I'll say it right now, out loud and at the outset, there is no physiologic reason that a woman can't successfully drive a Formula 1 car in competition. Let's look a little closer at the issue.
At the most basic level, the physical ability to drive the car, we need to consider muscular strength (especially upper body strength), coordination, endurance, and finally the ability to regulate core temperature.
If we look at what's known about muscular strength and endurance in men and women, when calculated in terms that take into account size differences, we find that there are no significant differences between the sexes. More importantly, the response of the muscles to identical levels of conditioning is the same, for example, in Jenson Button as it would be in Alice Powell. We need to remember that even if the "g"s developed by a Formula 1 car are phenomenal, these are not the most physically difficult cars an up-and-coming young driver will encounter. Which basically means that with enough commitment, acquiring the necessary strength and endurance to drive competitively at the highest level is eminently possible for a woman. It's also well known that there are no sex differences in coordination. And finally, women tolerate exercise-induced heat loads at least as well as men.
In terms of the unknowns, things start to get interesting. For example, the human brain contains receptors for androgens and estrogens - the sex hormones - starting during the embryonic stage. This means that the architectural layout of a baby boy or girl's brain will differ according to the hormonal milieu (among other influences) that it is exposed to during development. It's while obviously well known that learning and experience are key factors in determining patterns of behaviour, these genetic influences on brain development could also be responsible for differences between men and women's brains and therefore behaviour.
Recent and very preliminary work using functional neuroimaging suggest that women process emotional information, and especially the emotions of others totally differently than men. Similarly, the neural mechanisms for perceiving time, speed and spatial orientation seem likely to show important sex differences. While intriguing, these results still need to be confirmed by other research. Meanwhile, we can only wonder if it's here that we need to look to find an answer to the question so indelicately raised by Sir Stirling.
Once again it's Bernie who was right when he in essence said that women have the talent but not the opportunity. It's only when the vicious circle (no women because no sponsors, no sponsors because no women) is broken, hopefully by making the sport more attractive to women, that we can hope to see if the differences between men and women will lead to victories and podiums.