As you point out weeWX windchill and heatindex values track outTemp below 
certain minimums and above certain maximums respectively. The weeWX calculated 
appTemp uses the formulas mentioned in the post you linked and is quite 
different to a composite heatindex and windchill (by composite I mean windchill 
below 50F and heatindex above 81F). The key difference (other than the formula) 
is that appTemp is valid across all temperatures. appTemp is certainly affected 
by wind speed (just look at the formula), I often notice appTemp moving in time 
(and quite markedly) with wind speed changes on my realtime gauges.

I like to think of 'feels like' as being a term that means different things to 
different people and without an agreed understanding can be a source of 
confusion. It really is just a general term that tries to better approximate 
the effect of current weather conditions on the body, it could be based on a 
measure of heatindex, windchill, humidex, wet bulb globe temperature or 
apparent temperature. For me in Australia I think of apparent temperature, I 
expect in Canada humidex may be a more accepted measurement.

The use of the term 'apparent temperature' can also be confusing at times; does 
it refer to the accepted formula for Apparent Temperature (as you linked or as 
used by weeWX) or is it the more literal meaining. For this reason I prefer to 
refer to something like the 'weeWX appTemp field' or 'Apparent Temperature' to 
make it clear I am referring to the calculated value.

Gary

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