Bernd: How long do you leave them on the charger?
Much longer than you would a regular rechargeable, Bernt. Up to 24 hours for AAs (which are the ones I'm most concerned with). A typical AA cell has a capacity of just under 3Ah, which is about twice that of a NiMH rechargeable, and because you are using AC it's only being charged for half the time. Actually, rather less than half the time, because the sine waveform needs to rise to 2.2V: 0.7V before the diode will conduct, and a further 1.5V to start pushing electrons into the cell. For the other half of the time the cell is being discharged at about 20% of the charge rate.
The article uses a charge current of about 50mA.
Using 4.5V AC from the transformer, I = (4.5 - 0.7 - 1.5) / R2, where the 0.7 represents the voltage drop across the diode and the 1.5 is the voltage of the cell. So, where R2 is 47 ohms, I = 50mA (almost).
If you have a scrap transformer of different voltage V like 12V, find R2 using the same formula rearranged as:
R2 = (V - 0.7 - 1.5) / 0.05, where the 0.05 represents the 50mA charge current.
For R1, which comes into play in series with R1 during discharge, use the formula R1 = [(V + 1.5) / 0.01] - R2, where the 0.01 represents the discharge current which is set at around 10mA, being 20% of the charge current. During discharge the diode doesn't conduct, so doesn't come into this calculation.
I suppose the resistor ratings need to be increased if a higher voltage is used.
Remember that mains voltage is on the transformer primary
Despite my statement as to "no leaks so far", I don't use the thing on the polished dining table .....