To Lu:
First of all, I never called you an idiot. I said you have made yourself look like one by the
statements you have made. Obviously you have a lot of credentials. That makes you look even
worse. It's like a scientist going around saying the earth is flat and the planets, sun, and stars all
rotate around it as the center of the universe.
Yes I am biased. I happen to think that Frank Robinson has done as much to better the helicopter
industry as Sikorsky, Hiller, Piasecki, Young, Kaman or any of the other helicopter pioneers.
However, any bias, be it good or bad, cannot alter the physical laws of nature. My bias has nothing
to do with calling you on false statements.
On to your false statements. I'll start with your post to helo teacher on 04 Jan 2001 04:57.
Your statements are in capitals.
THE PURPOSE OF THIS ILLUSTRATION IS TO DISPROVE FRANK ROBINSONS'
PREMISE OF CONSIDERING A 90-DEGREE PITCH HORN IN THE DESIGN OF THE
ROBINSON ROTORHEAD.
IF HE HAD THE OPPORTUNITY TO CHOSE A 90-DEGREE PITCH HORN THEN ANY
VERTICAL MOVEMENT OF THE BLADE (CONING) WOULD TURN THE BLADE INO A
FIRST CLASS LEVER WITH THE CONE HINGE AS THE FULCRUM. IN THIS CASE,
WHEN THE BLADE CONED UPWARDS, THE PITCH HORN WOULD MOVE
DOWNWARDS AGAINST A FIXED PITCH LINK.
THIS RELATIVE MOVEMENT WOULD CAUSE THE BLADE TO INCREASE PITCH AS IF
THE PITCHLINK HAD BEEN MOVED RELATIVE TO THE BLADE.
Ok, here I agree, this is pitch cone coupling. And with a 90 degree pitch horn it would certainly be a
factor.
IN ORDER TO CONE, THE PILOT HAD TO PUT IN ENOUGH PITCH TO LIFT THE
HELICOPTER OFF THE GROUND.
False. Any increase in collective pitch will produce coning. Coning is a function of centrifugal
force and lift produced by the blade. Therefore any amount of lift produced by even the smallest
amount of collective will produce a certain amount of coning.
AT THE SAME TIME, THE CONING ACTION WITH A 90-DEGREE PITCH HORN WOULD
PRACTICALLY DOUBLE THE PITCH RESULTING IN BLADE STALL OR VERY CLOSE
TO BLADE STALL. IF THE PILOT HAD SUFFICIENT POWER TO GET THE HELICOPTER
OFF THE GROUND AND MOVED THE CYCLIC IN ANY DIRECTION HE COULD ADD
ANOTHER 5-6 DEGREES OR MORE TO THE ALREADY HIGH PITCH IN THE ROTOR
SYSTEM.
Wrong again. It would not double the amount of pitch in the blade as you will see later in this post.
You are saying this as if the blades won't cone at all until pilot has pulled in enough collective to
lift off, and then suddenly the blades will cone increasing the pitch just as suddenly nearly stalling
the blades and producing so much drag the engine can't produce enough power to maintain RPM.
This is ludicrous.
As for the cyclic. If the R22 had a 90 degree pitch horn there would be no pitch FLAP coupling.
When you apply cyclic the rotor tilts "flaps" in a direction. This means one blade goes up when the
other is down or vice versa. When this happens the coning hinges DO NOT move. The
TEETERING hinge DOES moves but our 90 degree pitch horns are in line with the teetering axis.
Therefore, there is NO resultant change in blade pitch from anything other than the actual cyclic
control input made by the pilot.
Now lets look at what would really happen if we were to try lifting off into a hover in an R22 with
a 90 degree pitch horn.
I am going through this step by step so there is no question about how I will arrive at my
conclusion. And it will be there for anyone to see in case I have made any errors.
First of all we need to establish some parameters.
1. how much do the blades actually cone when the R22 is in a hover?
2. how much will blade pitch increase from a given amount of coning with a 90 degree pitch horn.
Unfortunately I do not have the detailed specs for an R22 that I need to establish these parameters,
so they will be off a little, but they will be very close and if anyone wants to get the exact numbers
and run them, be my guest.
To calculate the coning we need to know two things.
1. the amount of centrifugal force acting on a single R22 blade at flight RPM
2. the amount of lift produced by a single R22 blade.
I will assume that an R22 blade weighs approx. 40 lbs. and that its spanwise center of mass is at
50% of the span.
Centrifugal force = Mass x Velocity squared. There are a couple of extras to go with that.
Velocity will be in the angular velocity unit of radians per second. And to put our blade weight into
the proper unit of mass we must divide the number of lbs by the acceleration force of 1g which is
32.2 ft/sec squared.
40 lbs divided by 32.2 = 1.2422
The R22 flight manual says, if I am not mistaken, that the 12.5 ft radius rotor has a tip velocity of
672 ft/sec at flight RPM.
Radians/sec = tip velocity divided by the rotor radius = 53.76 radians/sec
53.76 is of course the velocity so we have to square it.
2890.1376
multiply this by our mass.
1.2422
and we get
3590.1289
one last step, we must multiply this by the radius of the blade center of mass.
6.25 feet
Centrifugal force = 22,438.3058 lbs per blade
Now the lift part is simple, if we are at max gross weight that 1370 lbs. There are 2 blade so we
divide by two and find that we need to produce 685 lbs of lift per blade in order to hover.
Technically we need slightly more than that initiate the ascent into a stabilized hover.
Now we need some trig to figure out the coning angle from these two factors.
Lift divided by centrifugal force = 0.0305 ATAN = 1.7486 degrees of coning per blade.
whew! That solves our first problem. Now we need to know the pitch cone coupling ratio so we can
figure out how much more blade pitch we have at a hover with a 90 degree pitch horn.
Now, instead of running through exact numbers like: if the blade goes up 1.7486 degrees then the
pitch link will go down xx.xxx inches but since it can’t go down due to the swash plate then it will
rise relative to the blade feathering axis causing x.xxx number of degrees increase in blade pitch.
What I WILL do is establish a ratio for coning to feathering. And since I do not know the exact
dimensions of the pitch horn in relation to the coning and feathering axes. This will let us play with
a range of possibilities.
The pitch cone coupling ratio will depend upon two distances. The first distance is: from, the center
of the pitch link upper rod end bearing, to, the center axis of the coning hinge. The second distance is:
from, this same pitch link upper rod end bearing, to, the feathering axis about which the blade
changes pitch. I also must clarify that these distances are to be measured normal to, or
perpendicular to, the respective axes. By the way, if this gets hard for anyone to visualize from reading alone, draw it out, most of you probably know basically what a R22 rotorhead looks like.
The first distance decides how much the feathering axis will move below the pitch horn for a given
coning angle change. The longer the distance the more it would want to move. The second distance
decides how many degrees the blade will change pitch due to the feathering axis moving below the
pitch horn. The longer the distance the less the pitch angle will change. So if both distances are
equal, then one degree of coning will increase the pitch by one degree. If however the first distance
is let’s say half of the second, then 1 degree of coning will only produce 0.5 degrees of pitch
increase. So we can say that the ratio of the second distance to the first equals the ratio of coning to
pitch. Now, I don’t know the actual distances for the R22 but I would say from memory that the
pitch horn is farther away from the feathering axis than a 90 degree one would be from the coning
hinge axis. If this is the case then there would be less pitch change for an amount of coning. But lets
go with worst case and say they are the same. 1.7486 degrees of pitch would be compensated for by
the pilot unknowingly raising the collective I would guess about an inch and a half to 2 inches less
than he would for the 72 degree pitch horn without the pitch cone coupling properties. And of
course if the aircraft were to be certified this way they would simply have the controls rigged slightly
different. Remember I’m not using the real dimensions here, and more than likely the pitch cone
coupling ratio would actually be less and the pilot would probably have less than 1 inch collective
difference between the different pitch horn angles. If you must, find the actual dimensions and run
the numbers. See what you get.
[This message has been edited by helisphere (edited 14 January 2001).]