would have been adj. had?

Question

The massive influx of women cyclists-making up at least a third of the total market- was perhaps the most striking and profound social consequence of the mid-1890s cycling boom. Although the new, improved bicycle had appealed immediately to a few privileged women, its impact would have been modest had it not attracted a greater cross section of the female population. It soon became apparent that many of these pioneer women bicyclists had not taken up the sport as an idle pastime. Rather, they saw cycling as a noble cause to be promoted among all women as a means to improve the general female condition. Not only would cycling encourage healthy outdoor exercise, they reasoned, it would also hasten long-overdue dress reform. To feminists, the bicycle affirmed nothing less than the dignity and equality of women.

There is a sentence

... its impact would have been modest had it not ...

I can't understand what grammar of "would have been adj. had" is?

Answer 1

The construction its impact would have been modest had it not attracted a greater cross section of the female population is an example of a "reduced conditional". In this case it is the reduced, and more formal, version of the so-called third conditional:

Its impact would have been modest if it had not attracted a greater cross section of the female population.

The reduced conditional is often found with the protasis (the if-clause) first:

Had it not attracted a greater cross section of the female population, its impact would have been modest.

There is a brief section on reduced conditionals on the BBC webpage dealing with inversion. Here is one of its examples:

Had I stayed longer, I would have learned a new language.

Answer 2

... its impact would have been modest had it not attracted a greater cross section of the female population.

Normally the protasis of a conditional has the form of a PP with if as head and a content clause as complement.

But with remote conditionals with "has" (and "were") it is sometimes possible for it to take the form of an ungoverned content clause with subject-auxiliary inversion.

It’s the equivalent to if it had not attracted a greater ...