Windsun said:
Actually, in most places the best overall angle is around 30 minutes
after solar noon, due to the presense of morning haze in most places.
However... if you are pointed due south vs about 10 degrees either way,
the difference in power production is less than a 5% difference.
Now I'm not sure I understood the original question. When Gym* said
he heard the answer was "noon," I thought back to George Ghio's claim
that on a particular day, a fixed panel aimed south with an elevation
aimed at the noon sun would produce the most energy over that day.
George was wrong, of course, in the sense that a panel like that would
produce the highest instantaneous power at noon on that day, if it's
perfectly clear, when the cosine of the incidence angle is zero, but
a panel aimed closer to the horizon would likely produce more energy
over that day, with less power at noon and more at other times. Then
again, noon sun is brighter than morning and evening sun, on average,
since it travels through less air. And over a perfectly overcast
isotropic-sky day, a horizontal panel would produce the most energy.
But now it appears the question concerned azimuth vs elevation...
The drop off in power vs angle is a function of the cosine of the angle.
The power is proportional to the cosine of the solar incidence angle, ie
the angle between the sun and a perpendicular ray from the panel, which
depends on elevation as well as azimuth. That's close to the cosine of
the azimuth angle for small azimuth changes, but not exactly proportional
to the cosine of the azimuth angle.
So at 10 degrees sun angle you lose around 1.5%. At 30 degrees you lose
13.4%, at 45% you lose 30%. The 50% power loss point is 60 degrees...
Cos(60) = 0.5. This works if the sun has the same elevation all day

It might also work if we assume the panels change their fixed elevation
as they change their fixed azimuth. Max-energy East- and West-facing
panels would be closer to vertical.
Nick