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Mixing units, or how not to make buying decisions.

Mixing units, or how not to make buying decisions.

This popped up on my radar this morning, and I was so annoyed by the misuse of scientific data that I bumped today’s post to comment.

The advertisement, from a European maker of flashlights, claims that the sun produces 6,000 lumens; which, conveniently, is less than their flashlights at a claimed 10,000 lumens. Let’s give them the benefit of the doubt (though as you’ll see I don’t think they deserve it) and accept that their product does in fact put out that much light.

Here’s the thing: lumens are a non-directional measurement. In other works, lumens are used to measure the total output of a light source regardless of direction. If you hang a bare bulb from a cord in the middle of a white sphere and measure the light falling on the sphere, you can measure the total captured output in lumens.

So, if someone insists to you that the sun produces 6,000 lumens “when it reaches earth”, they’re either ignorant or lying — because the only thing we can measure here on earth is the luminance on a known area of our planet, which is expressed in lux. (Remember that the sun radiates in all directions and the huge, overwhelming amount of its output is going somewhere other than our little slice of heaven.)

Knowing that, however, we can calculate the output of the sun and find out if the claim holds water.

According to reference sources, the sun’s illuminance at the equator maxes out at about 130,000 lux — 130,000 lm/m^2. At our distance from the sun, the earth’s orbit describes a circle with a radius of about 150 million kilometers, or 1.5×10^11 meters. If we imagine the earth’s orbit as a sphere instead of a circle, it becomes an easy task to figure out how much total energy the sun is emitting — all we have to know is the inside surface area of that sphere.

The surface area of a sphere is calculated as (4*pi*r^2), which gives us a figure of 2.827 x 10^23 square meters. (That’s a whole lot of zeroes!) Multiply that by our 130,000 lumens per square meter figure, and we arrive at a total output for the sun inside of our imaginary sphere of 3.6751 × 10^28 lumens. Or, if you prefer: 36,751 trillion trillion lumens. This is within the ballpark of figures I found online, so I think my math is good.

That’s just a tad more than the 10,000 lumens that they’re claiming for their product.

Lumens, lux, cadelas, and candlepower are not the same, and you can’t mix them. If you already knew that, CenturioGroup, shame on you for trying to pull a fast one on your customers. If you didn’t, perhaps someone in engineering needs to go back to high school physics…freshman year.

-=[ Grant ]=-

  • Posted by Grant Cunningham
  • On June 13, 2011

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