A Plant Growth Lumen

Almost all consumer lamps are now labelled with watts consumption and lumens output. For humans, lumens per watt is a good measure of the efficiency of a lamp in meeting human ability to see, because it is based on the relative sensitivity of our eyes (the red curve at right).

Plants respond very differently to light than humans do. The green curve shows the relative effectiveness of light in producing plant growth. The black curve shows a common definition of plant growth effectiveness used by the lighting industry - as you can see, it matches the needs of plants only a little better than lumens do.

Plants respond to wavelengths other than the green curve for non-growth functions such as flowering initiation, just as humans respond to wavelengths other than the red curve for non-visual needs, such as the production of Vitamin D. However, fresh-water aquarists mostly aim for plant growth.

What we aquatic plant growers need is a true plant-growth lumen (PGL). Here is how to calculate one.

First, obtain the spectrum of the lamp output (you'll have to get it from lighting engineers at the manufacturer; you won't find it on the package or in stores), and its lumen rating. If the spectrum is supplied in energy units such as watts (most are), you must convert it to a photon scale by multiplying each intensity by its wavelength.

Then, using the table below, multiply each spectral value of the lamp by the matching spectral factor for plants. For example, multiply the lamp intensity at 450 nm by 0.213 The result will be the spectrum of the lamp as a plant sees it. Add up all the numbers and call the result P (for Plant).

Next, multiply the lamp spectrum by the matching spectral factors for lumens. The result will be the spectrum of the lamp as a human sees it. Again, add up all the numbers, call it L (for Lumens).

Finally, multiply the lamp lumens by P and divide by L to get the PGL.

Here is an example: a 60 W incandescent lamp, whose output is shown in the black curve of graph 2 at right. The lamp output is 855 lm. Following the above procedure, the red curve is the way a human sees the light, the green, the way a plant sees it. The ratio of P to L is 1.26, so it produces 855 x 1.26 = 1077 PGL.

If the spectral data is not in 10 nm bands, or covers less range than 350-750 nm, this method will still work as long as the data is uniformly spaced over its range. Simply use the nearest values in the table below, the same ones for both P and L. Since the method only calculates a ratio between human and plant lumens, the units of lamp spectral intensity don't matter, as long as they are in photons, not energy.

The result of such analyses is clear: very few 'plant growth' or 'aquarium' lamps outperform cheap standard-spectrum fluorescent tubes or compact fluorescent lamps for growing aquarium plants.

Graph 3 at right shows why. Three lamps are shown, with their output in relative photons per second in 10 nm bands. The black curve is a standard warm-white tube, the others two different plant-growth lamps. The extended spectrum of most plant-growth lamps is obtained at the expense of total output. And, the tiny production volume of the specialist lamps compared to standard warm-white makes them much more expensive.

human, plant and 'quantum' sensitivity

incandescent lamp performance

plant-growth vs. warm-white

typemodelwattsinitial lumensPGLPGL/watt
straight filament incandescent15T101512017211
coiled filament incandescent60A1960855107718
halogen incandescentPAR601050128021
warm-white fluorescent18"1583447832
warm-white fluorescent24"20125371836
cool-white fluorescent24"20120075038
warm-white fluorescent36"302123121641
2700 K compact fluorescent20120084142
warm-white fluorescent48"403117178545
Hagen fluorescentAquaGlo2040095047
Hagen fluorescentSunGlo20123098849
Hagen fluorescentPowerGlo201100104552
special purpose lamps
aquarium fluorescent#12075070735
aquarium fluorescent#22095074037
aquarium fluorescent#32087569034
plant-grow fluorescent#42048074037
plant-grow fluorescent#52075056028
plant-grow fluorescent#62067064032
metal-halide discharge503000189038
high-pressure sodium352240153444

Now that you have a Plant Growth Lumen, how do you use it to grow aquarium plants?

A commonly quoted measure of aquarium lighting in North America is 'watts per gallon': tube-fluorescent watts per US gallon for 10 hours per day. 1 watt per gallon is considered low light, 2 medium, 3 high. Although easy to criticise on the surface, it has proven to be an acceptably reliable measure in practise. So, how can it be converted to units that can be understood by the majority of the world that has access neither to US gallons nor to US lamps?

The efficiency of fluorescent lamps varies with length, as shown above. Most aquarium lamps here are 24", so 1253 lm for 20 W, 63 lm/W is a reasonable efficiency to use as a baseline for conversion. For a warm-white lamp, this is equivalent to 36 PGL/W. Since there are 3.785 liters in a US gallon, 1 'watt per gallon' converts to about 100 PGL-hr/l. For example, a 10 watt compact fluorescent lamp (420 PGL) operated for 12 hours per day over a 50 litre tank gives 420*12/50 = 100 PGL-hr/l, low light.

Now, you are ready to choose your plants based on their light requirements. Here is a listing of the best aquarium plants with their light requirements. Of course, plants respond to factors other than light - pH, fertilisers, trace elements, temperature, just to name a few. But, this note should help you get their light requirements in order.

John Sankey
other notes on physics

Notes
 
All light intensities on this page are in photons per second (Einsteins), not watts, as the activity of chlorophyll depends on the number of photons absorbed, not their energy.
 
Graph 1: The red curve is the CIE definition of the lumen (1924). The green is the average for 26 species of herbaceous plants from Inada, Plant Cell Physiol. 17(2):355-365 (1976). McCree has published similar results in Agric. Meteorol. 9:191-216 (1972), as have Sager et al. Trans. ASAE 31(6):1882-1889 (1988). Black shows the most common definition of Photosynthetically Active Radiation (PAR) approximated by "quantum light meters". PAR is also known as PPF, Photosynthetic Photon Flux. All are normalised for equal areas under the curves.
 
Graph 2: The black curve was calculated from the Planck radiation equation for 2856 K (CIE Standard Illuminant A). The lumens output for a typical 60 W lamp is from the US FTC Facts for Consumers. Note that economy 60 Wbulbs, such as those sold by Rona, produce only 520 lumens.
 
The filament temperatures of the 15T10 (2470 K) and halogen (3000 K) lamps were calculated from their published lumens output and the Stefan-Boltzmann equation. The outputs of warm white lamps are averages from a survey by Joseph Sellinger. All other data was obtained from manufacturers' web sites, and refers to specific lamps. Brands are shown only when they perform significantly better than standard fluorescent lamps. Most manufacturers list only "initial lumens", so the above tables are based on them. (Fluorescent lamps typically produce only 87% of their initial lumens averaged over their lifetime.)
 
The table of spectral factors below shows the values of graph 1.

Spectral Factors

nm   lumen  plant
350  .000  .041
360  .000  .047
370  .000  .056
380  .000  .071
390  .000  .098
400  .000  .134
410  .001  .165
420  .004  .198
430  .011  .222
440  .023  .232
450  .038  .212
460  .060  .198
470  .091  .201
480  .139  .212
490  .210  .224
500  .326  .237
510  .504  .241
520  .706  .242
530  .859  .248
540  .951  .263
550  .993  .289
560  .993  .313
570  .950  .340
580  .868  .369
590  .756  .397
600  .630  .420
610  .503  .443
620  .380  .461
630  .266  .476
640  .175  .493
650  .108  .509
660  .061  .523
670  .032  .535
680  .017  .525
690  .008  .421
700  .004  .273
710  .002  .122
720  .001  .081
730  .000  .062
740  .000  .046
750  .000  .032