Is there a meaningful formula to estimate time it takes for tap water to freeze in an specific outdoor area?

Question

This is to estimate freeze time required for backyard rink

I'm not interested in the obvious it depends on.....blah blah
I want a formula please.

Given a formula, one can normally deduce the dependancies....the following, which I did not mentioned in my question, for simplicity reasons, will be a factor, (Surface, Water depth,
Water start temperature,
Water Freezing temperature,
Evaporation rate, Outdoor temperature, Wind, Atmospheric pressure, etc...).

Having said this, now with your information I have a starting point to my question. Now lets break down TFA I TFG with assumptions. Can you still help?

Answer 1

Time = Volume * Btu/cube / (TFA * Surface Area *(32- Air Temp) + TFG *(32- Ground Temp))
In other words, the amount of heat held in the water on conversion to ice depends on the volume and the Btus per cubic measure and the time it takes depends on the surface area and the transfer function for water to air (TFA) and water to ground (TFG)
If course, the TFG and TFA depend on all those things you don't want us to mention like wind and evaporation. So there is no simple minded solution.
If it is cold enough and the ground is cold enough, the water will freeze before the rink is filled.

Answer 2

It depends on so many factors; surface area, volume, temperature of water and air, even things like humidity, sunlight and pressure would have an effect. Best to just try with a little water and see how long it takes.