Table 1: Direct Access to the Sub-Disciplines of Aerospace Engineering

DESIGN-CENTERED INTRODUCTION TO AEROSPACE ENGINEERING

9. PERFORMANCE

Under Performance, we think about issues like:

a) How long can the aircraft stay in the air (endurance)?

b) How far can it fly (range)?

c) How much payload can it carry on a given mission?

d) How long will it take to reach altitude (climb performance)?

e) What is its maximum speed?

f) How long a runway does it need to take off?

g) How long a runway does it need to land?

h) How quickly can it turn, pitch, and roll?

i) What is its minimum turning radius while flying?

j) What are the boundaries of its flight envelope?

The aircraft is considered to be a rigid body, with the lift (L), drag (D), thrust (T) and weight (W) acting on it. Flight Dynamics deals with the movement of the aircraft as it responds to these forces.

Equations of Motion

Consider an aircraft at point A, moving along a curved flight path. From Newton's 2nd Law of Motion, summing forces parallel and perpendicular to the flight path,

parallel to the flight path.

perpendicular to the flight path

and

Steady Level Flight

If acceleration =0, we get Static Performance: range, endurance, maximum speed etc., needed for aircraft design and operations.

Let and acceleration =0.

for most aircraft, so T=D; L=W for level, unaccelerated flight.

Thrust required for steady level flight

;

. So,

, or

Steady Climb

Hence,

. If

; then

, or

Rate of Climb

. Thus

. Maximum Rate of Climb:

. Depends on altitude.

Gliding Flight

T=0 : Equilibrium: no acceleration.

(parallel)

(perpendicular).Hence,

is the glide path angle. Rate of sink =

occurs at

Range and Fuel Consumption

Distance Flown per unit mass of fuel consumed =

Now

. So, Distance traveled per unit mass of fuel consumed =

Range =

.We will assume that the fuel consumption in descent and landing is at the same rate as during cruise (this is conservative).

For the climb phase, we will assume the fuel consumption for cruise plus an increment depending on the cruise altitude.

Altitude

% of takeoff weight as added fuel consumption

20,000 feet

0.75%

30,000 feet

1.25%

35,000 feet

1.60%

Takeoff and Landing Distances

Takeoff Distance: Let's assume that Net Thrust (which is the thrust minus the ground roll friction, drag etc.) is 0.2 Wto, where Wto is the takeoff weight of the aircraft. Then,

. Kinetic Energy =

where R is the takeoff run. This says that in distance R, we gained enough kinetic energy to be at the takeoff speed, accelerating at the rate corresponding to net thrust of 0.2Wto. Thus,

. Runway length should be twice this distance, in order to provide enough distance to stop if the decision to abort takeoff is made at the takeoff speed.

Landing Procedure:

Descent to 5000 feet. Vectored to 12 miles downwind, make a 180-degree turn. Extend flaps and landing gear, reduce speed to 150mph. This leaves 5 minutes of final approach.

Go to the next section: Stability & Control

Go to the previous section: Propulsion

Go to the Course Outline

Aerodynamics; Fluids

Structures;
Solids

Materials

Propulsion

Astronautics

Flight Mechanics

Controls; Avionics

Design;
Manufacturing

Altitude	% of takeoff weight as added fuel consumption
20,000 feet	0.75%
30,000 feet	1.25%
35,000 feet	1.60%