The copper cabling is the heat sink for the contact point in the connector. To prove this you can take something like a PP45 (Anderson Power Pole rated for 45A)
Attach 22AWG to one pair
Attach 10AWG to another pair
Run 10A continuous, check
Run 20A...
Run 30A...
Run 40A...
You will find that the exact same connector tied to 10AWG will tolerate much higher current than the connector terminated in 22AWG. Good connectors are actually specified to a given current ONLY when attached to a minimum gauge wire.
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So the point there, is that Heat is the issue you are addressing and that is I^2*R, so your current squared times your contact resistance.
The contact patch is basically constant, but the current (in the formula) is the AVERAGE running current. On an ebike (most ebikes) your average current will be quite low. Off the line you may dump gobs, but once the motor catches up the draw will fall back. If you are riding regularly (not going nuts) then ... you can pretty much run anything reasonable.
If on the other hand you are heavily over-volting, you have a soldered shunt (over-burst-currenting) you may actually get to the point where you can melt off a connector.
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The phase wires are small, but they run a high temperature insulation (teflon) so - ... the wires will likely not melt, but they also will not pull much eat away. I run 10AWG phase wires, but most controllers come with something much smaller.
Eh...
Just run a connector rated for 40A continuous and you will likely be fine. I have never melted an Anderson on a phase lead, even wired to pinner wires. I run (or ran) a hundred volts with 40 or 80 battery amp limit.
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Focus on Power instead of Current to simplify things.
A Kilowatt
2KW
3KW
4KW...
If you are seeing a KW or two on your battery side it will not be a big issue. Your motor will probably overheat FAR SOONER than your motor connections will. That is what I have found, but - that was dry. These days everybody runs oil in their motor or some kind of aggressive cooling.
While selecting a connector remember that you may have to sort the phases (when you change setups or controllers). This is why we originally used Anderson's
Good luck, let the smoke out of it.
-methods