The Factors in P-Factor – Flying Professors (2024)

When learning to fly, one of the first things that student pilots learn about is the phenomenon known as asymmetrical propeller loading, orp-factor. In aircraft with propellers, p-factor causes a yawing moment when the aircraft is at high angles of attack. For most single engine aircraft, this means that the aircraft will yaw to the left at high angles of attack unless an appropriate right rudder correction is applied. (This result applies to propellers which rotate clockwise as viewed from behind. For propellers that rotate counterclockwise, the yaw is to the right at high angles of attack.)

Wikipedia gives the standard explanation:

When an aircraft is in straight and level flight at cruise speed, the propeller disc will be normal (i. e. perpendicular) to the airflow vector. As airspeed decreases and wing angle of attack increases, the engines will begin to point up and airflow will meet the propeller disc at an increasing angle, such that horizontal propeller blades moving down will have a greater angle of attack and relative wind velocity and therefore increased thrust, while horizontal blades moving up will have a reduced angle of attack and relative wind velocity and therefore decreased thrust. Vertical blades 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 in or out along the wing.

That is, the effect is chiefly caused by an increase in the angle of attack of the downward moving propeller. Let’s call this the angle-of-attack effect.

ThePilot’s Handbook of Aeronautical Knowledgeis a bit confusing on this issue. In the section on p-factor, the first paragraph seems consistent with the Wikipedia explanation, saying that the “bite” of the downward-moving blade is greater than the “bite” of the upward-moving blade, which is consistent with the idea that p-factor is caused by a change in the angles of attack of the downward and upward moving blades. However, theHandbookgoes on to say,

This asymmetric loading is caused by the resultant velocity, which is generated by the combination of the velocity of the propeller blade in its plane of rotation and the velocity of the air passing horizontally through the propeller disc. With the aircraft being flown at positive AOAs, the right (viewed from the rear) or downswinging blade, is passing through an area of resultant velocity which is greater than that affecting the left or upswinging blade. Since the propeller blade is an airfoil, increased velocity means increased lift. The downswinging blade has more lift and tends to pull (yaw) the aircraft’s nose to the left.

That is, the effect is chiefly caused by the increase in the relative velocity of the downward moving blade, which is actually inconsistent with the angle of attack, or “bite” explanation. Let’s call this the velocity effect.

Austin Meyer, the owner and developer ofX-Plane, has an interesting aviation blog, calledAustin’s Adventures. In a recent post, A Few Myths Austin Wants to Bust, he argues that what most pilots believe ( that p-factor is caused by the angle of attack) is incorrect:

So why DOES the plane pull left in a climb even though the descending blade is NOT at a higher angle of attack? Look to helicopters for the answer. Their ADVANCING blade (the main rotor blade that is coming FORWARD) wants to put out a LOT more lift since it is moving at it’s rotational speed PLUS the speed of the aircraft.

So what causes p-factor, the angle-of-attack effect or the velocity effect? To find out, I’m going to use some ideas common to the analysis of rotor systems in aeronautics. I was actually quite surprised by the result! Because what follows is fairly technical, I’ll spill the beans and reveal the answer now: Both results are about equally important.

The Analysis.How should we do the analysis? A complete analysis, using CFD (computational fluid dynamics) or blade element theory is not really necessary. Instead, we can use a simplified analysis calledtypical section analysisthat gets the answer mostly right. For our analysis, it should certainly tell which effect is most important. The idea in typical section analysis is that we don’t analyze the entire propeller blade; instead, we analyze a “typical section” that stands in for the whole blade. Think of the typical section as representing the average blade behavior. The typical section is really a specific section of the blade, at a specfiic radius.

What is the right radius to analyze? The simplest analysis would suggest that we use the section at 50% of the propellor rotor radius — 50% is the average radius, after all! But that’s not right, since there’s more rotor area outside the 50% radius than inside. In fact, there’s three times as much! So the typical section radius ought to be greater than 50%. If we only cared about area, we would take the typical section radius to be 70.7% of the rotor radius, since that results in exactly half of the area inside and half outside the typical section. But the blades are more effective at greater radius, since they are moving faster there, so the typical section should be even further out. We’ll do the typical section analysis at the 75% radius.

Next, we have to understand what the typical section “sees” aerodynamically, that is, what is the relative wind at the typical section. To do that, we draw a so-called velocity triangle, which shows the contributions to the relative velocity from two sources: the motion of the aircraft relative to the air mass, and the motion of the typical section relative to the airframe. The velocity triangle for the downward traveling blade is shown below:

To make this velocity triangle, I used book numbers from my own airplane, a Cessna 172RG. The propeller diameter is 76.5 inches. In a max power climb configuration (the worst-case p-factor), the engine speed is 2700 RPM. That means the typical section has a velocity due to rotation of

(1) The Factors in P-Factor – Flying Professors (2)

(As a check, note that the tip Mach number The Factors in P-Factor – Flying Professors (3), which is about right).The velocity due to aircraft velocity is easier. In an 84 kt The Factors in P-Factor – Flying Professors (4) climb, it is simply

The Factors in P-Factor – Flying Professors (5)

The magnitude of The Factors in P-Factor – Flying Professors (6) is given by

The Factors in P-Factor – Flying Professors (7)

Now what happens if the angle of attack of the aircraft is increased by, say, 5 deg? The lengths ofThe Factors in P-Factor – Flying Professors (8) andThe Factors in P-Factor – Flying Professors (9) don’t change, butThe Factors in P-Factor – Flying Professors (10)is tilted up 5 deg, resulting in the following velocity triangle:

The geometry is a little harder now, since the triangle is no longer a right triangle. I’ll just give the important results, without showing the math. Specifically, for this new triangle,

The Factors in P-Factor – Flying Professors (12)

so that indeed the relative velocity does increase, by about 1.74%. In addition, although it’s not that clear from the figures, the angle of attack of the blade increases by The Factors in P-Factor – Flying Professors (13).

So both effects discussed at the beginning of this post do exist. Which is more important? We need to estimate the change in lift. For the first effect (change in magnitude of The Factors in P-Factor – Flying Professors (14), use the fact that lift at constant angle of attack is proportional to velocity squared. The sectional lift is

The Factors in P-Factor – Flying Professors (15)

where The Factors in P-Factor – Flying Professors (16) is the air density, The Factors in P-Factor – Flying Professors (17) is the sectional lift coefficient, and The Factors in P-Factor – Flying Professors (18) is the blade chord. So for small changes in relative velocity, the change in lift is

The Factors in P-Factor – Flying Professors (19)

The change in lift due to change in angle of attack is

The Factors in P-Factor – Flying Professors (20)

Now, the ratio of these two effects is

The Factors in P-Factor – Flying Professors (21)

If The Factors in P-Factor – Flying Professors (22) is much bigger than one, the velocity effect dominates; if The Factors in P-Factor – Flying Professors (23) is much less than one, the angle of attack effect dominates.

So what is The Factors in P-Factor – Flying Professors (24)? We already know for our example thatThe Factors in P-Factor – Flying Professors (25) and The Factors in P-Factor – Flying Professors (26). For a well-designed propeller in a highly loaded condition (as in our climb example), The Factors in P-Factor – Flying Professors (27). And for any airfoil,

The Factors in P-Factor – Flying Professors (28)

Putting all these results together, we have that

The Factors in P-Factor – Flying Professors (29)

In other words, the two effects are almost exactly the same size.Botheffects are needed to adequately explain p-factor!

Now, we actually don’t knowThe Factors in P-Factor – Flying Professors (30) very well, but we know that it is close to unity (probably within a factor of 2), but that doesn’t really detract from our result very much. The main point of this simplified analysis is that the two effects areroughlycomparable in size. Any careful analysis of p-factor therefore must include both effects.

The Factors in P-Factor – Flying Professors (2024)

FAQs

What is the P-factor in flight? ›

P-factor, also known as asymmetric blade effect and asymmetric disc effect, is an aerodynamic phenomenon experienced by a moving propeller, wherein the propeller's center of thrust moves off-center when the aircraft is at a high angle of attack.

What does the P-factor represent? ›

A general psychopathology factor (or “P-factor”) has been proposed to efficiently describe this covariance of psychopathology. Recently, genetic and neuroimaging studies also derived general dimensions that reflect densely correlated genomic and neural effects on behaviour and psychopathology.

What does the P-factor cause the airplane to yaw to the left? ›

P-Factor is an aerodynamic phenomenon experienced by moving propellers at a higher angle of attack. In such scenarios, the location of the center of the thrust changes. It forces the aircraft to yaw to the left. Pilots have to input the right rudder to counter this left-turning tendency.

How do you compensate for P-factor? ›

Compensation. The P-factor is compensated using different methods depending on the aircraft. In the helicopter case, the blades are mounted using hinges that allow them to be adjusted individually througout the rotation cycle.

What are the factors of flying? ›

Four forces affect an airplane while it is flying: weight, thrust, drag and lift.

What does P mean in flights? ›

F and A: first class. C, J, R, D and I: business class. W and P: premium economy. Y, H, K, M, L, G, V, S, N, Q, O and E: economy. B: basic economy.

What is the general factor P? ›

These correlated factors (e.g., Externalizing, Internalizing, Thought Disorders) constitute a correlated-factors model. The correlated first-order factors then load on a second-order factor, the general factor of psychopathology, or p, that is defined by the covariation of the first-order factors.

What is p factor of 8? ›

The factors of 8 in pairs are (2, 4) and (1, 8). 2 is the prime factor of 8.

What does the p-value represent? ›

Key Takeaways. A p-value is a statistical measurement used to validate a hypothesis against observed data. A p-value measures the probability of obtaining the observed results, assuming that the null hypothesis is true. The lower the p-value, the greater the statistical significance of the observed difference.

In what flight condition is P-factor the greatest? ›

This effect gets more pronounced as angle of attack increases, so it will be at its maximum when the airplane is flying at minimum airspeed and maximum power. This component of P-factor is responsible for the “critical engine” phenomenon on twin-engine airplanes.

What are the factors that cause yaw? ›

The yawing motion is being caused by the deflection of the rudder of this aircraft. The rudder is a hinged section at the rear of the vertical stabilizer. As described on the shape effects slide, changing the angle of deflection at the rear of an airfoil changes the amount of lift generated by the foil.

Why do pilots say rotate before takeoff? ›

Rotation at the correct speed and to the correct angle is important for safety reasons and to minimise takeoff distance. After rotation, the aircraft continues to accelerate until it reaches its liftoff speed VLO, at which point it leaves the runway.

How to explain p-factor? ›

P-factor is due to the ANGLE of ATTACK of the propeller, or in other words, the angle at which the air meets the propeller. The propeller takes a bigger “bite” of air on the right side producing more thrust from the right half of the propeller thus trying to turn the airplane left.

What are the 4 left turning tendencies? ›

The four left-turning tendencies are Slipstream, Gyroscopic Precession, P-Factor, and Torque.

What force makes an airplane turn? ›

The horizontal component of lift caused an airplane to turn. When an airplane is banked, part of the lift is directed horizontally, towards the center of the airplane's turn radius, resulting in a centripetal force that turns the airplane.

What does P stand for in flight? ›

(Note: The U.S. Army Air Service used the term “P” for pursuit aircraft, adapted from the French Avion de Chasse for pursuit or hunt airplane. After World War II, the term fighter was formally adopted by the USAF with the designator “F.”) R Reconnaissance Aircraft designed to perform reconnaissance missions.

What is P in flight number? ›

The P indicates a positioning flight.

In what flight condition is P-Factor the greatest? ›

This effect gets more pronounced as angle of attack increases, so it will be at its maximum when the airplane is flying at minimum airspeed and maximum power. This component of P-factor is responsible for the “critical engine” phenomenon on twin-engine airplanes.

What is the P lead in aviation? ›

P-Lead. Primary lead. The wire that connects the primary winding of a magneto to the ignition switch. The magneto is turned off by grounding its P-lead. source: FAA Aviation Maintenance Technician Powerplant Handbook (FAA-H-8083-32)

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