[Valarc]

EDIT: in my haste to write out the math here, I forgot a factor of 1/2 in the energy calculations... this is now the corrected numbers

The three top trays in a stack of 4 would of course have the same velocities as the three trays in a stack of 3, so the velocity in those wouldn't have any difference from before. I'm going to bore you all with a little math, just so we know exactly how much of a velocity difference we're dealing with here.

Everything I'm going to be calculating here is a theoretical maximum. This is the best possible velocity you could get without any air resistance, and no media changing flow direction and slowing the water down. This calculation is basically the water flowing straight down in a vaccuum. Actual velocities would be much lower, as would their difference.

Also, I can't find exact dimensions for the towers with some cursory googling, so I'm going to do a calculation GROSSLY over-estimating the size of the towers. Basically, I'm going to assume each section is a full meter high - which is of course MUCH taller than reality, so again the actual velocities and their differences would be much smaller.

The easiest way to do this calculation is with conservation of energy. It eliminates the hassle of using calculus to solve newton's equations, and makes the math short and sweet. That is, the potential energy at the top of the tower is conserved, and converted into kinetic energy at the bottom.

Potential energy - U = m * g * h

where m is the mass, g is the acceleration due to gravity, and h is the height. If we set the height to be 0 at the bottom of the tower, U at the bottom is then 0 as well.

As far as kinetic energy, E = (1/2) * m * v * v

Because we know energy is conserved E_bottom = U_top, therefore
0.5 * m * v * v = m * g * h, or v = square root (2 * g * h).

Therefore, for a 3 story bakki, with meter-tall units, the velocity AT THE BOTTOM OF THE LAST TRAY is...

v = sqrt(2 * 9.8 * 3 ) = 7.67 m/s

For 4 stories

v = sqrt( 2 * 9.8 * 4 ) = 8.85 m/s

So, for meter-tall units, the velocity at the BOTTOM of the lowest tray differs by a theoretical maximum of 1.87 m/s between a 3-tray and 4-tray system. To put this in perspective, adding a fourth tray gives a maximum theoretical velocity change of 15% at the end of the shower.

For half-meter trays, we get for 3 trays v=5.42 m/s, 4 trays - v=6.26 m/s. In this case, the difference is only 0.84 m/s, but this is again 15% of the 3 tray velocity.

I can't judge whether these velocity effects would be enough to make any difference in the filtration properties of the media, but I thought it was important for folks to understand the scale of the velocities we're talking about. I'm curious for those who have seen the effects of adding a fourth try - did you TRY it with the fourth tray stacked separately first, or did you just add the tray to the tower? My point is, it could simply be the extra media and accompanying biofilm that's making the difference, and not the extra height. The only way to know for sure would be to test both configurations.