Module 6

Aircraft Performance

Module 6

2Cruise and endurance

Where are we?

1 : Introduction to aircraft performance, atmosphere

2 : Aerodynamics, air data measurements

3 : Weights / CG, engine performance, level flight

4 : Turning flight, flight envelope

5 : Climb and descent performance

6 : Cruise and endurance

7 : Payload-range, cost index

8 : Take-off performance

9 : Take-off performance

10 : Enroute and landing performance

11 : Wet and contaminated runways

12 : Impact of performance requirements on aircraft design


Cruise Introduction

Definition of specific air range (SAR)

Calculation of SAR

Typical SAR chart

Cruise range calculation

Types of cruise

Temperature effects

Altitude effects

Wind effects


Cruise - Introduction

Range is defined as the distance that an aircraft can travel with a given fuel quantity and a given payload

• For example, the Bombardier Global Express has a (non-stop) range capability of 6,500 nm at a cruise speed of Mach 0.80 and with a payload of 8 passengers (1,600 lb)

Range is the sum of climb, cruise and descent distances

Efficient cruise performance is required in order to maximize range and minimize operating costs

The concepts associated with cruise performance will be discussed in the next slides


Cruise – Definition of Specific Air Range (SAR) SAR is defined as the air distance traveled per unit of mass of fuel during steady state and level flight cruise

conditions

SAR units

• Nautical air miles (nam) per lb of fuel (nam/lb)

SAR = true airspeed / fuel flow = V / Wf

SAR is independent of wind speed (if wind is constant)

Cruise air distance is proportional to SAR for a given fuel quantity


Cruise – Definition of SAR (Cont’d)

Specific Range (SR) is defined similarly but in terms of ground distance and speed

• SR = ground speed / fuel flow = Vg / Wf

• Vg = V + Vwind

• SR = SAR * (V + Vwind ) / V

• For mission performance analysis, headwinds are negative (negative impact on performance) and tailwinds are positive (positive impact on performance)


Cruise – Calculation of SAR

SAR can be calculated with an exact numerical method or with a theoretical method

Exact method :

• Specific cruise conditions are assumed : weight, altitude, Mach number, deviation from ISA , engine bleed extraction and number of engines operating (neng)

• V = ao 0.5

• q is calculated (q = 1481.3 M2 , q in lb/ft2)

• CL= W/(qS)

• From the high speed drag model of the airplane, CD is determined knowing CL and M


Cruise – Calculation of SAR (Cont’d)

• Total thrust required = Treq = D = CDqS

• T required per engine = Treq / neng

• Data supplied by the engine manufacturer is used to determine Wf per engine knowing altitude, Mach number, deviation from ISA, engine bleed extraction and Trequired per engine

• Wf = Wf per engine * neng

• SAR = V / Wf


Cruise – Calculation of SAR (Cont’d) Theoretical method is useful to understand the parameters that affect SAR

• SAR = V / Wf

• SAR = V / (Treq SFC)

• Knowing that Treq = W / (L/D) :

• SAR = (V/SFC) (L/D) (1/W)

• Knowing that V = ao 0.5 M,

• SAR = (ao 0.5 / SFC) (M L/D) (1/W)

Theoretical method shows that for a given weight and altitude combination, SAR is maximum when M L/D is maximized

• assumes that SFC is independent of the thrust level

• Maximum M L/D is equivalent to maximum CL0.5/CD


Cruise – Calculation of SAR (Cont’d) Tangent lines on CL – CD graph defines maximum M L/D

CL for maximum M L/D reduces as M increases

Maximum M L/D occurs when compressibility effects are becoming important


Cruise – Typical SAR chart


Cruise – Cruise range calculation Cruise range is defined as the cruise air distance traveled while burning a given quantity of fuel (given fuel burn)

Cruise range can be obtained by using SAR data or from a theoretical equation

For flight at constant altitude, cruise range can easily be determined from SAR data :

• R = SARavg * (W1-W2)

Where R = Cruise range (nam) (still air distance)

W1 = weight at beginning of cruise segment (lb)

W2 = weight at end of cruise segment (lb)

W1-W2 = fuel burn during cruise segment (lb)

SARavg = average SAR during cruise segment (nam/lb)


Cruise – Cruise range calculation (Cont’d)• Note : if SAR does not vary linearly with weight, it is necessary to analyze smaller cruise segments and to add them up

in order to obtain the cruise range

Cruise range can also be estimated with theoretical methods if certain assumptions are made:

• SFC is constant

• CL is constant

Cruise range is obtained by integrating the SAR equation over a weight range

Two cases are analyzed in the next slides

• Flight at constant altitude

• Flight at constant speed


Cruise – Cruise range calculation (Cont’d)Case 1 : flight at constant altitude

SAR equation : SAR = (1/ SFC) (V L/D) (1/W)

Knowing that V = (2 W / ( S CL))0.5 , we can rewrite SAR as

SAR = (1/SFC) (2 / ( S))0.5 (CL0.5/CD) (1/W0.5)

Integration of the SAR equation with respect to weight and conversion to nam gives:

R = [ 1.676 / (SFC ( S)0.5) ] (CL0.5/CD) (W1

0.5- W20.5) (nam)




Range is maximized by minimizing (i.e. high altitude) and by maximizing CL0.5/CD (i.e. CL = (CD0 / (3K) )0.5) if compressibility effects are neglected)


Cruise – Cruise range calculation (Cont’d)Case 2 : flight at constant speed SAR equation : SAR = (1/ SFC) (V L/D) (1/W)

Integration of the SAR equation with respect to weight and conversion to nam gives:

R = (V/ SFC) (CL/CD) (ln (W1/W2) (nam)

or

R = ( (661.5 0.5) / SFC) (ML/D) (ln (W1/W2) (nam)


V = TAS (knots)



Range is maximized by maximizing ML/D


Cruise – Cruise range calculation (Cont’d)

Constant speed and constant CL imply that the aircraft must climb as its weight reduces :

• CL = W / (1481.3 M2 S)

• W / must be constant

• As weight reduces due to fuel burn, the aircraft must climb

• Resulting climb angle is small (order of 0.02o) and the basic assumption that T = D is still essentially valid

If SFC, M or L/D are not constant, the integration can be done numerically


Cruise – Cruise range calculation (Cont’d) Range for the two cases can be compared with the following example:

- S = 450 ft2

- W1 = 45,000 lb and W2 = 42,000 lb

- FL370 / ISA / Mach 0.8- L / D = 15- SFC = 0.6 (lb/hr) / lb fuel

Flight at constant altitude :

• R = [ 1.676 / (SFC ( S)0.5) ] (CL0.5/CD) (W1

0.5- W20.5)

= 0.0006759 slugs / ft3

• q = 1481.3 M2 = 202.7 lb/ft2

• CL = W/ (qS) = 0.493

• CD = CL / (L/D) = 0.0329

• R = 778 nam


Cruise – Cruise range calculation (Cont’d)

Flight at constant speed :

• R = ( (661.5 0.5) / SFC) (ML/D) (ln (W1/W2)

= 0.7519

• R = 791 nam

Flight at constant speed and constant CL provides better range

Verify climb angle for flight at constant speed• W/ = 45000 / 0.2138 = 210,477 lb = constant

at end of cruise = W / (W/ ) = 42,000 / 210,477 = 0.1996

• Altitude at end of cruise = 38,437 ft

• Climb angle = atan ( 1437 / (791*6077)) = 0.017o


Cruise – Types of cruise

Cruise at constant speed and constant CL implies increasing altitude

• Not possible operationally

• Is approximated operationally by cruise segments at constant altitude followed by step climbs


Cruise – Types of cruise (Cont’d) During flight at constant altitude, range can be maximized (or fuel burn

minimized for a given range) by flying at the Mach number for maximum SAR – referred to as Maximum Range Cruise (MRC) Mach number

• MRC is not used very much operationally as it normally results in unacceptably low cruise speeds (long flight time)

• Flight at MRC implies that M and thrust are reduced as weight reduces

• MRC speed schedule can be derived from SAR chart


Cruise – Types of cruise (Cont’d)

Flight at Long Range Cruise (LRC) cruise speed or Mach number provides a good compromise between fuel efficiency and flight time

LRC speed is the speed that provides 99 % of max. SAR• Implies that Mach and thrust are reduced as weight reduces

• LRC can be derived from SAR chart



Flight at constant Mach number

• Commonly used operationally, specially on short range missions where flight at varying speed schedule (e.g. LRC) would only result in a small benefit in operating costs

Flight at maximum cruise speed

• Speed limited by maximum level flight speed capability (i.e. D = MCR or maximum cruise thrust) or Vmo/Mmo

• MCR limit varies as a function of temperature (MCR is lower at higher deviations from ISA)

• Results in low SAR

• Used when flight time is more important than fuel cost



Effect of different types of cruise conditions on cruise range


Cruise – Temperature effects Unless maximum cruise speed is used, temperature has a negligible effect on SAR and

range

• SAR = V / Wf

• In order to maintain a constant thrust level at a higher temperature, fuel flow increases

• The fuel flow increase is essentially compensated by the higher true airspeed V at the higher temperature

• Effect on SAR is typically less than 0.1 % for every degree of deviation from ISA conditions

Significant impact when max. cruise speed is limited by MCR


Cruise – Altitude effects

• Cruise altitude can have a significant impact on fuel required Example : CRJ200, 500 nm mission, 30 passengers

Climb: 250 kts/M 0.70 - Cruise: M 0.74

0

2

4

6

8

10

12

14

16

FL390

FL370

FL350

FL330

FL310

FL290

% increase inblock fuel forcruise belowFL390


Cruise – Wind effects When winds are present, it is desired to maximize nm/lb of fuel

SR (nm/lb) = SAR (V + Vwind)/V (tailwind positive)

With a tailwind :

• SR is greater than SAR

• Mach number for MRC and LRC are lower than in zero wind conditions

With a headwind :

• SR is lower than SAR

• Mach number for MRC and LRC are higher than in zero wind conditions

Range (still air distance) is corrected similarly in order to obtain ground distance


Endurance

Introduction

Conditions for best endurance


Endurance - Introduction

Endurance is defined as the length of time that an aircraft can remain airborne

Some aircraft are used for missions where it is required to maximize the time that the airplane remains airborne

• Ex. : surveillance mission

In addition, air traffic controllers may require that an aircraft stays in holding mode before proceeding with the planned mission

For such cases, it is desirable to fly at a condition where fuel flow is minimized

• Maximum endurance is obtained when the aircraft is operated at a flight condition where fuel flow is minimized


Endurance – Conditions for best endurance For practical considerations, level flight is assumed

Basic SFC definition leads to :

dW = - SFC T dt

dt/dW = -1 / (SFC T)

Knowing that T = D = W D/L in level flight :

dt = - (1/SFC) L/D 1/W dW

Integrating between beginning and end of flight segment :

E = (1/SFC) L/D ln (W1/W2)

Where E = Endurance (hours)

W1 = weight at beginning of flight segment (lb)

W2 = weight at end of flight segment (lb)

For the case where SFC is constant with varying thrust levels, maximum endurance is obtained during flight at maximum L/D or VMD


Endurance – Conditions for best endurance (Cont’d)

Typical data shows that minimum fuel flow occurs at a specific pressure altitude


Endurance – Conditions for best endurance (Cont’d)

In practice, the speed for best endurance or holding is normally defined by VMD

Other constraints may force a further increase of the holding speed

• Maneuvering margin prior to stall warning

• Maneuvering margin prior to buffet

Module 6

Documents

Transcript of Module 6