8/13/2019 Study 9

1/6

AE 451

Aeronautical Engineering Design

STUDY 9

LONGITUDINAL STABILITY ANALYSIS

Yaroslav Novikov

Ender Ozyetis

Emre Unay

Denizhan Yavas

28/12/2009

Middle East Technical University

Aerospace Engineering Department

8/13/2019 Study 9

2/6

ABSTRACT

This report presents all the work and calculations that were necessary to complete Study 9.

Longitudinal analysis performed in this study proves that our aircraft is stable for all configurations

which are to be described in the following pages of this report.

8/13/2019 Study 9

3/6

INTRODUCTION

Reader is first introduced to the calculation of neutral point of the whole aircraft. Static margin is

then determined for 4 different configurations for which the centre of gravity location is of great

importance.

8/13/2019 Study 9

4/6

NEUTRAL POINT

Position of the neutral has been calculated using the following relations (neglecting engine

contribution):

Here,

In these formulations, at and awb are lift curve slopes for the horizontal tail and wing-body,

respectively. Lift curve slope for wing-body is assumed to be equal to wings lift curve slope, and both

slopes are calculated using airfoil data through the following relation:

Lift curve slope for the wing was calculated in a previous study as 5,8959. F is the fuselage

contribution factor, and was computed in a previous study for the wing. This factor is taken as unity

for the horizontal tail.

Leading edge sweep angle, , for the horizontal tail is 10,631 degrees. Lift curve slope can be

obtained from airfoil data as 6,3025. Aspect ratio is 3,5 with a horizontal tail planform and exposed

area of 6,3 m2and volume ratio of 0,65. Substituting all numerical values for a flight at 0,3 Mach, the

lift curve slope for the horizontal tail can be calculated as:

Downwash factor is calculated using the following formula:

8/13/2019 Study 9

5/6

Ais the wings aspect ratio (6,68), stands for the wing taper ratio (0,544), hHand lHare the vertical(2,38 m) and horizontal (7,408 m) distances between wings and horizontal tails MACs, respectively. is the quarter-chord line sweep of the wing, and is a negative value for our design. Substitutingall numerical values,

Then,

Static Margin

CG location from the leading edge of the wing is calculated from known CG position and location of

wing MAC from datum (3,128 meters). Then, the static margin for different configurations of the

airplane can be calculated for the empty fuel tank case as follows:

Fully Occupied Configuration

Partially Occupied (Pilots & 2 last seat rows)

Empty Configuration

Air Ambulance Configuration

In these equations 2,308 represents the MAC length.

8/13/2019 Study 9

6/6

Ideally, the neutral point must be between 5-10% of MAC length. It is clear that this is fully satisfied

for all configurations, except for slight over-stability for empty configuration for which the static

margin is almost %16. However, this is an acceptable value.

Reader should be reminded that these values have been computed for empty fuel tank case. Fuel

tanks are to be positioned such that their center of gravity coincides with the center of gravity of the

aircraft in fully occupied commuter configuration. This means that with completely full tanks

longitudinal center of gravity location will remain the same as for the empty tank case.

Static margins for the 4 configurations with completely full fuel tanks can be calculated as follows:

Partially Occupied (Pilots & 2 last seat rows)

Empty Configuration

Air Ambulance Configuration

The following table summarizes all that we have done so far.

Empty Fuel Tanks Full Fuel Tanks

X CG

Location

Y CG

Location

Static

Margin

X CG

Location

Y CG

Location

Static

Margin

Fully

Occupied4,07 1,38 %8,94 3,99 1,52 %12,73

Ambulance

Configuration4,1 1,41 %7,4 4,01 1,55 %11,57

Partially

Occupied4,16 1,43 %5,3 4,05 1,58 %10,1

Empty

Configuration3,91 1,48 %15,8 3,83 1,64 %19,3

In fully occupied configuration there are 8 people on board plus 2 pilots.

Ambulance configuration assumes that all 4 stretchers are occupied by patients, and 4th

seat row is

taken by the medical team, plus 2 pilots.

Partially occupied configuration assumes that only last two rows of seats are completely occupied by

passengers, plus 2 pilots. This is not a very much realistic configuration, since people are eager and

will want to occupy fronts seats to see what is happening inside the pilot cockpit.

Empty configuration has only 2 pilots on board.