Rotary-Wing Flight Mechanics Simon Newman School of Engineering Sciences, University of Southampton, Southampton, UK 1 Variation of Power Required with Forward Speed 1 2 Climb 3 3 Maximum Range and Endurance 3 4 Autorotation 4 5 Flow Patterns in Axial Flight and Factors Affecting Vortex Ring State 7 6 Ground Effect 8 7 Summary 9 Nomenclature 10 Related Articles 10 Further Reading 10 1 VARIATION OF POWER REQUIRED WITH FORWARD SPEED A helicopter is not possessed of an ability to fly fast compared with fixed-wing counterparts. This is a result of considerations with the main rotor. The main rotor moves in a direction very close to its plane of rotation which naturally divides it into two halves which operate under different aerodynamic conditions. One side (called the advancing side) has the rotation and translation velocity contributions adding together whilst the other (called the retreating side) has them subtracting see Figure 1. This becomes more influential as the forward speed increases and the rotor has two principal problem areas caused by the main rotor needing to maintain a roll trim of the helicopter. In simple terms, the retreating side has lower air speeds over it when compared with the advancing side which, in consequence, requires the pitch angle to be greater on the retreating side. Eventually, the pitch required to maintain roll trim and to produce the necessary thrust, to overcome the drag force on the airframe, results in the retreating blade encountering stall. In addition, the advancing side also faces its own potential problem: at higher forward speeds, the advancing tip region has the combination of a high speed of rotation and a high forward speed over it. This can raise the Mach number to a level where transonic effects will limit the aerofoil performance and eventually trigger stall through the high Mach number. The main rotor is thus confined to a box which limits the thrust via the retreating blade stall limit and the highest speeds through the advancing blade stall limit. (Over most of the forward flight envelope, the rotor is limited by the retreating blade; the advancing limit is normally confined to the highest speeds, which may not Encyclopedia of Aerospace Engineering. Edited by Richard Blockley and Wei Shyy c 2010 John Wiley & Sons, Ltd. ISBN: 978-0-470-68665-2 Figure 1. Advancing and retreating sides of the main rotor.
2 Flight Mechanics Main rotor thrust limit Retreating blade limit Rotor operating envelope Forward speed Figure 2. The helicopter speed trap. necessarily be encountered). This is the well-known speed trap (see Figure 2) which is the price paid for an air vehicle with efficient hovering characteristics but also the ability to perform a transition to and from forward flight. Hover is seemingly easiest to model as it has axial symmetry. In fact, hover requires a considerable depth of analysis. The wake is generated by the rotor blades and because it is not washed away by any forward speed remains closer to the rotor itself and therefore interactions between the blades and the wake, flow through the rotor disc. A method of analyzing a helicopter rotor is available where the momentum change as the airflow passes through the rotor disc is used to determine the thrust force. The flow velocity through the rotor is assumed to be uniform and is known as the induced velocity. This simplification makes the method relatively easy to model but it carries a difficulty which will be discussed in a later section. The induced velocity in hover is expressed by the following equation: T V i = 2ρA Advancing blade limit (1) This shows the dependence of the induced velocity on the thrust per unit disc area. This is called the disc loading. Its importance is in the power required to generate the thrust force. Essentially, we have a thrust force moving at a velocity which is the induced velocity. The product of these two terms is the required power to produce the thrust. It is called the induced power and can be directly linked to the induced drag of a fixed aircraft wing. The difference is that the induced drag force acts on a rotor blade and when multiplied by the respective radial distance from the axis of the rotor shaft requires a torque to turn the rotor and when factored by the rotational speed gives rise to the induced power. There is also the profile drag force to overcome which, itself, gives rise to the profile power. In the hover, the induced power dominates the profile power and forms approximately 70% of the total. Therefore, an efficiently hovering rotor needs a low induced power, which, through equation (1), will need a low disc loading. This is usually accomplished by using a main rotor of large radius. Observation of helicopters, whose operation is lifting at low speeds, shows the benefits of a low disc loading. The fuselage does influence the rotor downwash since it lies directly in the path of the air mass passing through the rotor. This is known as blockage and Figure 3a shows how this occurs. As the helicopter moves into forward flight, the main rotor is now tilted forwards and the flow through the rotor disc now becomes a combination of two components. The induced velocity is still present, but to this is added the forward flight speed. The equation determining the induced velocity now includes the forward flight speed in the form of two components, V X parallel to the disc plane, and V Z perpendicular to it. V i = T 1 (2) 2ρA V 2X + (V Z + V i ) 2 Figure 3. (a) Main rotor blockage fuselage; (b) hub (parasite) drag. Courtesy of AgustaWestland.
Rotary-Wing Flight Mechanics 3 1200 Main rotor power components 1000 Power (kw) 800 600 400 Induced Profile Parasite Total 200 0 0 10 20 30 40 50 60 70 80 90 100 Forward speed (m s 1 ) Figure 4. Power component variation with forward speed. The solution of this equation is not as straightforward as in the hover and is solved by means of an iterative scheme. The effect of forward speed is to enhance the mass of air flowing through the rotor which therefore needs a smaller induced velocity to generate the momentum change and thereby produce the thrust. This means that the induced power reduces as the forward flight speed increases. The profile power also changes but increases slightly with forward speed. There is one more factor to consider. The induced power is the product of the rotor thrust and the induced velocity. However, there is a component of forward speed normal to the rotor disc plane which adds to the induced velocity and therefore when multiplied by the thrust will also generate a power. This can be shown to be equal to the power required to overcome the fuselage drag force and is therefore known as the parasite power. Figure 3b shows the manner in which the fuselage can be viewed as a body generating the parasitic drag. Also shown is the fact that the rotor head is a component of this drag, in fact, it forms approximately one third of the total drag of the helicopter. Figure 4 shows a typical variation of these various components with forward speed. This is for the main rotor. For the complete aircraft power the tail rotor power components need to be added. These will be the induced and profile powers. There is no parasite power as that is catered for by the main rotor. A contribution for powering auxiliary systems such as electrical generators and hydraulic pumps must also be included. Finally, the losses through the transmission are added which usually consist of a factor typically a 4% addition. The profile power calculation assumes a constant value of profile drag coefficient for the blades. As the helicopter approaches high speed, this assumption does not hold entirely. Some parts of the rotor blades begin to experience the effects of compressibility and the phenomenon of drag rise will be felt as a more rapid rise in profile drag and therefore profile power. 2 CLIMB Climb for a helicopter can be somewhat different from that of a fixed wing aircraft. As the main rotor provides the supporting force for the aircraft, the helicopter does not need to align itself with the flight path. The power consumption is determined by the horizontal and vertical components of flight speed over the rotors, the main in particular, as shown in Figure 5. The vertical component (V C ) adds to the downwash and causes the increase in power required for the aircraft to climb (W V C ), where W is aircraft weight. The incoming flow over the fuselage will be inclined downwards which can interact with any aerodynamic components at the rear of the fuselage. This can cause a trim change which is dependent on forward speed and pitch angle of the fuselage. 3 MAXIMUM RANGE AND ENDURANCE Having established the variation of power consumption with forward speed, the calculation of endurance and range can be addressed. Endurance is time of flight for a given mass of
4 Flight Mechanics Figure 5. Incident velocity components on a main rotor. Courtesy of AgustaWestland. fuel to be consumed, whilst range is distance traveled, again for a given fuel mass. It now becomes necessary to consider how the engine(s) consume fuel with respect to the power at which it (they) are operating. In order to model the fuel consumption it is sensible to view it in terms of fuel flow rate that is, mass of fuel per unit time. If this is plotted on a graph then a very good approximation to a straight line is found. Figure 6 shows a schematic of a typical situation. As can be seen from Figure 6, two situations are presented. The full law as it is termed is what would be expected of a typical engine and a linear relationship is a very good match for real engine data. However, a very important feature of this line is the positive intercept on the ordinate axis. The other fuel consumption variation, termed the simplified law, is obtained by artificially setting the full law intercept to zero but maintaining the same slope of the line. Whilst this might appear contrived, it provides a useful comparison since with this variation a constant specific fuel consumption value is obtained. Additionally, the existence of the intercept causes the fuel consumption to be directly influenced by the number of engines operating. This is manifest by the fuel consumption being directly increased when the power demand Fuel flow rate Power Figure 6. Fuel flow variation with power. Full law Simplified law is shared by multiple engines. Additionally, it shows the character of the variation allowing conclusions to be drawn as to the differences between the two methods. The endurance variation with speed is shown in Figure 7a. For both fuel flow variations, the same speed gives the maximum endurance condition, which is that of minimum power. The power variation shows the hover and high speed conditions to be high power consumption situations but the minimum power speed occurs at about 35m s 1. This is the condition at which a helicopter can loiter most effectively. Range, however, reveals a difference in the optimum speeds for the two fuel-flow situations. Figure 7b shows the range variation with speed for both fuel consumption laws. In Figure 7c the optimum speeds are plotted on the power consumption plots, and it can be seen that the maximum range speeds are shown as tangent conditions from different points on the ordinate. The simplified law (equivalent to constant specific fuel consumption) tangent springs from the origin, however, the full linear law from a point on the negative ordinate dependent on the fuel consumption law, that is, intercept and slope. 4 AUTOROTATION Power failure in flight does not mean that a helicopter is necessarily in any danger. If correctly handled, a power failure can be overcome with the aircraft remaining under full control of the pilot. The essential flight condition to be achieved is the windmill brake state. The situation and its handling is highly dependent on the number of installed engines and how many are lost. With a single-engined helicopter, power failure means that there is no power input and a landing is the only option. With a multi-engined helicopter, there will usually be some power remaining and the aircraft can maintain flight under circumstances where the power demand from the rotor system is supplied by the remaining engine(s). This normally would be with flight at speeds close to the minimum power speed. It could be that the remaining power is sufficient for all of the possible flight speeds to be achieved and a normal landing can take place. The difficulty is that hover requires a high power supply and the available power may not be sufficient. This is not necessarily a problem as a run-on landing may be possible. The ability of a particular helicopter to carry out a successful landing following the loss of an engine is defined in a plot of flight speed against altitude, known as dead man s curve (Figure 8). The shaded areas are those for which flight is not recommended. For brevity the discussion will be limited to a single-engined helicopter. If we focus on point A we have a high-altitude hover situation. As the engine fails, the
Rotary-Wing Flight Mechanics 5 1.0 200 0.8 150 Endurance (h) 0.6 0.4 Endurance-full Endurance - simple Range (km) 100 Range-full Range - simple 0.2 50 0.0 0 20 40 60 80 100 (a) Forward speed (m s 1 ) (b) 0 0 20 40 60 80 100 Forward speed (m s 1 ) 1400 1200 1000 800 Power (kw) (c) 600 400 200 0 200 400 600 0 10 20 30 40 50 60 70 80 90 100 Forward speed (m s 1 ) P TOTAL Best range simple Best range full Figure 7. Variation of endurance and range with forward speed. (a) Endurance; (b) range; (c) best range speed. reduction in power supply will cause the rotor to lose rotational speed. If nothing is done the rotor speed will diminish and the thrust generated will reduce accordingly. The aircraft will descend and the situation will become irretrievable. The crucial thing is to retain rotor speed. In order to keep the rotor speed up, a power input must be found. This is found in the ability of the rotor to behave like a windmill which requires an upflow to be generated. This is achieved by the helicopter entering a descending flight. This will require the pilot to lower the collective lever (one of the primary controls see Figure 9) and reduce the thrust allowing the helicopter to commence its descent this is the entry into autorotation and the dynamic characteristics of the rotor greatly influence the ease of performing this maneuver. As the descent velocity builds up the upflow keeps the rotor turning. A situation is reached where the collective lever can be raised, the upflow keeping the rotor speed constant and the rotor producing a thrust equal to the aircraft weight and a steady-state descending flight can be maintained. The descent rate necessary to achieve steady descent is too high for a successful landing
6 Flight Mechanics Altitude B A D C Figure 8. Dead Man s curve. Speed without significant damage to the airframe. The descent rate needs to be arrested which is achieved by the pilot raising the collective lever, increasing the rotor thrust and halting the descent in a maneuver known as the flare. However, this will cause the rotor to slow down and this means that the flare is a once-only situation so care must be taken in correctly flaring the autorotation. The ability to generate the thrust to arrest the descent rate is dependent on a high rotational speed during the descent phase of the autorotation. Effectively, the rotor becomes a kinetic energy store for use in the flare. This will be reflected in the inertia of the rotor and the rotational speed during the descent, where potential energy due to altitude is traded for this kinetic energy supply to the rotor. After the entry, the subsequent descent and flare all require a certain height loss to complete the autorotative landing maneuver. Point A is the lowest altitude necessary to successfully land the helicopter from a hovering condition. If the helicopter is hovering a small distance above the ground then a power loss can be handled by essentially the pilot doing nothing. The rotor speed will fall off, the rotor thrust will decay, and the helicopter will begin to descend. With a small altitude the impact will be slight and the undercarriage will take the loads accordingly. This corresponds to point B which is the maximum height from which this type of descent can be accomplished. Between points A and B, is a range of altitude where neither of these techniques can be successfully employed and so must be avoided. The upflow through the rotor can also be achieved if the helicopter is in forward flight when the engine fails. By easing back on the cyclic stick (see Figure 9), the forward speed can be directed partly through the rotor. The faster the forward flight, the greater potential there is for generating the required upflow through the rotor. Hence, the altitude limits defined by points A and B, are gradually removed as the helicopter flies faster. Eventually the limits merge at point C when this altitude limit problem disappears. As the helicopter flies increasingly faster, the difficulty in landing increases since the aircraft has to be rotated nose up to use the main rotor thrust to decelerate the aircraft. The high-speed-generated upflow can cause the thrust to build up unduly and the aircraft to balloon upwards making an eventual touchdown increasingly difficult to achieve. This is exacerbated at low altitude by the danger of a tail strike on the ground due to the extreme nose up attitude of the airframe. For this reason a second avoid region is added to the dead man s curve plot defined by point D. Figure 9. Primary controls of a Saunders Roe Skeeter. Collective lever is in the left hand controlling the main rotor thrust, the cyclic stick is for the right hand and controls the main rotor disc attitude and the foot pedals control the tail rotor thrust.
Rotary-Wing Flight Mechanics 7 Normalized induced velocity Axial flight-induced velocity variation 5 4 3 2 1 (c) (b) (a) 0 5 4 3 2 1 0 1 2 3 4 5 Normalized axial velocity Climb + ve root Descent + ve root Descent ve root Figure 10. Solutions of the actuator disc theory in axial flight. 5 FLOW PATTERNS IN AXIAL FLIGHT AND FACTORS AFFECTING VORTEX RING STATE The solutions of the climb and descent equations for the actuator disc in axial flight are presented in Figure 10. As can be seen, there are several solutions for the induced velocity which must be rationalized into realistic situations. Examination of the climb solution (a), as the axial velocity reduces to zero, sees a steady increase in induced velocity as hover is reached. This conforms to the physical situation, where the climb velocity adds to the induced velocity giving an enhanced mass flow through the disc. This means that, in order to keep the same thrust, a lower value of induced velocity is required to give the same momentum change. As the rotor moves into vertical descent, (b) the reduced inflow causes an increase in induced velocity, however this solution then begins to develop an odd behavior in that it asymptotes to a solution where the sum of the inflow and induced velocity tends to zero. This is plainly unrealistic as zero mass flow means that there is no hope of achieving a momentum change and thereby thrust generation. The other arm of the descent solution (c) also asymptotes to the zero total inflow condition but as the descent velocity increases it develop a behavior which is now physically realistic. The flow states surrounding a rotor in axial flight is shown schematically in Figure 11. Figure 11a shows the steady well defined streamtube for the hover where the downwash can be realistically modeled using actuator disc theory. However, the assumption of uniform downwash causes a difficulty in modelling moderate descending flight. In reality, vorticity is produced by the rotor blades, predominantly at the tips, which forms a ring-type structure around the disc periphery at low descent rates 11b. (Because it is limited in extent, actuator disc theory can be used.) As the descent rate increases, the region of the rotor affected by this vortex behaviour increases until it dominates the rotor with a recirculating flow. This is known as the vortex ring state 11c and is a distinct problem in helicopter operation. To describe this flow condition as a steady toroidal vortex would be naïve. It is a very unsteady condition dominated by interacting vortical flows. There is a considerable amount of high frequency vibration through the unsteadiness of the overall flow. To this is added the problem Figure 11. Schematic views of the overall flow structure with increasing descent rate.
8 Flight Mechanics Figure 14. Skew angle of wake (US Navy). Figure 12. Interpretation of ground effect via an image below the sea surface (US Navy). of vorticity tending to collect around the rotor and then releasing suddenly, which generates a low-frequency vibration. As the descent rate increases the vorticity is now allowed to move above the rotor to establish a flow pattern not unlike that behind a flat Plate 11d. For this reason it is known as the turbulent wake state. As the descent rate continues to increase, the vortical flows move further from the rotor disc plane and the tubular streamtube can now begin to re-establish 11e and eventually become the windmill brake state 11f. 6 GROUND EFFECT If a helicopter is operating close to the ground, the downwash is interrupted by the ground surface. This has a beneficial effect on the power consumption which can be used in two distinct ways. Firstly, a given weight of helicopter will be able to operate close to the ground at a reduced power or secondly, for a given power provision a greater weight of helicopter Figure 13. Ground effect.
Rotary-Wing Flight Mechanics 9 Figure 15. Sikorsky Blackhawk (a) and Westland Lynx (b) (US Navy). can be hovered. For this reason, performance is expressed in ground effect (IGE) or out of ground effect (OGE). Figure 12 shows an explanation of this phenomenon where the ground is replaced by an image helicopter hovering below the ground in an inverted orientation. This shows how the ground effect can be interpreted as a virtual upflow hence the improvement in performance. Figure 13 shows the variation of thrust available IGE v OGE for various heights (Z/R) and forward speeds. The forward speed is expressed in terms of wake angle which is a measure of the forward speed as a proportion of the downwash. The one axis is for the wake angle which is the amount that the downwash is skewed rearwards from the hover value of 0. Figure 14 shows this effect. The Rotor height/radius axis is the height of the rotor disc above the ground level with respect to the rotor radius. The vertical axis is the ratio of the rotor thrust in ground effect relative to that of a similar rotor in open air. It assumes that the rotor controls are the same for both and indicates how the ground has the effect of the rotor generating an enhanced thrust (the ratios are in excees of unity). As can be seen in Figure 13, the influence of ground effect diminishes as the helicopter moves further from the ground or increasingly into forward flight. 6.1 Main-rotor/tail-rotor interactions The tail rotor is often seen as the lesser of the two with the main rotor supplying control of five of the six degrees of freedom, with the sixth (yaw) being provided by the tail rotor (in the ubiquitous single main and tail rotor configuration). However, its placement is in a very difficult position on the aircraft being under the influence of the fuselage and, in particular, the main rotor wake. Figure 15 shows the extent of the main rotor wake in the hover and in forward flight. As can be seen, in hover the wake tends to avoid the tail rotor. As the helicopter moves into forward flight the main rotor wake Figure 16. Westland Lynx. Courtesy of AgustaWestland. is displaced aft and interaction with the tail rotor is possible. This can affect the aerodynamic performance of the tail rotor which, in turn, affects the yaw control. In addition, the placement of the tail rotor close to the fin, or vertical stabilizer, see Figure 16, can cause interference similar to the main rotor blockage. However, the mechanism for this is different but still has the same effect of the fin generating a force in direct opposition to the tail rotor thrust. The aerodynamic interaction between the rotors can also give rise to noise generation. Two important considerations for a tail rotor is whether it is a pusher (i.e., pushes the fin in the direction of the main rotor rotation) and its direction of rotation. For instance, in the case of Figure 16, it is a pusher, rotating backwards at the top. 7 SUMMARY This section discussed the various aspects of helicopter performance in hover, axial, and forward flight. The initial discussion was based on the use of momentum theory using
10 Flight Mechanics the concept of the actuator disc. This method is the most basic but provided that the helicopter is not operating close to a flight envelope boundary, it can be used to obtain a useful understanding and prediction of power required. This was then used to evaluate the fuel consumption of a typical turboshaft, with either a single or multi-engined installation. The effect of speed on endurance and range was then studied and the importance of the number of engines outlined. In axial flight, the limitations of the momentum theory were discussed. Climb, hover, low, and high rates of descent can be handled by an actuator disc, however, the moderate descent conditions of the vortex ring state, where the condition is dominated by unsteady vortical type flows render the mathematical solution of the momentum theory as of no practical value. The more complicated analyses or experimental data must be consulted for this condition. The effect on helicopter performance in the more involved flight conditions of autorotation and ground effect are then discussed. The final section is devoted to the tail rotor, which is a component that operates physically and aerodynamically under the influence of the main rotor. After completing this section, the reader should be aware that helicopter rotor aerodynamics is a very complicated affair. This chapter deals with the rotors as a lifting device and the overall performance estimation. Readers are encouraged to read the suggested linking chapters in this encyclopedia to further the understanding of helicopter aerodynamics. NOMENCLATURE A R T T IGE T OGE V C V i V X V Z W Z ρ Rotor Disc Area Rotor Radius Rotor Thrust Rotor Thrust In Ground Effect Rotor Thrust Out of Ground Effect Climb Velocity Induced Velocity Forward Velocity Component Parallel to Rotor Disc Forward Velocity Component Normal to Rotor Disc Aircraft Weight Height of Rotor Disc above Ground Level Air Density RELATED ARTICLES (see Unsteady Aerodynamics) (see High Angle of Attack Aerodynamics) (see Rotorcraft Aerodynamics) (see Ground Effect Aerodynamics) (see The Evolution of Analytic and Computational Methods for Fixed-Wing Flight Vehicle Aeroelasticity) (see Rotary-Wing Static Stability) (see Rotary-Wing Dynamic Stability) (see Rotary-Wing Control and Handling Qualities) (see Applied Aerodynamics and Propulsion Foundation: Rotary Wing) (see Performance: Rotary Wing Vehicles) (see Rotary Wing Vehicles) (see Rotary Wing Vehicle Design) (see Autonomous Flight of Rotary Wing MAV Using Infrared and Ultrasonic Sensors) (see Development of Centimeter-sized Aerial Vehicles) FURTHER READING Bramwell, A.R.S., Done, G., and Balmford, D. (2000) Bramwell s Helicopter Dynamics, 2nd edn, Elsevier Ltd, ISBN: 978-0-7506-5075-5. Cooke, A.K. and Fitzpatrick, E.W.H. (2002) Helicopter Test and Evaluation, AIAA Education Series, ISBN13: 978-1563475788. Gessow, A. and Myers, G. (1952) Aerodynamics of the Helicopter, Ungar. Johnson, W. (1994) Helicopter Theory, Dover Publications, ISBN: 0486682307. Padfield, G.D. (2007) Helicopter Flight Dynamics The Theory and Application of Flying Qualities and Simulation Modeling, AIAA Education Series, 2nd edn, Blackwell Science Ltd, ISBN13: 978-1-56347-920-5. Newman, S. (1994) Foundations of Helicopter Flight, Heinemann Butterworth, ISBN 13: 978-0-340-58702-7. Seddon, J. and Newman, S. (2001) Basic Helicopter Aerodynamics, AIAA Education Series, 2nd edn, Published by Blackwell Science Ltd, ISBN 13: 978-1-56347-510-8. Stepniewski, W.Z. and Keys, C.N. (1984) Rotary-Wing Aerodynamics, Dover Publications, ISBN: 0486646475.