SUBJECT 082 – PRINCIPLES OF FLIGHT – HELICOPTERS

(1)VOCABULARY OF MECHANICS Speed is a scalar quantity; it has only magnitude. Velocity is a vector quantity with magnitude and direction. The velocity of a point on a rotor blade, when rotating around an axis, is the ‘linear’ or ‘tangential’ velocity which can be expressed in revolutions per minute (rpm). Density is the mass of the fluid per unit volume (kg/m3) in the international system of units of measurement (SI (Système International)).

(2)AERONAUTICAL DEFINITIONS A rotor blade is a high-aspect ratio aerofoil attached by its root to the rotor hub with hinges or flexible elements. A blade element is a spanwise slice of the blade, so thin that the aerodynamic forces involved may be assumed not to vary. The forces produce lift (L), drag (D), and a pitching moment. Such a cross section has a contour, a leading and trailing edge, a chord line, a mean camber line, a maximum thickness or depth, and a thickness-to-chord ratio. The centre of pressure (CP) is defined as the point on the chord line where the resultant of all aerodynamic forces acts. The planform is the shape of a blade as seen from above. The pitch angle (of a blade or an element) is the angle between the chord line and the plane of rotation. The blade is not twisted when the pitch angle is constant from root to tip. A blade is twisted when the pitch angle of its elements’ sections varies with their distance from the root (in other words, the chord lines of the elements involved are not parallel). Washout exists when the pitch angle decreases towards the blade tip. The vector sum of the undisturbed upstream velocity (i.e. that found in the plane of rotation of the blades) and the induced velocity is the relative airflow. The angle between the relative airflow and the chord line of a blade element is the angle of attack (). Lift is the component of the aerodynamic force on a blade element that is perpendicular to the relative airflow. Profile drag is the component of the aerodynamic force on a blade element that is parallel to the plane of rotation. Induced drag is the component of the aerodynamic force on a blade element that is parallel to the relative airflow. Profile drag consists of pressure forces and skin friction acting on the surface of the blade element. The component of profile drag that arises from pressure forces (between the leading and trailing edges) is pressure or form drag. The component of profile drag due to shear forces over the surface is skin friction. The total rotor thrust is the vertical upwards force from the rotor disc as a whole, as the sum of all the blade thrusts. This term has been reinstated because there is already the term ‘rotor thrust’ that is used to denote the thrust along the axis of rotation that acts directly opposite the weight of the helicopter in a blade element.

(3)HELICOPTER CHARACTERISTICS Disc loading is the mass (M) of the helicopter divided by the area of the disc. Blade loading is the mass divided by the total planform area of the blades. The area of a rectangular blade is given by the chord multiplied by the blade tip radius. For tapered blades, the mean geometric chord is taken as an approximately equivalent chord. Rotor solidity is the ratio of the total blade area to the disc area.

(4)PLANES, AXES AND REFERENCE SYSTEMS OF THE ROTOR Shaft axis: The physical axis of the rotor shaft (mast). Hub plane: A plane perpendicular to the shaft axis through the centre of the hub. Tip path plane: The plane traced out by the blade tips. Virtual rotation axis: The axis through the centre of the hub and perpendicular to the tip path plane. Rotor disc: The disc traced out by the blade tips in the tip path plane. Plane of rotation: The plane parallel to the tip path plane that acts through the hub centre.

(5)ANGLES OF THE BLADES, INDUCED VELOCITY Pitch angle of a blade element: The angle between the chord line of the element and its plane of rotation, sometimes called ‘local pitch angle’. Blade pitch angle: Taken to be equivalent to the pitch angle of the blade element found at 75 % of the blade radius. Flapping angle: The angle between the longitudinal axis of the blade and the hub plane. Coning angle: The angle between the longitudinal axis of the blade and the tip path plane. Induced velocity is that induced by the engine power perpendicular to the plane of rotation. Aerodynamic forces on the blades and the rotor The thrust from a blade (blade thrust) is the sum of the thrusts from each blade element. The sum of the thrusts from all blades is the (total) rotor thrust acting perpendicular to the tip path in the direction of the virtual rotation axis. The result of the induced drag forces on all the blade elements of all blades is a torque on the shaft which, multiplied by the angular velocity of the blade, gives the required induced power. The result of the profile drag forces is a torque on the shaft which, multiplied by the angular velocity of the blade, gives the required profile power.

(6)TYPES OF ROTOR HUBS There are basically four types of rotor hubs in use:

1.Teetering rotor or seesaw rotor: The two blades are connected together; the ‘hinge’ is on the shaft axis, and the head is underslung. A variation is the gimballed hub; the blades and the hub are attached to the rotor shaft by means of a gimbal or universal joint (Bell 47). It is sometimes called semi-rigid because there is no movement of the blade in a drag-wise sense.

2.Fully articulated rotor: There are more than two rotor blades and each has a flapping hinge, a lead-lag (drag) hinge, and a feathering hinge or bearing.

3.Hingeless rotor: There are no flapping or dragging hinges. They are replaced by flexible elements (virtual hinges) at some part of the blade radius which allow such movements. A feathering bearing allows feathering of the blade.

4.Bearingless rotor: There are no hinges or rotating bearings. Flapping and dragging movements are obtained with flexible elements called elastomeric hinges. Feathering is obtained by twisting the element. When referring to their equipment, Airbus call this a ‘semi-articulated head’ (ref.: their training material). Two remarks:

1.Hinge offset and equivalent hinge offset The hinge offset is the distance between the shaft axis and the axis of the hinge. Hingeless and bearingless rotors have an equivalent hinge offset.

2.Elastomeric hinges This bearing consists of alternate layers of elastomer and metal. The flexibility of the elastomer allows flapping, dragging and feathering.

(7)DRAG AND POWERS Induced power is that required to generate the induced velocity in the rotor disc for the production of lift. For any given thrust, induced power is minimum when the induced velocity is uniform over the rotor disc. This can be approximated by using washout and ensuring that the blades are in track (a truly uniform velocity cannot be obtained). Rotor profile drag results from those components acting in the opposite direction to the blade velocities (i.e. the sum of all the profile drags from each blade element). The power required to overcome it is rotor profile power (the sum of the powers required to overcome the torque). Parasite drag is the drag from the helicopter fuselage including that from the rotor hub and all external equipment such as wheels, the winch, external loads, etc. (any drag from the tail rotor is included, but not from the rotor blades, which produce profile drag). The power to overcome this drag is parasite power. In level flight at constant speed, induced power, rotor profile power and parasite power are summed to give the total power required to drive the main rotor. Induced power and profile power for the tail rotor are summed to give the power required to drive the tail rotor. The power required to drive auxiliary services, such as oil pumps and electrical generators, is called accessory or ancillary power. It includes the power required to overcome mechanical friction in transmissions. The total power required in level flight at constant speed is the sum of all the above. When transitioning from the hover, the power required decreases as speed increases. This is called translational lift. The term limited power means that the total power required to hover out of ground effect (HOGE) is greater than the available power.

(8)PHASE ANGLE IN FLAPPING MOVEMENT OF THE BLADE The movement of the cyclic control tilts the rotor disc in the direction of the intended movement of the helicopter. For teetering heads, the flapping response is 90° later than the applied cyclic control movement (less than 90° for rotors with offset hinges). The pitch mechanism consists of the swash plate, and for each blade the pitch mechanism consists of a pitch link attached to the swash plate and a pitch horn attached to the blade.

(9)AXES THROUGH THE CENTRE OF THE HELICOPTER Longitudinal axis or roll axis: A straight line through the centre of gravity (CG) of the helicopter from the nose to the tail about which the helicopter can roll left or right. Lateral axis, transverse axis or pitch axis: A straight line through the CG of the helicopter about which the helicopter can pitch its nose up or down (this axis is also perpendicular to the reference plane of the aircraft, which is the plane either side of which the components that constitute the major part of the aircraft are symmetrically disposed in the port and starboard sense). Normal axis or yaw axis: A straight line perpendicular to the plane defined by the longitudinal and lateral axes and about which the helicopter can yaw. Note that the term ‘mass’ is used to describe a quantity of matter, and ‘weight’ when describing the force. However, the term ‘weight’ is normally used in aviation to colloquially describe mass. The professional pilot should always note the units to determine whether the term ‘weight’ is being used to describe a force (e.g. unit newton) or quantity of matter (e.g. unit kilogram).