Quoting DH106 (Reply 16):
*There's also a secondary effect - which I think is the effect I was addressing - that stems from the fact that the inner blade is closer to the CG than the outer (whether they be rising or falling).* |

Yes, P-factor. I'm sure 113312 is willing to spell out all the gory details.

The effect depends not on the distance from the CoG but on the downgoing blade getting a higher angle of attack than the upgoing blade if the angle of attack of the aircraft increases. Thus the downgoing blade generates more thrust than the upgoing blade, setting up a thrust assymetry over the propeller disc which generates a yawing force couple (torque).

Quoting DH106 (Reply 16):
*This yaw moment would decrease as the ratio of engine distance from CG to distance between rising and falling blade increases.* |

Ah, this is where you go wrong. The P-factor yaw moment will not be changed by where you put the engine. Let's do the math.

Assume that you have an engine generating thrust T at a distance y from the center of drag.

Assume that the propeller of this engine can be represented by a model having two thrust forces, T_d and T_u 1 m apart, thus at the distances of (y+.5) (T_d) and (y-.5) (T_u) from the center of drag. T_d is the thrust force from the downgoing half of the propeller disc and T_u is the thrust force from the upgoing half of the propeller disc.

At an angle of attack where the propeller will be at a positive angle of incidence, this will make it the critical engine, with more thrust being generated further out along the wing.

Assume that T_d is 0.6*T and that T_u is 0.4*T, for a total thrust of T.

Any moment on a rigid body around any axis can be calculated about any point, for the same result. Let us calculate the moment about the center of drag.

n = T_u * moment arm + T_d * moment arm =

= 0.4*T*(y-.5) + 0.6*T*(y+.5) =

= 0.4*T*y - 0.4*0.5*T + 0.6*T*y + 0.6*0.5*T =

= (0.4+0.6)*T*y + (0.6-0.4)*0.5*T + 0.6*T*y =

= T*y + .2*.5*T

T*y is the torque generated by the thrust, as you can see independent of the thrust assymetry over the disc and thus of the P-factor**.

This leaves the torque generated by the P-factor as .2*.5*T, or the distance between the thrust lines of the propeller halves times the thrust difference between them. The position of the engine is not a factor in this term.

To make it even clearer, replace the arbitrary figures for propeller half thrust line distance and thrust difference with constants. This is left as an excercise for the reader*.

Cheers,

/Fred

**) If you chose to look at the yaw torque about the engine instead, you would not get this term but, if the condition is steady flight and that is the only engine (T=D), an equal term D*y for the torque generated by the drag. Recall that the net torque on a rigid body is constant regardless of what point you calculate it about.

*) As always, this means "I cannot be arsed"...

I thought I was doing good trying to avoid those airport hotels... and look at me now.