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From the aforementioned discussions of continuity and the Bernoulli relationship, it might appear that the greatest pressure differential about the blade would occur at the point of greatest airfoil thickness. However, as illustrated in Figure 3-1, it is clear from examination of the pressure distribution about the airfoil that the greatest decrease in pressure actually occurs forward of the thickest section of the airfoil.

Figure 3-1 Pressure Distribution and Leading Edge Suction

This has been best described by Euler to be a result of leading edge suction. Looking at in the derivation of the Bernoulli equation by Euler (Figure 3-2), note the acceleration component in the first line (dV).

2

Figure 3-2 Bernoulli Equation as Derived by Euler

This acceleration term, which describes the rapid change in velocity from the stagnation point (where V=0) to the point of maximum thickness, accounts for the significant pressure differential forward on the airfoil. The acceleration term disappears with the derivation of the Bernoulli equation. However, this rapid acceleration forward on the airfoil does explain the pressure distribution, and has been termed “leading edge suction.” The three primary equations for studying pressure around an airfoil are recapped below.

Continuity: A

V

= A

V

Bernoulli: P

= P

+ ½ V

Euler: dP = -VdV

Figure 3-3 Continuity, Bernoulli, and Euler Equations 306. TWIST AND TAPER

The distribution of lift along a rotor blade is not uniform because speed varies along the span.

The linear velocity at a point on a rotating blade depends on the blade’s angular speed (often expressed in RPM), and the point’s distance from the center of rotation:

Velocity = (Angular velocity) x (distance from the axis)

The outboard portions of the rotor blades have the highest speeds and thus provide most of the lift. The increase in lift along the span does not vary with the radius, but with the radius squared.

This uneven lift distribution produces excessive blade bending and coning angles. To alleviate the problem, the rotor blades can be twisted so that the blade root has a higher AOA than the blade tip. This is known as geometric twist.

Geometric twist improves helicopter performance by making induced velocity distribution and therefore lift along the blade more uniform. When blade twist is used to even out the induced flow across the rotor disc it can significantly improve performance. A rotor without blade twist tends to produce higher induced velocities in the outer portion of the disc than in the inner portion (Figure 3-4). The optimum condition, however, is with uniform induced velocity over the entire disc. A blade with geometric twist has greater pitch at the root than at the tip. A progressive reduction in AOA from root to tip creates a balance of lift throughout the rotor disk.

It also delays the onset of retreating blade stall at high forward speed, due to reduced AOA. The application is usually modified by high-speed considerations. Experience has shown that the large amount of blade twist optimum for hover performance (as much as 30º) will generate high oscillating blade loads and vibration at high speeds. No twist or low twist angles reduces the vibration at high speed, but creates inefficient hover performance. The usual design compromise is to use moderate values of 6 – 12 degrees, which provide most of the benefits of ideal twist in hover while avoiding most of its disadvantages in forward flight.

Figure 3-4 Blade Twist

As an alternative to geometric twist, the shape of the airfoil may be altered. A blade with aerodynamic twist has an airfoil shape near the root that produces a greater lift coefficient at anticipated angles of attack than the airfoil shape used near the tip. Examples of geometric twist and aerodynamic twist are depicted in Figure 3-5.

Figure 3-5 Geometric combined w/aerodynamic and Aerodynamic Blade Twist

As yet another way to control lift along the blade’s span, surface area can be altered. Designers alter the lift profile in forward flight by maximizing the lift to drag ratio. Near the blade tip the chord is reduced thereby reducing the blade section lift and drag. This modification specifically addresses the advancing blade. If the tip sections have less surface area than the root sections it tends to even out the lift a little bit. The reductions in surface area are recognized as blade taper (Figure 3-6).

Figure 3-6 Blade Taper

Most helicopter rotor designs use a combination of geometric twist, aerodynamic twist, and blade taper to create a more ideal lift distribution.

307. INERTIA

Newton’s first law of motion: An object remains at rest or in uniform motion in a straight line unless compelled to change its state by the action of an external force. Inertia governs how an aircraft reacts to directional control inputs to the flight control system, but, more importantly for the helicopter pilot, governs the reaction of the rotor system to a loss of engine power.

A high inertia rotor system will tend to allow the pilot greater reaction time before rotor speed decays, but will be slower to regain lost RPM. A low inertia rotor system, on the other hand, loses RPM much more quickly if the collective is not lowered rapidly, but is able to regain RPM much more quickly than a high inertia system.

308. SOLIDITY

When using the basic lift equation, S represents the blade area.

SCl

However, when considering the total rotor thrust required by the rotor system, the process is a bit more complicated and designers start getting into the solidity ( or sigma) of the rotor disk, i.e.

how much of the actual disk area is rotor blades and how much is airspace.

Blade area, S, may be represented by:

, where

Rotor system solidity, , is defined as the ratio of the total blade area to the disc area.

Solidity can then be used with the coefficient of thrust (CT) to compute the blade loading coefficient (mean lift coefficient) or thrust coefficient or solidity for the entire rotor disk using the following equations:

Solidity and blade loading effect the size of the rotor blades and diameter of the rotor disk required to meet mission requirements. Given the solidity necessary for a particular mission and weight, selection of the appropriate number of blades, with additional consideration for forward flight performance (i.e. retreating blade stall) and autorotation characteristics, can be completed.

The assumption here is that the chord of the blade remains constant from the center of rotation to the blade tip. While this is a very simplified way to view the blade, it yields viable results for solidity because the inner portions of the rotor blade contribute little to the overall thrust production. Making corrections for the chord change on the blade tip is legitimate and is done by means of the equivalent thrust-weighted solidity, e.