16-helicopter performance 2008 - ulisboa · helicopters /filipe szolnoky cunha helicopter...
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Helicopters / Filipe Szolnoky CunhaSlide 1Helicopter Performance
Helicopter Performance
• Performance
– Estimation of the installed engine power require for a
given flight operation
– Determination of the maximum level flight speed
– Estimation of the endurance/range
– Since the ability of the helicopter is to hover, this
operation is more important than all the other factors
• Maximum altitude it can hover (in or out of ground effect)
Helicopters / Filipe Szolnoky CunhaSlide 2Helicopter Performance
Helicopter Performance
• Economic Performance
– Operation cost (hourly based)
• Fuel consumed
• Parts worn
• Maintenance cost
– Payload
– For military machines economics may not be the
overriding concern
Helicopters / Filipe Szolnoky CunhaSlide 3Helicopter Performance
Helicopter Performance
• Tactical performance (Manoeuvrability)
– Maximum load factor
– Tail rotor power
• Yawing ability
• Crosswind ability
– Range of CM positions
– Underslung weight
Helicopters / Filipe Szolnoky CunhaSlide 4Helicopter Performance
Helicopter Performance
• Safety
– Operating the helicopter outside its designed
performance envelope may result in excessive
stresses.
– The limits of the performance envelope must then be
established and made available to the operator
– Safety under abnormal situations is also important:
• Autorotation performance (engine power loss)
• Twin engine operation with one engine inoperative
• Operations under icing conditions
Helicopters / Filipe Szolnoky CunhaSlide 5Helicopter Performance
Hover Performance
• In hover T=W and the power estimation is:
• Notes:
– Valid for rectangular blade
– Hover power is a function of:
• Helicopter weight
• Air density
Helicopters / Filipe Szolnoky CunhaSlide 6Helicopter Performance
Hover Performance
• To standardise the air density (ICAO/ICAN):
• Values for a standard day:
– Temperature 15º C
– Barometric pressure 1013.3milibar (=101.3N/m2)
– Density 1.225Kg/m3
• Now we need the variation of these parameters with height (h)
Helicopters / Filipe Szolnoky CunhaSlide 7Helicopter Performance
Hover Performance
• In the lower atmosphere where helicopters
normally fly (below 6000m) the standard value of
the air density can be closely approximated by
the equation:
• With h expressed in meters and ρ0=1.225kg/m3.
Helicopters / Filipe Szolnoky CunhaSlide 8Helicopter Performance
Hover Performance
• Up to 11km the pressure p and temperature T´ are
related by:
• Where a standard lapse rate dT´/dh is 6.51º per
km of altitude. R* is the Universal Gas Constant.
• The temperature in the standard atmosphere is a
linearly decreasing function of altitude and can
be expressed by:
Helicopters / Filipe Szolnoky CunhaSlide 9Helicopter Performance
Hover Performance
• Integrating the previous differential equation gives the relation between temperature and pressure :
– With
• hp (pressure altitude) in meters
• 0 indicating sea level
Helicopters / Filipe Szolnoky CunhaSlide 10Helicopter Performance
Hover Performance
• The relation between altitude and density is given
by:
• With
– hρ (density altitude) in meters
– 0 indicating sea level
Helicopters / Filipe Szolnoky CunhaSlide 11Helicopter Performance
Hover Performance
• The previous expressions are obtained with the
temperature varying with altitude according the
expression:
• And therefore the pressure altitude is the same as
the density altitude
Helicopters / Filipe Szolnoky CunhaSlide 12Helicopter Performance
Hover Performance
• If not then we must correct for the non standard
temperature:
• As a rule of the thumb, density altitude exceeds
pressure altitude by 9.14m per ºC that the
temperature exceeds the standard value
Helicopters / Filipe Szolnoky CunhaSlide 13Helicopter Performance
Hover Performance
13% increase
Helicopters / Filipe Szolnoky CunhaSlide 14Helicopter Performance
Hover Performance
• Variation with altitude:
– FM can be considered as non-varying
– k can be considered as non-varying
– Engine power will decrease
• Reciprocating engine: A good approximation of this
variation is
• Turboshaft engine: A more complicated relationship but:
Helicopters / Filipe Szolnoky CunhaSlide 15Helicopter Performance
Hover Performance
Helicopters / Filipe Szolnoky CunhaSlide 16Helicopter Performance
Climb Performance
• We have seen that the induced velocity at a climb
velocity of Vc is:
• Remembering that:
For low rates of climb
Helicopters / Filipe Szolnoky CunhaSlide 17Helicopter Performance
Climb Performance
• The velocity VC can be obtained from the
relation:
• And we can writeFor low rates of climb
Helicopters / Filipe Szolnoky CunhaSlide 18Helicopter Performance
Climb Performance
Helicopters / Filipe Szolnoky CunhaSlide 19Helicopter Performance
Forward Flight Performance
• Forces acting on the helicopter:
Helicopters / Filipe Szolnoky CunhaSlide 20Helicopter Performance
Forward Flight Performance
• The power necessary for the helicopter in
forward flight can be written as:
• With:
– Pi the induced power
– P0 the profile power
– Pp the parasite power
– Pc the climb power
• Note that we should also add the Tail Rotor power
Helicopters / Filipe Szolnoky CunhaSlide 21Helicopter Performance
Forward Flight Performance
• Lets consider that the flight path angle θFP is
small:
• And the vertical equilibrium:
Tcos(αTPP-θFP)=W ≈T
Vc=V∞ θFT
Helicopters / Filipe Szolnoky CunhaSlide 22Helicopter Performance
Forward Flight Performance
• For the horizontal equilibrium:
Tsin(αTPP-θFP)=DFPcos θFP
• Assuming DFP independent of θFP, the last
equation can be written as:
T(αTPP-θFP)=Df or
Helicopters / Filipe Szolnoky CunhaSlide 23Helicopter Performance
Forward Flight Performance
• The power necessary to perform this manoeuvre:
• WVC is the Climb power PC
– And we can write:
Helicopters / Filipe Szolnoky CunhaSlide 24Helicopter Performance
Forward Flight Performance
• DfV∞ is the parasite power Pp
– And we can write:
• Sref is a reference area
• CDfis the fuselage drag coefficient based on Sref
• Therefore:
• Since Defining
Helicopters / Filipe Szolnoky CunhaSlide 25Helicopter Performance
Forward Flight Performance
• f is the “equivalent wetted area” or “equivalent
flat plate area”
• We can then write
• Typical values of f :
– Small helicopters 0.93m2
– Large utility helicopters 4.65m2
Helicopters / Filipe Szolnoky CunhaSlide 26Helicopter Performance
Forward Flight Performance
• We have already seen that for sufficiently high
forward velocity µ>0.1 the induced velocity can
be approximated by the asymptotic result:
• Also remember that
Large µ
Helicopters / Filipe Szolnoky CunhaSlide 27Helicopter Performance
Forward Flight Performance
• Using the BET the profile power can be
calculated using:
• If the radial component is taken into account:
• And CP0can be obtained by numerical methods.
• Neglecting the radial component of U
Helicopters / Filipe Szolnoky CunhaSlide 28Helicopter Performance
Forward Flight Performance
• An analytical expression of CP0can be obtained
• The results from Glauert and Bennet show that
the following approximation can be made:
• Where K varies from 4.5 at hover to 5 at µ=0.5.
In practice a single average value is used (4.6-
4.7)
Helicopters / Filipe Szolnoky CunhaSlide 29Helicopter Performance
• These results underpredicts the experimental
values because several assumptions were made.
• Among them:
– No compressibility effects were introduced
Forward Flight Performance
Helicopters / Filipe Szolnoky CunhaSlide 30Helicopter Performance
Forward Flight Performance
• Drag Divergence at a fixed alpha or Cl
• Drag rise due to formation of shock waves on the
advancing side, near the tip.
• Mdd: Mach number at which drag rises at the rate of 0.1
per unit Mach number. Curve slope=0.1.
M
Drag Divergence Mach No, Mdd
Cd
Helicopters / Filipe Szolnoky CunhaSlide 31Helicopter Performance
Forward Flight Performance
• The compressibility effects can be introduced
using the following estimation (Gessow and
Crim):
• Mdd is the drag divergence Mach number
Helicopters / Filipe Szolnoky CunhaSlide 32Helicopter Performance
Forward Flight Performance
• Another approach is suggested by Harris for
blades with different thickness-to-chord ratio:
• With
Helicopters / Filipe Szolnoky CunhaSlide 33Helicopter Performance
Forward Flight Performance
• With the introduction of these models the profile power
is overpredicted:
• This is essentially because there is a relaxation of the
compressibility effects at the edge of a lifting surface of
finite span.
– Approximations for the effect can be developed based on
transonic similarity rules
• The effect was first noticed in experiments on
propellers, which showed that losses in propulsion
efficiency did not occur until the tip Mach number well
exceeded the estimated 2D drag divergence number.
Helicopters / Filipe Szolnoky CunhaSlide 34Helicopter Performance
Forward Flight Performance
• Tip relief effects can be accounted for in the BET using
a effective local Mach number at each blade element in
the tip region that exceeds the drag divergence number:
• With:
– Mdd2 is the 2D drag divergence Mach number
– Mdd3 is the 3D drag divergence Mach number (with tip relief
that exceeds Mdd2 by 10-15%)
– ARblade is blade aspect ratio (R/c)
Helicopters / Filipe Szolnoky CunhaSlide 35Helicopter Performance
• Never the less there were still several
simplification introduced. Among them:
– Does do take into account the reverse flow region
• Remember the example in BET theory:
– Cd0is constant along the blade
• Not valid in separated region of the return blade. Assuming
double Cd0 in the reverse flow region
Forward Flight Performance
Helicopters / Filipe Szolnoky CunhaSlide 36Helicopter Performance
• Never the less there were still several
simplification introduced. Among them:
– No radial flow is included
• Including (numerically) can be approximated to:
– We could include reverse flow and radial flow
Forward Flight Performance
Helicopters / Filipe Szolnoky CunhaSlide 37Helicopter Performance
Forward Flight Performance
• Finally we can estimate the tail rotor power:
• The thrust can be smaller if the vertical tail
surface is used to create a side force.
• The interference between the main rotor and the
tail rotor can be accounted for using a induced
power factor kTR.
Helicopters / Filipe Szolnoky CunhaSlide 38Helicopter Performance
Forward Flight Performance
• Having calculate the necessary tail rotor thrust
the same procedure established for the main rotor
can be used for the tail rotor.
• Since the tail rotor requirements are relatively
low on a first estimation we can used that the
power for the tail rotor is a fraction of the main
rotor (typically 5 to 10%)
Helicopters / Filipe Szolnoky CunhaSlide 39Helicopter Performance
Forward Flight Performance
• The total power for the main rotor is therefore:
• Or for large values of µ:
Helicopters / Filipe Szolnoky CunhaSlide 40Helicopter Performance
Forward Flight Performance
Helicopters / Filipe Szolnoky CunhaSlide 41Helicopter Performance
Forward Flight Performance
Possible airspeeds
Helicopters / Filipe Szolnoky CunhaSlide 42Helicopter Performance
Forward Flight Performance
• We have seen that the necessary power is a
function of the helicopter gross weight:
Helicopters / Filipe Szolnoky CunhaSlide 43Helicopter Performance
Forward Flight Performance
• We also have seen that the necessary power is a
function of the air density (altitude):
Reduction of the power
available due to altitude
Helicopters / Filipe Szolnoky CunhaSlide 44Helicopter Performance
Lift to Drag ratio
• Remember that the rotor generates lift and
propulsion. The lift is:
L=TcosαTPP
• The effective drag can be calculated from the
power expended:
D=P/V∞
– If the calculation is for the rotor alone P=Pi+P0
– If the calculation is for the complete helicopter
P=Pi+P0+Pp+PTR
Helicopters / Filipe Szolnoky CunhaSlide 45Helicopter Performance
Lift to Drag ratio
• The Lift to Drag ratio can then be calculated:
– For the case of the rotor alone:
– For the case of the complete helicopter:
Helicopters / Filipe Szolnoky CunhaSlide 46Helicopter Performance
Forward Flight Performance
Helicopters / Filipe Szolnoky CunhaSlide 47Helicopter Performance
Climb Performance
• Rearranging the terms in the power equation we
can obtain:
Helicopters / Filipe Szolnoky CunhaSlide 48Helicopter Performance
Climb Performance
• It is realistic to assume that that for low rates of
climb (or descent) the rotor induced power, Pi,
the profile power P0, and the airframe drag D
remain nominally constant:
• Where Plevel is the power to maintain the same
situation without climb, that is at level flight.
Helicopters / Filipe Szolnoky CunhaSlide 49Helicopter Performance
Climb Performance
• To calculate the maximum climb velocity we just
have to substitute, in the last expression, P with
Pa which is the available power at that height
Helicopters / Filipe Szolnoky CunhaSlide 50Helicopter Performance
Climb Performance
Helicopters / Filipe Szolnoky CunhaSlide 51Helicopter Performance
Climb Performance
Helicopters / Filipe Szolnoky CunhaSlide 52Helicopter Performance
Important Forward Speeds
Helicopters / Filipe Szolnoky CunhaSlide 53Helicopter Performance
Speed for minimum power
• The maximum possible rate of climb is obtained
at the speed of minimum power in level flight.
– This is the Vmp velocity
• We have already established that:
• At lower airspeeds CP0is sufficiently small to be
neglected. Also consider that we have a level
flight. Then
Helicopters / Filipe Szolnoky CunhaSlide 54Helicopter Performance
Speed for minimum power
• To obtain the minimum power we differentiate
the previous expression in respect to µ:
• So the non-dimensional forward speed for
minimum power is:
Helicopters / Filipe Szolnoky CunhaSlide 55Helicopter Performance
• Recalling that :
• We can write
• The Vmp velocity is :
Speed for minimum power
Helicopters / Filipe Szolnoky CunhaSlide 56Helicopter Performance
Speed for minimum power
• Vmp is higher for:
– Higher W
– Lower ρ
• Higher Altitudes
• Higher Temperatures
• Vmp is also the speed at which the endurance is
higher
Helicopters / Filipe Szolnoky CunhaSlide 57Helicopter Performance
Endurance
• Generally it is sufficient accurate to estimate the
endurance by dividing the usable fuel on board
by the average fuel flow rate.
• A more precise estimation can be found using
(McCormick 1950):
• We will see the explanation of this equation
when we study the helicopter range:
Helicopters / Filipe Szolnoky CunhaSlide 58Helicopter Performance
Speed for maximum range
• Range: The distance an aircraft can fly for a
given takeoff weight and for a given amount of
fuel.
• This is obtained when the aircraft is operating at
the minimum P/V.
• Or it can be consider that it must operate a the
maximum V/P that is a the maximum L/D ratio
• This speed is called Vmr.
Helicopters / Filipe Szolnoky CunhaSlide 59Helicopter Performance
Important Forward Speeds
Helicopters / Filipe Szolnoky CunhaSlide 60Helicopter Performance
Speed for maximum range
• The ratio P/V can be approximated by CP/µ so
that:
• Differentiating to obtain the minimum:
Helicopters / Filipe Szolnoky CunhaSlide 61Helicopter Performance
Speed for maximum range
• Which gives:
• Or the velocity for maximum range Vmr:
• Vmr is higher for:
– Higher W
– Lower ρ
• Higher Altitudes
• Higher Temperatures
Helicopters / Filipe Szolnoky CunhaSlide 62Helicopter Performance
Range
• McCormick establish the basic analysis for an
aircraft, and this can be adapted for the
helicopter:
– The fuel flow rate in relation to the travelled distance
R´ is:
– Where :
• P is the power
• V the velocity
• SFC is the specific fuel consumption
Helicopters / Filipe Szolnoky CunhaSlide 63Helicopter Performance
Range
• The power required varies with gross weight anddensity
• The SFC varies with the power and density
• The following considerations have to be made:
– The Helicopter burns fuel during take-off, climb,descent and landing
– It must have a mandate fuel reserve
– As the fuel is burned the weight decreases
• For these reasons the previous expression mustbe integrated numerically to get the range
Helicopters / Filipe Szolnoky CunhaSlide 64Helicopter Performance
Range
• However the equation can be realistically
evaluated at a point in the cruise where the
helicopter weight is equal to the helicopter gross
take-off weight minus half of the initial fuel
weight. Therefore:
Helicopters / Filipe Szolnoky CunhaSlide 65Helicopter Performance
Range
Helicopters / Filipe Szolnoky CunhaSlide 66Helicopter Performance
Maximum forward velocity
• The maximum forward velocity will depend on:
– Installed engine power
– Gearbox (transmission) torque limits
– Rotor Stall
– Compressibility effects
– Aeroelastic and structural constrains
Helicopters / Filipe Szolnoky CunhaSlide 67Helicopter Performance
Maximum forward velocity
Helicopters / Filipe Szolnoky CunhaSlide 68Helicopter Performance
Co-Axial rotors
• Payne (1959) established a simple momentum study of
the co-axial helicopter:
• First assumption:
– Each rotor produces an equal amount of thrust, therefore the
total thrust is 2T
• Induced velocity:
• Induced power:
Helicopters / Filipe Szolnoky CunhaSlide 69Helicopter Performance
Co-Axial rotors
• If we take each rotor separately the inducedpower for each rotor is Tvi and the sum of the twois:
• Calculating the interference-induced power factor:
• Increase of 41% in the induced power
Helicopters / Filipe Szolnoky CunhaSlide 70Helicopter Performance
Performance
of coaxial helicopter
Helicopters / Filipe Szolnoky CunhaSlide 71Helicopter Performance
Tandem Rotors
• T1≠T2
• The induced power for each area is:
T2
T1
m(T1+T2)
Helicopters / Filipe Szolnoky CunhaSlide 72Helicopter Performance
Tandem Rotors
• The total induced power for the tandem rotor is:
• The total induced power for two independent
rotors is:
Helicopters / Filipe Szolnoky CunhaSlide 73Helicopter Performance
Tandem Rotor
• Harris suggest an approximation:
• Note that:
Helicopters / Filipe Szolnoky CunhaSlide 74Helicopter Performance
Tandem Rotor
Helicopters / Filipe Szolnoky CunhaSlide 75Helicopter Performance
Tandem Rotor
• It can be seen that even if the two rotors are
separated the power required for the rear rotor is
higher than the power required for the front rotor.
• This is caused by the fact that the rear rotor
operates at the slipstream of the front rotor.
• The total induced power can be calculated using:
Helicopters / Filipe Szolnoky CunhaSlide 76Helicopter Performance
Autorotation
• Definition:
– Self sustained rotation of the rotor without the
application of any shaft torque.
• The power to drive the rotor comes from the
relative airstream that passes through the rotor as
the helicopter descends.
• There is an energy balance between the decrease
of potential energy per unit time and the power
required to sustain the rotor speed.
Helicopters / Filipe Szolnoky CunhaSlide 77Helicopter Performance
Autorotation
• The pilot gives up altitude in a controlled manner
in return for energy necessary to turn the rotor
and produce thrust.
• The autorotation in low forward speeds takes
place in the turbulent wake state.
• At higher forward speeds the flow through the
rotor tends to be smoother in the autorotation
condition.
Helicopters / Filipe Szolnoky CunhaSlide 78Helicopter Performance
Autorotation
• Let's consider that there is no forward speed
during the autorotation manoeuvre.
• During autorotation the inflow angle must be
such that there is no in-plane force, and therefore
no contribution to the rotor torque
Therefore
Helicopters / Filipe Szolnoky CunhaSlide 79Helicopter Performance
Autorotation
• If we assume a uniform inflow over the disk:
• Over the inboard section is higher than over theoutboard section.
• So the driving force in the inboard section ishigher than in the outboard section
Helicopters / Filipe Szolnoky CunhaSlide 80Helicopter Performance
Autorotation
Inboard Outboard
Driving force>dD Driving force<dD
Helicopters / Filipe Szolnoky CunhaSlide 81Helicopter Performance
Autorotation
Helicopters / Filipe Szolnoky CunhaSlide 82Helicopter Performance
Autorotation
• The rotor will adjust its velocity (Ω) until the
equilibrium is obtained.
• This equilibrium is stable since:
– Increasing Ω will decrease and the driving region
will decrease inboard which will decrease Ω
– Decreasing Ω will increase and the driving region
will increase outboard which will increase Ω
• The fully established autorotative state is stable
• For a single section in equilibrium:
Helicopters / Filipe Szolnoky CunhaSlide 83Helicopter Performance
Autorotation
Helicopters / Filipe Szolnoky CunhaSlide 84Helicopter Performance
Autorotation in forward flight
Helicopters / Filipe Szolnoky CunhaSlide 85Helicopter Performance
Autorotation in forward flight
• In autorotation
• As a first approximation:
• Solving for λc
CQ=0
Helicopters / Filipe Szolnoky CunhaSlide 86Helicopter Performance
Autorotation in forward flight
Helicopters / Filipe Szolnoky CunhaSlide 87Helicopter Performance
Autorotative index
• The autorotative performance depends on several
factors:
– Disk Loading
– Stored kinetic energy
– Subjected assessments by pilots
• To help select the rotor diameter during pre-
design studies an “Autorotative Index” is often
used
Helicopters / Filipe Szolnoky CunhaSlide 88Helicopter Performance
Autorotative index
• The Autorotative index is basically an energy
factor:
– Bell used the ratio of kinetic energy to the aircraft
gross weight:
– Sikorsky used an alternative index
Helicopters / Filipe Szolnoky CunhaSlide 89Helicopter Performance
Autorotative index
• The absolute value of the AI is of no significance
• The relative values enables the comparison
between a new project and an existing helicopter
with acceptable autorotative performance
• Acceptable AI for a single engine helicopter is 20
• Acceptable AI for a multi engine helicopter is 10
• For pilots the Autorotative characteristics are
normally expressed in “Equivalent hover time”.
– The design goal is 1.5 s
Helicopters / Filipe Szolnoky CunhaSlide 90Helicopter Performance
Height-Velocity Curve
Helicopters / Filipe Szolnoky CunhaSlide 91Helicopter Performance
Height-Velocity Curve
• The power curve crosses the ideal autorotation
line at:
• For an ideal rotor κ=1, Vc/vh=-1.75
• In practice the value will be higher than this due
to the fact that beside the induced losses we also
have to overcome the profile losses
Helicopters / Filipe Szolnoky CunhaSlide 92Helicopter Performance
Height-Velocity Curve
• The climb (descent) velocity is
• T/A is then the primary factor influencing the
autorotative rate of descent and therefore the HV
curve
• The number of engines will also affect the HV
curve
Helicopters / Filipe Szolnoky CunhaSlide 93Helicopter Performance
Height-Velocity Curve
Single engine Helicopter
Helicopters / Filipe Szolnoky CunhaSlide 94Helicopter Performance
Height-Velocity Curve
Multi-engine Helicopter
Helicopters / Filipe Szolnoky CunhaSlide 95Helicopter Performance
Ground effect
• When a helicopter is close to the ground itsperformance is going to change.
• The rotor slipstream is going to expand rapidly asit approaches the ground.
• This alters the:
– Slipstream velocity
– Induced velocity
– Rotor thrust
• Although this is a well known fact theaerodynamics are still not fully understood.
Helicopters / Filipe Szolnoky CunhaSlide 96Helicopter Performance
Ground effect
• Cheesman & Bennet examined this problem
analytically using a image method:
• The ground effect can be seen as an increase of
thrust for the same power:
Helicopters / Filipe Szolnoky CunhaSlide 97Helicopter Performance
Ground effect
• Or it can be seen at a reduction of the rotor
induced velocity (for constant thrust)
• Betz suggested:
Helicopters / Filipe Szolnoky CunhaSlide 98Helicopter Performance
Ground effect
• Hayden curve fit experimental data and
suggested:
• With A=0.9926 and B=0.0379
Helicopters / Filipe Szolnoky CunhaSlide 99Helicopter Performance
Ground effect
Helicopters / Filipe Szolnoky CunhaSlide 100Helicopter Performance
Forward flight in near the ground
Helicopters / Filipe Szolnoky CunhaSlide 101Helicopter Performance
Forward flight in near the ground
Helicopters / Filipe Szolnoky CunhaSlide 102Helicopter Performance
Forward flight in near the ground
Helicopters / Filipe Szolnoky CunhaSlide 103Helicopter Performance
Forward flight in near the ground
Helicopters / Filipe Szolnoky CunhaSlide 104Helicopter Performance
Performance in manoeuvring Flight
• Manoeuvre requirements will set the ultimate
flight capability for a helicopter
• The prediction of rotor air loads under
manoeuvring conditions forms an essential part
of the overall design process
• This is a difficult task made even more
complicated by:
– The generally non-linear aerodynamics of the rotor.
– Complex rotor/helicopter kinematics
Helicopters / Filipe Szolnoky CunhaSlide 105Helicopter Performance
• Manoeuvre issues are of particular importance
for military helicopters:
– High load factor turns and pull-ups
– Steep turns and rollovers
– High rate of descent in combat landing zones
– Quick pop-up-pop-down manoeuvres for battlefield
observation
Performance in manoeuvring Flight
Helicopters / Filipe Szolnoky CunhaSlide 106Helicopter Performance
• The ability of the helicopter to manoeuvre
depends in part on:
– Excess power
– Excess thrust
• The load factor on the rotor, n, can be defined as:
Performance in manoeuvring Flight
Helicopters / Filipe Szolnoky CunhaSlide 107Helicopter Performance
• The ability to produce a given load factor on the rotor depends on:
– The ability of the helicopter to sequence a manoeuvre using the normal flight controls
– The effective management of potential, kinetic and rotor kinetic energy by the pilot
– Excess energy or power available at that speed
– Ability of the rotor to actually use the excess power and produce a load factor without stalling
– Structural strength and aeroelastic margins of the rotor
Performance in manoeuvring Flight
Helicopters / Filipe Szolnoky CunhaSlide 108Helicopter Performance
Steady manoeuvres
• For a steady manoeuvre the forces are at
equilibrium
• Let us consider a level banked turn with radius
Rturn
• There is a centripetal acceleration
aCT=V2∞/Rturn
• The centrifugal force will be
FCF=maCT=(W/g)(V2∞/Rturn)
Helicopters / Filipe Szolnoky CunhaSlide 109Helicopter Performance
Steady manoeuvres
• The rotor thrust must overcome both the weight
and the centrifugal force
Helicopters / Filipe Szolnoky CunhaSlide 110Helicopter Performance
Steady manoeuvres
• The load factor n on the rotor is:
• Also from the bank angle φ:
• And therefore
Helicopters / Filipe Szolnoky CunhaSlide 111Helicopter Performance
Steady manoeuvres
• The power required in turning flight bank angle
can be determined using the model based in the
momentum theory
• Note the addition on the tail rotor power (that can
be assumed to be a fraction of the main rotor
power)
Helicopters / Filipe Szolnoky CunhaSlide 112Helicopter Performance
Transient manoeuvres
• The analysis of transient manoeuvres can be
approached by energy methods.
• Potential energy
• Transitional kinetic energy
• Rotational kinetic energy
Helicopters / Filipe Szolnoky CunhaSlide 113Helicopter Performance
Transient manoeuvres
• The time rate of transfer of energy between these
three different energy states is equivalent to the
power required to change the energy level.
• The net excess power can be written as:
Helicopters / Filipe Szolnoky CunhaSlide 114Helicopter Performance
Transient manoeuvres
• Let us consider a helicopter undergoing a simple
pull-up manoeuvre
• The potential load factor also depends on the
ability to produce a acceleration through the
application of blade pitch.
Helicopters / Filipe Szolnoky CunhaSlide 115Helicopter Performance
Transient manoeuvres
• The excess power ∆P over the power required P
at a given airspeed V∞ is available to produce
extra rotor thrust ∆T and, therefore, to produce an
acceleration
• The helicopter load factor is:
Helicopters / Filipe Szolnoky CunhaSlide 116Helicopter Performance
Transient manoeuvres
• The ability to produce this load factor depends on
the stall margin of the rotor, which can be
defined in terms of the value
• If Msm>1 then the rotor stall boundary will be
exceeded before the power limit is reached