P-factor puzzles me

[Murmur]

A brief recall: when the aircraft has a significant AoA, the downgoing blade
of the propeller has a higher velocity (and a slightly higher angle of
attack as well) than the upgoing blade. So, the downgoing blade produces
more lift than the upgoing blade. This difference of thrust produces a left
yawing moment (for a counterwise rotating prop) that must be corrected with
right rudder.
(see also http://www.av8n.com/how/htm/yaw.html#sec-p-factor)

My doubt is: shouldn't we consider gyroscopic effects? In other words, the
torque produced by the difference of thrust between the blades, should
produce a PITCHING UP moment, and not a LEFT YAWING moment.

In effect, that's what happens with helicopter: when the pilot moves the
cyclic forward, the blades of the rotor reach (I'm considering a CCW
rotating rotor when seen from above) the HIGHEST PITCH (and lift) at 270
degrees (left side) and the LOWEST PITCH at 90 degrees (right side). The
gyroscopic effects then causes to rotor to PITCH DOWN, and not to ROLL
RIGHT.

What's the fault in my reasoning?

Marco

[Don Stauffer]

Yes, there IS gyroscopic reaction. However, generally the P-effect is
stronger.

For the rotor on a chopper, remember that we are talking about the
precession of the rotor, which is in effect 'gimballed'. The fraction
of the moment of inertia that is involved in the reaction is 100%. For
the propeller to torque an entire fixed wing aircraft, consider the
moment of inertia of the propeller is a small fraction of the moment of
inertia of the whole vehicle.

Also, gyroscopic reaction is a function of angular rate of pitch. One
needs to pitch up or down at a high rate for the gyro effect to take
hold. This is not true for the P-effect. It happens even when there is
NO pitch rate, only a fixed pitch angle between engine axis and relative
wind.

[Tom Sanderson]

> My doubt is: shouldn't we consider gyroscopic effects? In other words, the
> torque produced by the difference of thrust between the blades, should
> produce a PITCHING UP moment, and not a LEFT YAWING moment.

Nope.

For one thing, this isn't a gyroscopic effect. Gryo effects are the results
of the angular momentum of the propellor...as long as you don't change the
angular momentum (i.e. change the aircraft attitude) there aren't any gyro
effects.

As for the p-factor, you're right that the blade moving into the slipstream
sees a higher airspeed and higher blade AoA. This manifests as maximum
blade lift when the blade is at 9 o'clock (CCW prop, forward-looking-aft)
and minimum when the blade is at 3 o'clock, hence the left yaw. When the
blade is at 12 o'clock and 6 o'clock the blade velocity is perpendicular to
the a/c velocity so there's no thrust differential and, since propellors
usually don't have any dihedral, no moment.

> In effect, that's what happens with helicopter: when the pilot moves the
> cyclic forward, the blades of the rotor reach (I'm considering a CCW
> rotating rotor when seen from above) the HIGHEST PITCH (and lift) at 270
> degrees (left side) and the LOWEST PITCH at 90 degrees (right side). The
> gyroscopic effects then causes to rotor to PITCH DOWN, and not to ROLL
> RIGHT.

Once again, that's not a gyroscopic effect, but that's not really the issue.
There are a couple of things about helicopters that make the situation not
directly transferrable to an airplane prop. The biggest is that a
helicopter blade does not have fixed AoA while a propellor does. This is
not to be confused with variable pitch props; in this case we're talking
about variation within a single rotation.

When you push the cyclic forward, you move the swashplate in the rotor to
increase the angle of attach of the blades in the back half of the rotor and
decrease it in the forward half. This causes the blades at the back to
climb and the blades at the front to dive, creating a pitch down moment and
forward thrust. You also get a p-factor effect where the advancing blade
generates more lift than the retreating blade, but this isn't as large an
effect as the cyclic-induced differential thrust. Some helicopters also use
single-pin hinges on the blades which allow the blades to naturally swing
forward and aft, negating some of the speed difference between the sides of
the rotor.

Tom.

[Ken Rose]

> What's the fault in my reasoning?

Don't know that anything is wrong with your reasoning, it's just that
any pitch change is handled by the airplane's pitch stability (which is
already dealing with a lot), while the movement of the thrust center to
the right is only handled by the pilot's foot.

- ken

[Matthew Willshee]

Let me first say I don't know much about helicopters. Is the change in
rotor pitch really 90 degrees out of phase to the movement of the cyclic
control? I would have thought that was very confusing - but then I have
heard that flying helicopters is exactly that.

On the gyroscopic progression question I think you are probably confusing
moments with movements... That is a gyroscope's axis moves at 90 degrees to
the applied moment but that doesn't change the direction of the moment. So,
your prop plane flying pitch up is subject to a left yawing moment due to
the propeller aerodynamics plus a right yawing moment from the rudder. They
add up to no applied moment so there must be zero angular acceleration and
hence no change in attitude.

When a net applied moment remains because the moments from the prop and
rudder aren't balanced things probably get quite interesting...

The propeller on its own would move pitch-up when subject to a net
left-yawing moment because of gyroscopic precession but the plane itself is
not spinning so will react conventionally. What exactly happens to the
(plane + prop) system as a whole is going to be somewhere in between and
depend on the balance between these two influences. I feel like I'm hitting
the limits of my rotating dynamics knowledge - but surely there's some sort
of scale you could stick various devices on...

1) Prop-powered plane - Low gyroscopic influence - relatively slow
rotating mass, small compared to whole aircraft
2) Helicopter / Jump Jet - Important gyroscopic influence - large, fast
rotating mass
3) Boomerang - All gyroscopic - All mass is rotating.

The harrier notably has the two spools of its engine rotate in opposite
directions to try and balance out the gyroscopic effects.

The boomerang example I owe to one of my college lecturers, who was
Australian. Throw your with the axis horizontal and the upper surface of
the aerofoils pointing left. Flick your wrist so that the top blade is
advancing and the bottom blade receding. The top blade generates more lift
so there is a net moment. The boomerang responds to the moment by turning
left so that, if you get the centripetal force (also from aerodynamic lift)
and rate of turn just in the right balance, it flies round in a circle.

Regards,
Matthew

[Peter Wezeman]

Gyroscopic forces exist, but they are transitory, acting only while the
aircraft is undergoing angular motion. Once the aircraft is established
in a climb angle the gyroscopic forces would cease. Perhaps the most
notable example of the importance of gyroscopic forces are the old
rotary engines used in World War One fighters such as the Sopwith
Camel; the engine block, rotating at prop speed, was a good fraction of
aircraft's weight. It made a big difference between turning right and
left.

Peter Wezeman
anti-social Darwinst

[Murmur]

> When you push the cyclic forward, you move the swashplate in the rotor to
> increase the angle of attach of the blades in the back half of the rotor
> and
> decrease it in the forward half. This causes the blades at the back to
> climb and the blades at the front to dive, creating a pitch down moment
> and
> forward thrust.

That's not correct. See:

http://www.tpub.com/content/aviation/14018/css/14018_394.htm

"The spinning main rotor of a helicopter acts like a gyroscope.." [..] "A
downward force to the right of the disc area will cause the rotor to tilt
down in front." [..] "To simplify directional control, helicopters use a
mechanical linkage that places cyclic pitch change 90 degrees ahead
of the applied force. Moving the cyclic control forward will cause
high pitch on the blades to the pilot's left. At the same time, low pitch
occurs on the blades to his/her right. This combination of forces results
in the rotor tilting down in front."

or:

http://www.repairfaq.org/filipg/RC/F_RC3.html#RC_010

"In order to get the helicopter's rotor disk to tilt (for example) downward
at the front, you increase the lift on the right side of the rotor disk and
decrease the lift on the left side of the rotor disk. (This is assuming the
standard clockwise main rotor rotation.)"

Marco

[Tom Sanderson]

> http://www.tpub.com/content/aviation/14018/css/14018_394.htm
>
> "The spinning main rotor of a helicopter acts like a gyroscope.." [..] "A
> downward force to the right of the disc area will cause the rotor to tilt
> down in front." [..] "To simplify directional control, helicopters use a
> mechanical linkage that places cyclic pitch change 90 degrees
> ahead
> of the applied force.

It's right that the linkage is torqued off axis, but the reasoning is wrong.
Gyroscopic effects take place only when the angular momentum of the rotor
changes, such as transient conditions. During stable flight, you don't have
any gyroscopic effects.

When you push forward on the cyclic, the forward thrust comes from increased
blade lift at the rear half and decreased at the forward half (which points
the rotor lift vector forward). There is *also* a bias to increase lift on
the left side and decrease on the right to counteract the different
airspeeds each blade sees on each side and p-factor effects from the rotor
being tilted relative to the slipstream.

So, yes, the linkage tips the swashplate in a different axis than the cyclic
moves, to counter p-factor and forward velocity effects which change the
lift on each side, but that, by itself, doesn't give you any forward thrust.
When you first push the cyclic, gyroscopic effects will indeed tip the nose
down, but this torque stops as soon as the rotor reaches a stable attitude.

Tom.