This Summer the top of my head has been really feeling scorched by the sun. I'm suffering even on a day like today, when direct sunlight only fleetingly escapes past the big dollops of cloud that are floating through the heavens.
Prior to this year, I've never suffered from anything like this. And I had convinced myself before now that I still have a fair head of hair up top, but no, you can't argue with the feel of cranial radiation - my rug must be thinning; my thatch is losing its insulation; my pate will soon be skyclad.
Still, this sudden onset of Summertime-susceptibility to an overheated belfry has been quite interesting. There must exist some finely-defined critical mass of hair fibre density - drop below the requisite number of follices per unit surface area, and feel that scalp burn...
Now for the Science bit.
k = n/A
where k is the individual's scalp-hair fibre density constant
n is the total number of hair follicles
A is the surface area of scalp
if kA < n, then a nociceptive neural response is innervated