Steam Radiator Math

The amount of air in a radiator varies according to the type of radiator. For example, a column-type rad has more internal volume than a small-tube type. Go here and scroll to page 14 of the PDF to see:

https://www.heatinghelp.com/systems-help-center/balancing-steam-systems-using-a-vent-capacity-chart/

you really don't need to know the volume of the radiator, the edr is what is important, it tells you how much steam it can consume at a given ambient temp and steam pressure although in residential we assume the steam to be at around atmospheric pressure. if you are doing higher pressure systems that is more important to calculate than volume of the emitter.

the ratio of volume to surface area really isn't about efficiency, it is just construction style. you probably need to think about piping differences more than differences of ratio of edr to the radiator volume. probably a fixed ratio will be less error than other things that you can't measure.

once the radiator is full of steam you can calculate the condensate production from the edr and ambient temp(and steam temp if working at elevated pressures). i suppose if you wanted to figure out when the trap opened you would have to calculate how long it would take to collect 1/4"-1/2" of condensate over the trap which would depend on the profile of the bottom of the emitter, how the emitter connected to the trap, and the profile of the trap itself.

how long it takes steam to get to the trap is much more complicated because it is a function of how long it takes to heat each infinitesimally small piece of pie to steam temp then each increment of radiator to steam temp and of the rate of the radiator valve on a 2 pipe or the rate of the vent on one pipe. the steam won't progress until the surface just in front of it is the temp of the steam. it will produce a lot more condensate as this is happening vs steady state.

As I said before, the cycling rate of a radiator trap is not determinable from the BTUh power output of the radiator. It is determined by the trap design itself, and by the conditions surrounding it — if it cycles at all, which will only happen if the possible steam input rate exceeds the output capacity of the radiator.

This sort of thing can get kind of gnarly unless one is quite specific about the design and operation of the particular trap. There are trap designs, for instance, based solely on temperature. These often can modulate — that is vary the opening depending on temperature (exactly the same principle as the thermostat on liquid cooled engines, by the way). The sensing mechanism may be a liquid which expands. It may be a design which uses the change in vapour pressure of a liquid with temperature (often the liquid is methyl or ethyl alcohol, which have vapour pressures in convenient ranges). It may be a design which uses the expansion of a wax with temperature. And so on. Then there are designs which are purely mechanical, and use a bimetal element of some geometry; some of those modulate, some are two state (e.g. open or closed).

Then to add to the fun there are trap designs — the ones normally used in heating work with steam — which are not only temperature sensitive, but which also respond to the presence of water. They will contain an element of some sort which will float and open the trap when there is enough water, regardless of temperature, but also a thermal element which will allow gas to flow through up to a certain temperature. The common radiator trap is often of this type.

And they all have different response characteristics…