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Item 1002

OTHER: Aerodynamics - General - Blade Loading Coefficient (Mean Lift Coefficient) [C_T/σ]

Also called 'Thrust coefficient to Solidity' and 'Aerodynamic blade loading'.

"It is essentially blade loading normalized for rotational dynamic pressure." ~ from Sikorsky ABC report.

A measure of the mean blade lift coefficient. It represents the mean lift coefficient of the blade. Same things.

C_T/σ can be written as (T / ρA(ΩR)²) * (A /A_b) = T / ρA_b(ΩR)². [Source ~ PHA p.51] Where A = [see algorithm for disk area]

IMO, this coefficient may not be of any of any interest when using the Advancing Blade Concept. This is because retreating blade stall during cruise is not a problem. This coefficient may be of interest if there is the intent to have the RRPM low in hover, as well as during cruise and the justification for slow RRPM in hover could be that the blades already have a large chord for high speed cruise.

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

For more information see; [PHA p.50], [HT p.322] and [AH p.64]
Thrust Weighted Solidity [σ_T] (weighted by the square of the radial station)

The book 'Principals of Helicopter Aerodynamics', section 2.2.11 covers the subjects of Rotor Solidity and Blade Loading Coefficient. However, this section does not discuss the subject of varying the tip speed (ΩR)². Section 6.3.3 is on Rotor Solidity and it does say "Rotors that are designed for high speeds and/or high maneuverability requirements require a higher solidity for a given diameter and tip speed."

Note re Twin Rotor Configurations:

There is no consensus amongst the gurus as to what the disk area is for twin rotor helicopters. Therefor it is impossible to have a consensus as to the solidity ratio, for twin rotor configurations. Note that the algorithm above does not use disk area, because it is self-canceling.

Note re Advancing Blade Concept:

The report 'Advancing Blade Concept (ABC^TM) Development' says "While blade loadings up to C_T/σ ≈ 0.185 have been demonstrated, the full lift capacity of the rotor system is yet to be demonstrated."

The report 'The Impact Missions on the Preliminary Design of an ABC Rotor' makes much reference to L/D_eplotted against C_T/σ. The figures 8 and 9 compare Blade Load Coefficients between Thrust Weighted Solidity and Geometric Solidity. The difference is significant. I wonder how valid this is, when considering that there is dissymmetry of lift in forward flight and there should never be retreating blade stall?

Note re Stepniewski's Implications of the Low Tip Speed Design Philosophy ~ by Stepniewski, Wieslaw Z:

The above algorithm clearly shows that to maintain the same Blade Loading Coefficient and Thrust, any reduction in RRPM must be accompanied by an increase in the blade area. This is relevant to hover but I suspect that forward velocity and ABC will also benefit from the large blade area.

Related Page; at This Site:

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

Information on this page that is specifically on the subject of Blade Loading Coefficient is located here.

Aerodynamic Blade Loading: [C_T/σ] [Ct/sigma]

is a simple concept that lets us see how far from stall the rotor is operating, similar to the coefficient of lift for an airplane's wing. It is the coefficient of thrust divided by the solidity.

For most modern airfoil sections, deep rotor stall is experienced at a Ct/sigma of about .20 to .21 at hover. As retreating blade stall takes over, the Ct/sigma for stall at 160 knots is about 0.10 and by 200 knots, it is about 0.06.

For a tilt rotor, the blades are purposely made with less chord than a helicopter, because the thinner blades are then operating at a higher angle of attack in a hover, and are more efficient. This means that they can save power in a hover by operating at a high Ct/sigma. The downside is that there is little margin left over for maneuvering at low speed. For helos, the blade chord is sized up to allow flight at high speed, so it is way oversized for a hover. Tilt rotors don't need the extra chord for high speed because they are on the wing by then, and the rotors are props!

The V-22 has a hover Ct/sigma of 0.175, which means that it will stall at only about 1.2 to 1.3 g's in helo mode (.21/.175). A typical helo has a hover Ct/sigma of about 0.09, so it never gets close to stall at low speed (ever pull 2.4 g's at 40 knots? It's a wild ride!)

~ Nick Lappos

The Sikorsky ABC has demonstrated blade loadings up to 0.185, but the full lift capacity of the rotor system has yet to be demonstrated ~ (1976)

From Prouty "Helicopter Aerodynamics - p.68" "Most rotors are at the peak of their efficiency in forward flight when C_T/σ is about .08.

Reference the following rough and temporary info.

The UniCopter's Solidity is 0.1583 and the Blade Loading Coefficient is 0.0611.

The SynchroLite's Solidity is 0.0448and the Blade Loading Coefficient is 0.0434.

These intermeshing values are based on the Total Disk Area. There may be a problem here re Sigma and how to define it for the intermeshing configuration.

Last Revised: May 11, 2009