This post was triggered by a relevant discussion on the subject and the asymmetries in a SHSS that might be encountered in a prop aircraft.
There are a number of different propeller induced effects on the weathercock stability (Cn_beta) and dihedral effect (Cl_beta) of an aircraft. Although no rule of thump is applicable, the following provide some general tendencies.
Yawing moments (Prop effect on Cn_beta)
i) Prop normal force
Due to the airflow momentum directional change in a sideslip, the prop normal force (or sideforce) is the most significant contributor to the yawing moments. For the case where prop is fwd of CG the force is destabilizing both for left and right sideslip. No significant asymmetries are expected due to this effect.
ii) Spiraling slipstream
It is the result of the air circulating around the aircraft because the propeller imparts such motion to it and its magnitude and effect varies greatly between aircraft designs and flying conditions. The rotating air changes the direction of the local airflow at the side of the fuselage and vertical stabilizer, causing a yawing moment to the left (for clockwise prop rotation).
During wind-tunnel studies spiraling slipstream yawing moments are found to be much more significant to other asymmetric prop phenomena (p-effect). In straight level flight this asymmetry is counterbalanced by rigging, in side-slip flight some asymmetry is expected.
When the airflow into the propeller is n’t perpendicular to the propeller plane or disc, the thrust produced is n’t symmetrical about the disc. Again this varies significantly with flight conditions. Its asymmetric effect during most flying conditions is expected to be smaller than slipstream, and it could be argued than due to side-slip (side AoA) the p-effect is now encountered over the pitch axis, as the left going blade sees a different AoA than the right going blade.
iv) Other effects
Engine torque, gyroscopic precession and thrust axis offset. These effects are generally minor for our case, however it is important to note the coupling between roll and yawing moments, meaning that an asymmetry in roll moments due to torque or other effects resulting in different aileron deflections during the L and R side-slip will eventually be translated in yawing moment asymmetries due to aileron drag. Same with rudder deflection and rolling moments.
Rolling moments (Prop effect on Cl_beta)
A side-slip may induce a rolling moment with power-on because the slipstream
strikes more wing. Spiraling slipstream may contribute to a rolling moment if it alters the direction of the airflow over the wing.
In conclusion from all the above, my opinion is that the most significant factor in SHSS asymmetries encountered in prop aircraft is the spiraling slipstream and its interaction with the aircraft geometry.