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.

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

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

; . So,  , or  .

Hence,

. If  ; then  , or  .

. Thus  . Maximum Rate of Climb: . Depends on altitude.

T=0 : Equilibrium: no acceleration.

(parallel)

(perpendicular).Hence,

.  is the glide path angle. Rate of sink =  = .  occurs at 

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.

 

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.

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