Cessna 172M Skyhawk Performance Numbers

[Wm D. Cleveland]

A 172M has been set up for straight and level slow flight. You want to climb at 500 feet per minute. What is the RPM number that you use to get 500 feet per minute climb?

Would you increase the RPM by 500 RPM (ie 100 RPM for each 100 feet of vertical velosity)?

[canasdad]

As an Indian friend said recently, "That is an imponderable".
There is no rule that I know of, or would espouse. Why? Each airplane and circumstance is different. Different models, engines and loads plus speed at slowflight and flaps if any will all give different answers.
So, don't worry about it. Use the old rule that more power makes you climb and raise the RPM slowly until you get to the climb rate you want. You will probably overshoot on the first try, and have to adjust. If you fly a particular airplane long and often enough, you'll get to know it well enough to roughly guess how much to adjust power.
I sympathize with your attempt to reduce everything to reproduceable numbers - I am an engineer and thats what I do for a living. But the guess again priciple is the modus operendus here. It ain't graceful, but it works.