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OTHER: Helicopter - Outside - Side-by-Side - Cornu, Paul, 1907 - First flight

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Letter to the American Helicopter Society ~ Submitted, but Unpublished

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

Subsequent Paper and Response ~ added October 27, 2012

Performance Measurements of a 1/6-Scale Model of the 1907 Cornu Rotor by Leishman (2012)

Response to the Above Paper: Cornu vs. Revisionist History

Cornu's Rotorcraft and Its Specifications etc. For the consideration of lift with minimal power:

• The Helicopter, Paul Cornu; Author: A. Bracke; Translation: Bernard Mettler.
• History of the Helicopter ~ Jean Boulet (translated) Pages 21-24
• Cornu_1.jpg, Cornu_2.jpg, Cornu_3.jpg, Cornu_4.jpg
• Cornu's Helicopter ~ First in Flight? Article by Dr. Gordon Leishman in the 2001 Fall-Winter edition of of American Helicopter Society's publication Vertiflite.
• The two pages; Page 54 & Page 55. ~ Clicking on the pages will double their size. ~
• AHA:, 2007: Centennial of the Helicopter? From the AHS's Web site.

§ Engineering Analysis of the 1907 Cornu Helicopter by Dr. Gordon Leishman and graduate research assistant Bradley Johnson

• The Helicopters ~ Paul Cornu
• Paul Cornu and His 1907 Helicopter: A postscript. Article by Dr. Gordon Leishman in the 2007 Winter edition of of American Helicopter Society's publication Vertiflite.
• A Revised Version the above 'Engineering Analysis of the 1907 Cornu Helicopter ' ~ In the Journal of the American Helicopter Society (July 2009). ~ by Dr. Gordon Leishman and graduate research assistant Bradley Johnson
• A section on Cornu section was added to Leishman's revised book 'Principals of Helicopter Aerodynamics'
• Performance Measurements of a 1/6-Scale Model of the 1907 Cornu Rotor ~JOURNAL OF THE AMERICAN HELICOPTER SOCIETY 57, 032001 (2012). In computer but not on web site.

§ 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.

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.

P_ideal = Tv = T√T/2ρA

Wing - Blade Aspect Ratio Comparison:

	Aspect Ratio
Sailplane:	20:1	http://www.sailplanedirectory.com/zwf2.htm
Spitfire:	5.6:1	http://www.rdrop.com/users/hoofj/SpitIX.htm
Cornu:	4.2	Which includes the span of the large cutout.
SynchroLite	22:1	With 3-blades per rotor.

Calculations; MT and BEMT from Access Database Program:

• Specifications:
• Rotor radius; = 3 M = 9.842 ft
• Cutout: = 0.4 R
• Airfoil selected. NACA 0012. The Cornu airfoils were undercambered
• Twist: None
• Taper: None
• Chord = 2.34 ft.
• Gross weight; 260 kg. = 575 lbs.
• Pitch = 14.8º
• If the belts had not slipped, at 170 RRPM it should have flown, out of ground effect for under 20 hp.
• However, the pitch would have been 14.8º and this might have produced a leading edge stall.
• Momentum Theory, which is what Leishman used, shows 30 hp required. No tail rotor; 8-10% [Western], 10-12% [Kamov] = 10%. This would reduce the required power to 27 hp.
• DESIGN: UniCopter ~ Rotor - Disk - Large Chord & Low Tip Speed leads me to believe that the wide chord (Rotor solidity 0.151) and large cutout has an advantage.

Comparisons:

• De Bothezat claims lifts of 25lb/hp, and 133 lb/hp from the use of slow-turning undercambered blades.

See tables on these pages;

• OTHER: ~ Aerodynamics - Rotor Disk - Dual Configurations
• OTHER: Helicopter - Inside - Principal Assembly - Electrotor-Simplex (Ultralight & UAV)
• No tail rotor; 8-10% [Western], 10-12% [Kamov] = 10%
• DESIGN: UniCopter ~ Rotor - Disk - Large Chord & Low Tip Speed

Comparison Gyrobee to Cornu flying in ground effect.

• Gyrobee Gyrocopter, 500 lbs GW, 38-40 hp
• For the Cornu weight of 575 lb the power would have to be 575/500 * 39 = 45 hp.
• Mechanical vs. aerodynamic power transmission losses; (82% [Prop] * 82% [Rotor Figure of Merit]) - 5% [Mechanical ] = 72%. Therefore 72% of 45 hp = 32 hp
• In vs. out of Ground Effect; 15% - 20% [Leishman] = 17%. Therefore 32 Hp * .83 = 27 hp,

Threads on Forums:

· Thread on Rotary Wing Forum: Engineering Analysis of the 1907 Cornu Helicopter

· Thread on PPRuNe: 2007: Centennial of the Helicopter?

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

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]

Antoinette engine:

• "The Antoinette engine was designed and built in France by Léon Levavasseur. Named after the designer's daughter, it was Europe's most widely used engine until 1909-1910. The first Antoinette engine dated from about 1901 and was used in a speedboat. By 1905, Levavasseur had produced a water-cooled engine with eight-cylinders arranged in a 90-degree "V" and with direct fuel injection. It was safe, strong, and fairly powerful, generating 50 horsepower (37 kilowatts) and weighing about 110 pounds (50 kilograms). Its power-to-weight ratio was not surpassed for 25 years."

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:

• The Cornu Model: Leishman, in his latest article, has stated that "a model weighing up to 18 kg (40 lb) lifted by a 2 hp engine driving two contra-rotating rotors - was to make several sustained flights, in both hover and forward flight, and with many witnesses to the event." This is 20 lb/hp.
• The Flettner 282 Intermeshing: "It was capable of lifting 16 lbs. per horsepower - a figure not attained to this day by any of the modern helicopters." ["this date" - unknown]
• The Flettner had a GW of 2202 lbs and a 160 hp engine.
• The 282 had an Intermeshing configuration and this configuration has a Thrust/Power efficiency that is meaningfully below the Side-by-side configuration.
• The twin Rotor Factor for my SynchroLites and UniCopters in the Access database is 1.39 +/-. This seems to be too close to the Coaxial's 1.41. However, for the fun of it 16 hp * 1.39 = 22.24 hp.
• The Cornu Full size:
• 573.3 lb / 24 hp = 23.89 lb/hp Was this the GW weigh of his 13 November 1907 attempt when the craft was carrying a 121 lb sandbag?

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

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

To continue being the devil's advocate.

• A/ Momentum theory ~ Leishman in 'Aerodynamic Optimization of Coaxial Proprotor' mentions that momentum theory cannot be used to compare dissimilar configurations. Cornu's low aspect ratio, reverse tapered rotors are also very dissimilar to today's rotors. Why then does his evaluation use Momentum Theory?
• B/ Leishman's writes; "At first, the assumption of an aerodynamic efficiency of only 50% may seem low, but we must remember that even the best helicopter rotors that were to follow in the 1940s and 1950s had efficiencies of only 60% (i.e., figures of merit, FM, of 0.6), and this was using low solidity rotors with high aspect ratio blades...".
• Ba/ This is an interesting statement considering that in the early 1940s Flettner's FL282 had a FM of 0.72 (out of ground effect). It should be noted that Flettner's helicopter and Cornu's helicopter are not subjected to the tail-rotor power consumption.
• Bb/ In addition, an increased solidity ratio and decreased rotor rpm has been shown to significantly reduce the required power. Rotor - Disk - Large Chord & Low Tip Speed. From note (3) below, it appears that Cornu's rotors had a solidity ratio of 0.113, if the large root cutout of 0.40 is deducted from the disk area.
• C/ Where did the flat-belt efficiency of only 0.75 come from? Flat-belts are very efficient [up to a maximum of 98%]. In addition, could not Cornu have had instances where his modifications briefly eliminated the belt slippage? He certainly tried to, plus he was knowledgeable about belt drives since his bicycle manufacturing facility used them.
• D/ The article says; "The blades were also flat (no proper airfoil section) and untwisted, both chordwise and along their span." However, in this photo and in others it is shown that the blades were not flat but had a camber.

A different means of comparison ~

------	-----------------------------------	Cornu Helicopter:	Microlight Trike - GT Manufacturing SkyCycle
	Gross Weight:	518 lb (w/ 110 lb sand bag)	450 lbs
	Wing/Blade Area: ^(1)	4 * 14.4 sq.ft. = 58 sq.ft.	225 sq.ft.
	Engine:	Antoinette	Corsair Black Devil
	Power:	24 hp.	22 hp.
	Power Transmission:	Mechanical (flat belt) ~ 5-10% loss	Aerodynamic ~ 15% loss
	Velocity: ^(0)	.85R * 2 * 9.84 ft ^(2) * π * 85 rpm = 4,468 fpm = 50mph = 74 fps ^(0)	35 mph = 51 fps
	Rate of Climb at Gross Weight:	None - hovering flight	500 fpm. ^(3)
	Lift: L = (1/2) d v^2 s CL ^(3)	v^2 s CL = 74^2x 58 = 317,608	v^2 s CL = 51^2x 225 = 585,225
	Notes:

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,

5. I have no idea what the Coefficient of Lift is for Cornu's rotor-wing or the trike's wing is, however, the above suggests that Cornu's craft MIGHT have been able to produce sufficient lift to hover.

A further comparison after reading the Cornu section that was added to Leishman's revised book 'Principals of Helicopter Aerodynamics' ~ August 16, 2009

-------	--------------------------------------------------------------------	Cornu:	Mosquito:	Ultrasport-254:
	Airfoil:	Very thin undercambered, but Calculated using 8-H-12	Calculated using 8-H-12	VR-7
	Gross Weight: (lbs)	575 ^(5)	550	525
	Disk Area: (sq-ft)	608 | 512 ^(1)	254	346
	Disk Loading: (lb / sq-ft)	0.95 | 1.12 ^(1)	2.16	1.52
	Blade Area: (sq-ft)	58	10.88	11.72
	Blade Loading: (sq-ft)	9.91	50.55	44.80
	Rotor Speed: (RPM)	170 ^(6)	500	500
	Solidity Ratio:	0.095 |0.113 ^(3)	0.043	0.034
	Power - Momentum Theory: (HP) ^(4)	2 * 9.41 = 18.82 ^(7)	28.76	19.94
	Power - Momentum & Blade Element Theory: (HP) ^(4)	2 * 9.81 = 19.62 ^(7)	28.02	22.91

Notes:

• (1) The first number is the total area of both disks. The second number is with the large root cutout ratio of 0.40 deducted from the area of both disks
• (2) The two values are based on the two disk areas directly above
• (3) An increased solidity ratio and decreased rotor rpm has been shown to significantly reduce the required power. Rotor - Disk - Large Chord & Low Tip Speed.
• (4) A tail rotor consumes 8-12% of the available power and Cornu helicopter does not use a tail rotor.
• (5) Gross weight c/w pilot ~ from Leishman
• (6) The last given rotor speed by Leishman was 85 rpm. I have arbitrarily taken it up to 170. This will also reduce the torque and hence the belt slippage.
• (7) It looks like Cornu's helicopter, with its 24 hp engine, MAY have produced sufficient lift to hover.

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.

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.

Concluding Remarks:

• Rebuttal to Leishman/Johnson Figure of Merit argument;
• The paper states; "The blades were also flat (i.e., they had no proper Airfoil section) ..." and ".. the Cornu rotor system was further analyzed by using the blade element momentum theory ... the blades were modeled as thin flat plates."
• Response; Pictures clearly show that the rotor blades, and even the control surfaces, were not flat. They were undercambered.
• Outside quote; "The early aviation experimenters began with flat plate wings but soon realized that curvature [undercamber] improved efficiency; influenced most likely by the observation of birds' wings."
• Response; The bottom line in this table above is calculated from Prouty's blade element momentum theory.
• Response; Also, the side-by-side configuration, as used by Cornu, is the optimal one for high Figure of Merit.
• Rebuttal to Leishman/Johnson Transmission Efficiency argument;
• The paper states; "... a transmission efficiency of η=0.75 (note that a canvas belt can never be as efficient as a efficient as a geared transmission ...".
• Response; η=0.75 is far less than what flat-belt transmissions are capable of. Flat-belt transmissions can have up to 98% efficiency. This is one reason why they were used in Cornu's bicycle manufacturing facility and thousands of other plant at that time.
• The paper states; "One issue was that the belt was twisted several times from the engine to the rotors."
• Response; This is another of the flat-belt's attributes.

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.

Miscellaneous Stuff:

• Reynolds Number of Cornu's Blade;
• Mean chord length = 14.4 sq.ft. / 5.9 ft.[span] = 2.44 ft.
• Speed at 0.85 R = 74 fps at 85 rpm ~or~ = 148 fps and 170 RPM
• = chord (ft) x speed (fps) x 6378; at sea level. = 2.44 x 85 x 6378 = 1,322,800 ~or~ 2.44 x 170 x 6378 = 2,645,600

Summation:

• Leishman/Johnson infer an inability to fly, due to a need for-;
• 1/ "a larger rotor disk with a lower disk loading"
• 2/ "a higher aerodynamic efficiency"
• 3/ "a better method then a canvas belt drive"
• 4/ "a much more powerful engine"
• 5/ "Paul Cornu's claim to successful piloted flight with a helicopter, free of the ground and under positive control, is extremely dubious."

• Counter-argument to Leishman/Johnson arguments;
• 1/ The rotor disk was extremely large and the disk loading was very small. See 'Cornu's Disk', above.
• 2/ See 'Rebuttal to Leishman/Johnson Figure of Merit Argument'', above;
• 3/ See 'Rebuttal to Leishman/Johnson Transmission Efficiency Argument', above;
• 4/ No so if the Figure of Merit and the Transmission Efficiency are corrected. See Power comparisons, above.
• 5/ The control system probably was inadequate for meaningful flight. However, the above statement is an assumption lacking solid technical support.

· 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