Illuminating Merits

Engineers love Figures of Merit (FOM). We can come up we some pretty abstruse ones. Take this example used for Direct Digital Synthesizer (DDS) chips.

FOM = F_s * 2^ENOB/W

It takes the sampling frequency in Gigahertz times two raised by the effective number of bits, all divided by the power in Watts. Figures of Merit can be tailored to make one's claims stand out above others. In the above example, one group might not use ENOB (effective number of bits) and instead just use number of bits. They might have a really fast DDS, but its ENOB performance sucks, so they just omit the "effective" part of the FOM. Engineers also love acronyms, in case you couldn't tell.

So what does this have to do with cycling? I've been looking into night riding lights recently. As LED-based lights have surpassed HID in efficiency, all new lights arriving on the market are LED-based. It seems every company claims one of the following: a) the highest lumens, b) the longest run-time, or c) the lightest light. Some lights may sound really good, but suck in another way.  For example, what good is search light brightness that runs 12 hours if it requires a 25 pound lead-acid battery?  This just begs for a figure of merit to rank lighting systems. There is a pretty obvious one here. All light companies publish output in lumens, run-time in hours, and weight in grams. So I propose the following FOM:

FOM = Output (lumens) * run-time (hours) / system weight (grams)

Of course, I have only manufacturer's published numbers to work with here. It is easy to measure weight and run-time. Luminous intensity requires a calibrated detection sphere, which I don't own. Even if I did, I doubt any light company would send me free lights for characterization. Some would absolutely not do this, as they use calculated light output, not laboratory verified. I suspect many light companies publish highly optimistic numbers.

I'm looking for both a head mounted light and a bar mounted light. I would want the head mounted light to be compatible with both helmet and headband mounting. I plan to use it for cycling and night skiing. I categorized lights from a few companies in the table below. Run-time at maximum output is used for all lights.  Note the huge variation in the lumen-hours/gram FOM. It spans a range of 3:1.

Comparison of LED Light Systems

Some notable things pop out here. One is that the higher output lights tend to have higher FOM's. There are a multiple reasons for this. First, light companies tend to roll the latest LED technology into their highest power products first. Efficiency of LEDs continues to improve at a dramatic rate. So lights released to the market just two years ago now lag in FOM. One LED company, Cree, makes particularly efficient emitters in the XP-G family of devices. Several of the lights above now use them. A second reason the bigger lights have higher FOM is economy of scale. A bigger battery has more guts per outer packaging material. Thus the battery's volumetric efficiency is better. Same could apply to the lamp housing. Two double-emitter lamps will always weight more than one quad-emitter lamp.  I don't think the bigger lights have an inherent FOM advantage in terms of LED efficiency. Actually, the opposite is true. The harder these LED devices are pushed, the less efficient they are. It pays to use more LEDs in a lamp, with each LED operating at reduced power. This helps efficiency. Incandescent lamps tend to behave opposite to this.

Exposure Lights have the highest FOMs, with one at 11.25 lumen-hours/gram. I am a little suspect of their luminous output numbers though. They push the LED emitters pretty hard.  If specs are accurate, I believe they derive impressive FOMs by putting battery and lamp in a single, cylindrical housing. There are no bulky cables, no separate housings for lamp and battery. Thus Exposure wins by reducing weight to the absolute minimum.

I really like DiNotte's design philosophy. I spoke with Rob about how they achieve higher lumen-hours for a given battery. Basically, they use twice as many Cree XP-G LEDs as the other guys. Each LED is then operated at well below its maximum output. This means higher efficiency can be obtained, which can translate to using a smaller battery for a given run-time. DiNotte focused more on system weight, and they reduce it, ironically, by using more emitters in the lamp. This has a fringe benefit that the LEDs will run cooler and should last longer. The con here is these LED emitters are not cheap, so a brilliant, low-weight system will cost a few bucks more.

Lupine also makes some impressive lights using Cree XP-G emitters. Lupine makes a big deal about publishing measured luminous output, not theoretical. Kudos to them.  They are, however, crazy expensive. Any quality product out of Germany is expensive in the USA it seems. So this gets into a metric I chose to exclude from my FOM. If price were brought into the equation, the Jet Lites unit could shine brightly at $199. I excluded price because it can vary so widely depending on where you live and from whom you buy it. Some brands command more loyalty, and a premium can be charged for this.

I'm not sure what I will do yet. I like the fact DiNotte is a local New Hampshire company. I wish they would put a medium power head lamp based on XP-G emitters on the market. Their mature 400L light system has a pretty poor FOM. I'd like to see them produce a two emitter headlamp with greatly improved efficiency. Then I'd buy a complete bar and head system from them in a heartbeat. As it stands right now, I would buy 1200L+ (FOM=9.03) from DiNotte, and maybe the Joystick (FOM=9.18) from Exposure.