P-factor

P-factor, also known as asymmetric blade effect and asymmetric disc effect, is an aerodynamic phenomenon experienced by a moving propeller,[1] that is responsible for the asymmetrical relocation of the propeller's center of thrust when an aircraft is at a high angle of attack. This shift in the location of the center of thrust will exert a yawing moment on the aircraft, causing it to yaw slightly to one side. A rudder input is required to counteract the yawing tendency.

Causes

When an aircraft is in straight and level flight at cruise speed, the propeller disc is perpendicular to the relative wind. Each of the propeller blades will contact the air at the same angle and speed and thus the thrust produced is evenly centered across the propeller. As the aircraft's angle of attack increases and the propeller disc rotates toward the horizontal, the airflow will meet the propeller disc at an increasing angle. The propeller blades moving down and forward (for clockwise rotation, from the one o'clock to the six o'clock position when viewed from the front) will have a greater relative wind velocity and therefore will produce greater thrust, while propeller blades moving up and back (from the seven o'clock through 12 o'clock position) will have a decreased relative wind velocity and therefore decreased thrust.[2] This asymmetry displaces the center of thrust of the propeller disc towards the blade with increased thrust. In an aircraft with two or more propeller engines, P-Factor is what determines which engine is the critical engine.[3]

P-factor, change of relative speed and thrust of up- and down going propeller blades at increasing angle of attack

P-Factor is sometimes erroneously explained with the word "bite", as in "the descending blade has a bigger bite, or angle of attack, than the ascending blade". This faulty explanation does not take into account the forward motion of the blades as aircraft's angle of attack increases. In order to better understand this concept, imagine a propeller aircraft moving forward with a 90° angle of attack (vertical). This situation is identical to what a helicopter experiences, but a helicopter can reduce or increase the angle of attack of individual blades of the rotor (decreasing the angle of attack on the advancing blade, while increasing the angle of attack on the retreating blade) in order to keep the lift of the rotor disc balanced. Because the force of the air on the blades moving forwards through the arc is greater, they will produce more thrust than the blades that move backwards. If the blades of the rotor were unable to independently change their angle of attack there would be a constant backwards rolling motion due to the increased lift on the side of the rotor disc with the advancing blade. [4] In a fixed-wing aircraft, there is usually no way to adjust the angle of attack of the individual blades of the propellers, therefore the pilot must contend with P-Factor and use the rudder to counteract the shift of thrust.

Effects

Single engine propeller aircraft

(As viewed by the pilot), the aircraft has a tendency to yaw to the left if using a clockwise turning propeller (right hand), and to the right with a counter-clockwise turning propeller (left hand). The clockwise turning propeller is by far the most common. The effect is most noticeable during the climb phase after take off[5] and in flight conditions with high power and high angle of attack.[1]

Confusion about the effect of P factor exists due to gyroscopic precession. The asymmetric thrust produced by the descending blade produces a force to the propeller disc at an average location of 3 o'clock. The resultant force due to precession therefore acts on the propeller disc at 6 o'clock, causing a pitch up tendency as opposed to a left yaw tendency, as traditionally thought.

Multi engine propeller aircraft (clockwise rotation)

As with single engined aircraft, situations where the aircraft is at high power and has a high angle of attack (such as take off) will cause a slight, but noticeable yawing motion. The engine with the down-moving blades towards the wingtip produces more yaw and roll than the other engine, because the moment (arm) of that engine's thrust about the aircraft center of gravity is greater. Thus, the engine with down-moving blades towards the fuselage will be "critical", because its failure and the associated reliance on the other engine will require a larger rudder deflection by the pilot to maintain straight flight than if the other engine had failed. For most aircraft (which have clockwise rotating propellers), this is the left engine.

With engines rotating in the same direction the P-factor will affect VMC's, the minimum control speeds of the aircraft in asymmetric powered flight. The published VMC's are determined while the critical engine is inoperative. The actual VMC's after failure of any other engine is lower, safer, provided the pilot is aware of the limitations that apply with minimum control speeds.

Considering right-hand tractor engines (lines projecting from propeller discs represent the P-factor induced thrust lines):

At low speed flight with the left engine failed, the off-centre thrust produced by the right engine creates a larger yawing moment to left than the opposite case. The left engine in this scenario is the critical engine, namely the engine whose failure brings about the more adverse result. In the case of using counter-rotating engines (i.e., not rotating in the same direction) the P-factor is not considered in determining the critical engine (the engines are equally critical).

The asymmetric blade effect is dependent on thrust, and is proportional to forward velocity (specifically CAS) and, while generally insignificant during the initial ground roll for tail-wheel aircraft, will give a pronounced nose-left tendency during the later stages of the ground roll, particularly if the thrust axis is kept inclined to the flight path vector (i.e. tail-wheel in contact with runway). If a high angle of attack is used during the rotation (or indeed straight and level flight with high power and high angle of attack), then the effect can also be apparent. The effect is not so apparent during the landing, flare and rollout, given the relatively low power setting (propeller RPM). However, should the throttle be suddenly advanced with the tail-wheel in contact with the runway, then anticipation of this nose-left tendency is prudent.

See also

References

  1. 1 2 (Willits 3-49)
  2. ↑ Stowell, Rich (1996). Emergency Maneuver Training. Rich Stowell Consulting. pp. 26 – 28. ISBN 1-879425-92-0.
  3. ↑ Airplane Flying Handbook FAA-H-8083-3. Federal Aviation Administration. 1999. pp. 14–2.
  4. ↑ Rotorcraft Flying Handbook. Federal Aviation Administration. 2000. pp. 3–6. ISBN 1-56027-404-2.
  5. ↑ (Ramskill)

Bibliography

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