Chris
your assessment assumes i have not built and done such testing
what you state is patently false, and here is the reason
if you take a machine such as a 12 inch neo rotor job typical of those built here, (for the sake of discussion)
now rotate the rotor very slowly past one of the stator poles, and measure the voltage of that poll. you will find it to be very low
now speed the rotor up and you will find the voltage to increase, \
everything is the same, the magnets have not changed, so the magnetic flux has not changed, the coil has not changed so the flux linkages have not change, only thing that has change is the velocity, so...
velocity certainly has a function here.
lets do a little mental experiment here.
lets take a bicycle wheel that is say 24 inches in diameter, we will also affix to the wheel a smaller diameter wheel made of plywood that is 12 inches in diameter, when spinning both rotor turn the same speed in rpm, however rim speed of the outer rim is double that of the inner 12inch rotor.
if we affix the inner 12inch rotor a magnet, and using an arm to affix a coil with 30 thousand clearance, and we turn the wheel at 100rpm we end up getting X volts. the magnet passes the coil in this test at ~3770 inches per minute.
now if we move the magnet to the outer 24 inch rim, and move the arm which mounts the coil to the outer position, and set the clearance to 30 thou as the first test, and turn the wheel at 100rpm the impressed voltage will be proportionally higher at around ~2X volts. the reason being we have an outer rim speed in this case that is twice that of the previous test which is now ~7540 inches per minute.
this is no different than if we were to go back, remount the magnet to the inner rotor, and move the arm that mounts the coil, set the airgap, and then turn the wheel at 200rpm, the voltage will now be approx twice that of what it would be when turning at 100rpm.
there really is no difference!
my only point is we cannot summarily dismiss the effect of diameter on the voltage produced, diameter has a function in the formula, or at least can when it comes to designing an alternator.
one last point before i get told to go out and build something to prove your point.
long ago i learned from an instructor smarter than most of us will ever be, he posited this
"why do we draw, or use drafting, instead of just going out to the shop and building something?"
the answer
"paper is far cheaper than any building material"
now this doesn't have direct application here, but i figure it has a correlation when it comes to design of any machine.
"we study, we research, we learn and use theory/formula etc. we then draw it out on paper, use logic and when all else fails and we can't get the answer we need we then go out in the shop and build"
otherwise we never learn why something works, or perhaps more importantly why it works better than some other way. we can certainly determine if something works, but we generally cannot quantify or qualify our findings in a manner that anyone else is going to understand. we certainly cannot predict with any certainty what effect a change might make in a design before building it.
now having said all that,
i would not expect a doubling of voltage with a doubling of diameter, because of the time factor between poles, the gaps between the poles (assuming the same pole count as a smaller diameter unit) will certainly impact the change in voltage to the point the we won't generally see a doubling, but with careful design we can see an increase.
this was all i was saying to start with, we cannot summarily dismiss diameter effects on generated voltage.
now if we want to talk about what increased diameter allows in design, that would be a useful topic in my opinion.
bob g