William Robison

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Gentlemen, and twin builders too:

There are many misconceptions about “P-factor,” and the term is misused more often than not.

First, what it is.

When the airflow enters the propeller disc at any angle other than 90 degrees, we have P-factor effects.

For purposes of this discussion we will say our taildragger airplane sits on the ground with the nose pointed up at 15 degrees. We will also say the propeller pitch is 15 degrees, just to simplify things. Now, with the nose up 15 degrees, the prop shaft is also pointing up 15 degrees. Now, when the propeller turns, and the airplane starts its takeoff roll, the rising blade has the 15 degree pitch cancelled by the 15 degree up angle of the prop shaft, and the descending blade has that same 15 degree shaft angle added to its pitch. So, in effect, the descending blade has a 30 degree pitch, and the rising blade has zero pitch. The majority of the pulling power is developed by the descending blade, giving off center thrust, and that off center thrust is “P-factor.” The effect is zero at zero airspeed, and the effect builds until the tail wheel comes off he ground. This is why you have to gradually add right rudder as the airplane accelerates, and neutralize it when the tail wheel lifts, disregarding torque.

When the tail wheel comes off the ground and the airplane assumes a level position continuing the take off run, the air flow into the propeller disc is then on center, P-factor no longer has any effect, because it just isn’t there anymore.

With tricycle gear, and the plane sitting level at rest, there is NO affect on the plane from P-factor. It does not exist. If the plane sits slightly nose down or nose up, there is a small amount, but it’s so small it can be ignored. This is one of the reasons why a trike is so popular for training. Both in full scale and R/C. They are just easier on take off.

In normal flight P-factor will never affect the airplane, as the airflow, in relation to the airplane, never gets more than one or two degrees off axis. Key word here is “Normal” flight. Most aerobatics are done in a normal controlled flight regime.

When doing aerobatics that depart from normal flight, 3d, gyroscopic maneuvers, harriers, and so forth, p-factor can rear its ugly head.

But 99% of what people call P-factor in normal flight is truly nothing but torque reaction, and that’s another story for another time.

I welcome any and all comments pointing out my errors in this, amplifying my statements, or adding something I have forgotten.

Bill.

mucksmear

Well said Mr Robinson! Clearly explained, and as you said, often confused for/with torque.

A third, mostly neglected factor is the interaction the helical prop wash has on side area (fuselage/fin), both above and below the thrust line, as well as ahead and aft of the CG.

-E

ps2727

Mr Robinson,
Just a couple of comments about your post. Your explanation is right on the money, only on a taildragger it will cause a need for right rudder, not left if the descending blade is on the right side as most are.
The airflow through the prop changes with angle of attack on the wing so P factor exists throughout the flight envelope and is at its max when in a high power/low airspeed situation (high angle of attack). Since models can fly at considerable angle of attack there is the potential for much P factor in flight. As you pointed out its not a big player in normal flight as angle of attack is usually small when crusin'. But its very noticable on climbout after takeoff or when doing a go-around when right rudder is not used. The vast majority of model fliers don't apply right rudder on the climb and results in the model pulling to the left.
Paul

William Robison

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ps2727:

Paul, it was apparently senior moment time. I knew it was right rudder but typed left. I've changed it.

Regards P-factor in high alpha situations - when you get to the point where P-factor has any effect you are way "Behind the power curve," and while this isn't a dangerous situation in our normally overpowered model aircraft, it is a departure from normally controlled flight, so I plead its coverage under that clause.

The only "Normal" in flight condition where you have the airflow rising over the plane is during a low speed descent as on final approach, and thrust is used to control rate of descent. If you need to go around you lower the nose as you incrase power, and the airflow is again normal to the propeller disc. Again, with our overpowered models it's not necessary to lower the nose, but the power is so great that the duratuion of off line air flow is so short as to have no effect.

Okay?

Bill.

FLYBOY

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Well said! When I explain it to my full scale students, I hold up a model prop, and show what the pitch looks like normally. Then tip it back and show the forward flight path, but the extreme pitch on the right and no pitch on the left like you explained. It is a good way to show it. The visual helps a ton.

crashnfix

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Thanks guys, that explains what's been happening to me.

John

im_a_rcav8r

In a Full scale air plane, you have to deal with the slipstream created by the spinning air contacting the left side of the vertical stab/rudder. Do you think this has a noticeable effect on the model aircraft? I know it does on a full scale.

William Robison

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im_a_rcav8r:

The spiraling of the slip stream does indeed affect the handling of the airplane.

I'm intending to include that consideration in the installment on thrust lines.

You are invited to visit the second installment here:

http://www.rcuniverse.com/showthread...93&forumid=220

P-factor is the first in what I plan to be a series to qualify every body to be a scratch builder. The link takes you to number two.

Share your thoughts.

Thanks.

Bill..

rryman

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Wow! What an education I'm getting. First, the "critical" engine thing today, and now the "P" factor. Never understood either until today. Great job explaining them Bill. I must admit, I read the engine thread a couple of times, then drew some pictures on the board, and I think it finally soaked in. Great questions and great answers.
At least now I have some idea why my A-26 went belly up so suddenly when the left engine died just after rotation!
Randy

CAPtain232

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im_a_rcav8r


I would be willing to bet that the turbulant air movement from the prop has more effect on our models than it does in full scale......supposing a very scale model in relation to it's full scale counterpart. Why, well first of all, we all OVERPOWER our models, more engine and prop than what is needed. Secondly, if you were to scale down a full scale aircraft only in it's physical dimensions, you would end up with a plane that weighed exactly 1/4 (if that is the scale) of the full scale plane. Now you look at the current 1/4 scale planes out there, they weigh about 1/100 of the full scale plane. Example......full scale CAP 232 about 1300 lbs. 1/4 scale CAP 232 about 13 pounds. So if we are creating at least a scaled down amount of prop wash but have EXTREMELY scaled down the weight, we are going to have more issues with the slipstream on the fuse side. We have actually done more than scale down actual thrust, but the thrust to weight ratio is much high on our models.

Rotaryphile

In my own designs, I try to get as much rudder and fin area below the thrust line as above the thrust line. This, I think, should greatly reduce the effect of the spiral prop wash tending to yaw the airplane to the left at high power and low airspeed, such as during the takeoff run. This seemed to produce a very straight takeoff run with virtually zero rudder input, except, of course, in a crosswind. Subfins and subrudders, I found, are also very helpful while flying at near stall airspeed, when the airstream over the upper part of the fin and rudder is badly messed up by turbulence induced by the wing and fuselage, while the subfin and subrudder fly in virtually clean air. The result is a model that is much more solid in yaw at low speed, and thus resists the tendency to snap roll into the ground.

Several of the flyers in this area added subfins, and where practical, subrudders as well, and gained greatly improved low speed handling.

John Hawkins

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Hmmm.........I think there is something wrong there. That's a linear relationship isn't it when it should be cubic?

John

Rotaryphile

If you built an exact 1/4 scale replica of a full scale airplane, the replica would weigh 1/4 to the third power, or 1/64 that of the original, but it would have 1/4 to the second power, or 1/16th of the wing area of the original. It would thus have 1/4 the wing loading of the original.

A 1/4 scale Mustang P-51D makes an interesting illustration of the square-cube law. An all-metal replica built to the original factory drawings, but reduced to 1/4 scale, with about a 9 foot span, would weigh 1/64 that of the original, or about 104 pounds. (A tad on the heavy side, but just great on those gusty days) But here is the kicker: In its nose would reside a gorgeous 26 cubic inch V-12 that would be capable of revving four times as high as the original, since all its parts would be 1/64 as heavy as the full scale parts, but with 1/16 the strength, and it would have only 1/4 the stroke. It would thus make about 1600 x 1/16, or 100 HP. With nearly one horsepower per pound of aircraft weight, it would fly rings around the original, with unlimited vertical climb at around 300 MPH, and a top speed nearly as high as the original, at well over 400 MPH. (Renolds number effects would hurt it a bit.) It would also be capable of withstanding four times the G load of the original.

Playing around with scale effect math can be fun on rainy days.

Jared

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I have a few questions and suggestions to contribute. I think the taildragger example is a bit off, since the key player in the actual tail rising is also gyroscopic precession; think of it this way: by rotating the disc, you are "pulling" the top; as with all other gyroscopes, this "pulling" is felt 90 degrees early, so it results in a pulling on the right side of the prop, and thus a left turning tendancy. This is why just as the tail is coming up, you have to give a jab of right rudder to keep the tail straight. Point number 2: I don't think you can call high angle of attack situations abnormal; if you have a landing on the main wheels, you are flying at a high angle of attack. If you descend straight ahead with the airplane perfectly level, you still have a fairly high aoa, depending on the descent angle. Remember that the aoa is the difference between the direction you are going and the direction you are pointed. point number 3: The critical engine is determined almost entirely as a result of p-factor, since p-factor is what displaces the center of thrust further away from the longitudinal axis of the plane in the first place, and that is how accellerated slipstream works too. It is hard to explain critical engines to someone if he doesn't understand p-factor.

Also, be careful not to oversimplify propellor blade angle of attack; just because the blade angle is 15 degrees and the nose is 15 degrees doesn't mean that the blade is 30 degrees. In fact, it will be much much less than that, maybe 16. The rotation of the prop will greatly reduce its angle of attack, and the aoa of the blade is extraordinarily complex. In this case the aoa is still the difference between the direction it is going and the direction it is pointed, but the "it" is not the airplane; the aoa of the blade is the difference between the chordline of the blade's airfoil and the direction the blade is going, which is much more a matter of round and round than it is a matter of forward. If you have trouble seeing how complicated this matter is, remember that in addition to the prop blade rotating on a plane, and thus having a changing aoa along the length of the blade (bug on a record player), it is also inducing its own airflow, and that will reduce the aoa. As airplane airspeed changes, aoa will also change in the same way. This is why on the ground the engine may spin up to 18000, but it may climb much higher than that in a "winding up" dive from far aloft, as the blade aoa is reduced, and thus the blade's induced drag.

MinnFlyer

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Great Post Bill!

mulligan

P-factor IS an issue with trikes. Although you don't have P-factor while rolling down the runway, once you rotate and begin climbing, you do. So the difficulty is mananging the transition from no effect during the take-off roll to the angle-of-attack proportional effect during rotation and climb out.

Of course, this effect is more prevalent in full scale planes, and much less noticable in models, especially when compared to the relatively large amount of torque we can apply to our planes during take-off.

- George

William Robison

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Mulligan:

Sorry, but I still have to differ with you and all others who say P-factor has to be managed in normal flight. Key word is "Normal," look at my original post.

Even at a high rate of climb the off axis air flow is not far enough off-axis to need anything more than minimal correction, far less than required for minor turbulence.

I did remember one normal flight maneuver that does have a high angle off-axis air flow, but a sideslip is done with power off, so P-factor is still not relevant.

If you are foolish enough to get behind the power curve while you are riding in the plane, though... Will I see your real name in an FAA accident report?

My point is that if you eperience TRUE P-factor in a full scale airplane you are operating that plane outside of general aviation regulations, you are also beyond the normal aerobatic regime. You have either screwed up big time and are about to become a statistic, or you'll change your pants as soon as you can after landing.

With a powerful single you could well be confusing torque reaction with P-factor.

And you might have had an instructor who just told you wrong because he didn't know any better himself.

Bill.

FLYBOY

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P factor is an issue with all planes. It is more so when the plane is pitched up but still moving forward in a climb. On models, there is enough power that the plane is flying straight, with its longditunal axis flying straight into the relitive wind (angle of attack is almost 0). With full scale, they don't have the power to climb like a model, therefore when they climb, the longditudinal axis is not pointed straight into the relitive wind and they have a larger angle of attack. The nose is pointed up, but the plane is fllying a flatter climb angle than it is pointed. When the nose is high the plane is moving forward, there is more P factor. When the plane has as much power as a model, the plane is flying straight where it is pointing (the angle of attack is almost 0) and there is no P factor.

William Robison

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Jared:

I have to take you on also.
The weight of the propellor is such a small fraction of the total airframe weight that precessive forces are negligible. The WWI planes with rotary engines had a much greater percentage of their total weight spinning, a pilot who ignored precession in one of those often quickly became dead.
And in every instance you note, you are flying at idle power, or a very small amount of power on. P-factor negligible. Normal flight, remember?
Absolutely wrong, sir. The center of thrust is displaced by mounting the engines to either side of the airplane. And if you fly a twin engine out at a high angle of attack you too, will soon be a statistic. Offset thrust, rudder authority, and torque are the determinants of VMC, P-factor has nothing to do with it.

I will admit my 15 degree prop blade angle was a simplification, but it was sufficient to convey the needed information. A real propellor has a blade angle that changes from the root to the tip, since the tip travels a much greater distance per revolution than the root, it needs much less angle to have the same true pitch. If the blade were extended all the way to the root, the blade angle at the root would be 90 degrees regardless of the actual pitch, since the root has effectively zero rotation.

Bill.

William Robison

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Flyboy:

I repeat myself:
I did acknowledge the correction for P-factor, but it is so small that the experienced pilot will not notice it, the correction is so minor he will do it automatically without giving it any thought.

A low-time pilot, with low-time skills might notice it.

And I have already covered all this more than once in this thread.

Bill.

FLYBOY

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I understand that Bill, the point I was trying to make, but apparently didn't is that George said P factor was an issue with Trikes.

I wanted to make it clear that the plane doesn't care what kind of gear it has when it is in the air and nose high. Agreed that models don't deal with it as a full scale will, but I didn't want people thinking that they didn't have P factor because they had a tail dragger.

ps2727

Absolutely wrong, sir. The center of thrust is displaced by mounting the engines to either side of the airplane. And if you fly a twin engine out at a high angle of attack you too, will soon be a statistic. Offset thrust, rudder authority, and torque are the determinants of VMC, P-factor has nothing to do with it.

Bill, sorry I have to disagree with you here.
I used to fly Piper Navajo airplanes. The Chieftan has identical engines. Another version, the CR, has engines which counter rotate. Now on the Chieftan the left engine is the critical one and on the CR there is no critical engine. The only thing that changes with counter rotation is P factor. It most certainly is the reason that the center of thrust is offset and why losing one can be more detrimental than the other.

I don't know why you seem to deny the reality of P factor when it comes to models. It's there, although nothing to be overly concerned with, and easily seen and compensated for. On a normal flight a model will see high angle of attack as well as low. Generally high at takeoff and landing or slow flight, and low in cruise. When at high angle of attack and with power on P factor is there.
I do agree that there are other things which cause airplanes to want to go left and are probably more evident than p factor.
It's a nice debate but there are many happy model fliers who have never heard of p factor, et al; they just move the sticks to make the model do what they want!

Enjoying the thread
Paul

William Robison

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Paul:

You still overlook torque.

On the critical engine. the left, torque tends to counteract the offset thrust, making it easier to fly than with the right only, where the torque and offset thrust effects add.

With the CR version the torque and offset thrust are counteractive on both engines.

With either version, in a dive, VMC still holds. And in that dive the airflow into the props is as close as axial as you can get it making P-factor absent by definition. And you still can't hold yaw at full throttle until your speed comes back up. Torque and offset thrust, yes. P-factor, a resounding no.

Bill.

Jared

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Here are a few more ideas about your theories:

It has been a while since somebody told me about gyroscopes, but I believe the quantity one is concerned with is not the mass of the prop, but the angular momentum; after all, it isn't the mass of the wheel that keeps a bicycle upwright! it is the rotation of that mass. So, even though the prop is very light, it is also spinning very fast, and can thus has a high angular momentum, and its votes count more ("the lefts have it!" nevermind, that was a bad one) You might not notice it on your favorite sport plane, since it accellerates through the takeoff roll so quickly; but underpower a nice senior telemaster, or perform a reduced power takeoff with a sport plane, and you can certainly see the effects if you look for them.


Oh, I think I'm going to have to stand my ground on this one, but because I figured I could get away with omitting a word or two, I can see how you disagree. I meant to say that the p factor is what displaces the center of thrust further away from the airplane's longitudinal axis on the non-critical engine; of course the center of thrust is displaced for both engines by the distance from the long. axis, but the center of thrust on the non-CE is displaced further away because of the p-factor. The key to the CE theory is that there is an asymetric displacement of the center of thrust. This is why counter-rotating twins have no critical engine; the center of thrust is still displaced from the
longitudinal axis of the engine just like it is on almost all prop-aircraft. But, (in most counter-rotating cases) the center of thrust is displaced to the left on the right engine and the right on the right engine, and it all evens out, because there is no dissymetry between the distance from the aircraft long. axis and the center of thrust.


I think the interesting thing is that all of this discussion, and most aerodyamic discussions, are over-simplifications. The key to learning aerodynamics for a pilot is for him to be able to predict what will happen to his craft; he doesn't have to know formulas, etc. Instead, we teach pilots little "thought models" that help describe how airplanes fly. From time to time, we realize that those models are a bit too much of a simplification, and we have to add to them. Lets face it, I'm a pilot, not an engineer; I've never been in a wind tunnel, but I can tell you how a plane is going to react in most of its flight envelope.

Here is my next point: On my side of the river, the feds like to hear that critical engines are determined by four factors; p-factor, torque, accellerated slipstream (more lift further out on the wing) and spiralling slipstream. Critical engines are not determined by just one thing, but several factors; we don't have to decide on one and vote him "senior air marshal of all critical engine factors. Although, the spiralling slipstream and accellerated slipstream concepts rely on good ole' p-factor to displace the center of thrust further away on the left side (in america). The feds over here also like for pilots to know that VMC is very much affected by p-factor; VMC is almost never a problem, except in a high angle of attack, high power situation... "I've just got to clear those trees-mountains-clouds-ground-towers-runway-cows," or "lalalala see no airspeed indicator, hear no airspeed indicator, speak no airspeed indicator... Hey mr. airspeed indicator, if I can't see you you can't see me; after all, I'm busy trying to figure out why there's oil all over the wing" etc. After all, if you are going so fast that you have a low angle of attack, then you are going fast enough to have sufficient rudder effectiveness. VMC really matters at high power settings and high angles of attack; you remember that in what you call normal flight aoa is related to airspeed, right? Slow airspeed means more aoa to maintain altitude; you can't have a high power setting and a low aoa without building up airspeed (the stuff that makes your rudder able to do the job). Think about it, the only reason that an airplane will have a low speed when the engines are humming is because we are flying slow (high aoa in this case), and induced drag is high. When we reduce aoa, induced drag goes away, and the "brakes" that were keeping us slow are released. The airplane accellerates, and "away go vmc worries, down the drain." That is, unless you have an airplane with an extraordinarily high VMC; there are lots of factors that impact VMC, but the most obvious ones in a model might be high output engines, insufficient rudder, etc. Once again, I personally don't feel obligated to name one of those many factors "vice air marshall of all VMC," or "president of the VMC club." Or, "can't we aerodynamic-tendancies all just get along?"

Jared

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sorry for the discontinuity, but there is a limit on post lenght... maybe I should have said less. Anyway, here is the rest

Also, I have to question your note about flying behind the power curve in a real airplane. I'll skip the examples like wayne handley's turbo raven, which has more power than thrust... No really, even in a cessna, flight behind the power curve is not just a very convenient thing, it is a requirement! I don't know if we have the same thought model for how the "Bucket" speed works, but to elaborate very briefly, there is an airspeed at which an airplane will require the least power to maintain level flight (I know it is a simplification, but see above...) In a small Cessna single, that speed might be 70 knots; stall speed in the landing configuration of that same airplane is closer to 40. When learning to make spot landings, it is important to understand that an excessively fast final results in a float, and thus makes the judgement on very difficult. When it matters what spot the airplane lands on, the best way is to use a speed below that bucket speed, since it allows for less float during the flare. After all, the low speed means less kinetic energy to give away. When approaching a landing in a power off situation (engine failure, landing contest, whatever) management of the power curve is one of the best ways to ensure the desired glide path. Take my word for it; at one of the NIFA national power off landing contests, the winner had a combined score for two landings of 20... since he was penalized one point for each foot that he was away from the runway, averaging 10 feet per landing. The point is that sometimes feet matter. We have to tell pilots about the way an airplane handles behind the power curve, since it is very counter-intuitive! We even teach them manuvers so that they can practice it at a safe altitude. When you are gliding for a landing, at a speed below the speed on the power curve, and you are below the glide path, the corrective action is to dive. That's right, when you are low, you dive. In the short term, sink rate will increase, but in the long term, drag decreases and the airplane becomes more efficient. The dive results in a higher airspeed, and thus a reduction in induced drag; since induced drag is decreasing faster than parasite drag is increasing; and viola- the airplane will do the best it can to return to the glide path. Of course, if it is a bad approach, diving won't fix it, and that statistic stuff comes into play. The part of flight where the power curve is important is called the "region of reversed command" by some people, since a pilot will find that an increase in angle of attack, or elevator back, results in an increased sink rate, or airplane down. Elevator back, airplane down... that's reversed alright. But anyway, I didn't mean to lecture you on stuff you already know; instead, I wanted to make sure that you realize that flying behind the power curve does not lead to instant vaporization or death by spontaneous combustion (not to imply that you implied such); however, in the hands of a trained pilot, it doesn't necessarily lead to accidents either. I'd have much more confidence in a pilot who had explored that flight regime and could "thread a needle" during an off-airport landing than one who just avoided it because he was scared to die. In that case, the cautious one is more likely to die. In summary, sometimes flying behind the power curve is a normal procedure, and it doesn't become dangerous until a pilot gets behind it, or puts himself in a situation where he needs altitude that he doesn't have for the recovery.

One final note... I do enjoy discussing topics, and don't mind a little bit if disagreement... that is where the learning happens! But, let's be sure to stay friendly, rather than tending toward the urge to be short-tempered- after all, we do this for fun, right?