16-Helicopter performance 2008 - ULisboa · Helicopters /Filipe Szolnoky Cunha Helicopter Performance Slide 34 Forward Flight Performance • Tip relief effects can be accounted for

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)



• Economic Performance

– Operation cost (hourly based)

• Fuel consumed

• Parts worn

• Maintenance cost

– Payload

– For military machines economics may not be the

overriding concern



• Tactical performance (Manoeuvrability)

– Maximum load factor

– Tail rotor power

• Yawing ability

• Crosswind ability

– Range of CM positions

– Underslung weight



• 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


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


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)


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.


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:


Hover Performance

• Integrating the previous differential equation gives the relation between temperature and pressure :

– With

• hp (pressure altitude) in meters

• 0 indicating sea level


Hover Performance

• The relation between altitude and density is given

by:

• With

– hρ (density altitude) in meters

– 0 indicating sea level


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


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


Hover Performance

13% increase


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:


Hover Performance


Climb Performance

• We have seen that the induced velocity at a climb

velocity of Vc is:

• Remembering that:

For low rates of climb


Climb Performance

• The velocity VC can be obtained from the

relation:

• And we can writeFor low rates of climb


Climb Performance


Forward Flight Performance

• Forces acting on the helicopter:



• 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



• Lets consider that the flight path angle θFP is

small:

• And the vertical equilibrium:

Tcos(αTPP-θFP)=W ≈T

Vc=V∞ θFT



• 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



• The power necessary to perform this manoeuvre:

• WVC is the Climb power PC

– And we can write:



• 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



• 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



• 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



• 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



• 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)


• These results underpredicts the experimental

values because several assumptions were made.

• Among them:

– No compressibility effects were introduced




• 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



• The compressibility effects can be introduced

using the following estimation (Gessow and

Crim):

• Mdd is the drag divergence Mach number



• Another approach is suggested by Harris for

blades with different thickness-to-chord ratio:

• With



• 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.



• 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)


• 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



• 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




• 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.



• 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%)



• The total power for the main rotor is therefore:

• Or for large values of µ:





Possible airspeeds



• We have seen that the necessary power is a

function of the helicopter gross weight:



• We also have seen that the necessary power is a

function of the air density (altitude):

Reduction of the power

available due to altitude


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


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:




Climb Performance

• Rearranging the terms in the power equation we

can obtain:


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.


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


Climb Performance


Climb Performance


Important Forward Speeds


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



• To obtain the minimum power we differentiate

the previous expression in respect to µ:

• So the non-dimensional forward speed for

minimum power is:


• Recalling that :

• We can write

• The Vmp velocity is :




• Vmp is higher for:

– Higher W

– Lower ρ

• Higher Altitudes

• Higher Temperatures

• Vmp is also the speed at which the endurance is

higher


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:


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.


Important Forward Speeds



• The ratio P/V can be approximated by CP/µ so

that:

• Differentiating to obtain the minimum:



• Which gives:

• Or the velocity for maximum range Vmr:

• Vmr is higher for:

– Higher W

– Lower ρ

• Higher Altitudes

• Higher Temperatures


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


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


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:


Range


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


Maximum forward velocity


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:


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


Performance

of coaxial helicopter


Tandem Rotors

• T1≠T2

• The induced power for each area is:

T2

T1

m(T1+T2)


Tandem Rotors

• The total induced power for the tandem rotor is:

• The total induced power for two independent

rotors is:


Tandem Rotor

• Harris suggest an approximation:

• Note that:


Tandem Rotor


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:


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.


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.


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


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


Autorotation

Inboard Outboard

Driving force>dD Driving force<dD


Autorotation


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:


Autorotation


Autorotation in forward flight



• In autorotation

• As a first approximation:

• Solving for λc

CQ=0




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


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


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


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



• 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



Single engine Helicopter



Multi-engine Helicopter


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.


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:


Ground effect

• Or it can be seen at a reduction of the rotor

induced velocity (for constant thrust)

• Betz suggested:


Ground effect

• Hayden curve fit experimental data and

suggested:

• With A=0.9926 and B=0.0379


Ground effect


Forward flight in near the ground








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


• 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



• 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:



• 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



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)


Steady manoeuvres

• The rotor thrust must overcome both the weight

and the centrifugal force


Steady manoeuvres

• The load factor n on the rotor is:

• Also from the bank angle φ:

• And therefore


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)


Transient manoeuvres

• The analysis of transient manoeuvres can be

approached by energy methods.

• Potential energy

• Transitional kinetic energy

• Rotational kinetic energy



• 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:



• 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.



• 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:



• 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

Documents

16-Helicopter performance 2008 - ULisboa · Helicopters /Filipe Szolnoky Cunha Helicopter Performance Slide 34 Forward Flight Performance • Tip relief effects can be accounted for