Bally tends to operate at 43v, not 24v like other ems

I don't think you'll find much info on a DC equivalent, not something people trend to need to know.

That's a big question, and experimentation as you suggest might be the best answer.

Any coil will 'work' at any AC or DC voltage in the sense that when you put current through the coil, it will generate a magnetic field. So the coil itself does what it can with the available current. It gets complicated though when you try to harness that magnetic field into something useful with a mechanical linkage of some sort. Unless the magnetic field generated by the coil is strong enough to overcome the springs, armatures, plungers, levers, etc. that it's trying to move, the energy put into the coil ends up generating heat rather than motion.

On a relay for example, any current run through the coil is wasted until it reaches the level where the generated magnetic field can overcome the strength of the armature spring, the inertia of the armature and the tension of the switch leaves. It's like opening a glass jar for the first time. You can twist the lid a fair amount with no result until you apply enough torque to overcome the seal. Only then will the mechanical things start 'working'. Solenoids that pull plungers have the same problem, just more so. The solenoid's magnetic field has to overcome more spring tension and the inertia of moving parts.

Once you've supplied enough current to get things moving, there's still room for improvement. More current will make the relay or solenoid more reliable, or snappier, or more able to launch the ball up the ramp, etc. How much extra current is necessary above the minimum will depend on the situation. And of course at a certain point more current won't improve performance on some devices any more, it'll just make things run hotter.

When applying AC vs. DC current to the coil, you probably can get away with a lower voltage with DC than with AC. That's because the current from an AC supply spends a lot of the time at or near zero since it crosses between positive and negative many times per second. DC is constant so there is no time when the current drops. If you're using DC on solenoid coils you'll want to include diodes across the solder lugs to minimize arcing across whatever switch (mechanical switch or transistor) is turning the current on and off.

/Mark

Yep

A coil that's driven by AC has a higher resistance (actually impedance) than the same coil driven by DC. Therefore 24v DC will provide a greater current through the same coil than 24v AC. The force of a coil depends on current and number of windings.

In my experience an AC coil will start working at somewhere between 6v or 12v. Best way to test is to use a Lab power supply and just turn up the voltage.