Introduction

This assignment is based on the longitudinal stability and control of a conventional aircraft. The stability and control of the aircraft is theoretically obtained with the basic required values provided. Some of the basic calculations involved are obtaining elevator deflection angle, stick force and other essential data. The data obtained are for the aircraft when it is flying at different airspeed ranging from 200, 220, 240 and 260 knots. Graphs are plotted based on the values obtained to help further understand the data collected as well as further verification.

Assumptions

1. It is assumed that there is no induced drag acting on the aircraft.2. The aircraft has an engine of a 100% efficiency and all the power exerted is converted into

thrust so no power is lost due to drag.

Solutions:

Figure 1: Given Parameters for the Aircraft.

Relevant Data:

Pressure at altitude: h=8000 m (ISA)Aircraft Speed: V=200, 220, 240, 260 KTAS

Airspeed Conversion: 1 knot = 0.5144 ms

Ambient Temperature: T = T 0−L×h=236.15 ° K

Ambient Pressure: p=p0(pp0

)

For ISA: (pp0

¿=( TT 0 )

5.256

Atmospheric Conditions

TT0

=236.15288.15

=0.8195 4

pp0

=0.35133

p = 101325×0.35133=35599 Pa

ρ= pRT

= 35599287×236.15

=0.52525kgm−3

Dynamic pressure, q=12ρV 2

q=12×0.52525× (200×0.5144 )2=2780 Pa

Calculations of Parameters:

L=mgL=4000×9.81L=3924 0

CL=LqS

=mgqS

CL=392402780×42

CL=39240116760

CL=0.336051

V=l ×ST

c×Sl=lT+ (h−h0wb )c=6.45+0.45=6.45m

V= 6.9×124.2×42

V=0.469388

CMG=CM 0WB

+CL (h−h0wb)−V CLT

CLT=

CM0WB+C L (h−h0wb )

V

h−h0wb=

(h−h0wb) cc

CLT=−0.00851

CL0WB=CL−

ST

SCLT

CL0WB=0.338483

CLT=a1α T+a2δE+a3δT

α T=αWB (1− ∂ε∂α )+(iT−ε0)

α T=0.002404

δE=CLT

−a1αT+a3 δT

a2δE=−0.001128

FS=GE H

H=C Hq SEc

CH=b1αT+b2δE+b3δT

CH=0.000105H=2.110911FS=2.110911

hn−h0wb=V ( a1a )(1− ∂ ε

∂α )hn−h0wb

=0.19345

Kn=(hn−h0wb )−(h−h0wb )Kn=0.086307

a1=(a1−a2b1b2

)

Kn' =−(h−h0wb )−V ( a1a )(1− ∂ε

∂ α)

Kn' =−0.09332

Variable aircraft speed, Calculating elevator deflection angle and stick force.

VAircraft speed(m/s)

CL CLT CLwb wb T CH H(Nm)

E

(rad)FS

(N)

102.889 0.33605 -0.0091 0.33865 0.06513 0.00243 0.000113 2.26796 -0.0117 2.26796

113.1768 0.27632 -0.02369 0.28309 0.05444 0.00452 0.000331 8.05599 -0.0053 8.05599

123.4656 0.23337 -0.03418 0.24314 0.04676 -0.0095 0.000487 14.0489 -0.0006 14.0489

133.7544 0.19885 -0.04261 0.21102 0.04058 -0.0135 0.000613 20.7430 0.00316 20.7430

VAircraft speed(m/s)

hn−h0wb Kn Kn'

102.889 0.19345 0.086307 -0.09332

113.1768 0.196574 0.089431 -0.09310

123.4656 0.199996 0.092853 -0.09286

133.7544 0.203716 0.096573 -0.09259

0.18 0.2 0.22 0.24 0.26 0.28 0.3 0.32 0.34 0.36

-0.014-0.012

-0.01-0.008-0.006-0.004-0.002

00.0020.0040.006

f(x) = − 0.108561897801014 x + 0.0247524576797096

Delta E vs CL

Lift Coefficient, CL

De,Delta E

0 5 10 15 20 250

20406080

100120140160

f(x) = 1.66813261660184 x + 99.5756816917585

Fs vs V

Stick Force, Fs

Velocity, V

Question 5 and 6:

Static stability refers to the tendency of an aircraft to return to its equilibrium condition after being disturbed by a small perturbation, such as gusts etc. Dynamic stability refers to how the aircraft responds to a small perturbation as a function of time.

A statically stable aircraft when disturbed from its equilibrium condition would tend to return to its equilibrium position when the disturbance has passed. However, upon returning to the initial equilibrium condition the aircraft may overshoot its equilibrium condition and then oscillate about this equilibrium condition. The aircraft is dynamically stable if the oscillation eventually is damped down and the aircraft returns to its initial equilibrium position. However, it is possible that the oscillation lasts indefinitely because the amplitude of the oscillation remains constant with time, perhaps because the damping is non-existent or zero. Even worse is the case where the oscillation amplitude increases with time, in which case the aircraft is dynamically unstable and will eventually be destroyed.

The elevator is controlled by moving the control stick either forward or backward by the pilot. When the aircraft is trimmed, the stick may be held fixed by the pilot or it may be let go by the pilot. When the stick is held fixed. The elevator deflection is also fixed. On the other hand, when the stick is let go free, then the elevator is also free to float, which implies that the hinge moment acting on the elevator is zero. Generally speaking the static stability of an aircraft when the stick is held fixed is somewhat greater than when the stick is no held and is free to move.

Figure 2. Diagrams of the dynamically stable and statically stable stick.

Conclusion:Applying the knowledge learnt and the help of other resourceful books, it is possible to obtain all the values required. The stick free stability is not the same as the stick fixed stability except that the

aircraft contribution is modified by the factor(1− ∂ε∂α ). From the findings, it is possible to identify

that the stick fix is statically stable which refers to the stability when the elevator is fixed. Therefore the aircraft is in trim and we consider the static stability following a small disturbance. If a small disturbance such as gusts occurs, the stick will return to its neutral position. However, for the stick free, it is statically unstable as the elevator is free to move under the actions of the resultant aerodynamic forces. The stick free stability is less than the stick fixed stability.

References:Fundamentals of Aerodynamics, 2010, 5th edition, John D. Anderson, McGraw Hill, New York.