helicopter flight theory full report
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17-02-2010, 02:46 PM

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Helicopter is one of the earliest ideas for achieving flight. The advances in helicopter technology made it an extreme flying machine. In this seminar and presentation I discuss the historical backgrounds and early concepts of helicopter, then introducing the aerodynamic theory and principle behind helicopters, discussing the most potent mechanisms that are used in it. Also different configurations of helicopters have been described. Then discussing the first analytical theory to consider for a helicopter in forward flight (The momentum theory).Also discussed the strength and design requirements of the helicopter. Briefing the seminar and presentation with the describing some typical applications of helicopters.
The helicopter is arguably one of the earliest ideas for achieving flight. Over two thousand years ago, the Chinese constructed what are known as Chinese Tops, illustrated below. These simple toys consisted of a propeller attached to a stick that would be spun rapidly through ones hands to spin the propeller and achieve lift.
Fig-1 Chinese top Fig-2 Leonardo da Vinci's "Helicopter"
Later, in the 15th Century, famed inventor and artist Leonardo da Vinci designed one of the more aesthetically pleasing concepts for a helicopter, but such a craft was never actually constructed.
In England in 1796, Sir George Cayley constructed the first powered models of helicopters that were driven by elastic devices which attained an altitude of 90ft. In 1842, fellow Englishman W. H. Phillips constructed a model helicopter that weighed 20 pounds (9 kg) and was driven by steam. In 1878, Enrico Forlanini, an Italian civil engineer, also constructed a steam driven model helicopter that only weighed 3.5kg.
Fig-3 Sir George Cayley's helicopter
The first manned helicopter to rise vertically completely unrestrained was constructed by Paul Cornu, a French mechanic, in 1907. Cornu's helicopter had two propellers that were rotated at 90 rpm by a 18 kW engine. Cornu was most probably the first helicopter experimenter who was concerned with control. While cornuâ„¢s helicopter was historically significant, its performance and control was rather marginal and it was never a practical machine.
Fig-4 Cornu's helicopter
The next influential development in the field of helicopters was brought about by a man who never actually built a helicopter himself. In 1923, Juan de la Cierva successfully flew his C.4 autogiro, an aircraft that has two propellers, a powered one to provide thrust, and an un powered rotor to provide lift. Cierva's autogiro was noteworthy because it was the first to use an "articulated" rotor that allowed its blades to flap up and down in response to aerodynamic forces on the blades during forward flight.
The first recognized helicopter record was set in October 1930 by Italian Corradino D'Ascanio when he flew his helicopter over a distance of one half mile at an altitude of 59 ft (18 m) for 8 minutes and 45 seconds. D'Ascanio's helicopter had two contra rotating coaxial rotors (two rotors on the same shaft) that were controlled by flaps on booms trailing each blade near its tip.
Fig-5 D'Ascanio's helicopter
Just before and during World War II, Germany made several large, significant steps in helicopter development. The FA-61 helicopter, designed by Heinrich Focke, first flew in June 1936, and was later used in publicity stunts by the Nazis. The FL-282 helicopter, designed by Anton Flettner, became operational with the German Navy, and over 1000 of them were produced. This helicopter utilized twin-intermeshing rotors, had a forward speed of 145 km/h, and could operate at an altitude of 3,965 m with a payload of 360 kg.
Fig-6 Sikorsky's VS-300
The first American helicopter was the VS-300, designed by Igor Sikorsky of the Vought-Sikorsky Company. The VS-300 was the first helicopter to use a tail rotor to counteract the torque produced by the main rotor, and it was this innovation that solved the last major hurdle in making helicopters practical flying vehicles. This design is now the most common in today's helicopters.
An aerofoil is a streamlined body, which is designed to produce lift or thrust when passed through air. Airplane wings, propeller blades and helicopter main and tail rotor blades are all aerofoil.
Fig-7 Aerofoil features
Chord is the distance or imaginary line between the leading and trailing edge of an airfoil. The amount of curve or departure of the airfoil surface from the chord line is known as camber. Upper camber refers to the upper surface; lower camber refers to the lower surface. If the surface is flat, the camber is zero. The camber is positive if the surface is convex. The camber is negative if the surface is concave. The upper surface of an airfoil always has positive camber, but the lower surface may have positive, negative, or zero camber.
Bernoulli, an eighteenth century physicist, discovered that air moving over a surface decreases air pressure on the surface. As air speed increases, surface air pressure decreases accordingly. This is directly related to the flight of an aircraft. As an airfoil starts moving through the air, it divides the mass of air molecules at its leading edge. The distance across the curved top surface is greater than that across the relatively flat bottom surface. Air molecules that pass over the top must therefore move faster than those passing under the bottom in order to meet at the same time along the trailing edge. The faster airflow across the top surface creates a low-pressure area above the airfoil. Air pressure below the airfoil is greater than the pressure above it and tends to push the airfoil up into the area of lower pressure. As long as air passes over the airfoil, this condition will exist. It is the difference in pressure that causes lift. When air movement is fast enough over a wing or rotor blade, the lift produced matches the weight of the airfoil and its attached parts. This lift is able to support the entire aircraft. As airspeed across the wing or rotor increases further, the lift exceeds the weight of the aircraft and the aircraft rises. Not all of the air met by an airfoil is used in lift. Some of it creates resistance, or drag, that hinders forward motion. Lift and drag increase and decrease together. The airfoilâ„¢s angle of attack into the air, the speed of airflow, the air density, and the shape of the airfoil or wing therefore affect them.
Fig-8 Bernoulliâ„¢s principle
The amount of lift that an aerofoil develop depends on
1. Area (size or surface area of the air foil)
2. Shape (shape or design of airfoil sections)
3. Speed (Velocity of the air passing over the aerofoil)
4. Angle of attack (angle at which air strikes the aerofoil)
5. Air density (amount of air in a given space)
The production of thrust in helicopters is based on the propeller action. The rotation of propeller causes the air to accelerate from one side to the other side of it, which results in the development of thrust in the opposite direction of the flow. A propeller does the conversion of torque into axial thrust by changing the momentum of the fluid in which it is submerged. When a propeller submerged in an undisturbed fluid rotates, it exerts a force on the fluid and pushes the fluid backwards. The reaction to this force on the fluid provides a forward thrust, which is used for propulsion. Although the complete design of a propeller cannot be done according to the momentum theory, yet the application of this theory leads to some useful results s indicated by simple analysis of problem below.
Fig-9 Propeller
Let U be the upstream velocity and u be the downstream velocity. Let A be the propeller disc area and Q the mass flow rate of air. By Bernoulliâ„¢s principle we get the velocity through the propeller equal to average of upstream and far down stream velocities. Therefore the induced velocity u through the propeller equals,
If P is the power supplied and T the thrust developed then from momentum theory we have
This formula is applied for hovering condition of the helicopter where torque T equals weight to be supported. The actual flow through the propeller differs considerably from the model depicted above since the propeller works in an infinite sea of air ; there is no well-defined boundary between the fluid at rest and fluid motion; therefore the actual thrust will differ considerably from the values in the above expressions.
The most popular helicopter arrangement is that of single rotor using a tail rotor. The single rotor helicopter is relatively lightweight and is fairly simple in design with one rotor one main transmission and one set of controls.
The disadvantage of single rotor machine are its limited lifting and speed capabilities and a severe safety hazard during ground operation with the tail rotor position several feet behind the pilot and out of line of his vision.
Fig-10 Single rotor helicopter
This helicopter uses two synchronized rotor rotating in opposite direction. The opposite rotation of the rotors causes one rotor to cancel the torque of the other.
Each rotor is fully articulated and has three blades. It is capable of lifting large loads. A disadvantage of the tandem type is that it is not efficient in forward flight because one rotor is working in the wake of the other.
Fig-11 Tandem rotor helicopter
It has two main rotors mounted on pylons or wings positioned out from the sides of the fuselage. The side by side has rotors turning in opposite direction, which eliminates the need for a tail rotor.
The advantages are its excellent stability and disadvantage is having high drag and structural weight both resulting from structure necessary to support the main rotor.
Fig-12 Side by side helicopter
In this fuselage torque is eliminated by two counter rotating rigid main rotors mounted one above the other on common shaft.
Fig-13 Coaxial helicopter
The tilt rotor has the ability to combine the vertical take off low speed capabilities of the helicopter with high-speed performance of a turboprop airplane.
All rotor systems are subject to of Dissymmetry Lift in forward flight. At a hover, the lift is equal across the entire rotor disk. As the helicopter gain air speed, the advancing blade develops greater lift because of the increased airspeed and the retreating blade will produce less lift, this will cause the helicopter to roll. A non-articulated rotor in forward flight is shown in figure.
Fig-14 Velocities of rotor in forward flight
If the blades were to rotate at a fixed incidence, then this velocity differential would cause four-fifths of the total lift of the rotor to be created on the advancing side. The calculated pressure contours for a fixed incidence rotor with an advance ratio of =0.3 are shown below
Fig-15Calculated pressure contours for fixed blade incidence
Obviously, this large imbalance of force on the rotor would lead to large oscillatory stresses at the blade roots, along with a large rolling moment. This would make the helicopter very unflyable, both from a dynamics and structural viewpoint.
To reduce this large force differential, a cyclical variation of the blade incidence is needed. The most common way of reducing the blade incidence is with flapping hinges. When using flapping hinges, the blade is hinged as close as possible to its root, allowing the entire blade to "flap" up and down as it rotates.
Fig-16 An articulated rotor hub
When a blade is on the advancing side, its increased lift causes the blade to flap upwards, which effectively reduces its incidence. The opposite occurs on the retreating side. Due to the presence of the flapping hinges, none of the bending forces or rolling moments is transferred to the helicopter body. Centrifugal force is typically enough to prevent the blades from flapping to a large degree, but many helicopters also employ stops as an added preventative measure. The use of flapping hinges also creates a better force balance on the rotor, distributing the lift more evenly. Calculated pressure contours for a variable incidence rotor can be seen below.
Fig-17Calculated pressure contours for variable incidence
This diagram also denotes a region of reversed flow on the rotor. As the forward speed of the helicopter increases, a region near the blade roots on the retreating side actually experiences a reversed flow. Combined with the large blade incidence on the retreating side, as forward speed increases, the blades approach a stalled condition. At the same time, regions near the tips on the advancing side experience a very high velocity flow, approaching the point where shock waves form, leading to shock induced flow separation. Due to these limiting factors, the maximum forward speed of a helicopter is limited to about 402kph.
Helicopter lift is obtained by means of one or more power driven horizontal propellers, which is called main rotor. When the main rotor of helicopter turns it produces lift and reaction torque. Reaction torque tends to make helicopter spin. On most helicopters a small rotor near the tail, which called tail rotor, compensates for this torque. On twin rotor helicopter the rotors rotate in opposite directions, their reactions cancel each other.
The main rotor produces the lifting force. As they spin in the air and produced the lift. Each blade produces an equal share of the lifting force. The weight of a helicopter is divided evenly between the rotor blades on the main rotor system.
The tail rotor is very important. If you spin a rotor with an engine, the rotor will rotate, but the engine and helicopter body will tend to rotate in opposite direction to the rotor. This is called Torque reaction. The tail rotor is used to compensate for this torque and hold the helicopter straight. On twin-rotors helicopter, the rotors spin in opposite directions, so their reactions cancel each other.
The tail rotor in normally linked to the main rotor via a system of drive shafts and gearboxes that means if you turn the main rotor, the tail rotor is also turns. Most helicopters have a ratio of 3:1 to 6:1. That is, if main rotor turns one rotation, the tail rotor will turn 3 revolutions (for 3:1) or 6 revolutions (for 6:1). In most helicopters the engine turns a shaft that connected to an input quill in the transmission gearbox. The main rotor mast out to the top and tail rotor drive shafts out to the tail from the transmission gearbox.
The term gyroscopic precession describes an inherent quality of rotating bodies in which an applied force is manifested 900 in the direction of rotation from the point where the force is applied. Since the rotor of a helicopter has a relatively large diameter and turns at several hundred revolutions per minute precession is a prime factor in controlling the rotor operation.
The cyclic pitch control causes variation in the pitch of the rotor blades as they rotate about the circle of the tip path plane. The purpose of this pitch change is in part to cause the rotor disc to tilt in the direction in which it is desired to make the helicopter move. When only the aerodynamic effects of blades are considered it would seem that when the pitch of the blades is high the lift would be high and the blade would rise. Thus if the blades had high pitch as they passed through one side of the rotor disc the side of the disc having low pitch should rise and the side having low pitch should fall. This would be true except for gyroscopic precession.
Gyroscopic precession is caused by a combination of a spinning force and an applied acceleration force perpendicular to the spinning force. Thus if force is applied perpendicular to the plane of rotation the precession will cause the force to take effect 900 from the applied force in the direction of rotation.
As a result of the fore going principle, if a pilot wants the main rotor of a helicopter to tilt in a particular direction, the applied force must be at a angular displacement 900 ahead of the desired direction of tilt. The required force is applied aerodynamically by changing the pitch of the rotor blades through the cyclic pitch control. When the cyclic control is pushed forward the blade at left increases its pitch as the blade on right decreases pitch. This applies an up force to the left hand side of the rotor disc, but the up movement is therefore at rear of the rotor plane and the rotor tilts forward. This applies a forward thrust and causes the helicopter to move forward.
Any type of machine vibrates. However greater than normal vibration usually means that there is a malfunction. Malfunctions can be caused by worn bearings, out-of-balance conditions, or loose hardware. If allowed to continue unchecked, vibrations can cause material failure or machine destruction. Aircraft -- particularly helicopters -- have a high vibration level due to their many moving parts. Designers have been forced to use many different dampening and counteracting methods to keep vibrations at acceptable levels. Some examples are
1. Driving secondary parts at different speeds to reduce harmonic vibrations; this method removes much of the vibration buildup.
2. Mounting high-level vibration parts such as drive shafting on shock-absorbent mounts.
3. Installing vibration absorbers in high-level vibration areas of the airframe.
Lateral vibrations are evident in side-to-side swinging rhythms. An out-of-balance rotor blade causes this type of vibration. Lateral vibrations in helicopter rotor systems are quite common.
Vertical vibrations are evident in up-and-down movement that produces a thumping effect. An out-of-track rotor blade causes this type vibration.
High-frequency vibrations are evident in buzzing and a numbing effect on the feet and fingers of crewmembers. High-frequency vibrations are caused by an out-of-balance condition or a high-speed, moving part that has been torqued incorrectly. The balancing of high-speed parts is very important. Any build-up of dirt, grease, or fluid on or inside such a part (drive shafting for example) causes a high-frequency vibration. This type vibration is more dangerous than a lateral or vertical one because it causes crystallization of metal, which weakens it. This vibration must be corrected before the equipment can be operated.
Ground resonance is the most dangerous and destructive of the vibrations discussed here. Ground resonance can destroy a helicopter in a matter of seconds. It is present in helicopters with articulated rotor heads. Ground resonance occurs while the helicopter is on the ground with rotors turning it will not happen in flight. Ground resonance results when unbalanced forces in the rotor system cause the helicopter to rock on the landing gear at or near its natural frequency. Correcting this problem is difficult because the natural frequency of the helicopter changes as lift is applied to the rotors. With all parts working properly, the design of the helicopter landing gear, shock struts, and rotor blade lag dampeners will prevent the resonance building up to dangerous levels. Improper adjustment of the landing gear shock struts, incorrect tire pressure, and defective rotor blade lag dampeners may cause ground resonance. The quickest way to remove ground resonance is to hover the helicopter clear of the ground.
The tip path plane, or TPP, is the plane connecting the rotor blade tips as they rotate. While hovering, the thrust vector of a helicopter is oriented upward, perpendicular to the tip path plane. In order for the helicopter to travel forward, this thrust vector needs to be rotated slightly in the forward direction. To rotate the thrust vector, it is in turn necessary to rotate the TPP by the same amount, as illustrated below.
Fig-20 Tip path planes and thrust vectors for hovering and forward flight
Since tilting the rotor hub or rotor shaft is impractical, an alternative means of rotating the TPP is needed. Most modern helicopters use a system of swash plates. Seen in the following diagram, the swash plate system is composed of upper and lower swash plates.
Fig-21Cyclic control and swash plates
The lower swash plate remains stationary relative to the helicopter. The upper swash plate rotates with the rotor, while remaining parallel to the lower swash plate. By utilizing what is called cyclic control, the swash plates can be angled so as to vary the
Pitch of the blades depending on their azimuth angle. As the swash plates are tilted in the proper direction, there is an increased lift on the aft portion of the rotor, causing the blades to flap up, which in turn causes the TPP to rotate forwards. As the TPP rotates forwards, the thrust vector does as well, imparting a forward acceleration to the helicopter.
The first analytical theory to consider for a helicopter in forward (no axial) flight is the momentum theory. The analysis for vertical (axial) flight is very similar to that of a simple propeller, and will not be discussed here. One notable result of that analysis, however, is the induced velocity of the rotor in hover.
Where w is the disc loading, given by
In the terms of basic momentum theory, the thrust of a rotor in no axial flight is very difficult to derive. In the context of this discussion, a relationship for the thrust that was proposed by Glauert in 1928 will be used. A simple diagram of an actuator disk in no axial flow is depicted below.
Fig-22 Actuator disk in no axial flow
The thrust of the actuator disk can be given by
Far downstream from the disk, the downwash vf is doubled. Also, the term becomes the mass flow through the stream tube that is defined by the actuator disk. Some validity for these relationships can be inferred by comparing them to the formula for the lift of a wing having 2R span with a uniform downwash. The lift of such a wing is expressed by an equation similar to that shown above. After assuming that this equation is valid, determining the thrust requires that the induced velocity in forward flight be determined.
These two equations allow the determination of thrust and induced velocity of a helicopter in forward flight.
The helicopter structure must be strong enough to with stand all the loads expected to be experienced in service life. This comprises large loads, which are experienced rarely, and repetitive small to medium loads which are experienced in a normal flight. Where as large loads are important in designing the non-rotating parts of helicopter like the fuselage, the tail boom, the landing gear etc. The repetitive loads are important in designing the rotating parts such as the main rotor, the tail rotor, the shafts, the main rotor gearbox, the tail rotor gearbox etc.
The rotor blade structure must possess sufficient strength to with stand not only the aerodynamic loads generated on the blade surface but also the inertial loads arising from the centrifugal, the coriolis, the gyroscopic and the vibratory effects produced by the blade movement .the blade must also possess sufficient stiffness and rigidity to prevent excessive deformation and to assure that the blades will maintain the desired aerodynamic characteristics.
The vibration, its causes and reduction are as discussed previously.
While considering the expected service life of the helicopter or its components all types of expected loads must be considered. Three basic factors, which govern the service life, are
1. Corrosion
2. Creep and
3. Fatigue
Some of the important factors, which govern the selection of material for airframe and the primary load selection of material for airframe and the primary load bearing members of the helicopter, are
1. A high strength to weight ratio
2. Stiffness
3. Specific gravity
4. Resistance to impact loads
5. Temperature effects
6. Corrosion resistance
7. Fatigue strength
8. Rate of crack propagation
Even though the concept of the helicopter is arguably older than that of the airplane, there is still a great amount of research and advancement yet to occur. As the political climate of our world continues to change and military conflicts approach the small-scale urban warfare of recent years, the importance of the helicopter will continue to grow. It is rather ironic that an idea first conceived long before the Common Era will be key to winning military conflicts in the 21st century.
Rotary wing research and development is a complex interrelated challenge. The advanced tools used are Computational fluid dynamics (CFD), Finite element method (FEM), and Computational structural dynamics (CSD) for physical understanding of complex aerodynamics and structural phenomena. Integration of these will enable us to design rotorcraft, which will have superior productivity, enlarged mission capabilities and improved environmental acceptance.
The future of helicopter is bright with its ability to land in any small clear area; the helicopter finds use in air taxi service, police work, Inter city mail, and rescue work, power line patrolling and other areas. The development is still to continue.
1. Bhagwat, Mahendra J., et al. Flow Visualization and Measurements in the Wake of a Rotor with a Subwing Tip, Annual Forum Proceedings-American Helicopter Society, vol. 1, 1999, pp. 951-962.
2. Bramwell, A. R. S. Helicopter Dynamics. New York: Halsted Press, 1976.
3. Gessow, Alfred and Myers, Garry C., Jr. Aerodynamics of the Helicopter. New York: Macmillan Company, 1952.
4. Ghee, Terence A. and Elliot, Joe W. The Wake of a Small-Scale Rotor in Forward Flight Using Flow Visualization, Journal of the American Helicopter Society, vol. 40, no. 3, July 1995, pp. 52-65.
5. Gunston, Bill and Spick, Mike. Modern Fighting Helicopters. New York: Crescent Books, 1986.
6. Johnson, Wayne. Helicopter Theory. Mineola, NY: Dover Publications, 1980.
7. McCormick, Barnes W. Aerodynamics, Aeronautics and Flight Mechanics. New York: John Wiley & Sons, 1995.
8. Newman, Simon. The Foundations of Helicopter Flight. New York: Halsted Press, 1994.
9. Seddon, J. Basic Helicopter Aerodynamics. Reston, VA: American Institute of Aeronautics and Astronautics, 1990.
10. Stepniewski, W. Z. and Keys, C. N. Rotary-Wing Aerodynamics. Mineola, NY: Dover Publications, 1979.
11. Young, Raymond A. Helicopter Engineering. New York: Ronald Press Company, 1949.
12. Journal of Aeronautical Society of India-May 1997
13. Journal of American institute of Aeronautics and Astronautics.

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