0948

Item 0948

OTHER: Aerodynamics - General - Solidity [σ]

A solidity ratio of 1.5? ~

There is no consensus amongst the gurus as to what constitutes the disk area on twin rotor helicopters, let alone any meaningful disk area relationship amongst the various configurations. It is therefor impossible to have a consensus as to the solidity ratio, for these configurations.

Solidity Ratio: [σ] [sigma]

There is a Function rotor_solidity () but it is only the simplistic algorithm; at present.

Rotor solidity ratio = Total blade area / Disk Area. σ_rotor = A_b/A_sys

For constant chord blades, the local solidity and rotor solidity are identical.

Equivalent solidity ratio: [σ_e]

This is for use when comparing a constant chord to a tapered chord.

The following is for tapered blades.

Local solidity ratio: = The sum of the local ratios σ_local = ¹∫₀ σ * dr

Note: the programming Function: blade_area () takes into account taper, if it is linear.

For a linearly tapered blade;

σ_e= σ(r = 0.75) for thrust basis

σ_e= σ(r = 0.80) for power basis

The algorithm can be found in 'Helicopter Theory' - section 2 - 6.5.

Thrust Weighted Solidity.

If the blade is tapered then chord c must be modified to define thrust weighted solidity.

Power/Torque Weighted Solidity:

Rarely used in helicopter design.

Calculations re Varying the Solidity Ratio:

Tables that show the results of varying the solidity ratio; DESIGN: UniCopter ~ Rotor - Disk - Large Chord & Low Tip Speed ~ Hover

Solidity Ratio for Intermeshing:

The Access program uses σ = A_b/A_SYS, where

A_b = R * c * b ~ For more see: Blade Area

A_SYS = AT = (A_ONE- area of overlap segment) * 2 ~ For more see: Disk Area

My logic for using this means to determining the solidity ratio of intermeshing rotors is;

The solidity of a 4-blade single rotor is area of the 4 blades divided by the 1 disk area.

The solidity of two 2-blade rotors (side-by-side configuration) is area of the 4 blades divided by the 2 disk areas.

Therefore by using the above algorithm the solidity of an intermeshing or interleaving will be proportional to the area with 4 blades vs. the area with 2-blades. I.e. algorithm will agree with the above when the stagger reaches either of its extremes (0" or >2R).

Considerations for; wake contraction, swirl recovery, cutout ratio, Vee angle, etc. will be accounted for in subsequent calculations.

Solidity Ratio for ABC: [σ_ABC]

Rotor solidity σ = (b) x (chord @ 0.75R) / πR ~ From the Technical Documents on ABC ~ Forward Flight Performance of a Coaxial Rigid Rotor, by V. M. Paglino, dated May 1971, which is about the rotors in the Ames full scale wind tunnel.

Some thoughts.

Consider the change in Solidity Ratio if ABC is considered. This is relevant to the Disk Area and the Blade area as well, but there is no logic to changing them.

Perhaps this ratio will be a factor of the lateral dissimetry of lift ~ which in turn is based on the forward velocity and the RRPM? Advance ratio: μ = V_fwd / ΩR

My Prediction; from post #19 in PPRuNe thread 'Why are Helicopters with the Flettner-System so slow?'

This [preceding chart] suggests that a low solidity ratio is good for existing helicopters, for a number of reasons. One is the utilization of centrifugal force.

However very, very early attempts at hovering, were best served by a very high solidity ratio, to work with their slower rotational speed. Of course, to keep the weight down they used cloth for the airfoils and guy wires for the strength.

It appears that future helicopters will move back toward the earlier ones in that they will have large chords and slower speeds. Of course, the cloth and guy wires will be replaced by composite construction.

Additional Information;

'Aerodynamics of the Helicopter' ~ Gessow Myers. Pages 58 & 86.

Effect of Rotor Tip Speed and Solidity on Figure of Merit, page 62

"Practical considerations, of course, place a lower limit on the rotor speed.

One of the most important is the safety in case of sudden power failure, for the kinetic energy in the blades, the greater is the time margin possessed by the pilot to lower his pitch to a value that will permit autorotation.

Solution?;- The Flettner FL-282 had a rotor governor

Large coning angles and the poor psychological effects of slowly revolving blades also tend to fix a lower limit on rotor speeds.

Solution?;- today's stronger rigid blades reduce the need for centrifugal force to be used as a means of providing a low conning angle. Note that this will increase the radial load on the pitch bearings, but it will reduce the axial load on them.

Solidity Ratio V.S. Tip Speed

This Web Site:

DESIGN: UniCopter ~ Rotor - Disk - Large Chord & Low Tip Speed

Outside Web Site - NACA:

Static thrust analysis of the lifting airscrew, Knight, Montgomery; Hefner, Ralph A, 1937

"Of these changes the elimination of the solidity as an independent parameter is the most important."

Charts for estimating performance of high-performance helicopters, Gessow, Alfred; Tapscott, Robert J, 1956

Last Revised: Sunday, September 07, 2008