Lateral tilt

XXavier

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Hello all...

I think I've found it. In Gessow & Myers' Aerodynamics of the helicopter. Page 193.

Thanks, anyway...
 

Jean Claude

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Your Zbrozek's formula for b1 does not correspond to the one mentioned on page 193, Xavier

Why do you think that b1 couldn't be bigger than a1?
 

XXavier

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I saw Zbrozek's formula in this paper: https://booksc.xyz/book/52119531/086d29. Yes, I know it´s different from the one mentioned in page 193 of Gessow & Myers 'Aerodynamics of the helicopter'.

It seems to me strange that the lateral tilt may be higher than the blowback tilt... But that's just intuition... It's true that µ is smaller at low airspeeds, but there's the 4/3 factor...

BTW, I'm again stuck with the formulas in page 193 of Gessow & Myers. I may do as explained there and equate this

Captura de pantalla 2020-08-12 a las 15.18.00.png

to zero, but then I can't give a value to the variable r, the distance from the 'relevant section of the blade' to the rotation/flapping axis...

Any help will be welcome...
 
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Jean Claude

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In my opinion, r= 0.7R must be close enough to the truth, when the chord is constant
 

XXavier

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In my opinion, r= 0.7R must be close enough to the truth, when the chord is constant

That's what I was going to do at first, since the usual 'reference section' of a propeller is usually taken at 0,7R, but the rotor of a gyro doesn't work like a prop (or a helicopter rotor)...

Anyway, I'll try with r=0,7R and then see if the result looks plausible...

Thanks...

P.S. Editing after realizing that I had made an arithmetical mistake. Now I get b1 = 0,87º with Zbrozek's formula. The other angles are a0 = 3,3º and a1 = 2,5º. For my ELA @ 320 rpm and 100 km/h.

Those figures now seem right...

Editing again. Using the Gessow & Myers formula, and taking r = 0,7R, I get b1 = 0,91º Quite close to the results above...
 
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Jean Claude

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The values given by these formulas, are in excellent agreement...among themselves.
But are they as close to reality?

My doubt comes the algebraic analysis seems not take into account the non-uniformity of the induced velocity while it is not negligible at low Mu
The angle of attack of the blade sweeping in front is thus greater than that of the blade sweeping behind, and not only because of the coning.
This increases significantly b1at low forward speed.

Sans titre.png
 
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Jean Claude

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PS Table I of the Naca report 475 shows that the Pitcairn PCA 2's rotor gives an angle b1 greater than a1, to slow forward speed.

Flight n° 10 45 km/h a1= 1.1 degree b1= 2.6 degrees
Flight n° 7 75 km/h a1= 1.5 degree b1= 3.2 degrees
Flight n° 3 125 km/h a1= 3.1 degree b1= 3.5 degrees
Flight n° 6 145 km/h a1= 4.0 degree b1= 3.5 degrees
 
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XXavier

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Interesting... Very relevant data, as the values were actual values, recorded in flight with cameras.

Captura de pantalla 2020-08-13 a las 12.39.19.pngCaptura de pantalla 2020-08-13 a las 12.39.19.png
 

Jean Claude

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My calculation for an ELA (8.28 x 0.22 m, aerod pitch 2.8°) at 450 kg and 120 km/h and sea level gives:
381 rpm
A.o.A disc = 9°
a0 = 2,8°
a1 = 2,15°
b1 = 1,06°
It takes into account the non-uniformity of the induced speed.
 

XXavier

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My calculation for an ELA (8.28 x 0.22 m, aerod pitch 2.8°) at 450 kg and 120 km/h and sea level gives:
381 rpm
A.o.A disc = 9°
a0 = 2,8°
a1 = 2,15°
b1 = 1,06°
It takes into account the non-uniformity of the induced speed.

My figures are, for my ELA [8.50 x 0.20 m, pitch 3°, 390 kg, 120 km/h and 330 rpm at 1000m above sea level]:

AoA disc = 4,8°
a0 = 3,3°
a1 = 2,9°
b1 = 1,0°

For AoA disk, a0 and a1, I used formulas from 'Flugphysik der Tragschrauber', and for b1 I followed Gessow & Myers...
 

Jean Claude

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It is difficult to know the actual pitch of the blades in flight, because of the possible twisting .
However, your angle of attack of the disc seems to me very underestimated. This would imply an exceptional L/D ratio of 11.9, only believable at mu of 0.35
Are you sure it is not the angle of the shaft?
For my calculations I assume cD0 = 0.011
So, at 1000 m above sea level, 390 kg, and dia. 8.5 m, I obtains 7.6° (disc) or 7.6° - a1° = 4.6° (shaft)
 
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XXavier

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It is difficult to know the actual pitch of the blades in flight, because of the possible twisting .
However, your angle of attack of the disc seems to me very underestimated. This would imply an exceptional L/D ratio of 11.9, only believable at mu of 0.35
Are you sure it is not the angle of the shaft?
For my calculations I assume cD0 = 0.011
So, at 1000 m above sea level, 390 kg, and dia. 8.5 m, I obtains 7.6° (disc) or 7.6° - a1° = 4.6° (shaft)

In the book that I follow (Flugphysik der Tragschauber), the AoA is about 5º for 120 km/h... (Their gyro is a MTO, a copy of the ELA)

SSSgraph6 1.jpeg

That's more or less what I'm getting...

AlphaR is the AoA of the disk. This is the description of that variable in the book:

Captura de pantalla 2020-08-16 a las 15.46.44.png


(...) the angle between the flowing air and the rotor plane (...)

Captura de pantalla 2020-08-16 a las 16.06.28.png
 
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Jean Claude

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The angle of attack of the disc is related in parts to losses by profile power of the blades (Cd0)
I noticed that some studies consider Cd0 of the laminar profiles obtained in wind tunnel (0.006)
Hence, probably, the low mentionned angle.
However, this laminarity seems to me illusory on the rotary wings and cD0 = 0.011 seems more reasonable.

Note that disc AOA = 3.5° gives L/D>16, which has never been observed on a rotor.
 
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XXavier

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Well, it may be as you say, and I know that books are not always right, but 'Flugphysik der Tragschrauber' is a well-regarded book co-written by Holger Duda, an expert in aerospace research https://www.researchgate.net/scientific-contributions/75867332-Holger-Duda

The publisher –Springer Vieweg– is a very prestigious publisher in the field of scientific and technical books...



The book can be downloaded here: https://1lib.eu/book/2870637/39d9da

P.S. In this paper:

Captura de pantalla 2020-08-16 a las 21.33.23.png

I see these graphics, showing a L/D of 16+ for the MTOsport rotor...


Captura de pantalla 2020-08-16 a las 21.31.37.png
 
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Jean Claude

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NACA report n°515 report shows that for the rotor alone of the PCA2, the mesured L/D ratio never exceed 7
Sans titre.png
 

XXavier

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In this paper, https://booksc.xyz/book/62780721/f20813 a recent study using modern autogyros,

Captura de pantalla 2020-08-17 a las 9.30.09.png


there are important differences between calculated and real figures. For example, concerning the AoA of the disk...


Captura de pantalla 2020-08-17 a las 9.09.06.png
 
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Jean Claude

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L/D of our modern rotors is better that 7, due to the high aspect ratio of the blades. L/D max = 11 about (ELA, MTO, Magni's rotor alone)
Value 16 calculated by Dudda is unfortunately unrealistic due to assumed Cd0 (too low)
 

XXavier

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L/D of our modern rotors is better that 7, due to the high aspect ratio of the blades. L/D max = 11 about (ELA, MTO, Magni's rotor alone)
Value 16 calculated by Dudda is unfortunately unrealistic due to assumed Cd0 (too low)


Perhaps... But, for the book, they say they used a specially instrumented MTO, and –I translate the central paragraph– 'The position of the rotor blades in revolution and flapping were detected with two laser sensors fitted on the mast. The position of the rotor in space was determined in all flight situations by measuring the inclination of the control stick, the flapping angle and the inclination- and slip angles at the air flow sensor boom...'

SSSgraph6 3.jpeg


We amateurs might settle the question by carefully photographing a gyro, flying s/l against a clear horizon, from another gyro flying a parallel course at the same altitude... not too difficult and no need for special instruments...
 
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