P-factor is a differential thrust across the face of the blade due to localized changes in relative velocity and angle of attack. Sadly in most literature being published, only the angle of attack portion is being taught. First pardon my old school English measurements; I never made the transition to metric ;-)

A propeller spins at a certain RPM, for our discussions let’s only look at the tip of the propeller. For a given RPM the propeller tip is moving a specific velocity in feet per minute. For example a 4-foot propeller the tip is 2 feet from the hub. The distance the prop tip is traveling is the circumference of the circle or PI x D; (3.1416 x 4 = 12.58 feet) Now if the engine is turning a typical 2400 rpm on a Cessna type aircraft, the tip speed works out to 12.58 feet (one revolution) x 2400 revolutions per minute or 30, 200 feet per minute or for smaller units (dividing the minutes by 60) 503 feet per second. (88 feet per second equals 60 miles per hour) so the prop tip is doing 340 miles per hour.

Lift is a function of the following equation: Lift (or in the case of a propeller Thrust)
T= ½ CL ρ V2 A
CL is the Coefficient of lift. The CL is a function of the airfoil shape and its angle of attack; this is determined by wind tunnel work.
ρ RHO the density of the air
V2 the velocity through the air squared
A area of the wing. In the case of a propeller it gets more complex because there is an integration of the different angles of attack and speeds along the length of the blade. If we confine our discussion to just the tip, we only have to work with one value. Note that the Velocity is a squared value in the equation so a little a small change in velocity causes the most change in lift.

An airplane in a steady state climb, at a constant angle of attack (say 5 degrees and a constant airspeed (say 120 mph or 176 fps) causes the propeller to strike the on coming are at the same angle of attack the as the wing. From vector analysis that on coming airflow has a component that acts perpendicular to the front of the propeller and a vector that acts in the plane of the propeller’s rotation. If our airplane has a 5 degree angle of attack then from trig, the component of the in coming 120 mph air is 10.4 mph acting in the plane of the rotation, and 119.4 MPH perpendicular to the plane of rotation. We only need to focus on the 10.4 mph component.

As the propeller rotates in this in coming air it sees that 10.4 mph component reverse direction. At 12 and 6 o’clock it is zero, at 3 o’clock it’s PLUS+10.4 mph, at 9 o’clock it’s MINUS-10.4 mph.

Now add these two values to the propeller tip speed from the above discussion. At 3 o’clock the prop tip now has a speed of 350.4 MPH (340+ 10.4) and at 9 o’clock the tip now has a speed of 330.6 MPH (350-10.4) if we plug just these two values into our equation above

T= ½ CL ρ V2 A

And use an arbitrary 0.1 for CL, 0.01 for RHO and 10 for area we get
T @3:00=(.5)(0.1)(0.01)(350.4)(350.4)(10)=1,227 pounds of thrust (not a real number because of using the “1s” just something to work with)

But at the 9:00 position
T @9:00=(.5)(0.1)(0.01)(330.6)(330.6)(10)=1093 pounds of thrust

A difference of 134 pounds of thrust pulling harder at the right propeller tip causing a turn to the left.

And that is only due to the difference in rotational velocity. Buried in the CL term is the angle of attack. It to changes as the prop spins by +/- the 5 degree incoming air. Its effect are additive to the rotational values.

That is where P- factor comes from. Now for the first curve ball the strongest thrust is at the 3:00 position, that causes the highest airflow down the right side of the fuselage.

But due to gyroscopic precession it also pulls the nose of the airplane up!

Drat, I did this in word, and I just noticed the symbols dissappeard