Well, I took some scope photos with the bike in the workstand and spinning the wheel by hand.
I've taken photos with three different loads... one with no load, one with a 20 ohm load, and one with a 10 ohm load. For reference, the standard incandescent dynamo headlight used a nominal 12 ohm bulb.


For the no-load case, there is nothing connected to the dynamo but the scope leads.
The scope settings are 10 volts per division and 5ms per division.
From this, you can see that the amplitude is 26V peak (i.e. 26V from the zero volt position at the center of the screen to the top of the wave). The most obvious thing about the photo is that the waveform is definitely not sinusoidal! Due to the shape of the wave, it's hard to say what the RMS value is.
The period is about 35ms, yielding a frequency of 29Hz. This is equivalent to just a bit over 10mph, which I've measured as being 27.3Hz.
Of course, the relationship between the speed and dynamo frequency is determined by the wheel diameter. In this case, the wheel is 700C, and the tire was 700 x 28.





For a 20 ohm load, the waveform is closer to being a sinusoid, although it looks a lot like a triangle wave. The amplitude has dropped to 10V peak.
The frequency is 21.7Hz, which is a good deal slower than when it was unloaded. This is mostly because it is harder to spin up the wheel by hand when the dynamo is loaded. The slower speed is part of the reason why the voltage is lower, but primarily it is due to voltage being dropped across the dynamo's internal impedance.
Scope settings: 10v/div. 10ms/div.
amplitude is 1 div, or 10V peak.
period is 4.6 div, or 46ms. As such, the frequency is 21.7Hz.




For a 10 ohm load, the waveform is much more like a sinusoid. It draws more current from the dynamo, so the voltage is reduced. The peak voltage is 8V.
The frequency is roughly 23Hz.
Scope settings: 10v/div. 5ms/div.




So how do you predict what sorts of voltages and currents a dynamo will produce at different speeds? Well, each dynamo will be different, so it is hard to generalize. I've made some measurements on this particular SON28.
I did this with a relatively simple resistor network, a digital meter, and just rode at different speeds with different resistive loads, and took notes of the RMS voltage and the frequency.

Here's a shot of the test rig....




and here's the raw test data...




and when it's put into a table, where the voltage, current, and power are calculated, it looks like this:


The highlighted numbers are the max power that can be obtained from the dynamo at each of the speeds. As can be seen, the bike (with 700C wheels) had to be going about 9mph before the dynamo could generate 3 watts into a load that is about 15 ohms.
At 20mph, the dynamo could generate over 7 watts, as long as the load was 40 ohms.

For the sake of circuit analysis and simulation, this data can be used to generate a model for the dynamo. The model is about as simple as possible, so it isn't a perfect match for the test data, but it gets close.
The model is composed of three parts:

1. a voltage source that produces a sine wave whose amplitude is proportional to the dynamo's frequency. This is expressed by the equation Voc = K x f, where Voc is the dynamo's open circuit voltage (i.e. there is no load), K is the scaling constant, and f is the frequency of the AC voltage. I found that K = 0.53 gave me pretty good results.

2. inductance. This represents the inductance of the windings and the voltage drop that occurs when the AC current passes through it. I ended up with 0.145 Henries.

3. resistance. I got the best match between the model and the test data when I used 2.8 ohms for the dynamo's resistance. When I measure the resistance of the windings with a meter, I think it is closer to just 2 ohms.

The model is composed of these three elements wired in series.

This might be the longest post I've written on bikeforums, so I may have overlooked something or committed some other error. Let me know what I've missed or got wrong.


Steve in Peoria