Doing it a bit more exactly, and taking maximum values for the open circuit voltage and minimum internal resistance of a new battery off the net as 12.9 Volts and 0.02 Ohms, with the pull-in coil at 0.25 Ohms and the hold coil at 0.76 Ohms, the maximum surge current, when there is no other load on the battery but the two starter coils is as follows:
12.9 / (1/(1/0.25 + 1/0.76)+0.02) = 12.9 / (0.188+0.02) = 62 Amps.
The sustained current is much harder to do exactly without a value for the minimum cranking current. But I think it's widely accepted that 10 V is about all you can expect as a supply voltage while cranking (implying a cranking current of 145 Amps with an internal resistance of 0.02 Ohms), and the maximum sustained current through the hold coil is just 10/0.76 = 13.2 Amps. It might be a bit more, but it's nowt like the 62 amps of the surge.
However, those are for a new, freshly charged battery at STP (possibly NTP) probably after a couple of attempts to start have warmed the solenoid coils - when the battery ain't fresh charged anymore. But first thing in a morning after the car's been stood all night, resistances will be higher and voltages lower and the currents smaller.
So, with those values, 62 Amps is top value for surge current.
Maybe someone else knows how fast the solenoid pulls in, so what the duration of that surge would be. Then, given the resistance of the switch contacts, we could calculate the approximate maximum power dissipated in the switch, and, given some details of its thermal properties, etc. what that means. But I'm guessing that's all a bit much to ask.
But I still wonder if the cause of damage to the ignition switch isn't, at least in part, arcing across the contacts when the current to the solenoid is shut off, when you let the key spring back to run position. Problem is, I have no idea of the inductance of the hold coil nor the resistance, capacitance, and inductance of the wiring from the switch to the coil (which will disperse the Heaviside step function of the switch current to a sigma function at the coil, and attenuate the return voltage as well). So, all I know for sure is di/dt at the switch, which is infinite and a guess that the resistance, capacitance, and inductance of the wiring are all bugger all. I'm also guessing at the speed of propagation in the wire at about 2/3 C, so the return pulse is about 5 to 10 us after the switch opens. But even so, that the back EMF at the switch is above the magic 327 Volts when the contacts are the 7.5 um of the Paschen minimum (at STP) apart seems reasonably credible to me.
So, as well as isolating the ignition switch from the surge current while the solenoid pulls in, a relay will protect it from the back EMF from the hold coil when the contacts open. I'm guessing that most good relays will be reasonably reliable even when the load's a bit inductive.
Graham
_________________ The 16v Slant 4 engine is more fun than the 3.5 V8, because you mostly drive it on the upslope of the torque curve.
Factory 1977 TR7 Sprint FHC VVC 697S (Now all of, but still needs putting together)
B&Y 73 Dolomite Sprint UVB 274M (kids!)
1970 Maroon 13/60 Herald Convertable (wife's fun car).
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