What horsepower motor do i need to turn a 40:1 ratio gearbox at 25% over rating with a load of 77.5 fp?

Question

motor is 1745 rpm.

Answer 1

I'm not sure what you mean by "25% over rating", but here is a handy calculator: http://www.ajdesigner.com/phphorsepower/...

if gives 0.64hp for 77.5lb-ft @ 43.6rpm, (1745 / 40)

since there will be some friction in a gear box with that ratio, and allowing for your 25% (though I'm still not sure what you mean), and considering that motors are usually available in  limited increments, a one horsepower motor might be a good choice, 3/4hp  might be a little small, depending on what you mean by the 25%