Revealed: the true cost of powering the Death Star
25 November 2016 | OVO Energy
Dear Mr Vader, your energy bill’s arrived...and it’s really quite something. In fact, you might want to take a deep (hoarse) breath about now.
Yes, with the latest Star Wars spin-off set to zoom into cinemas soon, we got to thinking - just how much would it cost to power an evil empire? And what are the practical implications of running the Death Star? Aside from fuelling your planet-destroying laser there are, of course, more trivial matters to consider. Like feeding your crew, dealing with their laundry, taking readings on your smart meter and disposing of the rubbish. You see? Even super villains need to do chores.
See our graphic here for the figures at a glance. Or, for further details, see our in-depth workings below.
To help us make sense of the numbers, we spoke to Stephen Skolnick, editor of the American Physics Society’s Physics Central blog. He talked us through StarDestroyer.net’s calculations and helped us figure out the cost of the Empire’s astronomical energy bill:
“The good people at ‘StarDestroyer.net’ went and calculated the approximate amount of energy the Death Star's laser must have used to destroy Alderaan - assuming that it's a planet with roughly the same mass as earth. To do this, they found the gravitational binding energy of the planet—this is the amount of energy it would take to drag all the particles that comprise earth away from one another to an infinite distance.”
Still with us? Good. Because it gets trickier here...
“It might be surprising that you can pull attractive objects infinitely far apart on a finite energy budget, but it's possible due to the fact that the attraction between them falls off rather quickly. Using this knowledge, and a good bit of calculus, the Star Destroyer crew found that it would take roughly 10³² joules of energy to completely disintegrate an earth-like planet.”
A kilowatt-hour of energy is equal to 3.6 MJ, so it’s easy to convert our number to kWh, then all we need to do is apply our rate per kWh (15p), the unit used to measure energy that is used in homes and businesses, to the number of kWhs expended:
10³²J= £4.166667e x 1024
Recharging the weapon
Thanks to StarDestroyer.net, we know that the DS1 must have a power output of 10³³W, which is 72 million times the power output of the earth and three million times the power output of the sun.
In order to recharge the laser in the 24-hour time period specified in the movies, it would therefore cost us:
10³³W = 9.99999999999999879 x 1029 kW /24-hour recharge =4.1666667 x 1028 kWh =
£6.25 x 1027
What about ‘recoil’?
One aspect of the weapon’s capabilities that certainly doesn’t seem to be factored into the film, or any other calculations, is recoil. Professor Alexander Barnett, from Dartmouth University, discusses its possible side effects:
“Momentum carried by that much light energy is p = E/c ~ 1e24 newton seconds. The Death Star doesn't have that much mass - even if we assume it's 10% solid metal, it only has a mass of around 1x1017 kg. So, that means once it’s finished firing the beam, by conservation of momentum, the Death Star is now flying backwards at:
1 x 1024/1 x 1017 ~ 1 x 107m/s
“That’s around 3% of the speed of light, meaning it would travel 100 times its own diameter (100km) every second. I didn't notice any movement in the film, but maybe it shoots another beam behind it to balance itself out that we just don’t see!”
Jumping into Hyperspace
Our friends over at Star Destroyer have done a lot of the hard work again here and worked out that the much larger second Death Star (DS2) would require 5 x 1030J for a hyperspace jump. So, all we needed to do was find out how much smaller, in volume, the DS1 was, and apply that to the energy needed:
5x1030 J ÷ 2.36464088398 (DS2: 2,140,000,000,000,000 ÷ DS1: 905,000,000,000,000) =
2.114486 x 1030J = 5.87357222222222221 x 1023 kWh =
£8.8103583 x 1022
There are already tools out there to work out the amount of light needed to fit homes, based on the square footage of your house, so the next thing we needed to work out was the square footage of the Death Star. We know from Wookieepedia that the DS1 has dimensions of 120km x 120km, with a volume of roughly 9.05e14m3 and 21,588 floors, so:
9.05x1014 ÷ 21,588 = 4,192,300,437.25 (average volume) ÷ 5.5586436 (average height of each floor) = 754,194,861 (average square footage) x 21,588 = 1.6281558 x1014 m2
To work out the amount of light needed to fill that area, we needed to divide the square footage by the lumen rating of a standard 60W bulb to get the number of bulbs required:
Then we multiply the number of bulbs by the hourly rate per bulb (0.9p) and multiply by that by 24 to get the cost of lighting the structure for a day:
£4.137431313 x 1010
Eating and drinking
Fuelling evil people is pretty costly too, it turns out. To work out the cost of the energy needed to feed the staff on board, we used three example meals of porridge, bread, and casserole. We divided them into portions and then worked out how many times the required appliance would be used. These figures could then be applied to our average cost per use e.g. 11p per hob use, 23p per oven use, 2p per kettle use.
Breakfast: Porridge - 10 portions = 206,894 (hob uses) = £22,758.31
Lunch: Baked bread - 4 portions = 568,958 (oven uses) = £118,963.75
Dinner: Casserole - 6 portions = 344823 (oven uses) = £79,309.25
Cups of tea: 4 cups = 425,000 (kettle uses) x 2 cups a day = £16,500
Washing and drying
And you thought eating on a turbulent aeroplane was bad? Imagine how frustrating it must be to tackle a spaghetti bolognese while Mr Darth’s busy waging a full-scale battle? Stains must be a common occurrence on the space station, so how much would it cost to keep those uniforms looking clean? Well, the average wash cycle costs 15p and the average drying cycle costs 33p, so:
Washing clothes: 5 uniforms = 413,787 (cycles) = £49,654.45
Drying clothes: 5 uniforms = 413787.4 (cycles) = £136,549.84
Waste and recycling
We all remember the famous scene where Luke, Hann, Leia, and Chewy get trapped in the Death Star’s garbage compactor. Well this got us wondering about the amount of waste the station would create on a daily basis. The average person in the UK creates 1.13kg a day, which for the staff on board is:
2341016.39 kg = 2341.016 tonnes
To put that in context, we looked at West London Waste - a local council-run refuse centre that offers businesses a rate of £195 per tonne for waste removal. Using this as a basis for our calculation, this would mean a daily bill of:
So, the practical costs of running the Death Star? A whopping:
£6.2 octillion, 30 trillion times all the money on Earth.
What do you think of our calculations? Is there anything we missed?
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