Folie 1 - Department of Aerospace Engineering

AE 462
Design of Aerospace Structures
Minimum weight structural
design of a rectangular wing
Ömer Anıl Türkkan
Alexandra Balueva

Outline
Problem description
Aerodynamic load calculation
Initial layout
Approach to the problem
Results assesment

Problem description
Wing geometry:
Straight
Untapered
Rectangular
NACA 2412
AR = 6
Aircraft:
General utility
Single engine
MTOM1460 kg
Wing of minimum weight
should be designed
Design should:
satisfy airworthiness req.
be manufacturable

Flight envelope of the aircraft
Point Vel.(m/s) Load fac.
A 74.07 4.4
D 120.7 4.4
E 120.7 -2.2
G 52.36 -2.2

35000
30000
25000
20000
15000
10000
5000
0
70000
60000
50000
40000
30000
20000
10000
0
-500
-1000
-1500
0
Point A Point D
Shear Force
y(m)
0.00 1.00 2.00 3.00 4.00 5.00
Bending Moment
y (m)
0.00 1.00 2.00 3.00 4.00 5.00
Pitching Moment
0.00 1.00 2.00 3.00 4.00 5.00
35000
30000
25000
20000
15000
10000
5000
0
70000
60000
50000
40000
30000
20000
10000
0
0.00
-2000.00
-3000.00
-4000.00
-5000.00
Shear Force
y(m)
0.00 1.00 2.00 3.00 4.00 5.00
Bending Moment
y (m)
0.00 1.00 2.00 3.00 4.00 5.00
y (m)
0.00 1.00 2.00 3.00 4.00 5.00
-1000.00
Pitching Moment

Material chosen:
Aluminium 7075-T651
Property Value
Density 2800 kg/m3
Tensile Yield Strength 503MPa
Shear Strength 331 MPa
Modulus of Elasticity 71.7 GPa
Shear Modulus 27 GPa
Standard stiffener shapes are taken from the book by Bruhn
Thicknesses of available aluminium plates were taken from
www.matweb.com

Deciding on number of stiffeners
Buckling constant for straight plate in shear
After some trial and error it can be seen
that for our geometry decreasing the
width of the panels is as twice as effective
as decreasing the length of the panels.

Initial layout:
Both 3 and 4 bay configurations with step changes in properties are tested
Each iteration goes as follows:

Procedure
Spar locations were considered as fixed
All geometrical properties are calculated in MathCad due to
convenience
For iteration purposes a C++ code was written
Convergence criteria is the minimum weight point with a condition of
all MS being positive
Iterations are performed for all thicknesses and stiffener areas values
Both 3 and 4 bay configurations are checked
Both codes in MathCad and C++ are used interchangeably for results
verification

Rear spar location = 0.75*chord
Front spar location = 0.25*chord
START
When all possible configurations are traced
minimum weight is found.
step

Results: 3 bays @ point D
Bay 1
Bay 2
Bay 3
***All areas in m2, all thicknesses in m
As1
As5 As3
t3
t1 t2 t5
As2
t4
As6 As4
BAY # As1 As2 As3 As4 As5 As6
BAY 1 9.80643 e-4 1.29032 e-3 3.45161 e-5 6.4516 e-5 9.7677 e-5 3.45161 e-5
BAY 2 4.77418 e-4 5.16128 e-4 3.45161 e-5 3.45161 e-5 3.45161 e-5 3.45161 e-5
BAY 3 2.58064 e-4 1.93548 e-4 3.45161 e-5 3.45161 e-5 3.45161 e-5 3.45161 e-5
BAY # t1 t2 t3 t4 t5
BAY 1 0.001016 0.002286 0.001524 0.001524 0.000508
BAY 2 0.001016 0.0018034 0.00127 0.00127 0.0004064
BAY 3 0.000508 0.00127 0.0008128 0.001016 0.0004064
55 KG

Margins of Safety: Bay 1@ point D
0.176495
0.0314091
0.00300135
0.0382938
0.162106
0.0576388
0.197412 2.12591
5.4585
33.6149
0.62967
0.283007 0.348701 0.652871

Results: 4 bays @ point D
We found that for 4 bay configuration weight is 53 kg
For manufacturability we choose to have 3 bays

Results: 3 bays @ point A
Bay 1
Bay 2
Bay 3
***All areas in m2, all thicknesses in m
As1
As5 As3
t3
t1 t2 t5
As2
t4
As6 As4
BAY # As1 As2 As3 As4 As5 As6
BAY 1 9.80643e-4 9.80643e-4 6.4516e-5 6.4516 e-5 9.7677 e-5 6.4516e-5
BAY 2 4.77418 e-4 4.77418 e-4 3.45161 e-5 3.45161 e-5 3.45161 e-5 3.45161 e-5
BAY 3 2.58064 e-4 1.93548 e-4 3.45161 e-5 3.45161 e-5 3.45161 e-5 3.45161 e-5
BAY # t1 t2 t3 t4 t5
BAY 1 0.001016 0.002286 0.00127 0.00127 0.000635
BAY 2 0.0008128 0.0018034 0.001016 0.001016 0.000635
BAY 3 0.0004064 0.00127 0.0006358 0.0008128 0.0004064
47.5 KG

Divergence speed calculation:
Shear modulus was calculated by two methods:
Application of unit torque
Formula by Fung
Identical results were obtained
For uniform untapered wing divergence speed can be calculated as:
For our case a section at 75 % of the chord was taken:
= 643 m/s

Concluding remarks
Weight found is not necessarily the absolute minimum, to
ensure minimum weight an optimization method should
be applied
Weight could be lower if spar locations were variable as
well. But, 25% and 75 % chord are customary values (front
spar close to a.c., rear spar close to hinge line)
Aeroelastic stability of the wing is not ensured because
flutter determinant is not checked
All the calculations were accurately checked using two
independent codes