Auto RPM
Joined: Oct 1999
Aviation Qualifications: ATPL
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From: Den Haag
Crab,
if you consider the disc to be flat to begin (I know not correct but easier to explain and should not affect the figures), and the centre of mass of each blade to be at radius R from the centre.
As there is a linear relationship between angular momentum, rotational speed and polar moment of inertia, then if the rotaitional speed increases by 10%, the polar moment of inertia must decrease by 10%. As the mass does not change, this requires the effective centre of mass to be at 0.9R from the centre of rotation (okay, 0.909).
To achieve this, the blade must rise by anticos(0.9) degrees, which is 24.6 degrees.
Similarly, if you raise the blade by 10 degrees, the affective radius becomes 0.985R which would give a 1.5% rise in rotational speed.
This could be entirely flawed logic of course!
I don't dispute the Lynx has coning; of course all a/c have it to varying degrees, but these angles are very large.
What I actually believe is that there are a range of influences simultaneously acting to varying degrees. However it is far too complicated to explain them to student pilots, and so the CoAM theory is used as a simple explanation.
if you consider the disc to be flat to begin (I know not correct but easier to explain and should not affect the figures), and the centre of mass of each blade to be at radius R from the centre.
As there is a linear relationship between angular momentum, rotational speed and polar moment of inertia, then if the rotaitional speed increases by 10%, the polar moment of inertia must decrease by 10%. As the mass does not change, this requires the effective centre of mass to be at 0.9R from the centre of rotation (okay, 0.909).
To achieve this, the blade must rise by anticos(0.9) degrees, which is 24.6 degrees.
Similarly, if you raise the blade by 10 degrees, the affective radius becomes 0.985R which would give a 1.5% rise in rotational speed.
This could be entirely flawed logic of course!
I don't dispute the Lynx has coning; of course all a/c have it to varying degrees, but these angles are very large.
What I actually believe is that there are a range of influences simultaneously acting to varying degrees. However it is far too complicated to explain them to student pilots, and so the CoAM theory is used as a simple explanation.
Joined: May 2002
Aviation Qualifications: ATP+Mil
Posts: 18,633
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From: Downeast
I always heard that one teaches best what one knows the least about. If an instructor cannot understand nor explain what he is putting forth.....should he do so in the first place? Also....is there not a point beyond which "one does not have a need to know" and thus such philosophical discourses could best be left to the bar at the purchase of the nineteenth pint of the evening? This discussion is about as useful as memorizing the number of rivets in a UH-1 (Bell 205) tailboom for use on checkrides.
Joined: Oct 1999
Aviation Qualifications: ATPL
Posts: 7,371
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From: Den Haag
Mr. Selfish,
angular momentum is the product of the polar moment of inertia (sigma mass times radius) (sorry, can't do funny symbols here!) and the angular veocity in radians per second. Therefore the relationship between angular velocity and effective radius should be linear for a given angular momentum. We are not talking about airspeed and drag.
SASless, I take the point; call it idle curiosity!
angular momentum is the product of the polar moment of inertia (sigma mass times radius) (sorry, can't do funny symbols here!) and the angular veocity in radians per second. Therefore the relationship between angular velocity and effective radius should be linear for a given angular momentum. We are not talking about airspeed and drag.
SASless, I take the point; call it idle curiosity!
Joined: Apr 2000
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From: EGDC
I think this is where I make the standard CFS disclaimer that P of F is not an exact science, rather it is an acceptable explanation of something that can be seen to occur eg Nr rise in the flare.
To prove or disprove the CoAM argument will probably take pages of greek flute music (algebra) that would only make my brain melt. Equally to prove or disprove your theory of spanwise variation of driving and dragging sections would require flight test data, knowledge of aerofoil section, washout, taper, lock number, AoA, pitch angle, air density etc etc etc. ..... so I suggest we ask a test pilot - Nick are you there?
To prove or disprove the CoAM argument will probably take pages of greek flute music (algebra) that would only make my brain melt. Equally to prove or disprove your theory of spanwise variation of driving and dragging sections would require flight test data, knowledge of aerofoil section, washout, taper, lock number, AoA, pitch angle, air density etc etc etc. ..... so I suggest we ask a test pilot - Nick are you there?
Joined: Oct 1999
Aviation Qualifications: ATPL
Posts: 7,371
Likes: 926
From: Den Haag
Crab, I agree!
just to add a further dimension to the topic: why should there be conservation of momentum anyway? In autorotation there is a total energy concept, with rotor energy being one of the elements. By flaring or bunting you are changing the energy distribution between the rotor, airframe velocity and rate of descent, so there should be no real reason to assume that the roror enegy stays constant. Indeed, surely this is one reason for the flare at the bottom; to arrest the descent by transferring the enrgy to the rotor? (again, not exactly true, but generally so).
just to add a further dimension to the topic: why should there be conservation of momentum anyway? In autorotation there is a total energy concept, with rotor energy being one of the elements. By flaring or bunting you are changing the energy distribution between the rotor, airframe velocity and rate of descent, so there should be no real reason to assume that the roror enegy stays constant. Indeed, surely this is one reason for the flare at the bottom; to arrest the descent by transferring the enrgy to the rotor? (again, not exactly true, but generally so).
