Patent ID: 12197218

DETAILED DESCRIPTION OF EMBODIMENTS

Embodiments of the system and method disclosed herein mitigate blade supersonic airflow and RBS and permit rotorcraft operation at significantly higher velocity than conventional rotorcraft. Control of these aerodynamic limitations allows the rotorcraft to take off at higher weight as a greater RPM can be applied at low horizontal velocities with less concern for higher rotor velocities as the rotorcraft accelerates.

Conventional helicopters incorporate two mechanical systems that enable variations in rotor RPM and individual blade pitch angle control. These are the liquid fuel engine (gas turbine or internal combustion) with its associated transmission and the swashplate. Due to direct mechanical coupling from the transmission, any variation in main rotor RPM will cause a change in lift that will result in a climb or descent unless a change of blade AOA is applied. A change of RPM of the tail rotor will also cause a change in tail rotor thrust causing a yaw on the airframe unless compensating flight control input is applied. Operating the engine at a non-optimal velocity will also impact fuel flow and the capacity to manage rotor droop when the rotorcraft is subjected to aerodynamic loads such as applying incidence to the airframe.

Referring now toFIG.1, there is shown a rotorcraft, in this example a helicopter100with a fuselage102, landing skid104, a tail section106, an auxiliary thruster108, and a rotorcraft lift and thrust system comprising: one or more electronically controlled electric motors112coupled to counter-rotating first and second rotors, lower rotor118and upper rotor120, through rotor hubs122,124. The lower rotor118comprises a plurality of blades126coupled to rotor hub122and the upper rotor120comprises a plurality of blades128. The counter-rotating lower rotor118and upper rotor120can be independently controlled by the one or more electric motors112.

A plurality of electronically controlled actuators130,132are operatively coupled to the hubs122,124and to the blades of the lower and upper rotors126,128and are arranged to control blade pitch (or blade AOA). In the example ofFIG.1, each blade is controlled by a respective actuator, providing individual blade control (IBC).

A plurality of sensors (not shown) are located across the rotorcraft100and are arranged to measure rotorcraft air velocity, rotor hub angular velocity and other environmental parameters, such as external air temperature and rotorcraft altitude.

A control module134is located on-board the helicopter100and arranged to monitor velocity data received from the plurality of sensors, analyse the received data and generate at least one or more actuation signals. The control module, by using the received data, calculates air velocity over the plurality of blades; continuously analyse the received data; and generates, based on the analysis, one or more actuation signals to control the electric motors112and the actuators130,132in a manner such that lift is maintained. In addition, actuation signals can be generated to increase thrust and effectively improve the maximum air velocity and payload of the helicopter100.

Additional thrust can also be provided for the rotorcraft by auxiliary thruster108controlled by the control module134.

A variable velocity mechanical gearbox has been used in the art to control main rotor RPM and tail rotor RPM (where fitted). However, in this disclosure one or more electrically controlled electric motors112are used to obtain precise RPM control. The electric motors112offer rapid response to signals received by the control module134.

In the example described, high-velocity axial flux electric motors rotate the rotor hubs122,124. The motor is mounted directly adjacent to the rotor hubs122,124. The motors112are scalable and stackable enabling rapid power change by adding additional motors as needed. The motor used has: max RPM1500, motor Length (mm) 60, mass (kg) 14.3, Nominal power 20-25 kW @1000 RPM, peak power 45 kW@1000 RPM, peak torque (Nm) 430 Nm, continuous Torque (Nm) 191 Nm@1000 RPM. Those skilled in the art will appreciate that alternative motors may be used in accordance with the invention.

By using electronic control of the blade AOA for each blade126,128, the control module134can implement a virtual swashplate that can substitute the conventional swashplate. The individual blade AOA is electronically controlled in real-time for each blade126,128. For retreating blades this will reduce the likelihood of RBS. For advancing blades, individual blade angle control will allow lift to be maintained, increased or decreased and allow for increased maximum air velocity.

The control module134can allow maintaining roughly the same airflow across the advancing rotor blades by adjusting rotor RPM commensurate with net resultant airflow over the helicopter100. The faster the helicopter100flies the slower the RPM of the rotor hubs.

When the control module134calculates the reduction in RPM to maintain equilibrium, it considers the advancing hemisphere of the lower and upper rotors118,120, which is producing more lift, and the retreating hemisphere of the lower and upper rotors118,120, which is producing less lift.

Often when using a conventional swashplate design, the blade angle on the retreating blade will be higher than that of the advancing blade providing roughly the same amount of lift on the advancing side as is generated on the retreating side. This will ensure the helicopter remains in balanced flight.

Rotor RPM reduction will, however, cause retreating blades to approach the critical angle sooner. The control system134reduces the AOA accordingly on retreating blades to prevent retreating blades reaching the critical angle.

Blade pitch angle control is achieved by using electrically powered actuators130,132, which can be linear or rotary linear power transducers, actuators, torque motors or similar devices. Each rotor blade126,128has at least one actuator, torque motor, servo device or similar device (electrical, hydraulic or pneumatic powered) configured to individually control blade pitch.

The actuators130,132have a very fast cycling rate commensurate with the rotational RPM of the rotors118,120. For a 1200 RPM hub rotation the actuator operates at a frequency of 20 Hz. Each actuator is programmed to use variable throw (rotation or displacement) and variable rate to control different blade angle positions throughout each cycle or hub rotation. This allows different blade angles to be generated depending on the rotational position of the blades126,128. Advancing blades can have high angles of attack while retreating blades can have lower, zero or even negative AOA to prevent RBS. A force of about 90N is sufficient to rotate the blades126,128in flight. The actuators130,132can operate up to about 35 Hz. These actuators in conjunction with the axial flux drive motors will allow over velocity rotation of the rotor hub allowing much greater payload capacity.

To provide a simple understanding of the forces under consideration, the lift generated by the rotating blade can be resolved into two vectors. These are the vertical component which represents the lift to counter gravity and a horizontal component which represents thrust and is an accelerative force on the helicopter100.

As a helicopter accelerates the velocity of air over an advancing rotor blade increases and the vertical component that is the lift generated increases. The retreating blade generates less lift as the velocity of air over these blades is less. The lift equation shows the velocity is a squared relationship so when the resultant lift for the advancing and for the retreating blade is combined the overall effect is an increase in lift as the rotorcraft increases velocity.

For existing helicopters, to keep the vertical component of lift in equilibrium so the helicopter does not climb, less lift from the rotor system as a whole is required. Blade AOA considered mostly as collective is therefore reduced.

Rather than allowing the increase in velocity to be the determinant of lift requiring a subsequent reduction in blade angle, the control module134reduces the RPM of the rotor hubs122,124to values which maintain a similar net velocity of air over the blade. Assuming that the net airflow across the blade remains the same, the same amount of lift and thrust will be generated. Any desired increase in thrust or lift is achieved by increasing AOA primarily on advancing blades only. The control module134ensures that to ensure no transonic or supersonic airflow across the blade can occur.
VTip Velocity+VRotorcraft≈Constant

Once RPM reduction has been applied, the advancing blade should not encounter high velocity blade effects. The faster the helicopter100flies the lower the RPM of the rotor hubs122,124. The resultant net airflow over the retreating blade will only ever be equal to or less than the net airflow over the retreating blade.

Approach to retreating blade critical angle can be further reduced or eliminated by reducing the AOA on the retreating blade. As the helicopter100accelerates the control module134will reduce the retreating blade angle toward zero (or lower due to blade twist) to completely eliminate RBS. Given that L=CL*½ ρ V2S and knowing the performance lift drag curve for the blade, the number of degrees of retreating blade angle reduction is readily calculated.

Any loss of lift resulting from the reduction of RPM on the retreating blade on one rotor is applied to the other rotor by increasing the advancing blade angle to provide lift compensation.

As an alternative to that described in the net airflow method, lift compensation can also be achieved by holding RPM rotation higher and retreating blade angle below the critical angle hence generating additional lift on the advancing blades.

Referring now toFIG.2, there is shown, a schematic block diagram200of the rotorcraft system. The diagram200shows the control module202in the centre. The control module202comprises a processing unit204connected to the plurality of sensors206,208,210via a high-velocity communication link. The processing unit204is also connected to the blade actuators controllers212, the electric motor controller214, and auxiliary thrust controller216through a high-velocity communication link.

The plurality of sensors is such that helicopter100air velocity, rotor hub angular velocity and environmental data such as air temperature, pressure and wind velocity, are continuously streamed to the control module202via the high-velocity communication bus and the processing unit so that data can be analysed, and control actuation signals can be sent to the electric motor(s) or the actuators in real time.

The control module202comprises a memory unit218operatively coupled to the processing unit204. The memory unit comprises instructions suitable to generate, based on the helicopter100air velocity, rotor hub angular velocity and environmental data, at least one or more actuation signals to control the electric motor(s) or the actuators in a manner such that lift is maintained.

Static data which describe the physical attributes of the blade such as blade length as well as that of the rotorcraft are incorporated. Sensors which detect rotorcraft flight dynamics, flight control output from linkages or autopilot systems, rotor RPM, blade pitch angle, blade performance data and net resultant airflow will also be blended into the calculation. Atmospheric parameters such as density altitude can also be included. Data related to each specific rotorcraft can be accessed by the processing unit204through data libraries220.

By knowing the net airflow across the blade derived from wind velocity and rotorcraft velocity, the processing unit calculates an RPM to maintain a tip velocity well below transonic velocities.

As the helicopter100accelerates, roughly the same airflow across is maintained over the advancing rotor blades by reducing the RPM of the rotors commensurate with the increasing net resultant airflow over the helicopter100. This will eliminate high velocity effects on the advancing rotor blade.

Advance ratio (μ) provides a representative value of airflow over the retreating blade and is given by the formula μ=VFreestream/ωR. Rotor blade radius is represented by R and ω (omega) is the rotor angular velocity given in radians per second. When μ=1 there is no airflow over that section of the blade. For any particular AOA, the reduction in velocity of the air over the retreating blade as the true air velocity increases will cause the blade section to move closer to the critical angle.

When the advance ratio exceeds 0.7 RBS can occur. The control module202calculates μ for the current blade AOA of the retreating blade. If μ moves above 0.5, a buffer amount below 0.7, the blade angle is reduced.

The frequency of the sampling will be determined by the length of the rotor blades. The shorter the blades the more often the calculation will be required

A typical value for a 3 m rotor blade would be 10 Hz, once per revolution. Trend rate would be determined based on change of VFreestream. If ΔVFreestreamis 0 no further calculation is required. If VFreestreamis >0 and μ becomes higher than 0.5 a reduction of retreating blade angle will be applied. The amount of blade angle reduction will be proportional to ΔVFreestream. A small increase in VFreestream, for example 20 kts, would require a 0.1 degree reduction in blade angle. A larger increase in VFreestream, for example 50 kts, would require a 0.5 degree reduction in blade angle.

The control module202will then recalculate μ at the new AOA. If μ trends below 0.4, the blade angle will be progressively increased.

Advance ratio is then modified from
μ1=(VFreestream/ωR)
to
μ2=VFreestream/ωNr reductionR*(reduced blade angle factor)

The combination of RPM reduction and advance ratio control in this fashion will eliminate both high velocity and RBS limitations ensuring the rotorcraft can accelerate well in excess of the velocity of any comparable conventional rotorcraft.

RPM is reduced as net airflow increases to maintain near constant airflow across all blades. The net rotorcraft lift L is given by summing the lift for each rotor blade:
L=(CL½ρV2S)Blade 1+ . . . +(CL½ρV2S)Blade n

When the rotorcraft velocity is zero:
Lrotorcraft stationary=CL½ρV2rotorcraft stationaryS

As the rotorcraft accelerates the formulae become:
Lrotorcraft moving=CL½ρV2rotorcraft movingS andLNr reduction=CL½ρV2Nr reductionS
giving:
LNr reduction=Lrotorcraft moving−Lrotorcraft stationaryorLNr red′n=Lvelocity>0−Lvelocity=0
and subsequent Nr.

L is a calculus value determined by incrementally summing L for all blade sections. L can also be read from pre-determined blade property tables for the blade for any given blade AOA. VNr reductionrepresents the relationship between Vrotorcraft movingand Vrotorcraft stationary

Once L has been determined VNr reductionis calculated. This process will generate the same value of net lift L regardless of rotorcraft velocity.

The value calculated can be instantaneously verified by control module202. The control module202will sense vertical acceleration and should be zero once VNr reductionhas been applied. Buffers, bias and filters can be applied to ensure the granularity of the calculation is not so fine that excessive calculation beyond realistic and reasonable variations in air velocity occur.

Depending on the mission requirement and rotorcraft configuration the control module202can commence applying an RPM reduction to the rotors as soon as sensors detect helicopter movement, or once wind velocity over the helicopter is detected. Alternatively, the application of rotor hub RPM control can be delayed until the helicopter approaches its nominal limit velocity or at any velocity in between.

Approach to RBS can be further reduced or eliminated by reducing the AOA on the retreating blade as the rotorcraft accelerates. The control module202reduces the retreating blade angle toward zero to completely eliminate RBS. Given that L=CL ½ ρ V2 S and knowing the performance lift drag curve for the blade, the number of degrees of retreating blade angle reduction is readily calculated.

For the retreating blade:

Blade⁢⁢Angle⁢⁢(BA)=⁢Blade⁢⁢Angle⁢⁢Longitudinal⁢⁢(BALon)⁢+Blade⁢⁢Angle⁢⁢Lateral⁢⁢(BALat)⁢-Blade⁢⁢Angle⁢⁢Reduction⁢retreating⁢⁢blade

As velocity increases, un-stalling a blade can be achieved by driving the retreating blade to:
Blade Angle (BA)=0

When reducing retreating blade angle, it may be appropriate to increase the lift on one or more advancing blades to maintain the same net lift.

Knowing the loss of lift from the lower value of V and the loss of CLfor the retreating blade, the control module202will calculate the advancing blade angle change that will provide the same total L as was achieved prior to the RPM reduction and retreating blade angle reduction. Compensating lift is applied only to the advancing blades by increasing the AOA on those blades. The compensation would normally be applied to the alternate rotor disk advancing blades. This arrangement will keep the entire system balanced:
Lift Compensation=Lift lost from retreating blade due to AOA reduction+Lift lost from retreating blade dueNrreduction+Lift lost from advancing blade dueNrreduction.

For the advancing blade:
Blade Angle (BA)=Blade Angle Longitudinal (BALon)+Blade Angle Lateral (BALat)+Lift Compensationadvancing blade

Lift compensation for reduction in total lift of the retreating blades as retreating blade angle is reduced might also be achieved by holding Nrslightly higher than the nominal value computed by control module202.

Differential application of advancing blade AOA between the first and second rotor hub will enable pitch and roll control.

Vortex Ring State

Vortex ring state (VRS) occurs when a rotorcraft is at low velocity and tip vortices increase to the degree that lift is lost on the aerofoil. This state usually occurs when the rotorcraft is in a descent that increases the upflow of air through the rotor disks. A reduction of lift occurs as the tip vortices increase. This loss of lift is further amplified at the rotor hub as the low velocity of the blade combined with the increased upflow can cause that section of the blade to stall. As a result, the rotorcraft rate of descent will increase to a point where ground impact becomes inevitable.

It is assumed that the maximum all-up weight (AUW) to hover or descend and land will be limited by the power available and density altitude. When encountering VRS applying additional collective will increase the effect and there will only be a limited time before maximum power is demanded.

The system disclosed herein can mitigate or eliminate adverse aerodynamic flight vulnerabilities such as vortex ring state (VRS) and settling with power. A combination of dynamic RPM control in concert with IBC can change the airflow over the rotor blade once VRS is detected. A burst increase in RPM, significantly higher than the comparable lift capable of being generated by a conventional rotorcraft operating at low velocity, preceded by or combined with a reduction in blade pitch AOA will allow the rotorcraft to fly free of the VRS.

Once VRS is identified the control module202will use IBC to simultaneously decrease blade pitch angle and rapidly increase Nrto generate additional short-term lift to fly clear of the VRS condition.

Longitudinal Cyclic Pitch Control:

To move the rotorcraft forward, the angle of the rotors is tilted downward. The greater the forward pitch demand is, the lower the blade angle. To achieve this, the maximum blade angle decrement is applied at a position some time before the position of maximum rotors tilt. This position is given by the advance angle.

Once the amount of pitch change required has been determined by measuring the cyclic longitudinal control displacement or obtaining an electronic value adjusted for phase lag, the maximum and minimum blade angle changes can be calculated.

To emulate a mechanical swashplate the control module202calculates the rise and fall values for the blade to smoothly transition from maximum to minimum blade disk changes at θ=0 and θ=180. Phase lag must also be considered.

The basic formula used is, For θ0360:
Blade Angle Longitudinal (BALon)=Blade Angle in hover (BAH)−cos θ*(Blade Angle θ0−Blade Angle θAdvance Angle)+Density Altitude (DA) compensation.

Note that for rotation clockwise use Blade Angle θ0−Blade Angle θAdvance Angle, for rotation anticlockwise use Blade Angle θ0+Blade Angle θAdvance Angle.

Note that Blade Angle θ0will be less than Blade Angle in hover (BAH), i.e., a negative value for forward flight.

Note that Blade Angle θ0−Blade Angle θAdvance Angleis the maximum blade angle deviation in the longitudinal sense for any and every revolution.

Blade Angle in hover (BAH) is a pure Collective value.

Lateral Cyclic Roll Control:

To roll the rotorcraft, the angle of the rotor disk is tilted left or right. To achieve this the blade angle is decreased on the side the rotorcraft is rolling toward. Before considering phase lag, the lowest blade angle is at θ=90. The highest blade angle will be at θ=270.

The greater the roll demand is, the lower the blade angle will be.

The basic formula for lateral blade angle (roll) is, for θ0360:
Blade Angle Lateral (BAlat)=Blade Angle in hover (BAH)−cos θ(Blade Angle θ90−Blade Angle θAdvance Angle)+Density Altitude (DA) compensation

Note that for rotation clockwise use Blade Angle θ90−Blade Angle θAdvance Angle, for rotation anticlockwise use Blade Angle θ270+Blade Angle θAdvance Angle.

Note that Blade Angle θ90−Blade Angle θAdvance Angleis the maximum blade angle deviation in the lateral sense for any and every revolution.

Blade Angle in hover (BAH) is a pure Collective value

Full cyclic control can be accomplished by adding longitudinal cyclic pitch control and lateral cyclic roll control:
Blade Angle (BA)=Blade Angle Longitudinal (BALon)+Blade Angle Lateral (Balata)

FIG.3is a flow diagram300of a method for controlling a helicopter100using the system shown inFIG.1. The first step (302) requires the control module to receive air velocity data, first and second rotors rotational angular velocity data, external air temperature data and rotorcraft altitude data by the control module. Subsequently, using the received data, the air velocity over the plurality of blades is calculated (304). This allows the control module to establish whether one or more retreating blades of one of the first and second counterrotating rotors are generating insufficient lift and to calculate the amount of insufficient lift based on the following equation (306):
E=L+[cρR(3u−v)(v2−3vu+3u2)/6(v−u)]

Finally, one or more actuation signals are sent from the control module to the electric motor and/or actuators of the other one of the first and second counterrotating rotors to compensate for the insufficient lift (308).

Flight conditions that can generate loss of lift include blade critical velocity or a rotorcraft lift imbalance. For example, the blade critical velocity condition may be an RBS velocity or an advancing blade supersonic airflow.

Detailed Analysis of Rotorcraft Lift

Referring now toFIGS.4to6, there are shown a number of diagrams with lift and speed performance calculated using the standard and modified lift equation discussed in the sections above. These results do not account for any additional thruster, but just thrust generated by rotors.

Starting from the lift equations, since the helicopter rotor speed Ω is dependent on u, the time interval required to consider one revolution is also dependent on u. Therefore, for the standard lift equation the average value over one particular revolution with the alternative integral:

⁢Lstd,T⁡(u)=12⁢π⁢∫02⁢π⁢∫0R⁢12⁢ρ⁢⁢c⁡(v-uR⁢r+u⁢⁢cos⁡(θ))2⁢CL⁢drd⁢⁢θ.⁢Lmax,T=12⁢π⁢∫02⁢π⁢∫0R⁢max⁡(12⁢ρ⁢⁢c⁡(v-uR⁢r+u⁢⁢cos⁡(θ))⁢v-uR⁢r+u⁢⁢cos⁡(θ)⁢CL,0)⁢drd⁢⁢θ.

u is the forward velocity of the rotorcraft,

c is the chord length of the blades,

θ is the Azimuth angle of the blade along the rotor disk (Ωt),

ρ is the air density,

R is the blade radius, r is a point along the blade,

v is the speed of the blade(s) tip of the rotors.

FIG.4(a), shows that the models produce similar average lifts for low forward velocity as the effect of dissymmetry of lift is at its lowest influence. As the forward velocity increases, the lift produced by the blade decreases as the rotor speed must decrease. Once the negative lift is produced by the retreating blade at u=v/3 the lift from the standard and modified model diverge. The standard model increases lift as the forward velocity remains non-negative, this model does not take into account the RBS and therefore isn't realistic. However, The lift for the standard and modified model diverge.

For the modified model (center line), the overall lift decreases as the negative lift on the retreating blades counteract the positive lift produced by the advancing sides. If the angle of attack can be set to 0, the negative effect of the retreating blade diminishes, and the lost lift begins to recover. Since the retreating side of the rotor disk cannot produce any positive lift for velocities above 114.3 ms−1, only coaxial helicopters are able to rectify the issue. We also note the lift produced in these velocities varies between 50%-75% of the lift generated in static hover. This is primarily a consequence of the decreased rotor speed as u increases.

FIG.4(b)shows plots of the minimum for various weights with the theoretical maximum against forward velocity. The minimum threshold for Ω decreases as forward velocity u increases. While this allows the rotor disk to spin at a lower RPM, the maximum threshold imposed by Equation (1) decreases at a faster rate. The maximum speed limit is given by:

uM⁡(L)=v4+3⁢⁢Rc⁢⁢ρ⁡(3⁢Rc⁢⁢ρ⁢⁢v2-32⁢L)4⁢Rc⁢⁢ρ

FIG.4(c)shows the maximum speed uMagainst lift L for several blade lengths. If the forward velocity of a helicopter should exceed this limit (if u>uM), the rotor angular velocity must decrease and the lift produced will not be sufficient to maintain altitude. To compensate for this, other methods for producing lift will be necessary, such as wings or a modified fuselage shape.

FIG.4(d)shows a plot of the average lift over the advancing half of the helicopter rotor disk against forward velocity for the minimum values for required to maintain altitude for 1000 kg, 2000 kg and 3000 kg helicopters. As the forward velocity increases it reaches the maximum allowable limit uM, at which point the lift generated coincides with the lift obtained by the maximal rotor angular velocity.

FIG.5(a)shows the average lift over the advancing half of the helicopter rotor disk against forward velocity for several angles of attack. Lower angles of attack predictably produce less lift up to the stall threshold AOA≅10°. When the angle of attack exceeds this limit, the lift begins to decrease, as expected with retreating blade stall.

The lift generated on the retreating side of the rotor disk can be calculated as:

Lret⁡(u)=1π⁢∫π23⁢π2⁢∫0R⁢12⁢ρ⁢⁢c⁡(Ω⁢⁢r+u⁢⁢cos⁡(θ))⁢Ω⁢⁢r+u⁢⁢cos⁡(θ)⁢drd⁢⁢θ

The retreating side continues to build negative lift as forward velocity increases. The Inventors found that, for coaxial helicopters, the lift increase from the advancing side is sufficient to compensate the lift loss on the retreating side so that improved speed performance can be achieved by active electronic control of RPM and AOA.

FIGS.5(b) and5(c)show the lift coefficient and the difference between lift and drag against angle of attack and the average lift over the advancing half of the helicopter rotor disk against forward velocity for several angles of attack.

Angle of Attack Considerations for Coaxial Helicopters

In this section, we relax this assumption to derive conditions on the coefficient of lift that will enable lift to be generated equally across the rotor disk. For low forward velocities, the following formula can be applied:

CL⁡(θ)=LLstd⁡(u,θ),
where Lstd(u;θ) is the lift generated by the blade at forward velocity u and azimuth angle θ given by

Lstd⁡(u,θ)=ρ⁢⁢c6⁢Ω⁡[(Ω⁢⁢R+u⁢⁢cos⁡(θ))2⁢Ω⁢⁢R+u⁢⁢cos⁡(θ)-u3⁢cos2⁡(θ)⁢cos⁡(θ)]
This expression remains valid until the lift generated on the retreating blade is no longer capable of producing sufficient lift. That is, the first threshold is the forward velocity u1such that
Lstd(u1,π)=L.

FIG.5(d)shows the average lift over the retreating half of the helicopter rotor disk against forward velocity for different weights.

Assuming the rotor angular velocity is at its maximum as shown by equation (1), we may simplify the above equation to show u1satisfies

u13-43⁢vu12-23⁢(v2+Lρ⁢⁢cR)⁢u1-v9⁢(v2-6⁢Lρ⁢⁢cR)=0.
For velocities u>u1, the angle of attack on the retreating blades can be set to maximum and increase the angle of attack on the counterpart advancing blade to compensate the insufficient lift generation.
Lift Compensation for Retreating Blades

As the forward velocity u increases above the first threshold u1defined above, we must produce excess lift on the advancing blades to compensate the lack of lift produced on the retreating blades. Suppose each blade must generate L lift. If u<u1, Lstd(u; π)<L. Therefore, the excess lift E that the advancing blades must produce is given by:
E=L−Lstd(u,π)

FIG.6(a)shows that the advancing blade is capable of sustaining lift if the angle of attack can decrease lift on the retreating blades, as the lift on the advancing blade increases as forward velocity increases.

FIG.6(b)shows a plot of the average lift over the retreating half of the helicopter rotor disk against forward velocity.

The lift compensation E that the advancing blade must produce for its counterpart retreating blade. The curves inFIG.6(b)are proportional to the maximum lift produced with zero vertical velocity. The highest weight the rotorcraft may attain. Negative values indicate the retreating blade is producing sufficient lift and compensation is not necessary. As the forward velocity increases, the critical values E(u)=0 coincide with u1(L) are found.

The lift compensation required also increases up to the critical value v/3. Therefore, in the case that u>u1(L), the coefficient of lift will take the form:

CL⁡(θ)={2⁢L-min⁡(LLstd⁡(u,θ+π),1)⁢Lstd⁡(u,θ+π)Lstd⁡(u,θ)θ∈[0,π2]⋃[3⁢π2,2⁢π]min⁡(LLstd⁡(u,θ),1)θ∈[π2,3⁢π2]

Although the invention has been described with reference to a preferred embodiment, it will be appreciated by persons skilled in the art that the invention may be embodied in many other forms. It will be appreciated by persons skilled in the art that numerous variations and/or modifications may be made to the technology as shown in the specific embodiments without departing from the spirit or scope of technology as broadly described. The present embodiments are, therefore, to be considered in all respects as illustrative and not restrictive.

Throughout this specification, unless the context clearly requires otherwise, the word “comprise”, or variations such as “comprises” or “comprising”, will be understood to imply the inclusion of a stated element, integer or step, or group of elements, integers or steps, but not the exclusion of any other element, integer or step, or group of elements, integers or steps.

Any discussion of documents, acts, materials, devices, articles or the like which has been included in the present specification is solely for the purpose of providing a context for the present invention. It is not to be taken as an admission that any or all these matters form part of the prior art base or were common general knowledge in the field relevant to the present invention as it existed before the priority date of each claim of this specification.