[hoppycalif]

In the past I have argued that watts per gallon works no matter what the tank depth is, but:

For example - take two 100 gallon tanks, one with length and width of 20 inches by 20 inches, therefore with a depth of 100 x 231 divided by 20 x 20 equals 57.75 inches.

The second tank with length and width of 30 inches by 30 inches, therefore with depth of 100 x 231 divided by 30 x 30 equals 25.7 inches.

With both tanks having 200 watts of light. Both have 2 watts per gallon. Assume the light over each tank is a MH light that is significantly shorter than the tank top dimensions. The light intensity from that light will drop proportional to the distance from the bulb squared. So the deeper tank will have an intensity at the bottom of the tank that is 25.7 squared divided by 57.75 squared times the intensity at the shallower tank. That is about 1/5 th of the intensity.

The problem is that tank volume is proportional to tank depth, but light intensity at the bottom of the tank is proportional to one over the tank depth squared.

You can't really come up with a definite formula to account for tank depth in the watts per gallon requirement because the drop in light intensity is only roughly proportional to one over tank depth squared and only for light bulbs that are small in both dimensions compared to the tank top area. For a thin, but long bulb, like a T5 bulb, the drop is much closer to directly proportional to one over the tank depth. PC bulbs would be somewhere in between.

I think what is important is that the "rule" of 2 watts per gallon is referring to tanks of "normal" depth, and with lights shaped like a T8 bulb the same length as the tank length, and, also for PC bulbs with reflectors comparable to AH Supply reflectors. Then, if you use T5 bulbs you can divide the 2 watts per gallon by something like 1.3. And, if the tank is twice the "normal" depth, you need at least twice the 2 watts per gallon.

Even with those "corrections" you are still just crudely guessing how much light is needed - if your aquascape doesn't feature a carpet of plants and does feature a high driftwood centerpiece, the adjusted 2 watts per gallon will cause serious algae problems on the upper parts of the driftwood. And, if you want a really low carpet of HC, for example, but don't have any high stem plants or high rocks or driftwood in the tank, the adjusted 2 watts per gallon could be too low.

Perhaps some enterprising vendor will "develop" a divining rod that we can carry to the LFS and have it pick just the right light for us! I won't suggest which vendor will be first to offer it.

 

[hoppycalif]

Since the light intensity drops approximately by the "inverse square rule", meaning that every doubling of the distance from the bulb drops the intensity by a factor of 4, it has to be true that a pendant fixture hanging high above the tank provides a lot less light than that same pendant hanging right above the water.

But, the higher hanging pendant provides much more uniform light in the aquarium. For example, say you have a pendant hanging 2 feet above a 2 foot deep tank. At the surface the light is 2 feet away, and at the substrate it is 4 feet away, so the ratio between the intensity at the substrate and at the surface will be 1 to 4 - 25% of the surface intensity at the substrate. But if that light is 1 inch above the water surface (forgetting that this only applies directly under the light) the drop in intensity will be 1 divided by 25 squared or you would have only 0.2% of the surface intensity at the substrate.

This should explain why:
People get by with 250 watt MH pendants over 50 gallon tanks.
People get very good results with that light.

This works because the light is suspended high enough to drop the intensity at the water level low enough not to fry the plants. And, being suspended that high means the intensity doesn't drop off much at the substrate level.

This almost convinces me to buy a 250 watt pendant!