I hesitate to respond, and probably wouldn't, but I may need to explain what I meant. There is a pitch stated by the maker and then "Effective Pitch - The forward distance the prop actually moves on each revolution when operated in air."
The effective or mathematical pitch uses lap time, rpm, and distance traveled and then the effective pitch is calculated. Distance traveled would assume level flight and radius of handle to fuse center. It helps me estimate what rpm I might start at for a given line length or for changing line length, of when starting a setup. I have used that information for years before running across the term effective pitch and thought of it as calculated pitch. Using others data in "List your setup" will calculate fairly close to correct rpm and lap time, though in the end it is still trial and adjustment.
The effective/mathematical pitch of the 13 x 4.5 and the 13 x 4.5 F2B are different and I don't have to understand all of why to calculate motor rpm settings. The calculated or effective pitch of the F2B is closer to 5.5 than 4.5.
When discussed by email with APC a couple of year ago, there was some agreement with the concept and I excerpt the following reply. That reply may not be the definitive answer, but I was mostly using their props so asked them my questions.
"The pitch quoted on our propellers is in terms of the classic definition, forward travel per revolution.
In practice, the forward travel can be higher or lower than this number. It can be higher, because the airfoil produces lift and helps advance the propeller forward beyond the theoretical cork-screw value, even when slip is accounted for.
The pitch, flight rpm, and distance covered cannot be used to calculate flight speed for the above reason.
The 'effective' pitch (which will include slip, airfoil lift, airframe drag, etc.) can be calculated as you describe below.
The 12x6EP and 12x6EP(F2B) use different airfoils. The F2B prop is a thinner version of the 12x6EP. When the blade thickness was reduced the camber of the airfoil increased. Although the pitch has not changed, the F2B prop will produce more lift at the same rpm, this will result in a higher airspeed."
The formula is based on simple math not from the web or from calculators. I have tried the numbers of effective pitch is calculators instead of stated pitch for my interest and it seems to bring the simple calculators, such as E-Calc, closer to real life. I don't depend on them.
The calculation involves observed/measured data and math and does not try to explain the observation or how propellers move through air, nor does the effective pitch suggest which propeller would fly an airplane most desirably.
Dennis, sorry that my replies have turned to a hijack of the thread; didn't or don't mean to start a controversy.