How does the change in the pitch of the prop affect the plane, and how do you decide on which one to use. Or do you have to invest in something like Ecalc or motocalc.

Generally you use a higher-diameter, lower pitch prop for better climb and acceleration, and use a lower-diameter, higher pitch prop for more speed. The best place to start is in the range that your engine manufacturer recommends, and move on from there depending on what it is you want to do. The one investment you should make is in a variety of prop pitches/diameters that are appropriate to your engine. That'll let you feel the differences for yourself, and allow you to pick the one that best suits your style of flying.

I would have to agree with MikeL on the prop selections and getting yourself some test props. But if you really want to get scientific, along with the multitude of props to test based on the manufacturers recommendations, get a tachometer. This will help to find the maximum safe range for your engine.

I'd hate for you to go beyond the RPM range and burn-up/seize your engine. Yeah, the ears work, but if you have a 4-stroke, forget it! It’s generally harder to tune a 4-stroke compared to a 2-stroke, unless of course you have years of experience with a 4-stroke or have seized enough of those to know better.

My 4 cents…

How about within the the same diameter prop? If the pitch increases does speed increase and acceleration decrease?

raabid, the answer is yes.

Example:

10x7 slow acceleration but high speed
10x4.7 high acceleration but slow speed

One more and I'll leave you guys alone. If I take the same pitch prop and change only the diameter what will that do, provide my motor would handle it.

That will increase the thrust.

If you spin them at the same RPM, a larger diameter you will increase thrust, a smaller diameter will decrease thrust.

So if I was making a really heavy slow flyer that I wanted slow easy turns but ROG capability, I would go with a high gear 5:1 with a huge low pitch prop 10-11X5-6. Right?

Uhhh, how heavy is the plane? Plus be sure that your esc can handle the amp draw from the motor. What size battery pack are you running with what motor? Not knowing what cells, plane, esc, motor or battery you're running, I would guess the 10x 4.7 or 9x5 would be a good starting point?