The winning design for the Greener Gadgets 2008 competition comes from one Clay Moulton, a Master’s student at Virginia Tech. Moulton’s winning design is the Gravia lamp, which works not off of electricity, but by gravity. To “charge up” the lamp, the user lifts a weight to the top of a column, whereby it slowly drifts to the bottom. A hydraulic mechanism allows the gravitational potential energy to be converted into light energy, thus providing “up to 4 hours” of lighting usage with light output equivalent to that from a 40 watt incandescent light bulb.

It sounds great on paper, and the competition judges certainly thought so too. The lamp itself looks really neat.

There’s only one problem - the design can’t possibly work.

The calculation is so simple, that even pre-’O’ level students should be able to convince themselves that this design is physically impossible. The two-line calculation to prove this is given below the fold:

First, let’s gather some data. All but one piece of information can be obtained from the design sheet from the competition website, which is reproduced below:

Here’s the relevant data:

  • The lamp has a height h = 58 inches = 1.47 m.
  • The lamp uses a weight of mass m = 50 lb = 22.7 kg.
  • The lamp is meant to emit light for T = 4 hours with every one “charge” of the lamp, i.e. when the user moves the weight up the column.
  • The lamp is design to produce light of brightness 600-800 lumens. (This is stated on the main entry page.)

The only tricky datum is the brightness of the design, which is stated at 600-800 lumens. The lumen is a perceptual unit that measures how the human eye perceives brightness, and is known to be very sensitive to wavelength. This is because different colors are intrinsically brighter or darker to the human eye, even at the same power output. Green is intrinsically brighter then blue and red, and the brightness per power ratio peaks at green light of wavelength 555 nm, which has a brightness (technically, luminous efficacy) of 683 lumens per Watt.

Let’s be totally unrealistic and assume the lamp generates only green light at this wavelength. Then the lamp must output at least W = 600 lumens / 683 lumens per Watt = 0.878 Watts. This, then, is our very last datum required.

We can now calculate the energy input to the lamp using elementary physics using the formula for gravitational potential energy E = mgh. The energy output of the lamp is also given by WT, being simply power times total time taken.

Energy input = mgh = 22.7 kg x 9.81 m/s² x 1.47 m = 327 J

Energy output = WT = 0.878 W x 14 400 s = 12 643 J

This calculation hence tells us that the lamp is designed to produce approximately 40 times more energy than it accepts, which any student who passed physics can tell you is absolutely and utterly impossible. Bear in mind that to get this number, we already threw in the very generous assumptions of perfect energy conversion and maximum theoretical luminosity for ultrapure green light.  These simplifying assumptions already grossly underestimate the actual amount of energy required as output by at least a factor of 10 - an ideal white light source ought to have a luminous efficacy of 242 lm/W instead of 683 lm/W, and the most efficient light sources today don’t exceed 30% in efficiency.

Is there any way to rescue this design? Sure: make it taller, and use a larger weight. To be totally ridiculous, let’s use a weight of mass m = 472.5 kg, equal to the world record for weightlifting set by Rezazadeh Hossein in the Sydney Olympics of 2000. Applying the same assumptions as above, the height of lamp required would be 12 643 J / 472.5 kg x 9.81 m/s² = 2.72 m, which is quite a bit too high to fit in the average living room.

The conclusion is simple: If you’re a world record weightlifting champion, and you have a living room ceiling that’s at least 2.72 m tall, and you had perfect energy conversion efficiency, and if you were comfortable reading in green laser light, then perhaps you might be interested in this product. Otherwise, it’s simply not possible to create anything of such specifications.

The sorry conclusion of this exercise is blunt and simple: this design cannot possibly work, even we had the most efficient lights possible. All the quibbles about using better LEDs are irrelevant in the face of this most basic analysis.

Sorry Moulton; I’m sure you’re a great designer, but you’re no match for the laws of physics. Whoever awarded this physically impossible design an award ought to be forced to go back to school and learn physics from scratch.

Reference

  1. Greener Gadgets Design Competition 2008.
  2. International Weightlifting Federation’s World Records.