Transmissivity is a very "iffy" subject. It is intended to reflect the idea that the heat transmission through the atmosphere is attenuated by the heat absorbing molecules, primarily water, in the same manner that sound is attenuated by molecular dispersion.
I believe that the idea originated from one of Kent's papers (in about 1967 ?) where he had way of attenuating heat based on distance from his flame center. Unfortunately, the flame center he used may not have been real, so his formula may have been incorrect. Subsequently the formula now mainly in use seems to have developed along with Brzustowski's model.
It is included in the API RP-521 models in strange ways. In the API simple model it's a straightforward 2/3 reduction (?) and in the BRZ model its a more complex calculation involving distance from the flame center and Relative Humity. I have no idea where the RH% exponent (1/16) comes from. Perhaps there may be other readers who do (!!!)
In any event the formula is spurious because there is no temperature correction. If absorbtion by water vapor occurs, one would expect it to be related to the TOTAL quantity of water in the atmosphere and not the quantity RELATIVE to another amount, unless the formula is already standardized (and not knowing the basis makes it impossible to decide that)
One thing you have going for you is that the 4 pi solid angle formula you are probably using is no more accurate or inaccurate than the transmissivity factor or the emissivity which you have presumably selected out of thin air (as most designers do), or the wind speed that you have again selected for the radiation condition which you are considering (by the way is that a real case or theoretical?)
If I sound sceptical, I am!
You need to look carefully at ALL the factors in your formula and decide on the most realistic combination of conditions. Then you do the calculation and live with the results. If you expect to go out and measure the same values on test, forget it. At best, the standard calculations are wet finger estimates which (hopefully) encompass the worst conditions for (personnel?) exposure to radiant heat and give you a "feel" for the probable level of danger.
Sonic flare heh! Big long flame or short fat flame. In either case the chances of you having the right flame model are approaching zero, unless you did your own testing, (if you did, please publish!)
If you wish, you could take a look at my model "A proposed comprehensive model for flare flames and plumes" [AIChE Spring meeting 2006.] which might allow you to incorporate the benefits of high velocity into the flame size and shape .. or not..!
In any event you're stuck with the existing transmissivity formula or don't use it at all. You're probably better off looking at the emissivity - see my paper " Making the Flare Safe" [AIChE Spring meeting 1996]
