Sunday, August 31, 2014

Bicycling's "Light Up the Night" Suggestion for a Headlight

Or, Why This Is A Bad Approximation At Best

I was reading through the latest Bicycling issue (October, 2014). On page 26 is a one pager on lights and reflective stuff. Interestingly, the article states that a 100 lumen headlight should work "for most situations". But then down in the lower right hand corner of the page is a little picture that is titled "the right light" and which suggests that a 100 lumen light is good to a range of ten feet while a 500 lumen light illuminates to 50 feet and 1000 plus lumens to 75-100 feet.

Ten feet?? A commuter cyclist riding at 10 mph covers ten feet in about two thirds of a second. Assuming Bicycling has its numbers right on light range, 2/3 of a second is barely time to think "oh, shit" as you note the pothole or piece of lumber you are about to hit.

There is a lot more to lighting then lumens and more to this story than lumens. For one, the shape of the beam and thus the focusing lens determines how the light is distributed, which affects lux, which is actually more important.  Lux is a measure of how brightly something is illuminated, i.e., lumens per square meter, so a light that puts all of its lumens in a narrow beam will illuminate brightly for a longer distance but leave anything west or east of dead ahead in blackness. A well shaped beam concentrates illumination where you need it rather than in the eyes of oncoming traffic or out into space.The link from the Appalachian Mountain Club used the example of a full moon illuminating the earth to about 0.25 lux. Likewise, not all of us have equally good night vision and some of us need more lux than others. Luck, too. So let the buyer do some serious R and D before purchase.

But just taking that little graphic in the corner of pg 26 at face value, what can one say about how much light you need to get out to a distance of say, 1 to 3 seconds. 1 to 3 seconds is the broad measure of human reaction time in traffic. So what really matters to avoid that pothole is to be able to see it in time to do something besides hit it. I put Bicycling's range vs. lumens into a graph and used that relationship to solve for a 1 to 3 second range at various speeds. This is what I got.

Bicycling's 3 points put on a graph

At a given speed (abscissa), the number of lumens (ordinate) will, in Bicycling's model, illuminate the road 1 to 3 seconds ahead
As Stuart mentions in the comments, the linearity in Bicycling's article is a little strange given that if you assume the light is illuminating to a given distance and that the beam widens with an angle, say, theta, the area illuminated increases with the square of distance. Hence, you should need lumens to go up as the square of distance at constant lux. Is that correct? My hunch is that Bicycling's numbers are not rigorously scientific, but rough estimates as to what works. But I'd be surprised if it should be linear.

Mind you, this is more of a thought exercise and not hard and fast advice, but if you are thinking of buying a light (and Fall is coming up fast), you need to think about how fast you are going, the roads you are on, and therefore, how far out you need to see. You also need to think about whether you need a light that distributes light side to side (to avoid those raccoons darting out from the side of the road, etc).  That is a highly individualized decision and goes far beyond "...should work for most situations".

Other stuff on this blog having something to do with lights.


Steve A said...

If you are concerned about not blinding other road users, the light pattern is also important, though not very good in most bike lights.

Stuart T said...

Since light intensity decreases as 1/r^2, you should need 4 times the lumens to see twice as far. Why do the graphs seem not to show this?

Khal said...

I used Bicycling's estimates and it does seem a little fishy because the area being illuminated increases as the square of distance. Agree it should be a 1/r^2 relationship if you are illuminating equally brightly.

Chandra said...

Khal - Very important topic and thanks for posting on this topic.

I agree with Steve A - proper mounting of lights is very important also. I have a post coming up soon, where I will talk about that, not from a scientific POV, but from a 'Dang I can't see' POV.

Peace :)

PS. We only have 3 (Y,X) pairs and hence only have 1 df for error.