Study 9
-
Upload
kralraptor -
Category
Documents
-
view
216 -
download
0
Transcript of Study 9
-
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.