Power and Thrust for Cruising Flight

Power and Thrust for Cruising Flight

Robert Stengel, Aircraft Flight Dynamics, MAE 331, 2018

Copyright 2018 by Robert Stengel. All rights reserved. For educational use only.



1

U.S. Standard Atmosphere, 1976



2

1

Dynamic Pressure and Mach Number

= air density, function of height = e-h

sea level

a = speed of sound = linear function of height

Dynamic pressure = q V 2 2 Mach number = V a

3

Definitions of Airspeed

Airspeed is speed of aircraft measured with respect to air mass

Airspeed = Inertial speed if wind speed = 0

? Indicated Airspeed (IAS)

IAS =

( ) 2 p - p stagnation

ambient

SL =

( ) 2 ptotal - pstatic

SL

!

2qc SL

,

with

qc

!

impact

pressure

? Calibrated Airspeed (CAS)*

CAS = IAS corrected for instrument and position errors

=

( ) 2 qc corr #1

SL

* Kayton & Fried, 1969; NASA TN-D-822, 1961

4

2

Definitions of Airspeed

Airspeed is speed of aircraft measured with respect to air mass

Airspeed = Inertial speed if wind speed = 0

Equivalent Airspeed (EAS)*

EAS = CAS corrected for compressibility effects =

( ) 2 qc corr # 2

SL

True Airspeed (TAS)*

Mach number

V TAS = EAS

SL (z)

=

IAScorrected

SL (z)

TAS M=

a

* Kayton & Fried, 1969; NASA TN-D-822, 1961 5

Flight in the Vertical Plane

6

3

Longitudinal Variables

7

Longitudinal Point-Mass Equations of Motion

? Assume thrust is aligned with the velocity vector (small-angle approximation for )

? Mass = constant

V!

=

(CT

cos

-

CD

)

1 2

V

2S

-

mg

sin

(CT

-

CD

)1

2

V 2S

-

mg

sin

m

m

!

=

(CT

sin

+

CL

)

1 2

V

2S

-

mg

cos

CL

1 2

V

2S

-

mg

cos

mV

mV

h! = -z! = -vz = V sin

V = velocity = Earth-relative airspeed

r! = x! = vx = V cos

= True airspeed with zero wind = flight path angle

h = height (altitude)

r = range

8

4

Conditions for Steady, Level Flight

? Flight path angle = 0 ? Altitude = constant ? Airspeed = constant ? Dynamic pressure = constant

0

=

(CT

-

CD

)

1 2

V 2S

? Thrust = Drag

m

0

=

CL

1 2

V

2S

-

mg

mV

h = 0

? Lift = Weight

r = V

9

Power and Thrust

Propeller

Power

=

P

=

T

?V

=

CT

1 2

V 3S

independent

of

airspeed

Turbojet

Thrust

=

T

=

CT

1 2

V 2S

independent

of

airspeed

Throttle Effect

T

=

T T max

=

CTmax qS T ,

0 T 1

10

5

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