Ok, I was conflating two issues and being sloppy with my words earlier. Let me try again...
Looking at the waveforms, I am certain that the output from the dynamo is being rectified onto a capacitor in the lamp. This explains why there is no current flow below about 4V (No current will flow until the dynamo voltage is higher than the voltage on the capacitor.
Yes, definitely a rectifier in there, and a capacitor on the other side of it. The bigger question is what does the load beyond those look like?
And I'm suggesting that the answer is a diode, in terms of its current-voltage response. This basically means that it consumes very little current until you approach a threshold voltage, then quickly consumes a lot as you try to rise beyond that. Partly because that's what you'd expect from an LED and partly because it would explain the currents seen.
So if you are really putting in 7.4V, then you should be seeing full brightness. However, what is not explained is why you are only measuring 190mA (1.4W). What are you measuring the current with?
Well, if my hypothesis is correct then the current consumption is highly sensitive to voltage in this region. So if you were to apply 7.5 or 7.6V then the current would be significantly higher than 190mA.
You don't need a current limited source - there must be internal current regulation in the light, or the LED would only last milliseconds.
What I meant was a source which was actively controlled to limit current,
not apply a fixed voltage. i.e what I should have called a
current source. The point here is that because the load is very sensitive to voltage, if you were to try and apply any given
voltage source then you may end up with significantly different currents. The variation largely is due to manufacturing tolerances, and temperature change. So you ideally want a circuit that varies the applied voltage in order to achieve a given current supply accurately.
They are suggesting a conservative voltage limit because they're afraid someone might not understand the above, and want to keep them on the safe side of the actual limit. What isn't clear is what the real current/power limit is. My guess is it's thermal, and they don't want to say what because it depends on airflow and they want to clearly make sure they've recommended something is safe when homebrew nutters come back and blame them after they fry their LEDs.
There is a bit more information about the upper limit protection, and about applying dc, if you read down the quoted messages in the post I linked before.
It's a lipo battery with some circuitry, but clearly it's not current limited as it will happily supply two pairs of Ay-Ups at almost 300mA each = four times the current drawn by the Cyo.
It's not a case of a magic current limit for the battery - the battery has an effective internal impedance and voltage and this in combination with the load determines current. The highest current it can supply is when it's shorted and is only outputting at 0V. At open circuit with no current it will give largest voltage. As soon as you draw some current it goes down, but the result is highly dependent on the load I-V curve.
Assuming you don't have a bench power supply to check dc current against voltage, can you redo your test with a fully charged and a very low battery? And at the risk of being insulting, can I check you're measuring the battery voltage when loaded in both cases, not open circuit?
Similarly for your 7.4V answer - was that open circuit or at 190mA?
I just find it a bit hard to visualise. If I cut the wires and touched them alternately very very fast (creating a crude AC source, like a dynamo) the light would suddenly draw over 500mA?
No. Well, except in the instantaneous sense Kim said.