mesae

Multiflyer:

I have read several of your posts and find them refreshingly reasonable. I haven't found anything in your posts that disagrees with my own understanding of aerodynamics. I might assume you are an engineer, or at least very well read. I am glad you are contributing here--this sort of rigorous discussion can be beneficial.

LouW

You are exactly correct that cyclic pitch control made the helicopter a practical machine. If you check out the mechanics of cyclic pitch control, you will find that in order to control tilt of the rotor disc, the blade changes are introduced at ninety degrees to the desired reaction. In other words, for pitch, the blade changes occur as roll input causing the rotor to pitch and for roll control, the required input is pitch. When a helicopter moves too fast forward such that the retreating blade stalls, it doesn’t roll toward the retreating blade, but pitches up. As the cyclic pitch creates an asymmetric blade loading, the reaction is always at ninety degrees. In other words, the rotating blades of a helicopter and a propeller both react as any other gyroscope. Any force applied to the rim appears ninety degrees out of phase. P-factor is quite real, however it only affects pitch, not yaw.

When pitch angle increases, P-factor tends to increase pitch. This is opposite the stabilizing force from the tail and results in the longitudinal static stability being a little less power-on compared to power-off. But it doesn’t affect yaw.

mesae

Are you writing about airplanes or helicopters here? P-Factor (asymmetric propeller loading) very definitely and directly affects yaw in propeller-driven airplanes in upright or inverted flight when the propeller disk meets the relative wind at other than a right angle, as in a climb, slow flight, or even during rapid pull or push-ups (or downs). It is also one of the strong, yet little understood factors that affect pitch in knife-edge flight or at other times the fuselage is used to generate lift, as in a skidding turn.

When pitch angle increases while the propeller is producing thrust, the component of thrust perpendicular to the flightpath "lightens" the nose, effectively moving the CG back slightly, approximately as a function of the sine of the pitch angle, considering the arm at the prop hub. By "pitch angle" here, I mean the angle between the prop shaft and the flight path.

With a helicopter, in normal flight, would-be P-factor is corrected for with cyclic pitch variation. This is not the same as retreating blade stall, although it does result in momentary asymmetric lift distribution. The 90 degree "offset" in cyclic is due to the precession response of the rotating wing, unless I am mistaken. I am not an expert with helicopters.

mesae

Respectfully,

This question reflects an incredibly common misconception about how airplanes respond to wind. Any aircraft, from an indoor blimp or a foamy to a B747, has to crab into a crosswind (assuming "coordinated" flight) to maintain a desired flightpath. The only factors to consider to determine how much crab is necessary are the wind vector relative to the airplanes's velocity vector through the air, and the desired flightpath. Size, weight, fuselage side area, etc. matter not. Note that a crab angle has nothing to do with skidding or flying partially "sideways". It is the difference between the airplane's heading and it's flightpath over the ground as a result of the movement of the airmass through which it is moving.

Wind correction is solely the pilot's job and has nothing to do with the type or design of the aircraft. What those pattern pilots are talking about is really three main considerations: Airplanes with higher wing loadings tend to respond less to turbulence, and airplanes that are flying faster tend to respond less to turbulence, since they are exposed to a given vertical gust for a shorter time. Faster flying airplanes require smaller crab angles to maintain a desired flightpath in a given crosswind. The only aircraft whose heading would exactly equal it's flighpath in a crosswind would be one flying at an infinite airspeed.

MajorTomski

Great discussion guys, please allow me to interject several other points for your consideration; the source of P-factor and the value of the spiraling slipstream.

P-factor is a differential thrust across the face of the blade due to localized changes in relative velocity and angle of attack. Sadly in most literature being published, only the angle of attack portion is being taught. First pardon my old school English measurements; I never made the transition to metric ;-)

A propeller spins at a certain RPM, for our discussions let us only look at the tip of the propeller. For a given RPM the propeller tip is moving a specific velocity in feet per minute. For example a 4-foot propeller the tip is 2 feet from the hub. The distance the prop tip is traveling is the circumference of the circle or PI x D; (3.1416 x 4 = 12.58 feet) Now if the engine is turning a typical 2400 rpm on a Cessna type aircraft, the tip speed works out to 12.58 feet (one revolution) x 2400 revolutions per minute or 30,200 feet per minute or for smaller units (dividing the minutes by 60) 503 feet per second. (88 feet per second equals 60 miles per hour) so the prop tip is doing 340 miles per hour.

Lift is a function of the following equation: Lift (or in the case of a propeller Thrust (T)
T= ½ CL R V2 A
CL is the Coefficient of lift. The CL is a function of the airfoil shape and its angle of attack; this is determined by wind tunnel work.
R RHO the density of the air
V2 the velocity through the air squared
A area of the wing. In the case of a propeller it gets more complex because there is an integration of the different angles of attack and speeds along the length of the blade. If we confine our discussion to just the tip, we only have to work with one value. Note that the Velocity is a squared value in the equation so a little a small change in velocity causes the most change in lift.

An airplane in a steady state climb, at a constant angle of attack (say 5 degrees and a constant airspeed (say 120 mph or 176 fps) causes the propeller to strike the on coming are at the same angle of attack the as the wing. From vector analysis that on coming airflow has a component that acts perpendicular to the front of the propeller and a vector that acts in the plane of the propellers rotation. If our airplane has a 5 degree angle of attack then from trig, the component of the in coming 120 mph air is 10.4 mph acting in the plane of the rotation, and 119.4 MPH perpendicular to the plane of rotation. We only need to focus on the 10.4 mph component.

As the propeller rotates in this in coming air it sees that 10.4 mph component reverse direction. At 12 and 6 oclock it is zero, at 3 oclock its PLUS+10.4 mph, at 9 oclock its MINUS-10.4 mph.

Now add these two values to the propeller tip speed from the above discussion. At 3 oclock the prop tip now has a speed of 350.4 MPH (340+ 10.4) and at 9 oclock the tip now has a speed of 330.6 MPH (350-10.4) if we plug just these two values into our equation above

T= ½ CL R V2 A

And use an arbitrary 0.1 for CL, 0.01 for RHO and 10 for area we get
T @3:00=(.5)(0.1)(0.01)(350.4)(350.4)(10)=1,227 pounds of thrust (not a real number because of using the ones just something to work with)

But at the 9:00 position
T @9:00=(.5)(0.1)(0.01)(330.6)(330.6)(10)=1093 pounds of thrust

A difference of 134 pounds of thrust pulling harder at the right propeller tip causing a turn to the left.

And that is only due to the difference in rotational velocity. Buried in the CL term is the angle of attack. It to changes as the prop spins by +/- the 5 degree incoming air. Its effect are additive to the rotational values but they are linear not squared so they have much lower effect on the thrust.

That is where P- factor comes from.

Now back to slipstream spiral. I ask you to consider your discussions on spiral slipstream. About 5 years ago I began a study as to where spiraling slipstream came from, and why no one ever discusses the other effects that it should have on an airframe. Thankfully back in post number 10 of this thread, multiflyer finally points out the problem that I had, that the slipstream also affects the wings and stabilizer the same way that it does the fin, and the result is a mild roll to the right. This drove me to do a study. I have the fortune of working at a facility that has a huge old aviation library. My study of the slipstream spiral, at least in the 17 or so textbooks I looked at, didn’t exist before the publishing of Stick and Rudder. I came to the conclusion that spiraling slipstream is one of the rare aviation phenomena that has not been mathematically quantified. This combined with the lack of a photograph of a smoke stream actually wrapping around a fuselage lead me to believe that the spiraling slipstream is an aviation myth grounded in Stick and Rudder. However, I recently was directed to a 1930s NACA paper that DOES actually quantify the angle of the slipstream. It says that this twist is at MOST 3 degrees off the centerline of the aircraft. Not the huge force indicated in Stick and Rudder. Still working on this one.

This is fun, keep it up!

mesae

Hey, thanks, this is cool. I finally found a forum where people don't slam people for getting technical on aerodynamics.

I didn't know about that 3 degree angle. That's interesting and a little surprising. I never expected it to be 60 degrees or anything, in fact I suspected that the pictures I have seen in my studies exaggerated the density of the "coil" for illustration purposes but I didn't know how much.Still, it's effect is very observable in flight if you understand the principles.

LouW

Your analysis of the asymmetric thrust on a propeller when the airplane is in a climb is accurate. There is indeed a force acting on the propeller disc that tries to turn the nose to the left. That fact is not in question. The question is “how does that force manifest itself at the hub and how does the aircraft respond?� If you are not familiar with gyroscopes and a phenomenon called “precession�, I suggest you buy a toy gyroscope and study it some. A force applied to the rim always results in a movement at the hub ninety degrees out of phase with the applied force. The force on the propeller disc tending to turn the nose to the left affects the airplane as a nose up pitching moment. If the propeller is rotating it can’t react any other way.

As to propeller swirl, I would be the first to admit that the illustration in “Stick and Rudder� is misleading. The swirl (or more appropriately twist) is, of course, only on the order of a few degrees at the most. My airplane is a Piper Cherokee and has rudder trim. If I trim the rudder to eliminate any left turn in a steep high power climb it only takes two or three degrees of deflection. This is about what one would expect from propeller swirl alone. There is no need to add the infamous P-factor.

mesae

Not sure what you are getting at here. It's clear that P-factor is entirely different from gyroscopic precession, except that their forces are transmitted to the airplane through the propeller shaft.

I have done a bunch of aerobatics in Decathlons, and I found that if I pull up with at least 4.5 g loading at 140 mph or so, the precession generated approximately offsets the other left turning tendencies, minimizing rudder correction required to keep the heading, but only WHILE the airplane is changing pitch. That does not mean 4.5 g with another type of airplane will produce the same result. Once the airplane is flying again in a straight line, precession goes away. P-factor works any time the propeller is producing thrust AND the propeller shaft is not parallel to the flightpath. It is not a gyroscopic force, rather it is aerodynamically generated.

mesae

You seem to be implying here that you have done some experimentation and/or calculation to determine the expected number of degrees of rudder trim required to correct for spiral slipstream, and are using that as proof that P-factor is not occurring. Is that what you are saying?

stek79

Guys, I'm glad this thread is found interesting by many...

Thank you all! Tomsky, you did a great explaination, I never thought P-factor could yeld a 20% thrust difference!!! THANKS for that calcualtions!

I'm interested particularly in the slipstream issue, let's go deeper!

LouW

Not so. The force generated by P-factor is the same as any other force acting on the rotating propeller (gyroscope). Precession is simply the fact that any force that is applied to change the axis of rotation acts at ninety degrees from the applied force. It doesn’t matter if the force is generated aerodynamically or applied through the shaft. Precession happens. P-factor exists but it produces a pitching moment not a yaw.

LouW

My comment was not intended as proof of anything. It was simply an observation that the required correction is of about the same order of magnitude as would be expected due to slipstream twist alone.

mesae

On what basis are you asserting that P Factor produces a pitching moment? This is true in knife-edge flight or while skidding as I have written before, but it is generally thought of as a force that tends to cause left yaw in climbs and during slow flight with power, since those are more common flight conditions.

If P Factor is allowed to yaw the airplane left, as in a wings-level climb with insufficient right rudder (you use the rudder to keep the ball centered in climbs while flying your Cherokee), then precession will try to pitch the airplane up (or down while yawing right), but only while the airplane is yawing. This does not necessarily mean the nose will rise, as other forces may cancel the precessive reaction.

Are you saying that P Factor is the same as gyroscopic precession? If so, you are mistaken. P Factor is also known as assymetric propeller loading.

From the Pilot's Handbook of Aeronautical Knowledge (FAA-H-8083-25), page 3-25:

ASYMMETRIC LOADING (P FACTOR)
When an airplane is flying with a high angle of attack, the “bite� of the downward moving blade is greater than the “bite� of the upward moving blade; thus moving the center of thrust to the right of the prop disc area—causing a yawing (emphasis added) moment toward the left around the vertical axis. That explanation is correct; however, to prove this phenomenon, it would be necessary to work wind vector problems on each blade, which gets quite involved when considering both the angle of attack of the airplane and the angle of attack of each blade.

Majortomski posted a part of the vector analysis mentioned above. Thanks again Tom.

Here's the FAA's web link so you can read the whole explanation in context with illustrations (your tax dollars at work):
http://www.faa.gov/library/manuals/a...83-25-1of4.pdf


P.S. MajorTomski might find it satisfying that elsewhere this section refers to the downward moving blade having a higher resultant velocity--it doesn't solely refer to "bite" or angle of attack.

mesae

On what basis do you make the assertion that the required correction is of about the same order of magnitude as would be expected due to slipstream twist alone? Have you isolated the twist in a wind tunnel or done a study to determine that the amount of rudder input required to keep the ball centered is due to slipstream twist and no other factor?

mesae

I agree. Correct me if I'm wrong, majortomski: Be careful using that 20% figure, stek79. I don't believe majortomski's analysis was intended to be detailed enough to quantify the difference under any particular set of conditions. Tom's analysis made several assumptions, including the CL of the prop airfoil and only considered the 9 and 3 O'clock positions (the points at which the resultant velocity difference is greatest), and only at the tips of the blades, and the effect of vortices was not considered. To meaningfully quantify the difference would also require analysis at several different stations. Every change in angle of attack, airspeed and prop RPM or pitch will result a change in the "center of thrust". Majortomski's analysis does splendidly prove that there is a significant difference however, which I believe was his intent.

MajorTomski

Yes, a simple illustration that there is a difference across the face of the blade.

WRT gyroscopic forces, Louw and mesae you both are approaching the same problem from opposite directions.

mesae you're talking dynamic state in a high G pull up and Lou is talking about steady state climb, and you both are stating the correct answer for each situation.

LouW, in your first reference of the steady state climb in your Chokee (yeah, Cessna's rule!) don't forget that there is a certain amount of down thrust in all GA planes to help minimize pitch changes with power changes. And downthrust in turn minimizes the angle of attack on the propeller disk that in turn reduces P factor thrust. Now put on your biannual check-ride hat and lets go do some slow flight. Full power nose way up and right rudder stomped to the floor trying to hold heading. THERE is where P factor is most event. The high speed airflow off the prop is going down the right side of the fuselage, trying to pull the airplane left, AND that same constant force, as you have previously stated, is reacting through the prop, engine hub, and engine mounts trying to pull the nose up further due to gyroscopic precession.

Now mesae, you're pulling a positive g dynamic pull up. in that case at the 12:00 position of the prop is being forced aft by the airframe but the mass of the prop reacts 90 degrees later at the 3:00, causing as you pointed out, a zeroing of any left yaw due to the high alpha you're pulling

Fascinating isn't it!

gearup

VEERRY INNTTEERESSTING!!! Let's see now, we have the slipstream twisting around the fuse as it passes over the surfaces. Probably has pulses corresponding to the prop rpm times the number of blades on the prop, with diminished angular velocity between the pulses. Are we going somewhere? If we're going say 120 mph(176fps) and the engine is turning 2,400 rpm with about a 55 inch pitch, and assuming effective movement of 48 inches just for the sake of discussion, is it fair to say the slipstream should be winding around the fuse one complete circle every 4 feet? Of course not, because the slipstream would presumably be the vector sum of the forces acting through the prop disc, that is, the force perpendicular to the disc would be equivilent to the lift produced by an airfoil wing in constant-speed level flight, and the twisting moment would be derived from the combination of air friction and induced drag created from the propeller airfoil.

So, when I blow an oil cooler over the cascades at 11K and keep the fan turning all the way to touchdown, the 3 quarts of lost oil should produce a neat barber pole effect from the engine all the way to the tail. Streamer tape attached to the fuse should indicate the magnitude of the twisting moment. If the twist is the sum of the vectors, then is it in the ratio L/D of the prop? If it is any of these things, then it should be demonstrated by the oil slick or the streamer tape. If it's 20/1, the stream would still make about a half turn within the length of the fuse. BTW, we should also see more bugs on the left side of the vertical fin, if it is straight w/ the fuse and not canted, and for sure we should see more bugs on the bottom of the left wing, left stab and the top of the right ones, no?

Darned testing just doesn't want to add up to the assumed results. HMMM. If the slipstream is going to be turning like a horizontal tornado, we really need to identify the forces that will generate it and the mechanism that will make it behave as we assume it does. Fortunately, most of the net horsepower gets used up to create thrust perpendicular to the prop disc. A good number might be 80%, but you can feel free to substitute any actual tested numbers that contribute to the analysis. That leaves about 20% for various inefficiencies, including surface friction on the blades, noise generation, induced drag, etc. Some variables will change according to blade aspect ratio, prop airfoil variations, etc., but we might assume that in normal operation, only a small part of the horsepower might be available to produce a twisting slipstream.

Of the effects that can be demonstrated and have been tested, let's take a look at tip vortices, specifically as they might apply to rotating (prop)airfoils. We know that large air movements result from passage of heavily loaded airfoils, and we're constantly warned about prior passage of "heavys" even several minutes prior to our sharing the previously used airspace. Looking through the windows where things are upside down and you are low to the ground is not fun unless you are doing it on purpose. I digress. It seems logical that a heavily loaded airfoil, even though smaller would also generate significant tip vortices that would presumably behave in similar fashion to those generated by wings. This could be visualized as the turbulent interface between the stable surrounding air and the slipstream column. The demonstrated existence of vortices from the passage of any lifting airfoil combined with the other prop inefficiencies, would seem to leave very little engine horsepower available to twist the slipstream.

Let's see if we can twist the slipstream on purpose. What happens if we wind er up setting on the ground with the prop pitch flat, then pull the pitch to the feather position? Well now, looks like the prop airfoil went to critical pitch, stalled, then proceeded into an effective elevator perpendicular to the direction of rotation/airflow over the airfoil. Air movement went from almost none (only friction) through maximum efficient thrust to increased drag/decreased thrust, and finally to all drag/no thrust. In the full feathered position, it is definitely churning air and using lots of horsepower, but no thrust. If done in a static position, it appears that the air movement would be inwards towards the prop hub from the front and back of the prop disc, and outwards radially from the prop tips. In the full feathered configuration, the prop acts like a squirrel cage fan without the cage. BUT, it is interesting to note, there do not appear to be any major barber pole spiral airflows emitting from all this fuss.

Seems to me, we could demonstrate that twisted airflow on the ground with a tricycle gear airplane that sits in flight attitude. Just line up the surfaces, set everthing in a straight line, no offsets, fasten the gear to a bearing turntable with the center of the turntable on the cg and thrust/drag line of the airframe, set it at constant throttle and let er rip. Anyone wanna become famous?

mesae

I made reference to both static and dynamic states. The pullup was only one example, but my arguments are distributed through several posts. For simplicity, my arguments generally did not consider down thrust, except by implication when I made reference to the angle between the propeller shaft and the flightpath. That definition incorporates all thrust offsets by implication. P Factor is a slight right yawing force in level cruise flight because of down thrust.

Yes, it IS fascinating!

mesae

I am re-stating some points here because LouW has asserted more than once that P Factor is a pitching force, not a yawing force. Furthermore, I'm not sure he understands the difference between P Factor and gyroscopic precession. They are different forces, though in some conditions, they have the same result--in others, they tend to cancel each other. In still others, they act in oblique directions to each other.

In a steady state, straight climb, gyroscopic precession is not acting. It only acts while the airplane (actually the rotating propeller) is changing direction (pitch, yaw, or some combination of the two). While pitching toward the canopy, gyroscopic precession responds with a right yaw force. While yawing left, it responds with a pitch up force, and so forth.

The example I gave of a wings-level climb with insufficient rudder, is not a steady-state climb. The airplane will be yawing left slowly, depending mainly on the angle of climb and the power being produced. The heading will be changing slowly to the left. The ball in the turn coordinator will be deflected slightly right. In this case, P Factor (and spiral slipstream) is acting to yaw the airplane left, and gyroscopic precession applies a pitch up force.

If the proper amount of rudder is applied in a wings-level climb, the airplane's heading will be constant and the ball will be centered. This is a steady-state climb and gyroscopic precession is not acting, since the gyro (the propeller and other rotating components, even the alternators!) is not changing orientation.

mesae

That was fun! Especially the bugs.

Did you catch the part about the NASA study that makes out the spiral angle to be at most 3 degrees off the fuselage centerline? The horizontal tornado wouldn't even make it around the fuselage once during a full-throttle runup on the ground. The pressure waves are a different story entirely.

gearup

Just have always wanted to know how and why rather than just-the-facts. I wonder why the tip vortices off of a prop would act differently than off of a wingtip, if they in fact do. I wonder why the slipstream would retain a rotational component from the prop, when it seems likely that most of the induced prop drag generating the thrust and the rotational component would disipate radially off of the end of the airfoil/prop. (hence q-tips to try to limit the effect). I understand that fluids tend to spiral into areas of low pressure, and move radially away from high pressure, so I wonder why the slipstream, being relatively high pressure would provide a sustaining environment for the rotating component generated by the prop.

Notice taken of the NASA study reference. It would be interesting to look at the testing in detail to determine what controls and variables were examined and observe the range of data derived.

MajorTomski

Actually the paper is a NACA study from the 30's and in a 19 page report it skips over the one equation for the spiral in a half a column.

Now you're tripping over the vortex off the tip of the prop verses what the prop does to the air as it passes through it. They act exactly the same.

See this picture

http://www.zap16.com/images/kb04%20B...take%20off.jpg

The props are leaving tip vortices that are formed identically to the wingtip vortices. Here's where the catch kicks in if you look at the spiral,(and this may be what Stick and Rudder saw as the tight spiral around the fuselage) it goes the wrong way to support the slipstream spiral theory. Which is the air inside that outer defined spiral is slowly spiraling around the fuselage in the same direction as the propeller rotation due to the propeller imparting some energy to the airflow.

MajorTomski

There is where we disagree. In a steady state climb there is P factor yawing the plane to the left. That is a steady force applied to the propeller at the 3:00 position. Due to gyroscopic procession it has to result in a displaced nose up force acting throught the propshaft at the 6:00 position. The plane of the prop isnt changing but the forces are still there.

mesae

P Factor is attempting to yaw the airplane to the left. If the climb is performed correctly (sufficient right rudder is applied to correct), the airplane will not yaw, or change heading. If there is no yaw or pitch change, there is no precession reaction. If the pilot is lazy and allows the airplane to turn, then precession occurs while the turn is happening.

Excerpts from the Pilot's Handbook of Aeronautical Knowledge again, page 3-24 and 3-25 ( http://www.faa.gov/library/manuals/a...ilot_handbook/ ):

"GYROSCOPIC ACTION
... Precession is the resultant action, or deflection, of a spinning rotor when a deflecting force is applied to its rim. As can be seen in figure 3-32, when a force is applied, the resulting force takes effect 90 degrees ahead of and in the direction of rotation.

...

It can be said that as a result of gyroscopic action--any yawing around the vertical axis results in a pitching moment, and any pitching around the lateral axis results in a yawing moment...."

Emphasis added.

The last sentence requires that the gyro is free to change orientation as a result of the force applied to it. In the case of a steady-state climb, yes, P Factor is working, but right rudder is also working to cancel it out, so the gyro is not free to change orientation, hence no precession.

Your statement that, "The plane of the prop isn't changing but the forces are still there." is incorrect IF you are referring to gyroscopic precession. P Factor and precession are different phenomena with different causes. By the above, definition, if the plane of the prop isn't changing orientation, then precession does not occur. In a steady-state climb (aircraft attitude is constant), the plane of the prop isn't changing, and the P Factor force is occurring, (although it's being compensated for with rudder so the airplane isn't yawing), and precession is not occurring at all.

stek79

Someone has infos about prop pitch and diameter influence on spiraling slipstream strength?

I imagine this is the same thing of asking how wing incidence and span influence downwash... am I correct?

Thanks!