Monday, June 29, 2015
FREE AVIATION STUDY: Rotor Mechanisms for Forward Flight
FREE AVIATION STUDY: Rotor Mechanisms for Forward Flight: Rotor Mechanisms for Forward Flight The edgewise rotor In level forward flight the rotor is edgewise on to the airstream,a basically u...
FREE AVIATION STUDY: Flapping motion
FREE AVIATION STUDY: Flapping motion: Flapping motion To examine the flapping motion more fully we assume, unless otherwise stated, that the flapping hinge is on the axis of rot...
FREE AVIATION STUDY: Rotor control
FREE AVIATION STUDY: Rotor control: Rotor control Control of the helicopter in flight involves changing the magnitude of rotor thrust or its line of action or both. Almost th...
FREE AVIATION STUDY: Equivalence of flapping and feathering
FREE AVIATION STUDY: Equivalence of flapping and feathering: Equivalence of flapping and feathering The performance of the rotor blade depends upon its angle of incidence to the tip-path plane. A gi...
Equivalence of flapping and feathering
Equivalence of flapping and feathering
The performance of the rotor blade depends upon its angle of incidence to the tip-path plane. A given blade incidence can be obtained with different combinations of flapping and feathering. Consider the two situations illustrated in Fig. 4.19: these are views from the left side with the helicopter in forward flight in the direction shown. In situation 1 the shaft axis coincides with the TPA; there is therefore no flapping but the necessary blade incidences are obtained from feathering according to Equation 4.8. Blade attitudes at the four quarter points of a rotation are as indicated in the diagram. In situation 2 the shaft axis coincides with the NFA.By definition this means that feathering is zero: the blade angles however are obtained from flapping according to Equation (4.4). It is seen that if the feathering and flapping coefficients B1 and a1 are equal, the blade attitudes to the tip-path plane are identical around the azimuth in the two situations. The blade perceives a change in nose-down feathering, via the swash-plate, as being equivalent to the same angle change in nose-up flapping.
The performance of the rotor blade depends upon its angle of incidence to the tip-path plane. A given blade incidence can be obtained with different combinations of flapping and feathering. Consider the two situations illustrated in Fig. 4.19: these are views from the left side with the helicopter in forward flight in the direction shown. In situation 1 the shaft axis coincides with the TPA; there is therefore no flapping but the necessary blade incidences are obtained from feathering according to Equation 4.8. Blade attitudes at the four quarter points of a rotation are as indicated in the diagram. In situation 2 the shaft axis coincides with the NFA.By definition this means that feathering is zero: the blade angles however are obtained from flapping according to Equation (4.4). It is seen that if the feathering and flapping coefficients B1 and a1 are equal, the blade attitudes to the tip-path plane are identical around the azimuth in the two situations. The blade perceives a change in nose-down feathering, via the swash-plate, as being equivalent to the same angle change in nose-up flapping.
Rotor control
Rotor control
Control of the helicopter in flight involves changing the magnitude of rotor thrust or its line of action or both. Almost the whole of the control task falls to the lot of the main rotor and it is on this that we concentrate. A change in line of action of the thrust would in principle be obtained by tilting the rotor shaft, or at least the hub, relative to the fuselage. Since the rotor is engine-driven (unlike that of an autogyro) tilting the shaft is impracticable. Tilting the hub is possible with some designs but the large mechanical forces required restrict this method to very small helicopters. Use of the feathering mechanism, however, by which the pitch angle of the blades is varied, either collectively or cyclically, effectively transfers to the aerodynamic forces the work involved in changing the magnitude and direction of the rotor thrust. Blade feathering, or pitch change, could be achieved in various ways. Thus Saunders (1975)1 lists the use of aerodynamic servo tabs, auxiliary rotors, fluidically controlled jet flaps, or pitch links from a control gyro as possible methods. The widely adopted method, however,is through a swashplate system,illustrated in Fig.4.14 which shows the operation with collective pitch while Fig. 4.15 shows the operation with cyclic pitch. Carried on the rotor shaft, this embodies two parallel plates, the lower of which does not rotate with the shaft but can be tilted in any direction by operation of the pilot’s cyclic control column and raised or lowered by means of his collective lever. The upper plate is connected by control rods to the feathering hinge mechanisms of the blades and rotates with the shaft, while being constrained to remain parallel to the lower plate. Raising the collective lever thus increases the pitch angle of the blades by the same amount all round
Control of the helicopter in flight involves changing the magnitude of rotor thrust or its line of action or both. Almost the whole of the control task falls to the lot of the main rotor and it is on this that we concentrate. A change in line of action of the thrust would in principle be obtained by tilting the rotor shaft, or at least the hub, relative to the fuselage. Since the rotor is engine-driven (unlike that of an autogyro) tilting the shaft is impracticable. Tilting the hub is possible with some designs but the large mechanical forces required restrict this method to very small helicopters. Use of the feathering mechanism, however, by which the pitch angle of the blades is varied, either collectively or cyclically, effectively transfers to the aerodynamic forces the work involved in changing the magnitude and direction of the rotor thrust. Blade feathering, or pitch change, could be achieved in various ways. Thus Saunders (1975)1 lists the use of aerodynamic servo tabs, auxiliary rotors, fluidically controlled jet flaps, or pitch links from a control gyro as possible methods. The widely adopted method, however,is through a swashplate system,illustrated in Fig.4.14 which shows the operation with collective pitch while Fig. 4.15 shows the operation with cyclic pitch. Carried on the rotor shaft, this embodies two parallel plates, the lower of which does not rotate with the shaft but can be tilted in any direction by operation of the pilot’s cyclic control column and raised or lowered by means of his collective lever. The upper plate is connected by control rods to the feathering hinge mechanisms of the blades and rotates with the shaft, while being constrained to remain parallel to the lower plate. Raising the collective lever thus increases the pitch angle of the blades by the same amount all round
Flapping motion
Flapping motion
To examine the flapping motion more fully we assume, unless otherwise stated, that the flapping hinge is on the axis of rotation. This simplifies the considerations without hiding anything of significance. Referring to Fig 4.12, the flapping takes place under conditions of dynamic equilibrium, about the hinge, between the aerodynamic lift (the exciting function), the centrifugal force (the ‘spring’ or restraining force) and the blade inertia (the damping). In other words, the once-per-cycle oscillatory motion is that of a dynamic system in resonance. The flapping moment equation is seen to be
We shall return to this equation later. The centrifugal force is by far the largest force acting on the blade and provides an essential stability to the flapping motion. The degree of stability is highest in the hover condition (where the flapping angle is constant) and decreases as the advance ratio increases. Bramwell’s consideration of the flapping equation (p. 153 et seq.) leads in effect to the conclusion that the motion is dynamically stable for all realistic values of m. Maximum flapping velocities occur where the resultant air velocity is at its highest and lowest, that is at 90° and 270° azimuth. Maximum displacements occur 90° later, that is at 180° (upward) and 0° (downward). These displacements mean that the plane of rotation of the blade tips,the tip-path plane(TPP),is tilted backwards relative to the plane normal to the rotor shaft, the shaft normal plane (SNP). In hover the blades cone upwards at a constant angle a0, say, to the shaft normal plane. The coning angle is that at which the blade weight is supported by the aerodynamic lift. Its existence has an additional effect on the orientation of the TPP during rotation in forward flight. Figure 4.13 shows that because of the coning angle, the flight velocity V has a lift-increasing effect on a blade at 180° (the forward blade) and a lift-decreasing effect on a blade at 0° (the rearward blade). This asymmetry in lift is, we see, at 90° to the side-to-side asymmetry discussed earlier: its effect is to tilt the TPP laterally and since the point of lowest tilt follows 90° behind the point of lowest lift, the TPP is tilted downwards to the right, that is on the advancing side. The coning and disc tilt angles are normally no more than a few degrees. Since in any steady state of the rotor the flapping motion is periodic, the flapping angle can be expressed in the form of a Fourier series:
To examine the flapping motion more fully we assume, unless otherwise stated, that the flapping hinge is on the axis of rotation. This simplifies the considerations without hiding anything of significance. Referring to Fig 4.12, the flapping takes place under conditions of dynamic equilibrium, about the hinge, between the aerodynamic lift (the exciting function), the centrifugal force (the ‘spring’ or restraining force) and the blade inertia (the damping). In other words, the once-per-cycle oscillatory motion is that of a dynamic system in resonance. The flapping moment equation is seen to be
We shall return to this equation later. The centrifugal force is by far the largest force acting on the blade and provides an essential stability to the flapping motion. The degree of stability is highest in the hover condition (where the flapping angle is constant) and decreases as the advance ratio increases. Bramwell’s consideration of the flapping equation (p. 153 et seq.) leads in effect to the conclusion that the motion is dynamically stable for all realistic values of m. Maximum flapping velocities occur where the resultant air velocity is at its highest and lowest, that is at 90° and 270° azimuth. Maximum displacements occur 90° later, that is at 180° (upward) and 0° (downward). These displacements mean that the plane of rotation of the blade tips,the tip-path plane(TPP),is tilted backwards relative to the plane normal to the rotor shaft, the shaft normal plane (SNP). In hover the blades cone upwards at a constant angle a0, say, to the shaft normal plane. The coning angle is that at which the blade weight is supported by the aerodynamic lift. Its existence has an additional effect on the orientation of the TPP during rotation in forward flight. Figure 4.13 shows that because of the coning angle, the flight velocity V has a lift-increasing effect on a blade at 180° (the forward blade) and a lift-decreasing effect on a blade at 0° (the rearward blade). This asymmetry in lift is, we see, at 90° to the side-to-side asymmetry discussed earlier: its effect is to tilt the TPP laterally and since the point of lowest tilt follows 90° behind the point of lowest lift, the TPP is tilted downwards to the right, that is on the advancing side. The coning and disc tilt angles are normally no more than a few degrees. Since in any steady state of the rotor the flapping motion is periodic, the flapping angle can be expressed in the form of a Fourier series:
Rotor Mechanisms for Forward Flight
Rotor Mechanisms for Forward Flight
The edgewise rotor
In level forward flight the rotor is edgewise on to the airstream,a basically unnatural state for propeller functioning. This is shown in Fig. 4.1. Practical complications which arise from this have been resolved by the introduction of mechanical devices, the functioning of which in turn adds to the complexity of the aerodynamics. Figure 4.2 pictures the rotor disc as seen from above. Blade rotation is in a counter-clockwise sense (the standard adopted for all helicopters of the Western countries) with rotational speed W. Forward flight velocity is V and the ratio V/WR, R being the blade radius, is known as the advance ratiosymbol m,and has a value normally within the range zero to 0.5. Azimuth angle y is measured from the downstream blade position: the range y=0°–180° defines the advancing side and that from 180°–360° (or 0°) the retreating side. A blade is shown in Fig 4.2 at 90° and again at 270°. These are the positions of maximum and minimum relative air velocity normal to the blade, the velocities at the tip being (WR + V) and (WR - V), respectively. If the blade were to rotate at fixed incidence, then owing to this velocity differential, much more lift would be generated on the advancing side than on the retreating side. Calculated pressure contours for a fixed-incidence rotation with m=0.3 are shown in Fig 4.3. About four-fifths of the total lift is produced on the advancing side. The consequences of this imbalance would be large oscillatory bending stresses at the blade roots and a large rolling moment on the vehicle. Both structurally and dynamically the helicopter would be unflyable.
The edgewise rotor
In level forward flight the rotor is edgewise on to the airstream,a basically unnatural state for propeller functioning. This is shown in Fig. 4.1. Practical complications which arise from this have been resolved by the introduction of mechanical devices, the functioning of which in turn adds to the complexity of the aerodynamics. Figure 4.2 pictures the rotor disc as seen from above. Blade rotation is in a counter-clockwise sense (the standard adopted for all helicopters of the Western countries) with rotational speed W. Forward flight velocity is V and the ratio V/WR, R being the blade radius, is known as the advance ratiosymbol m,and has a value normally within the range zero to 0.5. Azimuth angle y is measured from the downstream blade position: the range y=0°–180° defines the advancing side and that from 180°–360° (or 0°) the retreating side. A blade is shown in Fig 4.2 at 90° and again at 270°. These are the positions of maximum and minimum relative air velocity normal to the blade, the velocities at the tip being (WR + V) and (WR - V), respectively. If the blade were to rotate at fixed incidence, then owing to this velocity differential, much more lift would be generated on the advancing side than on the retreating side. Calculated pressure contours for a fixed-incidence rotation with m=0.3 are shown in Fig 4.3. About four-fifths of the total lift is produced on the advancing side. The consequences of this imbalance would be large oscillatory bending stresses at the blade roots and a large rolling moment on the vehicle. Both structurally and dynamically the helicopter would be unflyable.
Example of hover characteristics
Example of hover characteristics
Corresponding to CL/a and CD/CL characteristics for fixed wings, we have CT/qand Cp/CT for the helicopter in hover. An example has been evaluated using the following data: blade radius, R = 6m blade chord (constant), c = 0.5m blade twist, linear from 12° at root to 6° at tip number of blades, N = 4 empirical constant, k=1.13 blade profile drag coefficient (constant), CD0 = 0.010 The variation of CT/s with q is shown in Fig. 3.8(a). The nonlinearity results from the CT term in Equation (3.28). The variation of CP/s with q is calculated for three cases:
• k=1.13, Equation (3.48), • k=1.0, Equation (3.46), the simple momentum theory result, • Figure of merit M = 1.0, which assumes k=1.0 and CDo = 0.
Over the range shown (Fig. 3.8(b)), using the factor k=1.13 results in a power coefficient 0–9% higher than that obtained using simple momentum theory. The curve for M = 1 is of course unrealistic but gives an indication of the division of power between induced and profile components. (Rotor performance characteristics are sometimes plotted as CP/s versus CT/s. This type of plot is known as a hover polar.)
Corresponding to CL/a and CD/CL characteristics for fixed wings, we have CT/qand Cp/CT for the helicopter in hover. An example has been evaluated using the following data: blade radius, R = 6m blade chord (constant), c = 0.5m blade twist, linear from 12° at root to 6° at tip number of blades, N = 4 empirical constant, k=1.13 blade profile drag coefficient (constant), CD0 = 0.010 The variation of CT/s with q is shown in Fig. 3.8(a). The nonlinearity results from the CT term in Equation (3.28). The variation of CP/s with q is calculated for three cases:
• k=1.13, Equation (3.48), • k=1.0, Equation (3.46), the simple momentum theory result, • Figure of merit M = 1.0, which assumes k=1.0 and CDo = 0.
Over the range shown (Fig. 3.8(b)), using the factor k=1.13 results in a power coefficient 0–9% higher than that obtained using simple momentum theory. The curve for M = 1 is of course unrealistic but gives an indication of the division of power between induced and profile components. (Rotor performance characteristics are sometimes plotted as CP/s versus CT/s. This type of plot is known as a hover polar.)
Tip loss
Tip loss
A characteristic of the actuator disc concept is that the linear theory of lift is maintained right out to the edge of the disc.Physically,recalling Fig.2.1a–2.1c,we suppose the induced velocity,in which the pressure is above that of the surrounding air, to be contained entirely below the disc in a well-defined streamtube surrounded by air at rest relative to it. In reality, because the rotor consists of a finite number of separate blades, some air is able to escape outwards between the tips, drawn out by the tip vortices. Thus the total induced flow is less than the actuator disc theory would prescribe,so that for a given pitch setting of the blades the thrust is somewhat lower than that given by Equation (3.22). The deficiency is known as tip loss and is shown by a rapid falling off of lift over the last few per cent of span near the tip, in a blade loading distribution such as that of Fig. 2.13. Although several workers have suggested approximations [Bramwell (p. 111) quotes Prandtl, Johnson (p. 60) quotes in addition Sissingh and Wheatley] no exact theory of tip loss is available. A common method of arriving at a formula is to assume that outboard of a station r = BR the blade sections produce drag but no lift. Then the thrust integral in Equation (3.21) is replaced by
A characteristic of the actuator disc concept is that the linear theory of lift is maintained right out to the edge of the disc.Physically,recalling Fig.2.1a–2.1c,we suppose the induced velocity,in which the pressure is above that of the surrounding air, to be contained entirely below the disc in a well-defined streamtube surrounded by air at rest relative to it. In reality, because the rotor consists of a finite number of separate blades, some air is able to escape outwards between the tips, drawn out by the tip vortices. Thus the total induced flow is less than the actuator disc theory would prescribe,so that for a given pitch setting of the blades the thrust is somewhat lower than that given by Equation (3.22). The deficiency is known as tip loss and is shown by a rapid falling off of lift over the last few per cent of span near the tip, in a blade loading distribution such as that of Fig. 2.13. Although several workers have suggested approximations [Bramwell (p. 111) quotes Prandtl, Johnson (p. 60) quotes in addition Sissingh and Wheatley] no exact theory of tip loss is available. A common method of arriving at a formula is to assume that outboard of a station r = BR the blade sections produce drag but no lift. Then the thrust integral in Equation (3.21) is replaced by
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