1119

Item 1119

OTHER: Aerodynamics - Rotor Disk - Dual Configuration - Coaxial

Outside Comments:

Representatives of the Kamov company have been present at the last two big UK Helicopter technical get-togethers and on both occassions have claimed that the co-axial rotor configuration, when properly designed is in fact more efficient than a single main rotor and tail rotor configuration. To the tune of about 15%! ~ CRAN

My note. If the net weight to payload ratio is 67/33, then this represents an increase of 45% in payload capacity.

My Thoughts Regarding Efficiency:

It is now believed that the coaxial configuration is more efficient than the main & tail rotor configuration by up to 15%. It appears that this is true when comparing craft with the same total number of rotor blades, such as a 4-blade single rotor and a 2-blade-per-rotor coaxial, or a 6-blade single rotor and a 3-blade-per-rotor coaxial. However, the addition of blades to a rotor decreases its efficiency. Therefore, it appears logical that a coaxial with two 2-blade rotors will not be 15% more efficient than a single rotor with only 2 blades.

For instance when comparing the two configurations with the same total count of blades; the coaxial will get an advantage from swirl recovery, but may suffer a disadvantage due to the downwash of the upper blades striking the lower blades.

Outside Web Pages:

Aerodynamic Features of Coaxial Configuration Helicopter ~ by Kamov; http://www.kamov.ru/market/news/petr11.htm

A Survey of Theoretical and Experimental Coaxial Rotor Aerodynamic Research; http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19970015550_1997024330.pdf
Operational considerations for a co-axial, contra-rotating rotor.

AERODYNAMIC OPTIMIZATION OF A COAXIAL PROPROTOR by J. Gordon Leishman & Shreyas Ananthan http://www.baldwintechnology.com/MTR_AHS06.pdf Have hard copy

Induced Power:

The Original Method:

The power requirements are initially calculated as if the helicopter was a side-by-side configuration. Then the required induced power (K_int) is increased depending upon the vertical distance (gap) between the rotor disks.

For gaps (g) that are 10% or less of the rotor radius (R), the required power is increased by a factor (K_int) f 41% (square root of 2).

For gaps (g) that are twice the rotor radius (R) , the factor (K_int) is 0.28.

For gaps (g) that are between 0.1 and 2.0 of the rotor radius (R), the factor (K_int) = 1.41 - ((1.41 - 1.28) * (g / (2 * R))).

The Revised Method:

Note: The above now appears to be incorrect. Newer evaluations suggest that the induced power factor (K_int) should be 1.16 [Source ~ PHA p.70]. This is in agreement with Figure 3.13 on [Source ~ RWA I, p.115].

My 'Blade Element Calculation for Hover' using Prouty's algorithms shows a slightly lower value then 1.16, and this lower value appears to be closer to the experimental dots in [Source ~ PHA, Figure 2.20, p.70]. See the following.

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A comparison between a single disk with 4 blades, to 2 disks of the same diameter, in a side-by-side configuration with 2 blades each. (I.e. combining the 2 disks and their blades into 1 disk so as to half the total disk area and double the disk loading) See: Required Power Comparison for Various Rotor Configurations, in Hover .

In Momentum Theory it requires 41% more induced power (K_int) if the gap is small.

In Blade Element Theory;

A 4-blade rotor requires 33% more induced power (K_int) than a comparable 2-blades rotor.

The pitch of the lower blade element is probable the same as that of the upper blade element. If the gap between the blades is very small then the angle of attack of the lower blade, as it passes through the downwash of the upper blade will be zero. The percentage reduction of lift in the lower rotor should therefor be equal to the solidity ratio of that rotor. But, since the induced drag is 80% of the total drag and this is reduced as well the increased power will only be 20% of the lower rotor's solidity ratio, which is about 1% more induced power.

Swirl cancellation should give an advantage of approximately 1%, and this will offset the above 1%.

In hover the induced power is 80% of the total power, therefor a 4-blade rotor requires (33% * 80%) = 26% more total power (K_total) than a comparable 2-blades rotor.

The elimination of the tail rotor results in a power saving of (8 to 15% ~ depending on source of information) 12%, therefor the 4-blade Coaxial rotor requires (26% - 12%) = 14% more total power (K_total) than a comparable 2-blades rotor.

The power for the single 2-bladed rotor was calculated from momentum theory using P = ((κ_intκ(2T)^3/2) / (√2ρA)) + (2σC_d0/8), where κ = 1.15, κ_int = 1.16 and C_d0 (zero lift drag coefficient) = 0.011. [Source ~ PHA p.71]

Which A is this?

Yaw:

The coaxial has excellent yaw control, which is done by varying the lift, and more importantly the drag, between the two counter-rotating rotors, while maintaining a constant total lift.

During autorotation, the airflow through much of the disks is reversed. A particular pedal input would now cause a yaw in the opposite direction, if it were not for 'pedal switching linkages' that automatically take place in Kamov's at the onset of autorotation.

"The problem of coaxial-rotor helicopters' directional stability in autorotation has been solved in full." ~ Quote from Kamov web page, but they do not say how it has been solved.

CRAN said ~ "Dr. Gareth Padfield picked the Russian engineers up on this point [weak yaw control during autorotation] at the conference and they sheepishly said that ...'yes, it is a problem, and we achieve direction control in autorotation with the moveable fins...' or words to that effect."

For a possible solution see: DESIGN: UniCopter ~ Rotor - Disk - Autorotation Yaw by Seperate Root and Tip Control

Other Potential Methods for Coaxial Rotors:

Air drag tip brakes. Gyrodyne

Friction brakes: Benson B-9 Little Zipster

Complex idea: Coaxial Transmission w/ Yaw Control

Rudder. Perhaps with adjustable axis that is linked to collective to give some effectiveness in autorotation.

Torque/Pitch Collective Rotor Hub. Hub-bar with piezoelectric actuator to change the differential collective.

Dual Rotor Configurations:

Coaxial | Intermeshing | Interleaving | Side-by-Side | Tandem

Last Revised: February 16, 2009