Item 1605.html
OTHER:
Helicopter - Outside - Side-by-Side
-
Cornu, Paul, 1907 - First flight

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Letter
to the American Helicopter Society ~ Submitted, but Unpublished
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Ms. Kim
Smith Subject:
Letter to the editor: The paper
'Engineering Analysis of the 1907 Cornu Helicopter' by Gordon Leishman and
Bradley Johnson, in the July 2009 issue of the Journal of the America
Helicopter Society, presents a very interesting story of Paul Cornu and
his efforts to advance the development of helicopters. However, I
question the paper's claim that "the engineering analysis described
in this article is unequivocal." My questioning relates to the
assumptions of; a Figure of Merit of 0.5, and a Transmission Efficiency of
0.75. This figure
of merit is based on the craft having flat blades, whereas pictures show that
the blades are undercambered. Secondly, calculations show that wide-chord,
slow turning rotors improve efficiency. Thirdly, Cornu used the side-by-side
configuration, which is the most efficient arraignment for hover. IMHO, a
meaningfully higher FM would be more reasonable. The power
transmission from motor to rotors was by flat-belt. Flat-belt were a well-known and much-used means of transmitting
power in machine shops, including Cornu's shop. Today's flat-belts are
capable of efficiencies up to 0.98, therefore it
could be assumed that the one-minute long eliminations of the belt slippage
would have temporarily increased the power at the rotors. There is
nothing indicating that Paul Cornu did not achieve short-term vertical
flight. Perhaps, his disappointment regarding the Deutsch Archdeacon Grand
Prix, and disenchantment with the future potential for his current design
caused him to refrain from further promotion, and return to engineering and
patenting advancements, such as a conventional swashplate
system. Dave
Jackson Vancouver, Canada |
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Subsequent Paper and Response ~ added October 27, 2012
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Cornu's
Rotorcraft and Its Specifications etc. For the consideration of lift with
minimal power:
§ Engineering Analysis
of the 1907 Cornu Helicopter by
Dr. Gordon Leishman and graduate research assistant Bradley Johnson
§ Consideration
about this paper in the Journal. In computer but not on web site. Reference file: ‘CornuVsRevisionistHistory.html’
~ in response to the following paper. Not yet posted on Internet. Eventually
link to from this long page.
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Leishman
uses Momentum theory to evaluate.
From
Helicopter Theory page 30
2-1.2
Momentum Theory in Hover
Consider
an actuator disk of area A and a total thrust T (Fig.2-1) It
is assumed that the loading is distributed uniformly over the disk.
Pideal = Tv = T√T/2ρA
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Wing - Blade Aspect Ratio
Comparison:
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Aspect
Ratio |
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Sailplane: |
20:1 |
http://www.sailplanedirectory.com/zwf2.htm |
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Spitfire: |
5.6:1 |
http://www.rdrop.com/users/hoofj/SpitIX.htm |
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Cornu: |
4.2 |
Which
includes the span of the large cutout. |
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SynchroLite
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22:1 |
With 3-blades per rotor. |
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Calculations; MT and BEMT
from Access Database Program:
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Comparisons:
See
tables on these pages;
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Comparison
Gyrobee to Cornu flying in ground effect.
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Threads
on Forums:
· Thread on Rotary Wing Forum: Engineering
Analysis of the 1907 Cornu Helicopter
· Thread on PPRuNe: 2007:
Centennial of the Helicopter?
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Bringing
Conventional Momentum Theory and Blade Element Theory Closer To Cornu's
Calculations:
o The conventional Momentum Theory and Blade Element Theory
should probably be reduced by 10% to account for the lack of tail rotor. See: http://www.unicopter.com/B329.html#Tail_Rotor
o
Then the value should probably be
reduced due to the very large cutout of 0.3R. 27 sq-ft
/ 304 sq-ft = -.9% off of the above value.
o Then the value should probably be reduced again due to the
very wide chord and the slow rotor rpm. See: tables on DESIGN: UniCopter ~
Rotor - Disk - Large Chord & Low Tip Speed
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Inverse Taper:
"...
from whatever payload advantage resulted from its
increased aerodynamic performance in hover and vertical climb. (Some
preliminary studies indicate that perhaps inverse taper holds some promise in
this regard.)"
~ by Prouty [RWP1 p.649]
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Antoinette engine:
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Access Forms:
The
following calculations are based on 1 of the 2 disks.
Test
Conditions:

The above note has been removed. It is Theta. The AofA is calculated for each element. See 'Elements' form.
After
August 16, 2009 review.
o The Collective pitch has been taken up to 14.8º.
Helicopter
Specifications:

After
August 16, 2009 review.
o The above program assumes a very small cutout ratio. It therefore
does not consider the cutout when calculating the rotor solidity ratio. In
addition, the revised measurement of Cornu's rotors shows a larger cutout of
0.4 of R. then that shown above.
o The airfoil has been changed from 8-H-12 to NACA 0012.
o The latest give rotor speed is 85 rpm. I have arbitrarily
doubled the rotor speed to 170 rpm and the Angle of Attack to 14.8º.
Momentum
Method:

After
August 16, 2009 review.
o The Power [P] is now showing 9.41 hp.
Flight
Hovering:

August 16, 2009 review.
o The Horsepower [hp] is now be
showing 9.8 hp. ![]()
Additional Information on
the Ability of the Cornu Helicopter to Hover in Ground Effect:
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Note Related to Coding of
Prouty's Momentum and Blade Element in Hover:
The
results of these calculations may give a 'required power values' that are too
low. This may be because the algorithms were meant for larger
helicopters.
See; OTHER: Helicopter - Outside - Single (1 seat) - Sikorsky VS-300
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A Revised
Version the above 'Engineering Analysis of the 1907 Cornu Helicopter ' ~ by
Gordon Leishman and Bradley Johnson: ~ The
Journal of the American Helicopter Society (July 2009). ~ August 16, 2009
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To
continue being the devil's advocate. ![]()
A
different means of comparison ~
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----------------------------------- |
Cornu Helicopter: |
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Gross Weight: |
518 lb (w/ 110 lb sand bag) |
450 lbs |
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Wing/Blade Area: (1) |
4 * 14.4 sq.ft. = 58 sq.ft. |
225 sq.ft. |
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Engine: |
Antoinette |
Corsair Black Devil |
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Power: |
24 hp. |
22 hp. |
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Power Transmission: |
Mechanical (flat belt) ~ 5-10% loss |
Aerodynamic ~ 15% loss |
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Velocity: (0) |
.85R * 2 * 9.84 ft (2) * π * 85 rpm = 4,468 fpm = 50mph = 74 fps (0) |
35 mph = 51 fps |
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Rate of Climb at Gross Weight: |
None - hovering flight |
500 fpm. (3) |
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Lift: L = (1/2) d v2 s CL (3) |
v2 s CL = 742 x 58 = 317,608 |
v2 s CL = 512 x 225 = 585,225 |
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Notes: |
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1.
Speed at 85% of blade span. 85% is
used due to very large cutout and reverse taper.
2.
These wings (blades) have a partial
elliptical shape and this might reduce the induced drag.
3.
The article states; "The
blade length was 1.8 m and had a chord of 0.9 m at their maximum point near mid-span.
This means that the total rotor radius was 0.9 m (radius of inner spoked hub) plus 1.8 m (blade length) to give 2.7 m (8.86
feet). ~ [By some accounts, however, the rotor radius was reported to be as
much 3.0 m.]". The views of the rotors show that that the root edge of
the blades are 10% of the span beyond the radius of the spoked
hub and this gives a rotor radius of 3m ( 9.84 feet).
In addition. The maximum chord appears to be near mid span of the blade and
this is near 70% of rotor radius.
4.
Prouty's Momentum theory (assuming that my coding in the Access database
for this was correct many years ago)
says that the power to hover must be increased by 52% to give a rate of climb
of 500 fpm,
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A
further comparison after reading the Cornu section that was added to Leishman's
revised book 'Principals of Helicopter Aerodynamics' ~ August 16, 2009
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-------------------------------------------------------------------- |
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Airfoil: |
Very thin undercambered, but Calculated using 8-H-12 |
Calculated using 8-H-12 |
VR-7 |
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Gross Weight: (lbs) |
575 (5) |
550 |
525 |
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Disk Area: (sq-ft) |
608 | 512 (1) |
254 |
346 |
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Disk Loading: (lb / sq-ft) |
0.95 | 1.12 (1) |
2.16 |
1.52 |
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Blade Area: (sq-ft) |
58 |
10.88 |
11.72 |
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Blade Loading: (sq-ft) |
9.91 |
50.55 |
44.80 |
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Rotor Speed: (RPM) |
170 (6) |
500 |
500 |
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0.095 |0.113 (3) |
0.043 |
0.034 |
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Power - Momentum Theory: (HP) (4) |
2 * 9.41 = 18.82 (7) |
28.76 |
19.94 |
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2 * 9.81 = 19.62 (7) |
28.02 |
22.91 |
Notes:
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In
addition, the latest edition of 'Principles of Helicopter Aerodynamics' by
Gordon Leishman includes his assessment of the power required for the Cornu
helicopter to hover, on pages 72 & 73. He calculates the Ideal Power to be
14.7 HP. This is then multiplied by a Figure of Merit of 0.5 and a Transmission
Loss of 0.75, to give a Required Power of 40 HP.
However,
no supporting information has been given for the guestimates of FM = 0.5 and TL
= 0.75. Whereas, the above sections; A/, B/, C/ & D/, give a rational
for significantly greater efficiencies.
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IMHO, the available information suggests that
the helicopter could have hovered and may have hovered for very short
intervals, but that the craft was unstable and uncontrollable. The Side-by-side
is the optimum one for efficiency, therefore It may be
the controllability that caused Cornu to look at alternative configurations.
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Concluding Remarks:
Cornu's
Figure of Merit may (or may not) have been sufficient. The flat-belt
transmission slippage may (or may not) have been solved. Improvements to the
craft's structure may (or may not) have been able to withstand the forces. The
controls may (or may not) have provided short-term stability. Not winning the
D-A Grand Prix Prize of Aviation may (or may not) have been
his reason for moving on to new ideas.
However,
in my opinion, the technical and the tenor in 'Engineering Analysis of the 1907
Cornu Helicopter' may (or may not) be an attempt to support a preconceived
notion.
IMHO, if
the Figure of Merit had be more realistic, if rotor speeds had been extend
beyond 140 rpm, if Cornu's pitch angle of 13º had been used, and the Efficiency
was to take into account temporary minimizations of slippage (partially due to
a larger driving pulley for the faster rotor speeds), then the power to lift
ratio should have looked attractive.
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Miscellaneous Stuff:
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Summation:
·
Conclusion: The above 'Counter-argument' certainly does not claim that
Cornu's craft did or could have successfully flown.
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Last Revised: October 27, 2012