakkith]

Because Nugatory brought up a relativistic baseball: http://what-if.xkcd.com/1/

 

[PAllen]

Because Nugatory brought up a relativistic baseball: http://what-if.xkcd.com/1/

Interestingly, this cartoon was analyzed here some time back. The consensus was that it is inaccurate:

- fusion would be insignificant
- 99+% of air molecules would go through the baseball unimpeded (based on mean free path data matching the speeds under consideration and the baseball composition).
- The ball would not be mostly disintegrated until a few kilometers beyond home plate
- All the same, the amount of radiation released between pitcher's mound and home plate would be more than sufficient to incinerate the pitcher and batter, but there would be no mushroom cloud.

 

[Nugatory]

Interestingly, this cartoon was analyzed here some time back. The consensus was that it is inaccurate:

- fusion would be insignificant
- 99+% of air molecules would go through the baseball unimpeded (based on mean free path data matching the speeds under consideration and the baseball composition).
- The ball would not be mostly disintegrated until a few kilometers beyond home plate
-All the same, the amount of radiation released between pitcher's mound and home plate would be more than sufficient to incinerate the pitcher and batter, but there would be no mushroom cloud.

Several threads, actually - a search for "xkcd baseball" will find them. I'm inclined to agree with that analysis; the xkcd piece is right that at the timescales involved we can consider air to be a solid, but wrong to have forgotten that it's still a very low-density solid so the energy release is spread across kilometers of distance.

I am assuming that because the density of rock is easily three orders of magnitude greater than the density of air, a relativistic collision with the ground will release the kinetic energy in a space of meters instead of a few kilometers. That's much more likely to be a mushroom cloud situation.

Of course we've also wandered far from the original question in this thread, and I'm much to blame . I was trying to make a point about just how enormously beyond the range of our normal experience relativistic speeds are... and I think I succeeded.