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questions on solenoid voltage and current limitations

So, I am a bit of a nut and bought a couple of the vintage robots a few years ago that were retired from a showbiz. They are pretty crazy. They run on 12v mac air valves. They take a massive air supply and are extremely loud. I am wanting to learn some about solenoids. to do little robotic like movements. I have read about magnetic fields and inductance. It appears that the strongest fields can be acquired by increasing the number of turns, but a larger diameter of solenoid is weaker. So, the smaller wire may be beneficial.

I know that larger wire diameter can tolerate high amperage, and that shorter wire runs have a smaller voltage drop. But, cant a small wire (say 28-30 gauge) undergo huge voltages or current flow for a fraction of a second without issues? What matters? What equations do I use? Do I just go by the heat rating of the wire? Im a little confused on it. I am going for the the best bang for the buck on size so am trying to determine what small wire gauges can tolerate.
 
If you double the voltage on a (100% duty) solenoid you double the pull and quadruple the dissipation, thus you have to reduce the duty to 25%.
A longer thinner solenoid will have a greater surface area than a "square" solenoid of the same mass, so it can be run harder. Fan cooling helps too.
Time is a factor too, the duty periods must not be too long related to the mass of the solenoid. It's the peak temperature that eventually will kill it.
The shape of the plunger tip has very much to say how the pull vs distance curve will look.
 
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