Not all people ask themselves this question, I know. Personally I have been thinking about this for about two months now and I have now finally found the time to do some calculations. The question is how powerful a light bulb would have to be to give the same light Sauron’s Eye does. Not life changing research but very intriguing nonetheless. In order to calculate this I have used a scene from the Return of the King. This means that everything is based on data from the movies and not the books.
It is a very beautiful scene with Sam and Frodo on a cliff in the foreground. In the distance is Barad-dûr crowned by the Eye of Sauron. The Eye itself is looking towards Frodo and illuminates the scene perfectly from behind in a glow that is best described as sunset.
In order to calculate the power of the light bulb we need to know the distance to the Eye i the scene. The distance can be calculated using this formula:
d = ( focal lenght (mm) * tower height (mm) * image height (px) ) / ( object height (px) * film height (mm) )
The image height is 570 pixels and the tower is 322 pixels high. Barad-dûr is in the movie depicted as approximately 1500 meters or 5000 feet tall. (1) If we assume this particular scene was shot in Super 35mm film the film height will be 14mm. (2) We also assume it was shot with a 50mm lens. All in all this gives us a distance of 9483 meters. With Pythagorean theorem the distance from the Eye to Frodo and Sam is calculated to be 9601 meters.
Let us now say that evening light is around 0,5 W/m2. (3) It is likely Sauron’s Eye outputs the same light in all directions. The searchlight characteristic is probably achieved by the construction suspending the Eye at the top of the tower. If this is true the total power can be calculated multiplying the area from a sphere with the radius of 9601 meters with 0.5 W/m2.
A = 4*π*96012 = 1158 358 002 m2
P = 1158 358 002 m2 * 0,5 W/m2 = 579 179 001 W
This means the power output of the bulb is 579,2 MW, a decent light source!
I think it is safe to assume it is an incandescent light bulb. Sauron most likely care very little for the environment and energy efficiency and will not have thought of LED or CFL. An incandescent bulb has an efficiency of only 5% which means the power of the bulb will have to be:
P = 579 179 001 W / 0.05 = 11 583 580 020 W
The total power of the bulb is 11.584 GW!
Something will of course have to power the bulb. I Mordor this is most likely a steam engine run by black coal. An old steam engine likely to have been used in Mordor typically had a thermal efficiency of 5 – 8% with a generator with an efficiency of about 90%. For the calculation I choose 6.5%.
P = 11 583 580 020 W / (0.065*0.90) = 198 009 914 872 W
This means the total input will have to be 198 GW and the energy usage 198 GWh or 4,752 TWh/day.
So how much does this equal in black coal? Black coal has an energy density of 24 – 35 MJ/kg. (4) If we choose something in the middle, 30 MJ/kg, the required amount of black coal will be 6600.3 kg/s or 23 761 tonnes/hour. With a density of 833 kg/m3 (4) the volume black coal will be 28 524 m3/hour which equals to a cube with 30.55 meters sides.
To put this into perspective the Kashiwazaki-Kariwa Nuclear Power Plant in Japan, the largest nuclear power plant in the world, would be able to power only 71% of the Eye of Sauron.
During Sauron’s reign in Mordor in the Third Age, from T.A. 2951 to T.A. 3019 they used 117944,64 TWh to power his Eye. This accounts for 89% of the total world enery consumption during a single year. (5)
(2) 35mm Digital Sensor Comparison Chart – (35mm Digital Sensor Comparison Chart)
(3) Light intensity in the afternoon and during a solar eclipse: effects on retreat underground in a diurnal mammal, Kamiel Spoelstra, Roelof Hut, Arjen M. Strijkstra, Gerard J. F. Overkamp and Serge Daan, Zoological Laboratory, Haren, the Netherlands
(4) Bituminous coal – Wikipedia (http://en.wikipedia.org/wiki/Bituminous_coal)
Now, we will never know the exact numbers and these are just approximations. If you have thoughts or questions please leave a comment below.
I have received a lot of advice from my good friend Robert. Thank you!