• Western Michigan University

• ENGR AE 3800

Western Michigan University 1

Department of Mechanical and Aerospace Engineering

AE 3800

Flight Vehicle Performance

Lecture 21 Climb Performance: Graphical Approach

Western Michigan University 2

Department of Mechanical and Aerospace Engineering

Equations of Motion for Climb

: cos sin

: cos sin 0

: Flight Path Angle (Angle of Climb)

For Steady Climb (γ=constant

sin 0

cos 0

), 0

W W

x z

dV

F T D W m

dt

F

T D

W L T

dV

dt

W

m Climb

t Altitude Increase

t Constant Speed Climb & Accelerated Climb

Western Michigan University 3

Department of Mechanical and Aerospace Engineering

Rate of Climb : Definition

Department of Mechanical and Aerospace Engineering

Graphical Analysis: Maximum Climb Angle & Maximum Rate of Climb

( ) ( )max

max

/

/ s

,

/

in

EP

R C EP TV DV

W

EP

R

W

R V

C C

g

¥ ¥

¥

= -

=

@

@

Western Michigan University 6

Department of Mechanical and Aerospace Engineering

Hodograph (Velocity Diagram)

V V V V H V (= - = ¥ ¥ 2 2 cosg )

(R C / )max g max

3 2

g

1

g ( ) R C / max

V( ) R C / max

V¥

= ROC

VV

g

V¥