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Thanks for the mechanical expertise! I guess this is an example of how virtual systems have less limitations than mechanical systems, so virtual-system interfaces can be more intuitive.

Can you explain further why "wiring the panel 'correctly' would make the fan take longer to do its job?" Would the fan take longer to get up to speed?

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Actually, it's an example of when it's wise to sacrifice intuitiveness for an economic benefit. I don't see any reason to believe that "virtual" systems are somehow exempt and there is obviously a cost in making something "intuitive".

The answer to your second question is a first-year calculus problem: Voltage=acceleration to some limit, which you can plot as angles over time across time and speed. It might be fun to work a protractor and some graph paper to see how it would differ with more than three settings.

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