Three T12 Bulbs Equals Six T12 Bulbs???

I have a 90 gallon AGA (All Glass Aquarium) with the AGA versa top. 
In the back side of the top, I've got about 9.5 inches of space, which
is just enough room to place six 40 Watt T12 (1.5 inch diameter) fluorescent
bulbs.  But is it such a good idea to pack them in like this? What if I used 
only three light bulbs?  What's the difference in available lumens for
these two designs?

First, I'll make some assumptions.

Each bulb produces 3000 lumens at 80 degrees F.

According to Sylvania's Engineering Bulletin 0-362, a T12 40 Watt lamp can
lose about 1/6 of it light output for each 40 degree F rise in temperature.

When light bulbs are closely packed in, light from the top half of the
bulb never makes it to the aquarium, since there's an adjacent bulb to block the
this reflected light.

I don't know how reflective a turned-on light bulb is, but I'll assume it is 50%.  
This means for the case of packed light bulbs, all reflected light comes from
light bouncing off of the adjacent light bulbs 50% attenuated.
(Does George Booth's experiments on bulbs with built in reflectors suggest that 
it is even less than this?)

For the 3 bulb case, there's enough room to place reflectors.  I'll
assume that 50% of the reflected light makes it down to the aquarium top.
Perhaps I'm being a little pessimistic in this case, but on the other hand
how can you believe the claim that these reflectors "Double the intensity
of any fluorescent tube".  Maybe close enough for the marketing types??? :-)

Fluorescent bulbs produce light 360 degrees around the tube.  However, not
all the light directly makes to the aquarium.  The amount of light directly
making it down to the aquarium top depends on the center to center spacing 
of the bulbs.  The angle which describes the amount of light directly striking
the aquarium top can be estimated from

         theta = 2 * ARCCOS(0.75 inches/D)

where: theta is the angle of light directly hitting the aquarium top
       0.75 inches -> comes from half the diameter of a T12 bulb.
       D is the bulb center to center distance
       ARCCOS() is the trigonometric inverse cosine function

As one can see only 1/2 the light ( theta = 180 degrees) makes it directly to
the aquarium top when the separation is infinity (very wide aquarium), and
only 1/3 of the light (theta = 120 degrees) when D=1.5 inches (packed in bulbs).  

The temperature of the aquarium water is 80 degrees F. 

I've done some measurements in a All Glass Twin Tube light fixture and
found that the steady state temperature just above the glass top inside the light
fixture to be around 120 to 130 degrees F. I'll assume that I can build a 
three bulb fixture that will produce a 40 degree rise when using 3 light bulbs.
Since I'll use the same fixture for the six bulb case, I'd expect another
40 degree rise in temperature for an internal hood temperature of 160 degrees F.
(The thermal impedance of the hood is the same for both cases, but the amount
of heat generated is doubled when using six bulbs.)

Anyways, let's see where this leads to ...

For the 3 bulb case, I can separate each bulb from each other
by 3 and 1/6 inches.  Thus, theta ends up being about 152.6 degrees.
Which means about 5/12 (152.6/360) of the light makes it directly to the aquarium
top.  One half one the remaining 7/12 of the light also makes it to the aquarium 
top( 1/2 * 7/12 = 7/24 ).
Since the hood temperature rises by 40 degrees, the the three bulbs only produce 
5/6 of their light.  (i.e. loss of about 1/6 of it light output for 
each 40 degree F rise in temperature.)

Total lumens available to the aquarium top three bulb case:

3 (lights) * 3000 lumens * ( 5/12 +7/24) * 5/6 (@120 degrees F) = 5300 lumens

For the 6 bulb case, 1/3 of the light is direct. 1/2 of 1/6 = 1/12 is reflected.
The hood temperature is 160 degrees F, so the light bulbs loses 2/6 of its light
compared to when the bulb temperature is at 80 degrees F.

Total lumens available to the aquarium top six bulb case:
6 (lights) * 3000 lumens * ( 1/3 + 1/12) * 4/6 (@160 degrees F) = 5000 lumens

Eeekkkssss, lumens available from 3 bulbs > 6 bulbs !!!!!!!!

Well - what happened?

Basically, in the six bulb case, half of the lighting is lost by not having
a separating gap between the bulbs.  The added heat also reduce the amount of

There are a few things one could due to improve the design.  At about 15 Watts
each, adding fan(s) to reduce bulb temperatures seems reasonable.

Using a hood made out of metal instead of plastic will also reduce the bulb
temperature by improving the amount of heat being dissipated from the hood.

Switching to the thinner T8 bulbs would make the reflectors more efficient 
since they will not block as much reflected light.

HO or VHO bulbs may also be a reasonable alternative, since one can get away
with less bulbs and allowing the use of reflectors.

One can't forget the compact fluorescent bulb either.  They produce a lot
of lumens in a relatively small space.  (Using pairs of 22 inch T5 55 Watt bulbs
in a 48 inch hood would be ideal if one could find them with a descent
color spectrum.)

Placing the lights above open water and allowing the heat to dissipate
into the aquarium water would also reduce the bulb temperature.  However,
I haven't tried this approach because I can't get past the issue of safety.
How do I make sure that the bulbs don't fall into the water or condensation
doesn't short the the tubes?  Commercial hood allow you to due this, but
they cost mega-bucks.

Electronic ballasts also help, but that the subject of another long winded

Ron Wozniak  Allentown PA, USA
rjw at aluxpo_att.com