Rotor Dynamics Vol 6 Final 40Set-1 PDF

1 FIS: ROTOR DYNAMICS INDEX Chapter No Topic Page No 1 Basic Definitions 2 2 History of Helicopters 6 3...

1 FIS: ROTOR DYNAMICS INDEX Chapter No Topic Page No 1 Basic Definitions 2 2 History of Helicopters 6 3 Theories of Rotor Dynamics 10 4 Torque Reaction 15 5 Movement of Main Rotor Blade 18 6 Dynamics of Hover 29 7 Dynamics of Forward Flight 33 8 Dynamic Lift Overshoot 48 9 Autorotation 52 10 Stretching The Glide 62 11 Height Velocity Diagram 70 12 Helicopter Performance 78 13 V-N Diagram 93 14 Vortex Ring 97 15 Loss of Tail Rotor Effectiveness 101 16 Ground Resonance 109 17 Static and Dynamic Rollover 111 18 Mast Bumping and Droop Stop Pounding 113 19 Cyclic Saturation 115 20 Stability and Control 120 21 Helicopter Design 130 22 Main Rotor Design 148 23 BERP 161 24 NOTAR 163 25. Uncommon Configurations 166 26. Helicopter Vibrations 171 27 Helicopter Noise 179 28 Helicopter Weight and Balance 185 Glossary of Terms 195 FLYING INSTRUCTORS SCHOOL  2 FIS: ROTOR DYNAMICS CHAPTER - 1 BASIC DEFINITIONS General Definitions 1. Mass. It is the quantity of matter contained in a body. Unit: Kilogram (Kg) Dimension: M 2. Inertia. The reluctance of a body to change its state of rest or uniform motion in a straight line is called its Inertia. It is a quality possessed by the body and is dimensionless. 3. Speed. For a body in motion, the rate of change of position is called its speed. The speed is a scalar quantity. Unit: m/s Dimension: LT-1 4. Velocity. The rate of change of position along a particular direction in a straight line is called velocity. Unlike speed, velocity is a vector quantity. Unit: m/s Dimension: LT-1 5. Equilibrium. When two or more co-planar force act on a rigid body, the body is said to be in equilibrium, if following conditions are satisfied:- (a) All the forces acting on the system should cancel each other i.e. algebraic sum of all the forces should be zero. (b) Algebraic sum of moment of all the forces at any point in their plane should be zero. (c) The algebraic sum of resolved parts of all the forces, in the direction at right angles to the first direction, should be zero. 6. Force. Force is that which changes or tends to change the state of rest or of uniform motion in a straight line of a body. It is a vector quantity. 2 Unit: Newton Dimension: MLT- 7. Weight. It is the force with which a body is attracted towards the centre of the earth. W=Mg where M is mass of the body and g is acceleration due gravity. 8. Density. Density is defined as mass per unit volume. It is denoted by Greek symbol ρ (Rho). Unit: Kg/m3 Dimension: ML-3 8. Pressure. Pressure is defined as force per unit area. Unit: Newton/m2 Dimension: ML-1T-2 10. Centre of Gravity. It is the point through which the weight can be considered to act. FLYING INSTRUCTORS SCHOOL  3 FIS: ROTOR DYNAMICS 11. Work. A force is said to do work on a body when it moves the body along its line of action. The amount of work done is equal to the product of the force and the distance moved in the direction of the force. W = FS Unit: Joules Dimension:ML2 T -2. 12. Energy. The energy of a body is its capacity to do work. 2 E=Fs. Unit: Joules Dimension: ML T-2. 13. Power. The power of an agent is its rate of doing work. P=FST=Fv Unit: Watt Dimension: ML2 T -3. 14. Moment of a Force. The moment of a force around a point is the product of the force and the perpendicular distance between that point and the line of action of the force. The moment (or turning effect) of a force can be either clockwise or anti- clockwise. The net effect of a system of forces can be calculated by adding all the moments algebraically. The clockwise moments by convention are taken as positive while the anti-clockwise moments are negative. 15. Couples. A system of two equal, unlike, parallel forces is called a couple. A couple can cause no motion in translation but only causes rotation. The moment of a couple is equal to the product of one force and the perpendicular distance between the two forces. The work done by a couple is the product of the moment of the couple and the angle in radians described by the arm. Rotor Dynamics Definitions 16. Helicopters may be single or multi- rotor, each rotor having several blades, usually varying from two to six in number. The rotor blades are attached by a rotor head to a rotor shaft which extends approximately vertically from the fuselage. They form the rotor, which turns independently through the rotor shaft (Fig 1.1). 17. Shaft Axis. The shaft axis is the Fig 1.1 Rotor Head Arrangement axis through the main rotor head about which the blades are permitted to rotate. 18. Axis of Rotation. The axis of rotation is the line through the head of the main rotor shaft about which the blades actually rotate. Under ideal conditions of nil wind hover, the axis of rotation will coincide with the shaft axis; however, this will not always be the case since the rotor disc is permitted to tilt under certain conditions of flight Fig 1.2 Axis of Rotation (refer Fig 1.2). FLYING INSTRUCTORS SCHOOL  4 FIS: ROTOR DYNAMICS 19. Plane of Rotation. The plane of rotation is at right angles to the axis of rotation at the head of the main rotor shaft and is parallel to the tip path plane. 20. Tip Path Plane. The tip path plane is the path described by blade tips during rotation and is at right angles to the axis of rotation. 21. Rotor Disc. The area contained within the tip path plane is referred to the rotor disc. 22. Coning Angle. It is the measure of the angle between the span wise length of the blade and blade’s tip path plane. 23. Blade Pitch. The angle between the chord of the aerofoil section and the plane in which the blade is free to rotate is known as the pitch angle. 24. Induced Flow. The rotor blades when rotating act like a fan and continuously pump air downwards. The column of descending air is called induced flow. (Refer para9 Chapter 3 for explanation) 25. Relative Air Flow. A rotor blade experiences different airflows:- (a) Airflow due to rotation of blade. (b) Induced flow (c) Flow due to forward motion of helicopter. Thus Relative airflow( RAF) is the flow as experienced by an element of blade and is a resultant of all the three. 26. Rotor Thrust. The component of total reaction acting perpendicular to the Plane of Rotation is called rotor thrust. 27. Angle of Attack. Similar to a fixed wing aircraft AoA or ᵅ is the angle between RAF and blade chord. 28. Rotor Drag. The component of total reaction acting along the plane of rotation opposing the motion of the blade is called rotor drag. 29. Total Rotor Thrust. The resultant of the rotor thrust provided by each blade is called the total rotor thrust. Provided all the blades produce equal rotor thrust, the total rotor thrust will act through the hub, at right angles to the plane of rotation. 30. Blade Loading. It is weight supported by unit area of rotor blade. It is determined by dividing the gross weight of the helicopter by the combined blade area. A helicopter rotor blade always possesses a high blade loading. 31. Collective Pitch Control. Control mechanism either manually or automatically operated, by which the pitch of all rotor blades is varied equally and FLYING INSTRUCTORS SCHOOL  5 FIS: ROTOR DYNAMICS simultaneously is called collective pitch control. Since it changes the pitch of all blades by same value simultaneously, it is called the Collective pitch control or collective. 32. Cyclic Pitch Control. Control mechanism which individually changes the pitch of each rotor blade during a cycle of rotation to control rotor disc tilt is called cyclic pitch control. Since pitch is changed by a fixed value in a cycle of one rotation it is called cyclic pitch control or cyclic. 33. Disc Loading. Just as we have ‘wing loading’ in fixed-wings aircraft, so we have disc loading and blade loading in helicopters. Disc loading is the ratio of the all up-weight to the rotor–disc area. 34. Torque Reaction. As per Newton’s Third Law, “To every action there is an equal and opposite reaction”, in a helicopter, when the fuselage mounted engine applies torque to rotates the main rotor, the reaction for the fuselage is to turn in the opposite direction. This is called torque reaction. 35. Gyrodyne. Rotating wing aircraft whose rotor(s) is (are) normally engine- driven for take-off, hovering, landing, and forward flight through the low part of its speed range and in cruise flight may be powered and unpowered. Its primary means of propulsion, usually propeller(s) is independent of the rotor system. 36. Gyroplane. Rotating wing aircraft whose rotor (s) is (are) not engine – driven except for initial starting, but are made to rotate by the action of the air when the rotorcraft is moving, and whose primary means of propulsion, usually propeller(s), is independent of the rotor system. Both Gyrodyne and Gyroplane produce lift by rotor above and thrust by independent engine driven propeller. 37. Helicopter. Rotating wing aircraft whose vertical and horizontal motion is dependent on engine-driven lifting rotor(s) (Fig 1.3).Both lift as well thrust are produced by engine driven rotor. Fig 1.3 FLYING INSTRUCTORS SCHOOL  6 FIS: ROTOR DYNAMICS CHAPTER-2 HISTORY OF HELICOPTERS 1. It is a curious fact that the idea of helicopters is about 5000 years old! Around 3000 BC in ancient China, there appeared a toy called the ‘Chinese top’. It was a simple and yet an aerodynamically sound device, consisting of a stick with a simple propeller attached to it. The stick was given a rotation by rubbing it between both the palms and let go. Because of the rotation, the toy would rise a short distance and then in an autorotational manner fall to Fig 2.1 the ground. 2. Unfortunately, the Chinese top remained only a toy and did not create any breakthrough in man’s desire to fly. The next development occurred around 1483 AD, when Leonardo da Vinci, applied his extraordinary intellect to the problems of human flight. He designed a helical vane (Fig 2.2 something like a screw but with flat surfaces in place of the threads on the screw) He argued correctly that if this helix was rotated fast enough, it would bore through the air and go up. However, the major problem during Da Vinci’s time was to find an engine which could supply enough Fig 2.2 power to rotate the helix. Never the less, his contribution is such that he is today regarded as the ‘Father of the Helicopter’. 3. Further development in helicopter was achieved only through toys. Almost three centuries later, at the 1783 science conference in Paris, two Frenchmen named Launoy and Biencenu, demonstrated a toy they had developed. It was a modification of the Chinese top, with propellers at either end of the stick, which rotated in opposite direction and thus prevented the body from rotation. This toy climbed to a height of about 70 ft and autorotated to the ground. Needless to say, this attracted a lot of attention. What these French men had accomplished was to Fig 2.3 invent the first true rotary-wing toy. It was logically argued that, what could work in a model big enough to carry a man. FLYING INSTRUCTORS SCHOOL  7 FIS: ROTOR DYNAMICS 4. The next milestone came almost after another 60 years in 1843. Sir George Clyley, an Englishman, unveiled the first helicopter model ever. It had two sets of rotors, situated side by side and was powered by a steam engine. Of course, it failed to take off; the weight of the engine was too great. In spite of its failure, it influenced future design of helicopters. Around mid-nineteenth century, a Frenchman named Ponton D’ Amecourt also produced a model of helicopter with a co-rotating wing, powered by the then latest model steam engine. His craft also failed to take off though it attempted to lift off by getting slightly light on the ground. It was D’ Amecourt who coined the word ‘helicopter’ from two Greek roots; helico meaning spiral and ‘pteron’ meaning wing i.e spiral wing. 5. The first helicopter model which took to air was an unmanned craft weighing about 3 kgs developed by the Italian Enrico Foranini, around 1870. This was also a steam powered model, and it rose to 40 ft and remained in air for about 20 min. Manned helicopter flight was about to become a reality. 6. In 1907, just four years after the Wright brothers demonstrated manned flight at Kitty Hawk in 1903, a French man, Paul Cornu, became the first man to fly in a rotary wing aircraft. His craft (Fig 2.4) was powered by a 24 hp internal combustion engine and had two rotors arranged in tandem. He rose only a few feet and remained airborne just for a few seconds. At Fig 2.4 about the same time another Frenchman, Louis Charles Breguet, also achieved helicopter flight for a few seconds with his design which had four rotors arranged in a box fashion, but his ac was tethered to the ground. 7. Even though rotary wing flight was only four years behind the first fixed wing flight, subsequent developments were not as rapid as in the latter’s case. World War I intervened and progress was slow. One of the main problem which was not solved, till after the war, was control of the rotor craft in flight. 8. After WW-I, many models were built in France, USA, UK and Spain. Amount of stability and controllability were established but it was still a far cry from having a practical helicopter. The next major development was a hybrid combination of fixed wing and rotary-wing known as Cierva’s Autogyro. 9. Juan de la Cierva was a Spanish aircraft designer. In the early 1920’s one of his three-engine bombers crashed on its second flight, due to slow speed stall. While investigating these problems, an idea struck him- why accelerate the entire aircraft to create lift even at low speeds? This was a brilliant idea. He designed an aircraft with wings on side and on top also. He reasoned that even at slow speeds, the airflow would be able to rotate the rotors like in the case of wind mills, and that should produce enough lift for a takeoff. The earlier scale models worked nicely but the actual aircraft rolled over and crashed as they initiated forward flight. It was back to the drawing board again. One day, when he was watching the play ‘Aida’ with his FLYING INSTRUCTORS SCHOOL  8 FIS: ROTOR DYNAMICS wife, a sudden inspiration came to him. He realized that his scale models were made of wood that was flexible whereas his actual aircraft was made of rigid rotor blades. If they were also made flexible to move up and down with respect to their plane of rotation, probably there would be no roll over on takeoff. So, he introduced a hinge at the hub to allow the blades to flap up and down-(now known as the flapping hinge). This was a great breakthrough in rotor design, on which future helicopter designers would build. Due to dissymmetry of rotor thrust between advancing and retreating side and the rotor system earlier being rigid, aircraft was rolling over to retreating side. When Juan de la Cierva made a flexible system by adding flapping hinges, the blades started to ‘flap to equality’. This as we know now causes ‘flapback’ in forward flight which is countered by pilots, by moving the cyclic forward that is by cyclic ‘feathering’. We will come back to these terms later in this book. 10. The 1930’s saw the ‘dawn’ of helicopters, as we know them today. The first practical helicopter was built by the German designer, Heinrisk Focke in 1936. This aircraft was named FW-61 or Focke- Acheglis helicopter. In 1937, it gave a demonstration of its maneuverability inside a Hall measuring 100 ft in length and 100 ft in width, in which the helicopter flew forward, backward and sideward over a single spot and carried out 3600 turns on the spot. Another unusual aspect about Fig 2.5 this demonstration was that it was flown by a women test pilot – the famous “Hanna Reitch”. It was a side-by-side, twin helicopter without a tail rotor. This was also the first helicopter, which went into production as ‘Focke Fa 223 Drache’. However, only a few aircraft were produced before the end of WW II. 11. The concept of having a tail rotor for torque compensation was first propounded by BN Yuriev, an early Russian Rotorcraft pioneer. His idea was initially tried out on a helicopter by the Dutchman Von Baumhaver in 1924. However, it was not a success as Baumhaver had a separate engine to drive the tail rotor, which made it too heavy for lift off. In 1939, Igor Sikorsky, a Russian Émigré’ in USA, tested the first successful helicopter with a tail rotor. This historic model, VS–300, soon broke the records set by FW-61 and went on to pave way for most of the current helicopter designs. Many of the subsequent Sikorsky model were produced under license in other countries also and used almost worldwide. The first helicopters to be obtained by the IAF were also Sikorsky’s S-55. 12. With the advent of jet engines, there was a flurry of activities aimed at harnessing these engines to the helicopters. A Ram Jet/pulse jet engines which operate efficiently only at high speeds, were tried out by fitting them at the rotor tips. They were not very successful as it involved complicated arrangements. The next major breakthrough came with the development of turbo-shaft engines for aircraft. By adopting it to helicopters, a greater power/wt ratio and better fuel economy could be brought about. Because of this development, helicopters like the Russian Mil Mi-12 could be built with a max AUW of about 105 tons and payload of about 40 tons. This FLYING INSTRUCTORS SCHOOL  9 FIS: ROTOR DYNAMICS helicopter is no longer operational now. The current heaviest operational helicopter in the world is Mi-26 with a max AUW of about 56 tons and a payload of 20 tons. 13. Even though there have been impressive achievements in the weight carrying capabilities of the helicopter its achievement in speed has not been so dramatic. The first world record set up by FW-61 in 1938-39 had been 76 miles/hr. The max speed reached now is around 249kts by Westland Lynx. It does appear that increasing the max speed poses insurmountable problems to the helicopter. Some designers have taken other routes to beat this problem like the compound helicopters and convertiplanes. 14. Compound Helicopter. Compound helicopter is a helicopter with small wings and with one or more additional propulsion units (usually jet engines). Some experimental models have been tried out. The highest speed achieved by any compound Helicopter is 274kts by Bell UH-1 compound with two additional jet engines for propulsion. Due to compounding the rotor is relieved of its lifting and propulsive duties there by eliminating retreating blade stall, which is the most serious limitation to high-speed helicopter flight (covered in subsequent chapters). 15. Convertiplane. Convertiplane is an aircraft that can convert from a helicopter to a fixed wing aircraft in flight to take advantage of the best characteristics of each. An early model was the Fairey Rotodyne. It had rotors on top and two turbo-props on a conventional wing like in a fixed wing transport ac. For initial take off, the power from the two engines was fed to the rotor in the form of jets at the wing tips and the ac lifted off like a helicopter. Upto 80 kts of speed, the power was fed only to the rotor. Between 80 to 120 kts, power was slowly withdrawn from the rotor and fed to the propellers. Above120kts, the rotor was left to windmill or auto rotate and the turbo-props took over. This ac reached a speed if 170 kts but was not a commercial success. A similar model was also tried out by McDonnel XV-1, which remained a research ac and never entered production. A more advanced convertiplane was the Sikorsky S-57 or XV-2. This was another experimental aircraft with a single jet engine. For takeoff, the jet power was used to run a compressor, which in turn was ducted through jets at the rotor tips. In flight, the compressors as well as the rotors were stopped and the jet engine and the wings took over. The latest entrant into the market in the tilt rotor V-22 osprey of the US, which initially started off as XV-3. For take –off, the two propellers at the wings tips of the ac are tilted up and behave like rotors of a helicopter. In flight, the propellers tilt, forward and behave like normal turbo-props. For landing, the sequence is reversed. It has taken about 40 years from conception to production for this ac. We will have to wait and watch as to how successful this aircraft will prove itself to be. 16. Helicopters have come a long way since the first model flew in 1907. They have proved themselves to be extremely versatile, can adopt themselves to many roles and have become an indispensable part of both civil and military operations. When some extremely imaginative and difficult task is to be performed by a flying machine, especially at an inaccessible place, more often than not you invariably will hear - ‘get a helicopter’ There will always be such tasks, whether in peace or war, and therefore helicopter development is expected to continue at a fair pace in the future. FLYING INSTRUCTORS SCHOOL  10 FIS: ROTOR DYNAMICS CHAPTER – 3 THEORIES OF ROTOR DYNAMICS 1. Helicopter derives its thrust from rotors. Each blade of a rotor is similar to a wing in that it is aerodynamically shaped to be an efficient producer of lift through the flight envelope. The blade can be described in terms of shape of its cross section (chord, thickness, camber, etc) and the shape of its planform (span, aspect ratio, taper, twist, sweep, etc). As in fixed wing, the aerofoil shape may change span wise, and a geometric twist is usually built in, so that the tip sections are ‘washed out’ that is, have lower incidence, towards the tip. The generation of lift in helicopters can be described by two theories namely Momentum Theory and Blade Element Theory. 2. Momentum Theory. The momentum theory is based on Newton’s third law of motion “for every action there is an equal and opposite reaction”. For the hovering helicopter, the action is the downward velocity imparted to the air in the rotor wake and the reaction is found in the production of an upward rotor thrust. Since the air is unconstrained, it moves downward through the rotor disc, accelerating from state of rest far above the rotor to some velocity Vi at the rotor, and then proceeding down to some final downwash velocity Vj about one to two rotor diameters below the disc (in free air hover only – the presence of ground changes the scenario called ground effect). 3. Newton’s second law of motion states that a body will accelerate at a rate proportional to the force applied, divided by the mass of the body, e.g., this applies directly to a cannonballs being pushed out a gun barrel; however to apply it to a rotor requires that we turn Newton’s second law around by saying that a force is equal to the product of acceleration and mass. In the case of a helicopter in a steady hover, the force is the rotor thrust; the acceleration is the change in air velocity from far above the rotor (where it is zero) to a steady value below the rotor; and the mass is the mass flow of the air being pushed through the rotor disc every second. 4. The mass flow is the product of the mass in a cubic foot of air, the disc area and the induced velocity at the rotor disc. Since, both the mass flow (ρaV) and the acceleration (V/t) depend on the induced velocity, the rotor thrust is proportional to the product square of the induced velocity and the rotor disc area. For this reason, a small rotor must induce a higher velocity then a large rotor to produce the same thrust. 5. Blade Element Theory. Although the momentum theory provides a good general explanation of hover power, it fails to deal with the detail of what is actually happening to the blade, or the dependence of rotor thrust on rotor speed or collective pitch setting; for this we need Blade Element Theory. 6. The fundamental difference between the blade of a rotor and a fixed wing is that each section of a rotor blade experiences a significantly different airspeed (hence dynamic pressure) than its neighboring section or some other span location. The angular velocity ω causes a linear velocity Vr at any section which is directly proportional to the distance of the section from the centre of rotation (Vr =ωr). The FLYING INSTRUCTORS SCHOOL  11 FIS: ROTOR DYNAMICS highest velocities occur at the tip where r is the largest. The typical tip velocities range from 350 to 500 Kts. The tip speed of Chetak is around 408 Kts. 7. Similar to a fixed wing, lift generation by a blade section of area ΔS is given by the basic equation ΔL =CL ½ ρ Vr2 ΔS. Where Vr is the particular velocity associated with the location of ΔS spanwise and CL is the lift coefficient of the section determined by the shape of the aerofoil at that location and the AOA at that location. In general each section has a different CL and Vr. 8. Fig 3.1 shows the conditions at a typical blade element in a hover. The blade experiences air both due to rotor rotation and due to downward induced velocity. These two velocities combine to form a resultant velocity vector that is pointed slightly down. Since, by definition lift is perpendicular to the local vector velocity (or relative airflow), it is titled slightly back. The rearward component of the lift is known as drag. Since both the rotational airflow as well Fig 3.1 Forces on a Blade Element at Hover as induced flow will vary along the rotor blade, the direction of RAF and magnitude of AoA will differ. This will vary the direction of lift generated by individual blade elements. Unlike fixed wing AD where TR is divided into mutually perpendicular lift and drag; in Helicopter AD, TR is divided into Rotor Thrust and Rotor Drag which are parallel and perpendicular to the axis of rotation. By this arrangement Rotor thrust and Rotor Drag of all the blade elements can be added correctly. 9. Lift. The lift produced on a wing of an aircraft results from a combination of various factors and is commonly expressed in the formula 2 CL1/2V S. Lift from a helicopter rotor blade can generally be expressed in similar terms but because the blade moves independently of the fuselage, the velocity (V2) in hovering conditions in still air is purely the result of the rotation of the blade (Fig 3.2). The Fig 3.2 Lift/ TR on the Blade forward flight modifies both direction and strength of RAF for a blade. FLYING INSTRUCTORS SCHOOL  12 FIS: ROTOR DYNAMICS 10. Blade Pitch. The wing of a fixed wing aircraft is fitted to the fuselage at some specified angle. The datum are the chord of the aerofoil section and the line longitudinally down the fuselage. The angle between the two is known as the angle of incidence. The rotor blade, when attached to the rotor head will also have a Fig 3.3 Blade Pitch Angle basic setting. The datum are the chord of the aerofoil section and the plane in which the blade is free to rotate. The angle between the two datums is known as the Pitch Angle (Figure 3.3). 11. If the blade has a constant value of pitch throughout its length, problems would arise relating to blade loading because each section of the blade will have a different rotational velocity and therefore a different TIP ROOT value of lift. As lift is proportional to V2 each time the speed is doubled the lift will increase four times and the pattern of lift or loading on the blade would be as in Fig 3.4 which will cause it to rise. 12. To avoid this considerable variation of lift, it is Fig 3.4 Washout necessary to increase lift at the root end and decrease some of the lift at the tip. The blade is therefore, either tapered, given a washout ( reduction of pitch angle from root to tip) or a combination of both. Chetak has washout of 6o 30”. Lift from the blade will still have its greatest value near the tip but its distribution along the blade will be more uniform Figure 3.4. FLYING INSTRUCTORS SCHOOL  13 FIS: ROTOR DYNAMICS 13. Determining the Direction of the Air Relative to the Blade. Relative wind is created by the motion of an airfoil through the air, by the motion of air past an aerofoil, or by a combination of the two. Relative wind may be affected by several factors, including the rotation of the rotor blades, horizontal movement of the helicopter, flapping of the rotor blades, and wind speed and direction. For a Fig 3.5 Induced Flow helicopter, the relative wind is the flow of air with respect to the rotor blades. When the helicopter is hovering in a nil-wind condition, relative wind is created by the motion of the rotor blades through the air. If the helicopter is hovering in a wind, the relative wind is a combination of the wind and the motion of the rotor blades through the air. When the helicopter is in forward flight, the relative wind is a combination of the rotation of the rotor blades and the forward speed of the helicopter. Consider a column of air through which a rotor blade is moving horizontally, the effect will be to displace some of the air downwards. If a number of rotor blades are travelling along the same path in rapid succession (with a three bladed rotor system rotating at 240 rotor rpm, a blade will be passing a given point every twelfth of a second), then the column of still air will eventually become a column of descending air(Fig 3.5). 14. This downwards motion of the air is known as the INDUCED FLOW. The direction of the air relative to the blade will therefore be the resultant of the blade’s horizontal travel through the air and the air which is descending. 15. If the force acting on the aerofoil (Total Reaction) is split into components, lift and drag. Lift at right angles to Relative Air Flow, is not providing a force in direct opposition to the weight as in the case of fixed wing aircraft. The lifting component of the Total Reaction must therefore, be that part of it, which is acting along the axis of rotation. This component is known as ROTOR THRUST. The other component of the total reaction will be in the blade’s plane of rotation and is known as ROTOR DRAG. 16. Total Rotor Thrust. If the rotor blades are perfectly balanced and each blade is producing the same Rotor Thrust, then the TOTAL ROTOR THRUST can be said to be acting through the hub at right angles to the plane of rotation. Fig 3.6 Total Rotor Thrust FLYING INSTRUCTORS SCHOOL  14 FIS: ROTOR DYNAMICS 17. Coning Angle. The Rotor Thrust will cause the blades to rise until they reach a position where their upwards movement is balanced by the outwards pull of the centrifugal force being produced by the blades’ rotation. In normal operation the blades are said to be coned upwards, the Coning Angle being measured between the span-wise length of the blade and the blade’s Fig 3.7 Coning Angle tip path plane. The coning angle will vary with combinations of Rotor Thrust and rotor rpm. The weight of the blade (and its distribution) will also have some effect but for a given helicopter this will be constant (Figure 3.7). 18. Rotor Disc. The rotor disc is the area enclosed within the circle described by the rotor blade tips. Because this area decreases as the coning angle increases, the coning angle must never be allowed to become too big. As coning angle increases, horizontal component of Rotor Thrust (facing towards centre/hub) will keep increasing at cost of vertical component of Rotor Thrust. 19. Limits of Rotor Rpm. As the centrifugal action through rotor rpm gives a measure of control of the coning angle, provided the rotor rpm are kept above a laid down minimum, the coning angle will always be within safe operating limits. There will also be upper limits to the rotor rpm due to engine and transmission considerations and end loading stresses where the blade is attached to the rotor head. Rotor rpm limitations will be found in the relevant pilot notes. With rotors stopped only weight is determining the blade position. As rotor start rotation the centrifugal force modifies the tip path till sufficient RPM is achieved when aerodynamic force also starts affecting its position. 20. Pre Coning. Most helicopters have a pre-coning angle built into the rotor hub to reduce stresses on the blades, that is, the rotor blades are attached to the hub at a small positive coning angle. This reduces bending stress on the main rotor head. 21. Overtorqueing. Overtorqueing is possible on turbine driven helicopters when the transmission system cannot absorb the high torque that turbine engines are capable of producing. Overtorqueing can be avoided by careful monitoring of the torque gauge and careful use of the helicopter controls. 22. Overpitching. Overpitching is a dangerous condition reached following the application of pitch to the rotor blades without sufficient engine power to compensate for the extra rotor drag. The rotor rpm decays, coning angle increases, disc area and rotor thrust reduce. A need is felt to increase the collective further which again decays rotor rpm. This can be prevented only by reducing the pitch angle of the blade by reducing collective. This entails a loss of height which can be dangerous close to ground. FLYING INSTRUCTORS SCHOOL  15 FIS: ROTOR DYNAMICS CHAPTER – 4 TORQUE REACTION 1. Torque Reaction. In a helicopter since the source of power is on the fuselage, rotation of main rotor will cause the fuselage to rotate in opposite direction. The tendency of the fuselage to rotate in opposite direction to the main rotor is called Torque Reaction. If the source of power were to be located on the blade itself, e.g., small ramjet engines on blade tips, there TAIL would be no torque reaction. There are a ROTOR number of ways by which this reaction can be overcome but the only method considered here would be the fitting of a tail rotor. When the moment of the tail rotor thrust equals the torque reaction, then the fuselage will maintain a constant direction (Refer Figure 4.1). As the torque reaction is not a constant one, some means must be provided to vary the thrust Fig 4.1 from the tail rotor. This is achieved by the pilot moving yaw pedals which COLLECTIVELY CHANGE the pitch and thereby the angle of attack on the tail rotor blades, the pitch increasing or decreasing depending upon which yaw pedal is depressed. 2. In a nil-wind hover, the tail rotor provides all of the anti-torque compensation. As the aircraft moves into forward flight, the tail rotor is assisted in this compensatory effort by the weather-cocking effect and the vertical stabilizer. The increased parasitic drag produced on the longitudinal surface of the aircraft as the relative wind increases causes the aircraft to "steer" into the relative wind. This weather-cocking effect will increase proportionally with square of EAS and provide assistance to the tail rotor anti-torque effect. 3. At higher speeds, tail rotor power requirements are significantly reduced by mounting a vertical stabilizer shaped like an aerofoil, which produces lift opposite the direction of the torque effect. By reducing the power required by the tail rotor, more engine power is now available to drive the main rotor system. 4. Additional Tail Rotor Functions. Apart from the primary function of producing an anti-torque reaction force the tail rotor is also available for additional functions as follows:- (a) To Alter the Direction of the Fuselage While Hovering. By operating the yaw pedals to produce a tail thrust greater or less than the torque reaction, the heading of the fuselage can be altered while the helicopter is hovering over a spot. Yaw pedals operate in the correct sense in that a yaw to the right results from pushing on the right yaw pedal and vice versa. Taxiing on ground is also achieved by similar manner. FLYING INSTRUCTORS SCHOOL  16 FIS: ROTOR DYNAMICS (b) To Maintain a Balanced Condition in Forward Flight. By using the yaw pedals to keep the ball in the correct place (Centre/Offset depending upon the helicopter type.) (c) To Stop the Fuselage Rotating in Power Off (Autorotative) Flight. When the rotors are being turned purely by the reaction from the air and without assistance from the engine, friction will cause the fuselage to rotate in the same direction as the rotor. Directional control is maintained by changing the pitch on the tail rotor to such a degree that tail rotor produces a thrust in a direction opposite to that required when the rotor is being driven by engine power. The tail rotor blades are symmetrical in shape and must be capable of being turned to produce plus or minus values of pitch. 5. Tail Rotor Drift. Consider a metal bar, which is being turned under the influence of a couple YY1 about a point X. The rotation will stop if a couple ZZ 1 of equal value pulls in the opposite direction (Figure 4.2a). The rotation would also stop if a single force ZZ1 was used to produce a moment equal to the couple YY1 (Figure 4.2b), we now have a force of ZZ1 opposing Y1 as Y1=Z1, there is a residual force Z acting in the same direction as Y1. There will now be a side force on the pivot point X (Figure 4.2c). The tail rotor of a helicopter produces a moment to overcome the couple arising from torque reaction which in turn causes a Fig 4.2 side pull on the pivot point or axis of rotation of the main rotor. This side force produces a movement known as TAIL ROTOR DRIFT and unless corrected would result in the helicopter moving sideways over the ground. Since the value of the moment is the product of force x distance, the greater the distance that the tail rotor acts from the main rotor axis of rotation, the smaller the force required. In practice, the tail rotor is normally positioned just clear of the main rotor. The tendency of tail rotor drift will vary according to how much power is being transmitted to the rotor. More the torque reaction more will be the tail rotor force and thus more the tail rotor drift. 6. Correcting for Tail Rotor Drift. Tail rotor drift can be corrected by tilting the rotor disc away from the direction of the drift. This can be achieved by: (a) The pilot making a movement of the cyclic pitch stick. (b) Rigging the controls so that when the stick is in the centre, the disc is actually tilted by the right amount. (c) By mounting the gearbox so that the drive shaft to the rotor is offset. (d) By causing the disc to tilt laterally when the collective pitch lever is raised. FLYING INSTRUCTORS SCHOOL  17 FIS: ROTOR DYNAMICS 7. Tail Rotor Roll. If the tail rotor is mounted on the fuselage below the level of the main rotor hub, the tail rotor drift corrective force being produced by the main rotor, will create a rolling couple with the tail rotor thrust, this will cause lateral shift of Centre of Gravity. This in turn will cause correcting couple of weight and vertical component of TRT to balance the couple. This will cause the helicopter to hover one wheel low (Figure 4.3). Remember that here tail rotor thrust is considered a force and therefore any mechanism that creates a force to counter the torque reaction will have a tail rotor drift and therefore a tail rotor roll(provided above Fig 4.3 conditions is met).This can be overcome if the tail is raised to the level of the main rotor by cranking the fuselage, or fitting the tail rotor to a pylon (see figure 4.4 a & b), but this condition will only be achieved if the fuselage loaded with the C of G in the ideal position. The tendency of helicopter to fly one wheel low will depend upon:- (a) Tail rotor Force. (b) Vertical distance between main rotor hub and tail rotor. (c) All up weight. Higher the AUW and tail rotor force higher the moment of couple, so more the tail rotor roll. Fig 4.4a Fig 4.4b FLYING INSTRUCTORS SCHOOL  18 FIS: ROTOR DYNAMICS CHAPTER -5 MOVEMENT OF ROTOR BLADE 1. Feathering. It is the rotational movement of the blade about the chord axis and takes place as a result of changes in collective or cyclic pitch. 2. Flapping. This describes the angular movement of the blade above or below the plane of the hub. Flapping will occur following collective and cyclic pitch changes, variation in rotor RPM, and as a result of changes in the speed and direction of the airflow relative to the disc which occurs in certain in-flight conditions. To alleviate bending stresses, which would otherwise occur, the blade is allowed to flap about a flapping hinge, or in some helicopters the blades are allowed to seesaw about the hub. Flapping hinge gives flexibility to main rotor as described in Chapter 2 Para 10 to avoid toppling over as forward flight is initiated. 3. Dragging. This describes the freedom given to each blade to allow it to move in the plane of rotation independently of the other blades. To avoid bending stresses at the root, the blade is allowed to drag about a dragging hinge but the movement about the hinge is constrained by some form of drag damper to avoid undesirable oscillations. Dragging occurs because of :- (a) Periodic Drag Changes. When the helicopter moves horizontally, the blades’ angle of attack is continually changing during each complete revolution. This variation in angle of attack results in variation in rotor drag and consequently the blade will lead or lag about the dragging hinge. Additionally, in forward flight the velocity vector of aircraft adds on to the rotational velocity on advancing side and vice versa on retreating side. This also changes the drag on blade continuously.  19 FIS: ROTOR DYNAMICS (b) Changing Position of the Blade C of G Relative to the Hub. Consider the helicopter stationary on the ground in still air conditions, rotor turning. The radius of the blade’s C of G relative to the axis of rotation will be constant. If the disc is tilted forward the radius of the blade’s C of G relative to the axis will be changing continuously through each 360˚of travel. The law of conservation of angular momentum states that, Mass x Velocity x Radius = Constant. Thus if the radius is reducing, it will cause the blade to speed up about the dragging hinge and vice versa. The same effect will occur when the helicopter first moves into horizontal flight. (c) Hooke’s Joint Effect. The movement of blade to reposition itself relative to other blades when cyclic stick is applied. Its effect is very similar to the movement of the blades’ C of G relative to the hub. Consider a rotor hovering in still air. (Figure 5.4a) When viewed from above the shaft axis, the blades A, B, C and D appear equally spaced relative to the Fig 5.4 shaft axis (Figure 5.4b). When a cyclic tilt of the disc occurs (Figure 5.4c) the cone axis will have tilted but if still viewed from the shaft axis, which has not tilted, Blade A will appear to increase its radius and Blade C decrease its radius. (Figure 5.4d) Blades B and D must maintain position as in Figure 5.4c in order to achieve their true radial position on the cone. It follows therefore, that they must move relative to the shaft axis and position themselves as in Figure 5.4 d. FLYING INSTRUCTORS SCHOOL  20 FIS: ROTOR DYNAMICS 4. Flapping of Equality. Moving the cyclic stick does not alter the magnitude of total rotor thrust but simply changes the disc attitude. This is achieved by the blades flapping to equality when the cyclic pitch change is made. Consider a blade of a Fig 5.5 helicopter in the hover where the angle of attack is 60 (Figure 5.5a). A cyclic stick movement decreases the blade pitch and assuming that initially the direction of the relative airflow remains unchanged, the reduction in pitch will reduce both the blade’s angle of attack and rotor thrust (Figure 5.5b). The blade will now begin to flap down causing an airflow from below, thus reducing induced flow and increasing the blade’s angle of attack. When the angle of attack is back to 6 0 ,rotor thrust will return to its original value and the blade will continue to follow a path to keep the angle of attack constant(Figure 5.5c). Thus cyclic pitch will alter the plane in which the blade is rotating but the angle of attack remains unchanged. The reverse takes place when a blade experiences an increase in cyclic pitch. Therefore any change in angle of attack through control action or in-flight conditions causes the blades to flap, and they will do so until they restore the rotor thrust. They have “Flapped to Equality”. 5. Equivalence of Flapping and Feathering. For a given airspeed the tilt of rotor disc is entirely by the requirement to overcome the parasite drag and rotor drag force. At the same speed the fuselage may ride either nose up or nose down with respect to the rotor tip path plane depending upon CG position and moments produced by the aerodynamics of the fuselage and the horizontal tail stabiliser. As far as the blade is concerned its angle of attack with respect to the tip path plane is the only thing of importance. Figure 5.6a, b and c show a helicopter in forward flight (a) (b) (c) (a) (b) (c) Fig 5.6 FLYING INSTRUCTORS SCHOOL  21 FIS: ROTOR DYNAMICS at a constant speed, but with three different trim conditions. Assuming that the fuselage lift and drag are the same in each case, the rotor thrust vector and hence the tip-path plane attitude will be the same. The angle of attack of a blade element on the retreating side is shown for illustration. In the first case, the tip-path plane is perpendicular to the shaft – so there is no flapping, but feathering is used to obtain the correct blade angles of attack. Imagine aerofoil section of a blade advancing towards you, when your eyes are in same level as tip path plane. For example if you see aerofoil nose up as it moves towards you, 180˚ later you will see the same section facing nose up away from you. In the last case 5.7c, there is no feathering but nose-up/down flapping is used to achieve the same result. When you look at the disc at the level of the mast you will see one side of disc flapping below and other side above the mast level. 6. The middle case is in between, where both feathering and flapping are being used to trim the helicopter. The blade sees a 10 change in nose up flapping as given the same angle of attack change as 10 of the feathering achieved with a nose-down swash plate tilt, thus illustrating the equivalence of feathering and flapping. The rigid rotor system is more effective in changing the fuselage attitude vis a vis disc attitude change. This is because, apart from the moment of rotor thrust acting about the CG of helicopter, the couple acting at rotor mast about the effective flapping portions of the disc will also cause a strong moment. Hence, the lag between disc attitude and fuselage attitude change in rigid rotor system is less which causes less flapping. In Teetering rotor only the moment of rotor thrust acting about the CG of helicopter is used to change the fuselage attitude, hence it requires more tilt of rotor disc (to produce change in fuselage attitude). 7. Although we have been looking at only the retreating blade, the same argument can be made for the blade at any point of rotation. The use of cyclic pitch makes it possible to eliminate the flapping hinges in a hingeless rotor system. If a rotor with hinged blades is trimmed with cyclic pitch so that the tip-path plane is perpendicular to the shaft – as in the first case in Figure 5.7a then it’s possible to freeze the flapping hinges with no change to rotor conditions, since there was no hinge motion in the first place. This and eliminating the lead-lag hinges by using sufficient structural material will convert a fully articulated rotor into hingeless rotor. PHASE LAG AND ADVANCE ANGLE 8. Control Orbit. In its simplest form of operation, movement of the collective lever causes a flat plate mounted centrally on the rotor shaft to rise and descend. Movement of the cyclic stick causes it to tilt, the direction of the tilt being controlled by the direction in which the cyclic stick is moved. Rods of equal length, known as Pitch Operating Arms, connect the flat plate to the rotor blades. When the flat plate is tilted the pitch operating arms move up or down, increasing or decreasing the pitch of individual blades. The change in pitch angle depends on the amount and direction in which the flat plate is being tilted. The flat plate can be more accurately described as a control orbit because it represents the plane in which the pitch operating arms are rotating. To enable reference to be made to a control orbit for mechanical FLYING INSTRUCTORS SCHOOL  22 FIS: ROTOR DYNAMICS systems which do not incorporate a flat plate, the Control Orbit can be defined as the plane of rotation of any common point on the pitch operating arms. 9. Pitch Operating Arm Movement. Consider now the effect of the movement of a pitch operating arm when the control orbit has been tilted 20in fig 5.7. (It is assumed that the control orbit tilts in the same direction as the stick is moved). A plan view shows clearly the Fig 5.7 amount by which the control orbit has been tilted at four positions, namely A, B, C and D. If the movement of a pitch operating arm through its 3600 of travel is plotted on a simple graph the result would be as shown in Figure 5.8 & 5.9. Fig 5.8 Fig 5.9 FLYING INSTRUCTORS SCHOOL  23 FIS: ROTOR DYNAMICS 10. It will be noted that RATE at which the pitch operating arm is moving up and down is not uniform. It is akin to a sine curve where first 300 (1/3 travel) causes fifty percent of pitch change (Sin 300 = 0.5) This can be shown more clearly if a comparison between the control orbit in plan view is made with the control orbit in side elevation and noting how much vertical movement takes place during each 300 of travel, for a range of 900. 11. Resultant Change in Disc Attitude. The rotor blade will respond to the cyclic pitch change by flapping up or down and the resultant change in disc attitude can be determined by following the movement of each blade of a two- bladed rotor fitted with flapping hinges through 1800 of travel. Consider the rotor blades to be positioned at A, and C when the control orbit is tilted and the pitch operating arms are attached to the control orbit directly beneath the blades (figure 5.10). 12. As the blade moves clockwise from position A, it will experience an increase in pitch and the blade will begin to flap up. RATE of flapping varies with the amount of pitch change so the blade will be experiencing its greatest RATE of flapping up as it passes position B (maximum pitch change). In the next 900 of travel the pitch is returning from +20 Fig 5.10 back to 00 so the RATE at which the blade is still flapping up will slowly die out and disappear entirely when the blade has reached position C. So the blade which started at A is flapping up for 1800 of travel and will therefore, reach a high position at C. 13. The reverse will take place with the other blade. As it rotates clockwise from C to A the reduction in pitch will cause the blade to flap down, the maximum RATE of flapping occurring as the blade passes position D. Beyond this point the RATE of flapping down begins to slow down but will not disappear entirely until the blade has reached position A. So the blade that started at C is flapping down for 1800 of travel and will reach its low position at A and the disc will now be tilted along an axis (BD) 900 removed from the tilt axis of the control orbit (AC). If the Movement of Fig 5.11 0 the blade through 360 of travel is plotted on a graph similar to the one showing movement of the pitch operating arm the result FLYING INSTRUCTORS SCHOOL  24 FIS: ROTOR DYNAMICS would be as shown in Figure5.11.For the same reason as explained in paragraph 3 the RATE of flapping is not uniform. By superimposing the movement of the pitch operating arm, it will be seen that the blade flapped position will always be at 90°out of phase with the control orbit. The advancing blade will encounter its highest rotational speed 90° prior to a position over the nose of the aircraft, but does not experience the highest degree of flapping at this point. In fact, this maximum flapping (max flap up position) occurs over the nose, 90° later. This is termed Phase Lag. When the cyclic pitch is applied the blade will automatically flap to equality. In doing so the disc attitude will change, the blade reaching its highest and lowest position 90° later than the point where it experiences the maximum increase and decrease of cyclic pitch (Fig 6.4). The variation between the tilt of the control orbit in producing this cyclic pitch change and subsequent tilt of the rotor is known as PHASE LAG. Phase lag will also occur when the blades experience a cyclic variation resulting from a change in speed or direction of the relative airflow as occurs in horizontal flight. 14. Advance Angle. If the control orbit tilts in the same direction as the cyclic stick is being moved, and as a result of these changes in cyclic pitch the rotor disc tilts 90°out of phase with the control orbit, then the disc will also be tilting 90° out of phase with the cyclic stick. Thus, unless the system is compensated in some way, moving the stick forward would cause the helicopter to move sideways. One way to overcome this undesirable feature is to arrange for the blade to receive the maximum alteration in cyclic pitch change 90° before the blade is over the highest and lowest points on the control orbit. Another way would be to make the control orbit tilt so that it is out of phase with the cyclic stick by the required angle (Fig 5.12). 15. The angular distance that the pitch operating arm is positioned on the control orbit in advance of the blade to which it relates is known as the ADVANCE ANGLE. When the control orbit tilts to follow the stick, to compensate fully for phase lag the advance angle would have to be 900. On Chetak the advance angle is 60°.Control orbit tilt is 30°out of phase with the stick movement hence the advance angle required is just 60°,to make full compensation Fig 5.12 for phase lag. FLYING INSTRUCTORS SCHOOL  25 FIS: ROTOR DYNAMICS 16. Symmetry of Rotor Thrust. If a nil air hover the speed of relative air flow over each blade will be equal to the speed of rotation of the blade. With all other parameters (pitch, blade area, planform, density) affecting thrust generation being same the Rotor Thrust by the individual blades will be uniform across the disc and considered to be symmetrical. The velocity of this airflow is equal to the blades’ speed of rotation this airflow will be referred to as VR. 17. Dissymmetry of Rotor Thrust. If the conditions change and the helicopter now faces into a wind, during the blade’s rotation through 3600 half the time it will be moving into wind and for the remainder of the time it will be moving away from the wind. The disc can therefore, be divided in half, one half being the ADVANCING SIDE and the other the RETREATING SIDE (Figure 5.13). Fig 5.13 18. When the blade is at right angles facing into the wind (position A), the velocity of the relative airflow will be VR plus VW where VW is the value of wind speed. As the blade continues to rotate the value of VW will decrease and when the blade reaches position C the velocity of the relative airflow will have become VR minus Vw. If no changes has taken place in the blades' plane of rotation the rotor thrust being produced by the advancing blade at position A will be equal to cl 1/2p (Vr+ Vw)2s and for the retreating blade at position c, cl1/2p (Vr- Vw)2s.The value of rotor thrust across the disc will no longer be uniform and unless some method is employed to provide equality the helicopter would roll towards the retreating side. This condition where one side of the disc has more rotor thrust than the other is known as DISSYMMETRY OF ROTOR THRUST. This was the reason why earlier helicopters used to topple over as they initiated forward flight. 19. Flapback. To maintain control of the helicopter it is obvious that this dissymmetry must not be allowed to take place and one method of preventing it is to decrease the angle of attack of the advancing blade and increase the angle of attack of the retreating blade, so that each blade again produces the same value of rotor thrust. With the fully articulated rotor head this change in angle of attack takes place quite automatically but as a result, the disc attitude changes. The manner in which it changes and the reason why this change in attitude prevents dissymmetry can be seen by following the movement of a blade through 360 o of travel. FLYING INSTRUCTORS SCHOOL  26 FIS: ROTOR DYNAMICS C D B Fig 5.14 A 23. Referring to Figure 5.14 and starting at position A as, the blade begins to travel( anti-clockwise) on the advancing side the speed of relative airflow will increase. Rotor thrust begins to increase and because it is free to do so the blade will begin to flap up about the flapping hinge. As the blade flaps up the angle of attack will begin to decrease, rotor thrust decreases and the blade will proceed to follow a path to maintain the same value of rotor thrust as it was producing before it began to flap up. The blade in fact is flapping to equality. As the blade progresses on the advancing side ( A to B) the greater will be the velocity of the relative air flow, so to maintain a constant value of rotor thrust the RATE at which the blade is flapping will steadily increase, with maximum RATE of flapping and therefore, minimum angle of attack occurring when the blade reaches position B. For the next 900 of travel the velocity of the relative airflow begins to decrease so the RATE of flapping will decrease however the blade continues to rise. When the blade reaches position C, relative airflow will have the same value as at position A so the RATE of flapping dies out completely but because the blade has been rising all the time from position A the blade will reach its highest position at C. The reverse will take place on the retreating side with the blade having its maximum RATE of flapping down and therefore, its maximum angle of attack at position C and reaching its lowest position at D. In flapping to equality the disc will therefore; have flapped away from the wind. This change of disc attitude, which has occurred without any control movement by the pilot, is known as FLAPBACK. 21. By comparing figures 5.15a and b, it is seen that when the helicopter is subjected to wind, the disc attitude is altered although no cyclic stick has been applied. This disc has flapped back relative to the wind and to the control orbit and FLYING INSTRUCTORS SCHOOL  27 FIS: ROTOR DYNAMICS the blades are moving about their flapping hinges. The rotor thrust being produced will however be the same as before the disc flapped back. If the pilot now moves the stick forward to return the disc to its original position (Figure 5.15c), it will be seen that the disc is now flapped back only in relation to the control orbit and not to the wind and that movement is no longer taking place about the flapping hinges. Thus Fig 5.15a Fig 5.15b Fig 5.15c flap back has been counter-acted by cyclic feathering (by moving cyclic forward), and as the cyclic stick only changes the disc attitude the value of the rotor thrust force remains unchanged. When the helicopter is airborne and moving in any horizontal direction the effect will be the same as a helicopter on the ground facing into wind, with flap back being prevented by cyclic feathering. The first movement of the cyclic stick will tilt the disc to initiate horizontal flight then a second movement will be necessary to prevent the disc from flapping back. It should be noted however, that some movement about the flapping hinges will still take place if the C of G of the helicopter is not in the ideal position. Flapback is caused due to lateral dissymmetry of rotor thrust. Flapback increases with increase of speed. If the rotor was not flexible to flap to equality (i.e. if it was attached rigidly to the main rotor head), the dissymmetry of thrust on advancing and retreating side will cause the helicopter to roll over on retreating side as the helicopter initiates forward flight. 22. Inflow Roll. The effect of moving air horizontally across the disc causes a reduction in the induced flow (Figure 5.16). However, this reduction is not uniform, because air passing across the top of the disc is being continuously pulled down by the action of the rotors. Thus air, which is moving horizontally towards the Fig 5.16 disc, will cause the greatest reduction in induced flow at the front of the disc and the smallest reduction at the rear of the disc. The reduction in induced flow for the disc as a whole will produce an increase in rotor thrust but because the increase in angle of attack is not uniform it will also produce a change in the attitude of the disc. Assuming that flap back has been corrected; consider the effect of variation in angle of attack for a blade starting FLYING INSTRUCTORS SCHOOL  28 FIS: ROTOR DYNAMICS at position A (Figure 5.17). As the blade moves towards position B, increasing angle of attack will cause the blade to flap to equality. Rate of flapping will be maximum as the blade passes position B, because this is the point where there has been the greatest reduction in induced flow. In the next 90o of travel RATE of flapping will slow down dying out completely when the blade is at position C. Thus the blade will be rising all the time it is travelling from position A to reach a high position at C. The reverse will take place for the next 180o of travel with the blade having its maximum RATE of flapping at D and its lowest position at A. The disc will therefore, tilt about the axis XY towards the advancing side. Inflow roll is caused due to longitudinal dissymmetry of rotor thrust. One more factor which adds to inflow roll is that when the disc is coned up even by a small amount some airflow in forward flight will impact rotor from below in front part. This increases the angle of attack on front portion of disc causing effects as discussed above. 23. The combined effect of inflow roll and flap back is therefore, to tilt the disc about an axis ZZ (Figure 5.17). As inflow roll will have its greatest effect at low speed and flap back its greatest effect at high speed the axis about which the disc will tilt will vary with forward speed. In Chetak/Cheetah the cyclic has to be moved forward and to right for forward flight to counter Flapback and inflow roll respectively. Thus to counteract Flapback and Inflow roll the cyclic is moved forward and to the retreating side. Fig 5.17 FLYING INSTRUCTORS SCHOOL  29 FIS: ROTOR DYNAMICS CHAPTER – 6 DYNAMICS OF HOVER 1. Definition. Hover is defined as that condition of flight where there is no horizontal and vertical motion of a helicopter and it maintains a constant direction. 2. Pick Up and Climb to a Free Air Hover. To lift the helicopter off the ground, a lifting force must be produced equal and opposite to the weight which is acting vertically downwards through the aircraft centre of gravity. When the rotors are turning at takeoff RPM, and when collective pitch lever is fully down, very little rotor thrust is being produced. As the collective pitch level is raised the blades will cone up and eventually the rotor thrust will be exactly equal to the weight. The oleos of the helicopter will be completely extended and the wheels will be in light contact with the ground. If the collective pitch lever is raised further, the rotor thrust will again increase becoming greater than the weight. The helicopter will, in still air conditions, accelerate vertically upwards (Fig 7.1). In practice, that phase of the takeoff (pick up) where the helicopter is light on its wheel is passed through as quickly as possible to avoid setting up a condition called ground resonance. 3. After a short while, the acceleration will become a steady rate of climb, the helicopter will continue in this state, assuming constant power Fig 7.1 available, until such time as the pilot lowers the collective pitch lever. Consider the helicopter to be 200 feet above the ground when the collective pitch lever is lowered just the right amount to stop the helicopter from climbing. The helicopter will come to hover and being well clear of the ground it is referred to as a FREE HOVER. To present the hover, in terms of figures, consider that 40 is the angle of attack required to produce the necessary rotor thrust to balance the weight and that this is being achieved with say 80 of collective pitch. 4. Vertical Descent. From the free air hover if the collective pitch lever is lowered the angle of attack will reduce, rotor thrust becomes less weight and the helicopter will begin to accelerate downwards. The airflow resulting from the helicopters descent will be opposing the induced flow through the disc and the resultant change in direction of the relative airflow to the blade will cause the angle of FLYING INSTRUCTORS SCHOOL  30 FIS: ROTOR DYNAMICS attack to increase. When it again reaches 40 rotor thrust will equate the weight and the downward acceleration will become a steady rate of descent. Compared with the free air hover, in a vertical descent less collective pitch and power is being used to produce a rotor thrust equal to the weight, but the required angle of attack can of course only be maintained provided the helicopter continues its steady rate of descent. 5. In a vertical climb the reverse take place. Increased pitch increases the angle of attack, rotor thrust becomes greater than weight and the helicopter accelerates upwards. The airflow rate of climb is in the same direction as the induced flow and the resultant change in airflow direction to the blade will gradually reduce the angle of attack. When it again reaches 40, rotor thrust equals weight and the acceleration upwards will become a steady rate of climb. When climbing or descending there will also be some parasite drag from the fuselage to be overcome but the amount it relatively small, a rate of climb or descent of 1200 F/P/M being only 13 mph. 6. Ground Effect. In a free air hover the airflow through the rotor disc begins at zero velocity some distance above and accelerates through the disc and into the air below (Momentum Theory). There is little resistance to the downward movement of air. If the helicopter is hovered close to the ground the downwash meets the ground, is opposed, and escapes horizontally. A divergent duct is Fig 7.2 produced causing an increase in pressure. From basics of aerodynamics, we remember that ρAV is constant. In a pipe, when a fluid is coming out of a venturi, the cross section area increases, speed reduces and the static pressure increases. Similarly below the rotor close to ground the flow is Fig 7.3a Fig 7.3b diverging away causing the pressure at the core, i.e. below helicopter to increase (Fig 7.2). The increased pressure of the air beneath the helicopter opposes and reduces the induced flow so that angle of attack and hence Total Rotor Thrust are FLYING INSTRUCTORS SCHOOL  31 FIS: ROTOR DYNAMICS increased for a given pitch setting. In order to remain at a constant height the collective pitch must be reduced, to reduce the angle of attack and keep the Total Rotor Thrust equal to AUW. The Total Reaction will have moved closer to the axis of rotation producing a reduction in rotor drag and in power required to hover in Ground Effect. Helicopters are said to hover Inside Ground Effect (IGE) or, when in free air hover, Outside Ground Effect (OGE). 7. The formation of this high pressure dome can be explained in one more way. The downward airflow from the rotor is reflected by the ground into flows (Fig 7.3 Fig 7.4 a) towards the centre below helicopter and (Fig 7.3 b) towards outside, which is dissipated against the surrounding air. Flow (a) meets under the disc and is brought to rest, as all the horizontal component in approximate circle cancel out each other, forming a dome of stagnant or slow moving air this dome of ‘dead air’ GROUND CUSHION (slightly increase pressure and causes a reduction in induced flow). The direction of the flow relative to the blade changes, increasing angle of attack, or, the same angle of attack can be maintained in GROUND EFFECT (IGE) with less collective pitch and power than that required out of ground effect (OGE). The reduction in power is possible because of reduced rotor drag. 8. Factors Affecting the Ground Cushion: (a) Ground cushion is inversely proportional to hover height. The ground disappears at a height equal to approximately three-quarters of the diameter of the rotor disc. (b) Nature of the ground. (Rough ground dissipates the cushion) (c) Slope of the ground, which will produce an uneven, ground cushion. (d) Wind. (The cushion is displaced downwind) 9. Recirculation. Whenever a helicopter is hovering near the ground some of the air passing through the disc is recirculated and it would appear that the recirculated air increases speed as it passes through the disc a second time. This local increase of induced flow near the tips gives rise to a loss of rotor thrust. Some recirculation is always taking place, but over a flat even surface the loss of rotor thrust due to recirculation is more than compensated by the ground cushion effect. However if the helicopter is hovering over tall grass or similar types of surface, the loss of lift due to recirculation will increase, and in some cases the effect will be greater than the ground cushion. The downwash can be imagined to be flowing inside a concave bowl. The induced air in downwash cannot escape away from helicopter horizontally (as is the case over plain clear ground) and has an upward component as it moves up and away from the bowl created by the tall grass This FLYING INSTRUCTORS SCHOOL  32 FIS: ROTOR DYNAMICS upward component of induced flow is once again sucked into the rotor from top and hence increases the tip vortices and induced velocity at tips When this situation arises, more power and collective pitch would be required to hover near the ground than to hover in free air. Recirculation will increase when any obstructions on the surface or near, where the helicopter is hovering, prevents the air form flowing evenly away (Fig 7.5). When hovering over water energy of induced flow is also dissipated in creating ripples. Recirculation is more over water. A shallow concave bowl is formed over surface of water because of lesser cohesion of water molecules vis a vis solid ground. Power required to hover hence is more over a water body. 10. Interference Effects. A Recirculation phenomenon that effects hover performance was discovered several years ago from motion pictures of a rotor on a whirl tower on a damp day. It was observed that the tip vortex from one blade, made visible by condensation-stayed approximately in the plane of the tip until the next blade Fig 7.5 Recirculation near Obstruction came along. The proximity of the vortex to the second blade produce a distorted local induced velocity pattern over a small region of the tip, which can cause some very high angles of attack, sometimes exceeding the stall angle of the aerofoil. Sikorsky has made an attempt to overcome this problem by providing a high nose down twist just inboard of the tip where the high angles of attack occur. 11. Running off the “Ground Cushion”. It has been found out during experiments that at rotor heights of less than half rotor diameter, the ground vortex (caused by the down wash ahead of the rotor disc), is overrun at some low forward speed. Before it is over run the ground vortex adds onto the Induced flow at forward edge of rotor, and hence reduces AOA. Hence it affects the rotor as if it was in a climb. This is evident as slight loss of height when initiating a cushion creep T/O. This is also one of the reasons for increase in power requirement while initiating forward flight from hover IGE. Refer power required/power available graph in chapter FLYING INSTRUCTORS SCHOOL  33 FIS: ROTOR DYNAMICS CHAPTER – 8 DYNAMICS OF FORWARD FLIGHT 1. Forces in Balance-Hover. The total Rotor Thrust produced by the rotor is taken as acting through the axis about which the blades are rotating and at right angles to the plane of rotation. In the perfect hover the Total Rotor Thrust will, therefore, be pulling the fuselage vertically upwards and the total weight of the helicopter, acting through the centre of gravity, will be pulling the fuselage vertically downwards. If the fuselage is loaded Fig 8.1a Fig 8.1b to position the centre of gravity (CG) exactly below the blade axis of rotation no change in fuselage attitude will occur when the helicopter leaves the ground during a pick up. Figure 8.1a. 2. If, however, the CG is not below thrust line, then as soon as the helicopter leaves the ground during a pick up a couple will exist between the Total Rotor Thrust and the weight, and the fuselage will pitch until both forces are in line. It will cause a pitch up if the CG is behind the Thrust axis and pitch down if the CG is ahead of the Thrust line. Figure 8.1b shows CG behind the thrust line. 3. Forces in Balance - Forward Flight. Consider a helicopter in the perfect hover with the centre of gravity in the ideal position (Fig 8.1a). Assume that the helicopter moves into forward flight but that no change takes place in fuselage attitude. The rotor disc will be tilted forward and the disposition of the forces on the helicopter will be as shown in Figure 8.2. The forces acting will be:- (a) Vertical component of Total RT. (b) Horizontal component of total RT. (c) Weight. (d) Parasite Drag. Fig 8.2. Forces in Balance Transition FLYING INSTRUCTORS SCHOOL  34 FIS: ROTOR DYNAMICS 4. Total Rotor Thrust will now be inclined forward and produces a nose down turning moment about the centre of gravity. The vertical component of total Rotor Thrust and weight remain in line but a couple now exists between the horizontal component of Total Rotor Thrust and fuselage parasite drag as the aircraft gains speed. Under the influence of this couple Fig 8.3 Level Attitude with Pitching the fuselage will pitch down endeavouring Moment to bring these forces into line. As soon as the fuselage pitches DOWN an opposing couple will be produced between the vertical component of Total Rotor Thrust and the weight, which will try the fuselage to pitch UP. Therefore, once the cyclic has been moved forward, the fuselage will only pitch down, until a condition is reached where the two couples are in balance and this will occur when the centre of gravity is again in line with the total Rotor Thrust (Fig 8.2b). Thus, the centre of gravity will control the position of the fuselage in relation to the disc (fuselage attitude) both at hover and at forward flight, but this relationship can be affected in forward flight by the aerodynamic shape of the fuselage and loading on the stabiliser. 5. The load on the stabiliser if the amount of downwash on it at any given point in time. More the downwash more the downward force on the stabiliser and will cause a pitch up. Therefore, from a given collective position if the collective is raised, it will cause an increase in downwash and therefore will cause a pitch up and whenever the collective is lowered it will cause a decrease in the downwash causing a pitch down. The effect is there in both hover and in forward flight. However, the effect gets aggravated in forward flight due to an added effect of static AOA stability. 6. Transition. When the helicopter is hovering in still air conditions the Total Rotor Thrust produced by the rotor is equal to the weight. There will, in fact, be some fuselage parasite drag to be overcome but for simplicity this drag will be considered to be included in the weight. To achieve forward flight the rotor disc has to be tilted forward and the Total Rotor Thrust must now provide not only a vertical force to balance the weight but a horizontal force in the direction in which the helicopter is moving. This change in state from a hover to movement in a horizontal direction is known as TRANSITION, the same term being used to describe a change from horizontal flight back to the hover. This change from forward speed to hover can be gentle and progressive deceleration or by executing a FLARE i.e rapid deceleration of speed. When this method of reducing speed is employed, collective pitch and power changes to control the manoeuvre will differ considerably from those required to produce a more gentle transition. The mechanics and effects of flare are discussed in detail in chapter on Autorotation. While the helicopter crosses transition there are definite vibrations that are set in the helicopter. These vibrations are more prominent during the approach than during takeoff. The primary reason for this is that helicopter stays in its own wake for a longer time during approach. This phenomenon is dealt in detail in chapter on Vibrations. 7. When the helicopter is travelling forward at uniform speed, the horizontal component of thrust will be balanced by the parasite drag of the fuselage and since FLYING INSTRUCTORS SCHOOL  35 FIS: ROTOR DYNAMICS the parasite drag increases as the square of the speed, the faster the helicopter is moving forward the greater must become the tilt of the disc, to provide the thrust. But for level flight the vertical component of Total Rotor Thrust must remain equal to weight. To meet this requirement it follows, therefore, that when the helicopter moves forward from a hover state the total Rotor Thrust must increase and that the faster the forward speed the greater must become the Total Rotor Thrust being provided by the rotor. 8. As Total Rotor Thrust is a direct function of collective pitch applied, it would appear from the foregoing that the collective pitch lever must be progressively raised for any given increase in forward speed, with power being increased to overcome the rising rotor drag. However, it is found in practice that for speeds up to minimum power speed i.e approx 45-55 kts, depending upon the type of helicopter, both the collective pitch and power can be progressively reduced and it is only for speeds beyond this figure that the pitch and power have to be increased. This gain in rotor efficiency when moving forward is known as TRANSLATIONAL LIFT and the same effect will occur if the helicopter is hovering stationary over the ground in wind conditions. 9. Translational Lift. When the helicopter is in the perfect hover in still air conditions, for a given rotor RPM a certain value of collective pitch, say 80, will be required to support it in the air. A column of air, the induced flow, will be continually moving down towards the rotor disc and this downwards flow of air must be Fig 8.4 considered when determining the direction of the air flow relative to the blade. (Fig 8.4). It will be noted that the angle of attack, say 50; is less than the pitch angle. The angle of attack depending up on the value of the induced flow. If there were no induced flow the angle of attack would be the same as the pitch angle. 10. Consider the effect now if the helicopter is facing into a 20 knot wind and assume that it is possible to maintain the hover without tilting the disc. The horizontal “wind” flow of air will blow across the vertically induced column of air and deflect it “down wind” before it reaches the disc. The column of air which was flowing down towards the disc will therefore be modified and gradually be replaced by a mass of air which is moving horizontally across the disc. The rotor will act on their air mass to produce an induced flow but the velocity of the induced flow is greatly reduced (fig 8.6). Therefore, airflow parallel to the disc must reduce the induced flow and increase the angle of attack. Fig 8.6 Translational Lift FLYING INSTRUCTORS SCHOOL  36 FIS: ROTOR DYNAMICS 11. However, to maintain the hover condition when facing into wind the disc must be tilted forward. The horizontal flow of air will not now be parallel to the disc and a component of it can now be considered to be actually passing through the disc at right angles to the plane of rotation, effectively increasing the induced flow, (Fig 8.7a). To consider an extreme case, if the rotor disc was tilted 90 to this horizontal flow of air then all of it would be passing through the disc at right angles to the plane of rotation. 12. The effect of this horizontal air flow across the disc when hovering facing into wind is, therefore, to reduce the induced flow but because the disc has had to be tilted forward, a component of this horizontal airflow will now be passing through the disc, effectively increasing the induced flow, and both of these effects must now be taken into consideration when determining the direction of the air flow relative to the blades. If the reduction in induced flow is greater than the component of horizontal airflow passing through the disc, then the relative airflow will be nearer to the plane of rotation than when the helicopter is in the hover in nil winds and the angle of attack will increase. Therefore, the collective pitch can be decreased to Fig 8.7 Airflow through a Disc say, 70 while still maintaining the SAME angle of attack (Fig 8.7b). The lift/drag ratio for this angle of attack remains unchanged so the total reaction must move FORWARD when the collective pitch is reduced. There will therefore be less rotor drag and rotor RPM can be maintained with less power. 13. The reduction in induced flow, causing an increase in lift called the TRANSLATIONAL LIFT, first takes effect when air moves towards the disc at approximately 12 knots. The reduction in induced flow is appreciable at first and although it continues to reduce as the velocity of horizontal airflow increases, the rate at which it reduces becomes progressively less. 14. The rotor disc has to be tilted forward to provide a thrust component equal to parasite drag. Parasite drag is low at low forward speeds so only a small tilt of the disc is required to provide a balancing amount of thrust, and with only a small tilt of the disc only a small component of the horizontal airflow will be passing through the disc at right angle to the plane of rotation. As the parasite drag increases as the square of the speed the greater must be the amount that the disc must be tilted to provide the necessary increase in thrust, and as the velocity of the horizontal air flow approaching the disc increases the greater will be the component of it passing through the disc at right angles to the plane of rotation. If the information given in Fig 8.7a and 8.7b is now related to one graph it will be seen that the flow of air at right angles to the plane of rotation decreases at first then increases again being a minimum when the two airflows have the same value. As the flow of air through the disc decreases less collective pitch and power will be required to maintain the required angle of attack. When the flow of air through the disc begins to increase again, collective pitch and power must be increased if the required angle of attack is to be maintained. FLYING INSTRUCTORS SCHOOL  37 FIS: ROTOR DYNAMICS 15. In order to decelerate a helicopter from steady level flight to the hover the balance of forces must be changed. The general method of coming to the hover from forward flight is by the pilot executing a flare by tilting the disc in the opposite direction to that in which the helicopter is moving. The handling techniques needed to control the manoeuvre differ from those required for a more gentle transition. 16. The Flare. To execute a flare the cyclic stick is moved in the opposite direction to that in which the helicopter is moving. The harshness of the flare depends upon how far and how fast the stick is moved. The flare will produce a number of effects. Flare Effects 17. Whenever a flare is executed the following effects take place. (a) Thrust Reversal. Fig 8.8(a) represents a helicopter in normal forward flight and fig 8.8(b) a helicopter in forward flight with the pilot executing a flare. By tilting the disc away from the direction in which the helicopter is travelling the thrust component of the total rotor thrust will now act in the same direction as the fuselage parasite drag causing the helicopter to slow down very rapidly. The fuselage will respond to this rapid deceleration by pitching up because reverse thrust is being maintained whilst parasite drag decreases. If the pilot takes no corrective action the Fig 8.8 Change in Airflow in disc will be tilted back further till causing an Flare even greater deceleration. (b) Increase in Total Rotor Trust. Another effect of tilting the disc while the helicopter is moving forward is to change the airflow relative to the disc. As explained in translational lift a component of the horizontal airflow due to the helicopter moving forward is passing through the disc at right angles to the plane of rotation in the same direction as the induced flow. When the disc is flared a component of the Fig 8.9 Increase in horizontal airflow will now be opposing Total Rotor Thrust induced flow and the changed direction of the airflow relative to the blade will cause an increase in angle of attack and therefore, an increase in total rotor thrust (Figure 8.9). If no corrective action is taken the helicopter would climb. The collective pitch lever must therefore, be lowered if constant height is to be maintained. FLYING INSTRUCTORS SCHOOL  38 FIS: ROTOR DYNAMICS (c) Increase in Rotor RPM. Unless power is reduced when the collective pitch lever is lowered to maintain height, the rotor RPM will obviously rise. This will also increase rapidly in the flare for two other reasons, conservation of angular momentum and reduction in rotor drag. (i) Conservation of Angular Momentum. The increase in total rotor thrust will cause the blades to cone up. The radius of the blades CG from the axis of rotation decreases and the blades rotational velocity will automatically rise. Power must therefore, be reduced to maintain rotor RPM constant. (ii) Reduction of Rotor Drag. Rotor drag is reduced in the flare because the total reaction moves towards the axis of rotation as a result of the changed direction of the relative airflow (Figure 2A and 2b). In figure 3a and 3b lift and drag vectors have been used to position the total reaction and to show that in the flare even allowing for a worse lift/drag ratio as a result of a greater angle of attack, the total reaction does in fact move forward reducing the rotor drag. As engine power is being used to match the rotor drag for a given rotor RPM, if the drag decreases then power must be reduced to maintain constant rotor RPM. (d) Change in the Tail Rotor Drift. We all know that tail rotor drift is directly proportional to the torque of the fuselage, which in turn is a function of the power applied to the main rotors. Thus, when the helicopter is flared, the power is reduced, which in turn reduces the tail rotor drift and as such cyclic will have to be moved to left in case of Chetak/Cheetah to maintain ground position. Once the flare effects die down power is increased thereby increasing the tail rotor drift, hence the need to move the cyclic to the right if any drift is to be avoided. However, when a flare is executed in autorotation(i.e. without engine power) the scenario. This has been explained in chapter on autorotation. Landing (Sit Down) 18. If collective pitch is reduced slightly in a hover IGE, the helicopter will descend but settle at a height where ground effect has increased total rotor thrust to again equal all up weight. Therefore a progressive lowering of the collective lever is required to achieve a steady descent to touchdown. When the helicopter is close to the ground the tip vortices are larger and unstable causing variation in the thrust around the rotor disc and turbulence around the tail and makes control difficult. For this reason, and to help to prevent ground resonance, the helicopter is normally landed firmly to decrease the chance of drifting when touching down. FLYING INSTRUCTORS SCHOOL  39 FIS: ROTOR DYNAMICS 19. Symmetry of Rotor Thrust. If the helicopter is hovering in still air conditions, rotor turning, with some collective pitch applied then the rotor thrust produced by each blade will be uniform. The RAF over any section of any blade of a four bladed system will be the resultant of the rotational velocity and the induced flow. For ease of understanding as the magnitude of Induced flow will be constant, we will be considering only the horizontal vector that is the rotational velocity. As the helicopter is hovering in still air conditions magnitude of this vector or the speed of the relative air flow over each blade will be equal to the speed of rotation of the blade, and will have the same value Fig 8.10 Symmetry of Airflow irrespective of the position of the blade during its 3600 of travel. (Fig 8.10) As the velocity of this airflow is equal to the blades’ speed of rotation this airflow will be referred to as V R. Therefore the lift produced over any side of disc will be CL ½ VR2S and as the VR is same and all other factors constant the lift produced across the disc will be symmetrical as its reciprocal side. 20. Dissymmetry of Rotor Thrust. If the conditions change and the helicopter now faces into a wind, during the blade’s rotation through 360° half the time it will be moving into wind and for the remainder of the time it will be moving with the wind or downwind. The disc can therefore, be divided in 2 halves, one half being the ADVANCING SIDE where the blade is advancing into the wind and the other the RETREATING SIDE where the blade is retreating away from the wind. Fig 8.11. The same situation will exist when the helicopter is in forward flight. 21. When the blade is a right angles facing into wind, position B, the velocity of the relative airflow will be a maximum and if the value of Fig 8.11 Dissymmetry of airflow the wind speed is referred to as VW then at position B the velocity of the relative airflow will be (VR+VW). As the blade continues to rotate the value of VW will decrease and when the blade reaches position D the velocity of the relative airflow will have become (VR -Vw). If no changes has taken place in the blades' plane of rotation the rotor thrust being produced by the ADVANCING BLADE at position B will be equal to CL 1/2(VR+VW)2S and for the RETREATING BLADE AT POSITION D, CL1/2(VR-VW)2S. The value of rotor thrust across the disc will no longer be uniform and unless some method is employed to provide equality the helicopter would roll towards the retreating side. This condition where one side of the disc has more rotor thrust than the other is known as DISSYMMETRY OF ROTOR THRUST. FLYING INSTRUCTORS SCHOOL  40 FIS: ROTOR DYNAMICS 22. Flapback. To maintain control of the helicopter it is obvious that this dissymmetry must not be allowed to take place and one method of preventing it is to decrease the angle of attack of the advancing blade and increase the angle of attack of the retreating blade, so that each blade again produces the same value of rotor thrust. With the fully articulated rotor head this change in angle of attack takes place quite automatically but as a result, the disc attitude changes. The Fig 8.12 Flap back manner in which it changes and the reason why this change in attitude prevents dissymmetry can be seen by following the movement of a blade through 360 ° of travel. 23. Referring to Figure 8.12 and starting at position A as, the blade begins to travel on the advancing side the relative airflow will increase. Rotor thrust begins to increase and because it is free to do so the blade will begin top flap up about the flapping hinge. As the blade flaps up the angle of attack will begin to decrease, rotor thrust decreases and the blade will proceed to follow a path to maintain the same value of rotor thrust as it was producing before it began to flap up. The blade in fact is flapping to equality. The f