Every book I've read didn't really explain P Factor in details. I understand the descending blade has higher AOA but Why is that only when we increase the aircraft AOA? I mean if you look at both blades in level flight the descending blade still has higher AOA. I'm trying to find good illustration on the subject besdies the ole descneding/ascending one I see in every book. something that explains how relative wind is changing. on that note... would the ascending blade have higher AOA in a descend or if we lower the aircraft AOA? Thanks.
P-Factor and Relative wind!
- Thread starter VDEE7
- Start date
I dont see how the relative wind is perpendicular to the rotational velocity!! isn't the angle between the cord line of the blade and the relative wind?
Do you have one for the ascending blade? I tried to zoom in to read the vectors (Vs) and what they mean on your illustration!
Thank you.
Do you have one for the ascending blade? I tried to zoom in to read the vectors (Vs) and what they mean on your illustration!
Thank you.
tgrayson
New Member
We must be careful about terminology here. There are two relative winds. One if them is produced by the forward motion of the aircraft; the other is produced by the rotation of the propeller. I've tried to limit my use of the term to that produced by the aircraft's forward motion, in order to be consistent.
When the aircraft isn't moving, the only angle of attack seen by the propeller is produced by its own rotation; as it starts moving forward, the relative wind of the aircraft adds to the relative wind produced by the rotation to produce a new, total relative wind, with a new direction and new velocity.
No. First understand this side, then we'll talk about the other.
fish314
Well-Known Member
You have to be careful with your terminology here, because it is very easy to wind up talking about two different (yet both correct) relative winds.
So let's make it very clear which relative wind we are talking about. Realize that there will be a relative wind that is associated with the entire airplane, and that is the relative wind that is seen by the wing. (Actually, there are some small effects that change that relative wind slightly around the wings, but it's close enough for government work to think of them as the same). Basically, this relative wind is what we are normally talking about when we use the term. In the picture that Tgrayson posted, that's the V that is at the bottom of the triangle. I can't quite read the label he put on there on my computer, but it looks like Vs or maybe V with an infinity sign on it. That's the relative wind of the AIRPLANE as a whole. And of course the angle between the chord line of the wing and the relative wind of the AIRPLANE is the airplane's angle of attack.
But remember that the propeller blade is basically just a little tiny wing. It has a chord line and a motion to it, and therefore it has a relative wind and an angle of attack all it's own as well. The propeller has motion from two sources. First the whole AIRPLANE is moving forward, and second the blades of the propeller are spinning. In the picture Tgrayson drew, the motion from the blades spinning is Vrot. Of course the motion from the whole airplane moving forward in space is the same Vs or V infinity. (I wish I could read that symbol
). If you put those two together you get the relative wind that the propeller sees, which is different than the relative wind seen by the whole airplane. Tgrayson labelled the relative wind as seen by the propeller as Vres, which probably stands for "resultant", which is what you call it when you add two vectors (or two arrows) together. I'll follow his lead and call the relative wind for the whole AIRPLANE, Vs, I'll call the relative wind for the propeller, Vres (for resultant), and I'll call the motion of the air around the propeller that is due to JUST the rotation, Vrot.
So on to the answer to your question. Why is the relative wind of the AIRPLANE perpindicular to the Vrot (at zero angle of attack)? Well, from the discussion above hopefully you can already see why. Assume for sake of argument a zero angle of attack for the AIRPLANE. The AIRPLANE is travelling straight forward (along it's longitudinal axis), and the propeller is travelling in a circle that is perpindicular to that direction.
Now what happens when you increase angle of attack (OF THE AIRPLANE)? Well, that circle that the propeller is spinning in gets tilted. Specifically the bottom of the circle (the prop arc, as it's usually called) moves forward and the top moves back. So some of the relative wind OF THE AIRPLANE, Vs, is now moving along the same direction as Vrot, which causes the length of Vres to get bigger. In other words the speed of the relative wind of the PROPELLER (Vres) goes up on the descending blade, which causes the descending blade to produce more "lift".
Of course "lift" on the propeller blade is really just THRUST. So that effect produces more thrust on the descending propeller blade.
The other effect is this: Because the Vs and the Vrot are more aligned (still talking about just the descending blade, now), Vs doesn't cause the angle between Vrot and Vres to be as big. If that angle shrinks (the angle between Vres and Vrot) than the angle between Vres and the chord of the propeller must grow, since the chord of the propeller and the direction of rotation are FIXED. If you are having trouble seeing this, imagine the airplane at 90 degrees of angle of attack. In that case, the Vs and the Vrot would be perfectly aligned, so adding them together, Vres would also be perfectly aligned. Which would mean that the angle between the chord of the propeller and Vres would have become the same as the angle between the chord of the propeller and Vrot.
But the angle between the chord of the propeller and the Vres is the angle of attack of the PROPELLER blade! Since that angle grew, it also means that the "lift" of the descending blade would increase due to that effect as well!
So BOTH effects produce more "lift" on the descending propeller blade (or, really it's more THRUST).
VDEE7 said:
The ascending blade is going to behave the exact opposite. If you get comfortable with and understand the descending blade, you won't have any trouble understanding the ascending blade, either.
So, back to the big picture: When we fly at a positive angle of attack (OF THE AIRPLANE) we get more thrust out of the descending blade and less thrust out of the ascending blade. If your propeller spins clockwise, as seen by the pilot, that means more thrust from the right side of the prop arc, and less from the left side. Hence, you get a yaw to the left, and you need to add right rudder due to that effect.
Not to mention needing to add right rudder due to spiraling prop wash, gyroscopic effect, and torque, which are the other 3 effects that contribute to the yaw in a propeller aircraft.
tgrayson
New Member
Perhaps it's just my ESP that enables me to sense what fish is thinking at the moment, and urgency to be first motivates me to distill the knowledge to the bare minimum in order to type it more quickly.
tgrayson
New Member
On a simplistic level, you'd have to know what airfoil the prop blade is based on and then look at a diagram called a "drag polar" for that airfoil. Propellers are often based on a "Clark Y" airfoil. Since I'd have to search to find a drag polar for that airfoil, I'll grab one at random...looks like a 9 degree AOA for a NACA 0009.
Still, that's for an airfoil with an infinite aspect ratio and it doesn't take into account the environment of a propeller blade, which is spinning in the wake of other blades. There are most likely a lot of fudge factors that would have to be applied, but at least that gives you the flavor.
<<Also, can you explain why the RPM increases in a descend, and decreases in a climb on fixed pitch propellers?>>
Take a look at the diagrams in my first post, and figure out what influence on the AOA of the blade that slowing/increasing the a/c forward velocity has. You'll see that slowing the airplane increases the AOA seen by the blade, slowing it down; increasing the velocity of the airplane lowers the AOA of the blade, speeding it up. It's not the climb or descent, per se, that produces this effect.
I thought it would be the AOA where Vres and Vrot are the same, which is the highest AOA which gives highest amount of thrust since nothing else besides airspeed would control the thrust (assuming fixed pitch props). maybe thats 9º for that specific airfoil ? or am i missing something ?
tgrayson
New Member
The only time that Vres and Vrot will be the same is at rest. Is the blade most efficient here? Well, no, a fixed pitch blade is partially stalled when the airplane isn't moving. But let's say we advance the forward speed to just the point where none of the blade is stalled, and Vres and Vrot will be a close as they're ever gonna be, is this the most efficient AOA? Again, no. Remember that efficiency isn't measured by the maximum amount of thrust being product, but is instead a ratio of the thrust/drag.
fish314
Well-Known Member
The only times that Vres and Vrot would be the same are:
1. The airplane isn't moving, so Vs is 0, and hence Vres is made up entirely of Vrot.
2. The airplane was moving at an angle of attack (for the airplane, not the propeller) of 90 degrees. In this case, Vs and Vrot would be perfectly aligned, so Vres would also be aligned. Of course this condition is unrealistic, also, because the airplane would be stalled. Most airplanes stall somewhere between 10 and 20 degrees of angle of attack, so 90 is probably impossible to reach, and definitely impossible to hold for any length of time!
That 9 degrees IS for a specific airfoil. The airfoil was called the NACA 0009, which Tgrayson was using as an example, because he didn't have access to the information for an airfoil called the Clark Y. Anyways, there will be a particular angle of attack that is the most efficient for every airfoil, and it will normally be somewhere in the middle.VDEE& said:
The way you find it is by looking at a graph of that airfoil's coefficient of drag versus it's coefficient of lift. What you're basically looking for is the most CL for the smallest CD. Once you have that CL, that corresponds to a particular angle of attack, which you find on plot of coefficient of lift versus angle of attack.
By the way, this is exactly the same idea as L/Dmax for an airplane's airfoil. That happens at a particular angle of attack on the wing. Well a propeller IS a wing, it just happens to spin around. There's some angle of attack that corresponds to the propeller's L/D max. And lift on the propeller blade is really THRUST.
Of course, there probably are some other minor effects due to each propeller following in the wake of the previous propeller. So there may be some adjustment factor or fudge factor, but that's at least the basic idea.
No. First understand this side, then we'll talk about the other.
Okay.. I think I understand this side now.. Let's talk about the other side! I'm having a hard time figuring out where Vres would be. I'm also trying to figure out the difference in thrust between a stationary plane and a plane in 90º angle from the horizon or flight path. shouldn't both blades have the same AOA? or is it more of a speed function kinda like helicopter?
fish314
Well-Known Member
From this statement it sounds like you're still misunderstanding some concepts. Let's start with a stationary airplane.
STATIONARY:
Ok, Vs is the velocity of the airplane, so if the airplane is stationary, that makes Vs equal to 0. If Vs is equal to 0, then the ONLY velocity (and hence the only relative wind) seen by the propeller blades is due to hte motion of them SPINNING, so it's Vrot. Since there is no Vs, the only component available for Vres, is Vrot, so they are the same.
Also, since P-factor is caused by the difference in angle of attack and difference in velocity of the air going over the downgoing blade versus the up-going blade, with no Vs there IS NO DIFFERENCE. So for a stationary airplane, there is no P-Factor.
90 degrees to the Horizon (90 degrees of PITCH):
Now, in the next part of your statement you said "90 degrees to the horizon or 90 degrees to the flight path." Realize that these are 2 VERY different things. Imagine a loop for a second. An airplane in the first part of the loop flying straight up has a flight path that is straight up (90 degrees to the horizon). As the exact moment the airplane is TRAVELLING straight up, it might have a pitch angle very close to 90 nose up, but probably slightly above it, say 92-95 degrees of pitch or so. This aiplane is about 95 degrees to the horizon, but only about 5 degrees to the flight path, since the flight path is straight up. And of course the flight path is exactly 90 degrees to the horizon. So in short, these things are different and you have to be careful about which angle you are thinking about. AOA is the important one. Pitch doesn't matter and flight path doesn't really matter either.
By the way, the angle from the chord line to the flight path is the same as the angle of attack (of the wing). This is because the relative wind is the opposite of the flight path. They are the same lines, just opposite directions.
So long story short is that PITCH angle is irrelevant when talking about P-factor. Also, flight path angle (to the horizon) is unimportant. What IS important is the AOA. 0 AOA will produce no P-factor, positive AOA's will produce some, and negative AOA's will produce some as well, but in the opposite direction (i.e. the nose will go the other way). HOW you get to that AOA is really independent of your airplane attitude.
Yeah I did misspoke there, I meant the plane in 90º pitch but flying straight. which blade would produce more thrust and why?
Now, looking at the upgoing blade picture, what I'm not understanding is why the Vres is coming from right to left instead of left to right since the airplane is traveling in that direction. I keep thinking the Vres should be on the other side of the airfoil! Sorry if I'm boring you guys.
Now, looking at the upgoing blade picture, what I'm not understanding is why the Vres is coming from right to left instead of left to right since the airplane is traveling in that direction. I keep thinking the Vres should be on the other side of the airfoil! Sorry if I'm boring you guys.
tgrayson
New Member
With the relative wind parallel to Vrot, there would be no change in the AOA; however, the downward moving blade will still experience an increase in velocity, so it will generate more thrust, just a like a helicopter.
Because Vrot is *much* faster than V∞. Vrot comes from right to left and V∞ can't affect that much; it just make the angle shallower. If V∞ got very, very fast, it would eventually come from left to right.
fish314
Well-Known Member
Ok, I think I've got what you were asking. Ok, couple of quick assumptions just to simplify things. First, we'll assume that the chord line of the wing and the longitudinal axis of the airplane and the axis of rotation of the propeller are all the same. Basically, all we're saying there is that the wings and the engines are mounted on the airplane "straight" the way you'd "normally" think of them. Only reason that I bring it up is because frequently they aren't. Sometimes engines are mounted just a little bit "crooked" to eliminate yaw in cruise, or the wing may be mounted with some incidence angle for some reason, like stall characteristics. But for the sake of this argument, we'll assume that none of these oddities come into play.
If by "straight" you mean that it is travelling parallel to the horizon, or basically not climbing or descending, but at 90 degrees of pitch, then the airplane is ALSO at an angle of attack of 90 degrees. By the way, this isn't a very realistic scenario in real airplanes, but probably a very good one in terms of basic teaching and understanding.
Ok, so the angle of attack of the propeller then would be whatever the angle is between the propeller blade and the plane of rotation. For a fixed prop, it would simply be the installation angle. And because the Vs and the Vrot are along the same line, both the down going propeller blade and the up going propeller blade would have the same AOA (of the blades, now).
But they wouldn't produce the same thrust. The down going blade (as seen by the pilot) will be moving into or "opposite" the relative wind and the upgoing blade will be moving "with" the relative wind. So even though both blades would have the same angle of attack, the Vres of the downgoing blade would be Vrot PLUS Vs, and the upgoing blade would have a Vres of Vrot MINUS Vs. So the downgoing blade would produce more thrust in this scenario than the upgoing blade, but due to ONLY the difference velocities. This is a peculiarity of the 90 degrees of AOA scenario that you presented.
Now at any AOA (of the airplane) between 0 and 90 the Vs and the Vrot would NOT be aligned, but at exactly 0 degrees AOA both the downgoing blade and the up going blade see the exact same relative wind (same propeller AOA and same Vres, so no P-factor). And as we just discussed at 90 degrees AOA (of the airplane) the upgoing and downgoing blades see the same propeller AOA, but different velocities, so there will be some P-factor (but only from 1 of the 2 causes of P-factor).
Now that you've looked at 0 and 90 degrees of AOA try making a sketch for yourself of the situation at 45 degrees of AOA (of the airplane).