Tendencias

Lift is the component of the total aerodynamic force of an airfoil that is perpendicular to the relative wind (Figure 2-30). The illustration of the lift equation, accompanied by a simple explanation, helps the understanding of how lift is generated. The point is not the math but understanding what an aviator can change and what he cannot.

The lift equation is as follows:

SCl

V

L ²

2 1



Where L = lift force

1/2constant

 (rho) = density of the air (in slugs per cubic foot) V² = airspeed (in feet per second) squared

S = surface area (in square feet) CL = coefficient of lift

The shape or design of the airfoil and the AOA determines the coefficient of lift. The aviator has no control over the airfoil design. However, he has indirect control over the AOA through manipulation of pitch angle. This is one element of the lift equation over which the aviator has some control. The aviator cannot affect the value of rho, but must be cognizant of the significant performance degradation associated with high DA. S represents the surface area of the airfoil, a design factor also unaffected by aviator input. Finally, there is V, representing relative wind velocity or airspeed.

Linear Velocity Linear Velocity Induced

Velocity

Figure 2-30 Forces Acting on an Airfoil 223. DRAG AND THE DRAG EQUATION

Drag is the component of the total aerodynamic force of an airfoil that is parallel to the relative wind (Figure 2-30). It results from pressure differences between the front and rear faces of an object (airfoil) in an airflow, as well as frictional losses between the surface and the passing air.

Drag is often defined as the force that opposes the motion of an airfoil through the air.

The illustration of the drag equation accompanied by a simple explanation can help (in addition to the lift equation) in understanding how drag is generated. The point is not the math but understanding what an aviator can change and what he cannot.

The drag equation is as follows:

D = ¹/2 V² S CD

Where D = drag force

1/2constant

 (rho) = density of the air (in slugs per cubic foot) V² = airspeed (in feet per second) squared

S = surface area (in square feet) CD = coefficient of drag

Just as in lift, the most readily apparent effects are due to dynamic pressure and surface area. An increase in q (½  V²) or S results in more interactions between air particles and airfoil surfaces which result in greater overall drag. The many other factors effecting the creation of drag are represented by CD.

The shape or design of the airfoil and the AOA determines the coefficient of drag. As with the lift equation, the aviator has no control over the airfoil design. However, he has indirect control over the AOA through manipulation of pitch angle. This is one element of the drag equation over which the aviator has some control. Again, the aviator cannot affect the value of rho, but must be cognizant of the significant performance degradation associated with high DA. S

represents the surface area of the airfoil, a design factor also unaffected by aviator input. Finally, there is V, representing relative wind velocity or airspeed. It is the only other factor that the aviator can change.

CD may be plotted against AOA for a given aircraft with a constant configuration. Note that the CD is low and nearly constant at very low angles of attack. As AOA increases, the CD rapidly increases and continues to increase. Since there is always some resistance to airflow, drag will never be zero; therefore, CD will never be zero. Figure 2-31 shows a generic plot of CL and CD

for varying AOA and then the ratio of lift over drag (L/D), which designers use to find the optimal operating range for an airfoil/aircraft. However, while L/D calculations work very well for fixed wing aircraft, due to the many extra variables in helicopter flight with a turning, rather than stationary airfoil/wing, rarely will you see helicopters analyzed based on L/D calculations.

Figure 2-31 CD vs. AOA

The total drag on a helicopter has three components: parasite drag, profile drag and induced drag.

Drag/Airspeed Relationship. Figure 2-32 illustrates the relationship between the different drag components and airspeed.

Figure 2-32 Drag and Airspeed Relationship

Parasite drag is the drag incurred from the non-lifting portions of the aircraft. It includes the form drag and skin friction associated with the fuselage, engine cowlings, mast and hub, landing gear, wing stores, external load, and rough finish paint. Form drag is related to both the size and shape of the aircraft or substructures. Skin friction drag results from the various layers of air near the aircraft skin surface sliding over one another and creating a force retarding the aircraft’s motion (drag) because of the viscosity of the air. Surface roughness generates turbulent flow which increases skin friction drag. Many operators’ manuals contain two sets of performance charts, one set for clean configuration and one set for high drag associated with the mounting of optional external fuel tanks or other mission equipment. Parasite drag increases exponentially with forward airspeed and dominates the drag curve at high airspeeds (Figure 2-32).

Profile drag is the drag developed by moving the rotor blades through the air. It has three components: skin friction, form, and wave drag. This is parasite drag, but called by a different name for the following reason. At a hover the rotating blades will generate parasite drag even if the aircraft is stationary without any forward speed. This is unlike an airplane which must move its fuselage (and attached wings) through the air to generate parasite drag.

At a stationary hover the blade tips may be at a speed of 300 knots, thereby generating skin friction and form drag on the blades, even though the fuselage has no forward speed.

Accordingly, the blade parasite drag is labeled “profile” drag to differentiate it from the standard parasite drag which will affect the non-lifting portion of the aircraft as forward airspeed is increased. The name “profile’ is used because blade parasite drag is a function of the shape of the blade airfoil, which is its two dimensional “profile.” Profile drag is nearly constant at middle forward flight speeds, but increases moderately at higher airspeeds. At very high airspeeds, profile drag increases rapidly with the onset of blade stall or compressibility.

Skin Friction drag is drag due to wasted energy as the air rubs against the airfoil surface. It increases with surface roughness.

Form drag is the result of the very large difference in static pressure between air flowing near the leading edge (stagnation point) and that moving along the trailing edge. Just as high pressure below an airfoil combined with low pressure above it causes lift, high pressure on the forward portion of an airfoil combined with lower pressure on the after portion of the airfoil causes drag.

Wave drag is the result of shock wave formation and is present only at transonic and supersonic speeds; it is effectively zero for subsonic speeds below a very high speed known as the Drag Divergence Mach number. This form of drag would only be encountered in high speed operations, at the tip of the advancing rotor blade.

Induced drag is a result of the induced flow trailing edge downwash created by blade tip vortices. These vortices (previously discussed in Section 219) are only generated when the blades are producing lift. Due to the tip vortices, the relative wind actually departs the trailing edge of the blade with a downwash angle it did not have at the nose of the blade. If the relative wind at the nose of the blade and the trailing edge downwardly modified relative wind are combined, the average relative wind over the entire blade is inclined downward at the rear as compared to the free stream relative wind. Since lift is perpendicular to the “average” relative wind, the lift generated is inclined aft at the same angle that the relative wind is inclined downward by the induced velocity. This results in a component of lift acting in a rearward direction, which is known as “induced drag” (Figure 2-33). High angles of attack, which produce more lift, generate stronger vortices and greater trailing edge downward velocities that increase induced drag. In rotary-wing aircraft, induced drag is highest while hovering and decreases with increasing airspeed (Figure 2-32).

Figure 2-33 Production of Induced Drag 224. PITCHING MOMENT

Now let us investigate the different aerodynamic characteristics of airfoils regarding the AC and center of pressure for each type. The center of pressure is the point along the chord where the distributed lift is effectively concentrated. On a symmetrical blade, the moment is zero. For a nonsymmetrical airfoil, the AC is the point along the chord where all changes in lift effectively take place and where the sum of the moments is constant for any AOA.

On symmetrical airfoils, the center of pressure is co-located with the AC. The center of pressure of the upper and lower surfaces of a symmetrical airfoil act directly opposite each other.

Because the AC and center of pressure are co-located, no moment is produced even though the total lift force changes with change in AOA (Figure 2-34, left).

On nonsymmetrical airfoils, the center of pressure of upper and lower surfaces do not act directly opposite each other, and a pitching moment is produced. As the AOA changes, the location of the distributed pressures on the airfoil also changes. The net center of pressure (sum of upper and lower) moves forward as AOA increases and aft as AOA decreases; producing pitching moments (Figure 2-34, right). This characteristic makes the center of pressure difficult to use in aerodynamic analysis. Since the moment produced about the AC remains constant for pre-stall AOA, it is used to analyze airfoil performance with lift and drag coefficients. The AC is located at the quarter chord position on most subsonic airfoils and near half cord on most supersonic airfoils.

Figure 2-34 Pitching Moments in Airfoils

Pitching moments are an important consideration for airfoil selection. Torsional loads are created on the blades of positively cambered airfoils due to the nose down pitching moment produced during increased AOA. These torsional loads must be absorbed by the blades and flight control components, and initially this resulted in structural blade failure and excessive nose-down pitching at high speeds. Early helicopter engineers consequently chose symmetrical airfoils for initial designs, but have since developed cambered blades and components with high load-bearing capacity and fatigue life.

For the TH-57, rotor blade designers combined the most desirable characteristics of symmetrical and nonsymmetrical blades, resulting in the “droop-snoot” design (Figure 2-35). This

incorporates a symmetrical blade and a nonsymmetrical "nose" by simply lowering the nose of the blade. The resulting nonsymmetrical blade performance characteristics include low pitching moments and high stall AOA.

Figure 2-35 “Droop Snoot” Design Airfoil

The definitions of Center of Pressure and Aerodynamic Center are reviewed below:

Center of Pressure. A point along the chord where the distributed lift is effectively

concentrated at a given AOA and the sum of the moments is zero. On symmetric airfoils its location is fixed; on cambered airfoils it moves forward as AOA increases.

AC. The point about which no change in pitching moments occurs with changes in AOA.

The AC is normally located at the quarter chord position on most subsonic airfoils and near half cord on most supersonic airfoils.

Summary of differences between symmetric and cambered airfoils. By looking back at Figure 2-29, the reader should discern that symmetric and cambered airfoils perform differently in at least three important ways:

1. Symmetric airfoils produce no lift at zero degrees AOA; cambered airfoils produce some lift at zero degrees AOA.

2. In general, a cambered airfoil produces more lift at a given AOA than a symmetric one.

3. Cambered airfoils tend to have higher maximum lift coefficients than symmetric airfoils.

Consideration of pitching moment reveals one other important difference:

4. Symmetric airfoils have zero pitching moment about the AC. Cambered airfoils have a nose down pitching moment about the AC (Figure 2-34). This is an important consideration in the design of rotor blades due to the constantly changing AOA during each revolution.

225. AERODYNAMIC FORCES ON THE AIRCRAFT/TOTAL ROTOR THRUST Up to this point, we have been discussing aerodynamic forces on the rotor blades and system.

When we start discussing how the helicopter flies in later chapters, you must also look at how the forces apply to the aircraft itself. Main rotor thrust is the sum total of all the force/thrust

vectors produced by the rotor blades along its entire span and throughout 360° of rotation. As previously discussed, it is perpendicular to the rotor disk or plane of rotation; therefore it is the vertical force if the plane of rotation is horizontal. In terms of Newton’s Second Law (F= m ● a), rotor thrust is the mass of air through the rotor, multiplied by the change in velocity of the air (T = m ● v).

Newton’s law of acceleration states that the force required to produce a change in motion of a body is directly proportional to its mass and the rate of change in its velocity. This means that motion is started, stopped, or changed when forces acting on the body become unbalanced. Rate of change (acceleration) depends on the magnitude of the unbalanced force and on the mass of the body to which it is applied. This principle is the basis for all helicopter flight: vertical, forward, rearward, sideward, or hovering. In each case, the main rotor thrust, also called total rotor thrust or just rotor thrust, generated by a rotor system is always perpendicular to the tip-path plane (Figures 2-36 through 2-39). For this discussion, this force is divided into two components, vertical and horizontal. The vertical component opposes aircraft weight while the horizontal component opposes drag and acts to accelerate or decelerate the helicopter in the desired direction. Aviators direct the aircraft in a desired direction by tilting the tip-path plane.

At a hover in a no-wind condition, all opposing forces are in balance; that is, they are equal and opposite. Therefore, the vertical component of thrust and weight are equal, resulting in the helicopter remaining stationary (Figure 2-36).

Figure 2-36 Balanced Forces, Hovering, No Wind

To make the helicopter move in some direction, a force must be applied to cause an unbalanced condition. Figure 2-37 illustrates an unbalanced condition in which the aviator has changed the attitude of the rotor disk resulting in the displacement of the thrust vector from vertical and increased the magnitude of the total rotor thrust. The total rotor thrust vector can now be viewed

as being made up of two components, a vertical (lift) vector and a horizontal (thrust) vector, resulting in a total force forward of the vertical. No parasite drag is shown because the aircraft has not started to move forward yet.

Figure 2-37 Unbalanced Forces Causing Acceleration

As the aircraft begins to accelerate in the direction of the applied horizontal thrust, parasite drag develops. When parasite drag increases to be equal to thrust, the aircraft will no longer

accelerate because the forces are again in balance (Figure 2-38) as the aircraft has achieved steady-state (unaccelerated) flight. Total rotor thrust had to be increased to maintain lift equal to weight.

Figure 2-38 Balanced Forces, Steady-State Flight

To return the aircraft to a hover, the aviator must change the disk attitude to unbalance the forces (Figure 2-39). By tilting the rotor disk aft, the horizontal (thrust) force acts in the same direction

as parasite drag and airspeed decreases.

Figure 2-39 Unbalanced Forces Causing Deceleration

Although the vertical component is often called lift, and the horizontal component is often called either thrust, or the propulsive force, these alternate terms are not recommended for use by the student due to their potential for confusion with other variables. Lift and Total Aerodynamic Force will be used in this course only as they apply to the blade element diagram.

226. MAIN ROTOR DRAG (IN-PLANE AND H-FORCE)

The horizontal component of the lift vector on the blade element diagram represents the induced drag at a specific location on one blade and can be added to profile drag to arrive at rotor drag.

When this rotor drag is integrated along the entire span of the rotor blade and throughout 360° of rotation, in-plane drag for the rotor system is calculated. Because the drag of the retreating blade (lower linear velocity) is less than that of the advancing blade, the resultant rotor drag opposes the aircraft’s movement. This drag has been termed the H-force because it is acting about the hub. Analyzing H-force is beyond the scope of this course.