Two sources, worked out
Four hundred and fifty people at a quarter of a pound an hour each is 112.5 pounds of water an hour walking into the building. The outdoor air is the other half: 4,000 CFM at 0.075 lb per cubic foot carries 18,000 pounds of dry air an hour, and if that air is 84 grains per pound while the bowl is held at 28, each pound of it drops 56 grains — 0.008 pounds — which is 144 pounds an hour. Add eight pounds for wet floors and evaporation and the building is making 264.5 pounds of water an hour, or nearly 32 gallons.
A machine rated 180 pounds an hour at these conditions leaves 84.5 pounds an hour in the air. That is the surplus, and the surplus is what causes fog, drips off the roof steel, wets the glass and lands on the ice.
Why frost costs so much heat
Vapour going directly to ice gives up the heat of condensation and the heat of fusion together — around 1,220 Btu a pound with the default in the field. At 46.5 pounds an hour reaching the sheet that is 56,700 Btu an hour, or 4.7 tons of refrigeration the plant is carrying purely because the building is wet. It is a bigger number than most operators expect and it is invisible: no gauge in the plant room says frost.
The thickness that is not a thickness
The same 46.5 pounds an hour over ten hours is 465 pounds of frost. Over 16,327 square feet at 57.2 lb per cubic foot that is 0.006 inches. Ten of those days would be six hundredths of an inch, less than a single resurfacer flood puts down. Frost is not how sheets get thick. Floods are how sheets get thick.
What this cannot know
It has no view on what humidity you should hold, which is a question for whoever specified the building and for what you are doing on the ice that day. It cannot tell you whether your machine is the right one, because the removal figure it works from is one you read off a submittal. And the split between the ice and every other cold surface is genuinely unknown — the page asks you rather than pretending.
Questions people ask
What are grains per pound?
A humidity ratio: how much water vapour rides along with each pound of dry air, measured in grains, of which there are 7,000 to the pound. It is the reading that matters for moisture load, because relative humidity on its own tells you nothing without the temperature it was measured at.
Why not just use relative humidity?
Because 60 per cent at 70 °F and 60 per cent at 40 °F are wildly different amounts of water. The bowl of a rink is stratified — warm wet air near the roof, cold dry air over the ice — so two relative humidity readings in the same building can be honest and useless at the same time. Grains compare directly.
Does dehumidification make the ice colder?
No, it takes work off the plant. Every pound of vapour that lands on the sheet as frost gives the ice about 1,220 Btu, so drier air means less of that heat arriving and a plant with more room for the floods. What the plant does with the room it gets is set by your controls.
My machine is rated much higher than the number the page asks for.
Catalogue ratings are quoted at conditions, usually warmer and wetter ones than a held-down rink bowl. Removal falls off as the air dries, and refrigerant and desiccant machines fall off along very different curves. Use the line off the submittal that matches the grains and temperature you actually run.
Where does the moisture go if there is no surplus?
Into the equipment and out as condensate or regeneration exhaust. If the removal figure covers the load, this route puts nothing on the ice, and the page says so rather than inventing a number.