Pilot Courses of Instruction

Aerodynamics

P-factor, Torque, Propwash, and Gyroscopic Precession

The Four Elements of Power-Based Directional Instability

P-Factor

P-factor, also known technically as "asymmetric blade effect" and "asymmetric disc effect," happens when a propeller-driven aircraft is flying at a high angle of attack. The "high" angle of attack occurs, in this instance, when the angle of attack (of the airplane; i.e., the airplane's wings) is great enough to cause the angle of attack of the propeller blades to vary during the course of the rotation of the propeller. The varying angle of attack of the propeller blades results in the center of thrust of the propeller to be offset to one side of the centerline of the aircraft (for single-engine aircraft or centerline thrust multiengine aircraft) or of the nacelle (for multiengine, non centerline thrust aircraft).

Technically, this is referred to an an "asymmetrical relocation of the propeller's center of thrust." This is similar to what happens when a helicopter moves forward in flight, during "translational lift," with the center of lift moving towards the side of the advancing blades, as those advancing blades create more lift than the retreating blades (and more lift is created overall than from a stationary aircraft). Given sufficient forward airspeed the helicopter will roll uncontrollably toward the side of the retreating blades.

Causes of P-Factor

When an aircraft is in straight and level flight at cruise speed, the propeller disc will be normal to the airflow vector:

• "normal" being a term from physics, meaning "perpendicular to," as in
  • "the normal force is the force that acts perpendicular to the surface of which an object is resting"
• "airflow vector" — also a physics-based term — meaning what is otherwise termed the "relative wind," meaning that the extended centerline of the engine(s) along the crankshaft (i.e., "the centerline of the engine") is directly into the relative wind.

The airplane is designed this way, which directly implies that the centerline of the engine would be so situated as to not be offset — vertically, up or down — from the longitudinal axis of the aircraft (the line from the nose to the tail, the roll axis), assuming the longitudinal axis is parallel with the direction of flight at normal cruise.

As selected airspeeds are decreased, to maintain level flight the wing angle of attack is increased, and the engines(s) will begin to point upward; therefore, airflow will meet the propeller disc at an increasing angle, such that horizontal propeller blades (i.e., the individual blades when horizontal in their rotation) moving down will have a greater angle of attack and relative wind velocity and therefore increased thrust, while moving up will have a reduced angle of attack and relative wind velocity and therefore decreased thrust. Vertical blades (i.e., the individual blades when vertical in their rotation) are not affected. This asymmetry in thrust displaces the center of thrust of the propeller disc towards the blade with increased thrust, as if the engine had moved left or right from the longitudinal axis or in or out along the wing. Regardless, the effect of this will be yaw in the direction of the reduced angle of attack.

Torque

Torque is the force that tends to change the rotational motion of an object. When an object is made to rotate (a screw being driven by a screwdriver, for example), the screw is subject to torque. Likewise, when the propeller is rotated, it is being subject to torque. Not surprising, perhaps, is the fact that the propeller would prefer to stand still and rotate the airplane (or helicopter, powered-lift aircraft, blimp, etc.). The resulting counter force must be countered. Fortunately, the airplane itself is far more massive than the propeller, so the propeller's force on the aircraft is quite small in comparison to the aircraft's force on the propeller. Aircraft also have various surfaces that mitigate against rotation, such as wings and tails. The way this plays-out is a yawing movement in the direction in which the aircraft is being rotated.

Propwash

Propwash is the effect of the rotating propeller moving air not just directly backward but also in a corkscrew fashion. The corkscrew rotation is in the same direction as the rotation of the propeller, arrives at the rudder on the same side as the downward moving propeller, and deflects the nose of the aircraft toward the downward the same side as the downward moving propeller.

Gyroscopic Precession

To some an unusual concept, a spinning object, such as a gyroscope, deflects force 90°, so that when a force is encountered the resultant of the force is offset 90° from where the actual force took place. The propeller is such a rotating object, and a force which effects a movement of the rotational disk of the propeller is offset, so that the resultant is advanced 90° around the rotation of the propeller in the direction of that rotation.

Effects of the Four Elements

Single engine propeller aircraft

P-Factor

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 right-hand propeller is by far the most common. The effect is noticeable during take off and in straight and level flight with high power and high angle of attack (i.e. "flight at minimum controllable airspeed" or "slow flight").

For the typical airplane, the plane yaws left and requires right rudder for correction.

Torque

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 right-hand propeller is by far the most common. The effect is noticeable during take off and in straight and level flight with high power and low airspeed (i.e. "flight at minimum controllable airspeed" or "slow flight").

For the typical airplane, the plane yaws left and requires right rudder for correction.

Propwash

All qualifiers noted above for P-factor and torque holding, the rotation is clockwise around the airplane, and arrives at the tail on the left side (looking forward), deflecting the tail to the right and — with respect to the vertical axis — the nose to the left.

The effect is proportional to power, and the response required is proportional to speed: higher power settings increase propwash, which increases the leftward deflection of the nose of the aircraft; higher airspeed increase rudder effectiveness, which decreases the rudder required at any given power setting.

Gyroscopic Precession

Gyroscopic precession only occurs when a force, an action to change the vector of the aircraft, is occurring; that means that only when a control input in applied such that the nose of the aircraft is moved will the effect of progression be created.

This is most critical in a conventional gear aircraft when the tail is raised during the takeoff roll: raising the tail has the effect of lowering the nose, pivoting the aircraft on the main gear and substantively applying forward pressure on the top of the rotational disk of the propeller.

All qualifiers noted above for P-factor and torque holding, this force is then advanced 90° around the rotational disk of the propeller, which equates to forward pressure on the right side of the of the rotational disk of the propeller, thus deflecting the nose of the aircraft to the left.

For both conventional gear and tricycle gear aircraft the force will reoccur at rotation, when the nose is raised, essentially a forward force at the bottom of the rotational disk of the propeller, advancing the force clockwise 90° to the left side of the rotational disk of the propeller, therefore deflecting the nose to the right. This is the only time a force described here works opposite to the other forces.

P-Factor, Torque, Propwash, and Gyroscopic Progression Together

It should be noted that P-factor, torque, propwash, and gyroscopic precession are all distinct phenomenon from each other. In a standard single-engine airplane (forward-facing propeller; standard, clockwise-turning engine & propeller; tail in the back, no canard in front), all of these forces — with the one exception noted of gyroscopic precession when raising the nose — will always work in the same direction, all of which will require right rudder for correction. For this reason it is often difficult to understand the differences among the four as they are occurring.

Multi engine propeller aircraft

All of the forces described above will appear in analogous fashion in multiengine aircraft. However, among the forces, P-factor will have a unique roll to play in the design and operation of multiengine aircraft.

Critical Engine

When a twin-engine aircraft has two identical engines, which both turn in the same direction, the engine with the down-moving blades on the side with the wingtip produces more yaw and roll than the engine with the down-moving blades on the side with the fuselage. Technically, this is because the moment (the arm) of that engine's thrust about the aircraft center of gravity, the distance between the center of thrust of the propeller disk and the center of gravity of the airplane (the center of gravity laterally, in this case, which should be along the middle of the fuselage, not offset to the right or left) is greater for that engine. That is, the downward moving blade will be further from the fuselage on one side than on the other side. 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. Note that "critical engine" represents the engine that fails, causing the greatest loss of control, not the engine that continues to operate, causing the greatest loss of control.

With engines rotating in the same direction, P-factor will therefore affect V_MC (minimum control speed).

At high angles of attack, with standard right hand rotation, the thrust disk is shifted toward the fuselage with the left engine and away from the fuselage with the right engine. This means that the arm (i.e., the distance from the longitudinal axis to the center of thrust) is greater with the right engine than with the left engine, that the right engine exerts more turning force than the left engine (longer arm equals longer lever equals greater force), so that the failure of left engine creates more yaw than the failure of the right engine.

A failed engine yaws the aircraft from the operating engine toward the fuselage. With clockwise rotating propellers, the off center thrust produced by the right engine operating with the left engine failed creates greater yaw to left than would be the case with the left engine operating with the right engine failed. In fact, with the left engine failed the yaw from torque, p-factor, slipstream, and yaw from dead engine effect will all work to the left (requiring greater yaw correction — right rudder — ultimately limited by rudder authority). A failed right engine yaws the aircraft to the right, along with p-factor on the operating left engine (comparatively less than for the right engine), while torque and slipstream yaw the plane to the left, (requiring less yaw correction — left rudder — again ultimately limited by rudder authority, but requiring less rudder authority for any given power setting, thus decreasing the functional V_MC below the published V_MC, which is determined based on the critical engine). Precession, like p-factor, yaws toward the fuselage and has a shorter arm on the non-critical engine, but since this only an episodic effect its overall import is negligible. This is the only time P-factor works against torque and slipstream.

The left engine in this scenario is the critical engine, namely the engine whose failure brings about the more adverse result.

Counter Rotating Engines

In the case of using counter-rotating engines (i.e., not rotating in the same direction):

Center line thrust

While center line thrust aircraft do not yaw towards a dead engine, and this is an explicit element of the "centerline thrust only" restriction to a multiengine rating, there will be the various p-factor, torque, etc., affects during all phases of operation. For example, yaw will be working in the same direction from both fore and aft of the vertical axis as a result of p-factor, torque, and precession; who knows what slipstream will be doing?

Operational Notes

The asymmetric blade effect is dependent on thrust, and is proportional to forward velocity (specifically to TAS); thus,

• Greater thrust (i.e., higher power settings) produces more force;
• Higher airspeed produces more force.

Relatedly, torque, gyroscopic precession, and slipstream will be constant at any given level of thrust regardless of the airspeed:

• At constant thrust and angles of attack, changes in airspeed will affect the rudder:
  • Increased airspeed will increase the effectiveness of the rudder,
  • Decreased airspeed will decrease the effectiveness of the rudder.
• In flight at a stable airspeed and angle of attack, regardless of airspeed and angle of attack, p-factor, torque, & slipstream will be in balance with a constant rudder setting and precession will not exist.

In various phases of flight, given a standard right-hand engine, the following considerations exist:

• At takeoff,

  1. During the initial phase of the takeoff roll, as power is advanced to takeoff power,
     • Torque will require an abrupt and significant application of rudder to maintain directional control;
     • P-factor will generally be insignificant.
     • Gyroscopic Precession will not exist
  2. As the takeoff roll progresses,
     • For conventional-gear aircraft,
       1. prior to elevating the tail (i.e. while the tail-wheel remains in contact with runway), as the airplane accelerates down the runway, P-factor will be increasing, increasing the nose-left tendency during the later stages of the roll;
       2. while elevating the tail, precession will push the nose to the left;
       3. following elevating the tail, P-factor will be reduced or eliminated.
     • For tricycle-gear aircraft, there should be no noticeable effect.
     • In either case, as speed increases at a constant angle of attack (tailwheel or nose wheel still on the runway), rudder effectiveness will increase as speed increases; therefore,
       1. Rudder becomes more effective,
       2. Torque and slipstream remain constant: therefore, less rudder is needed;
       3. P-Factor increases: therefore some degree of change in need for rudder occurs:
          • more rudder is needed: P-Factor increases faster than rudder effectiveness increases;
          • less rudder is needed: P-Factor increases slower than rudder effectiveness increases;
          • no change in rudder is needed: P-Factor and rudder increase at the same rate.
       4. Overall, the increase in rudder effectiveness generally means that following the initial application of rudder to compensate for torque that there will be a constant decrease in rudder required, slightly adjusted when the tail of a conventional gear aircraft is lifted of the ground during the roll.
  3. At rotation,
     • Given a sufficiently high angle of attack, P-factor will produce a yaw to the left:
       • For conventional-gear aircraft, the effect will return abruptly;
       • For tricycle-gear aircraft, the effect will become apparent abruptly.
       and the effect will remain until power and/or angle of attack are reduced.
     • In multiengine aircraft,
       • Both propellers produce the same amount of P-factor;
       • the left engine produces yaw to the right, while the right engine produces yaw to the left;
       • P-factor related effects (related to the length of the arm from the downward moving propeller to the fuselage) will mean the critical engine (presumably the right engine) will produce somewhat more yaw to the left than the left engine will produce yaw to the right;
       • the effect will be some amount of yaw to the left, but not as much as in a single-engine aircraft.
     • As rotation takes place, but only as it takes place, precession will deflect the nose to the right.

• In flight,

  when operating with low airspeed, high power, and high angle of attack, the effects can be apparent for P-factor, torque, and slipstream, and it will be difficult to understand which has the greater effect.

• Landing,

  during the rollout and flare, the effect is not so apparent, given the relatively low power setting, except
  • For soft field landings in tricycle gear airplanes, where power applied may approach cruise power following touchdown, high power, low airspeed, and nosewheel off the ground is a recipe for loss of control;
  • During rolling-out in conventional gear airplanes, should the throttle be abruptly advanced with the tail low or the tail-wheel in contact with the runway (e.g., a delayed aborted landing or a touch and go following the settling of the tail wheel) there will likely be an abrupt nose-left tendency;
  • Both of the above would be the result of P-factor, torque, and slipstream.

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