WING SPAR Presentation

Design of Front and Rear Spars for The

Trainer Aircraft Wing.

TEAM

Team Members :

Akshay A.

Pradeep S. Shet

Pavan Kumar N. R.

Raghunandan M.

Lakshmana H. B.

Chetan A. V.

Guide

:

Mr. H. N. Athavale

Co-ordinator

:

Mr. Umanath Nayak

CAE

OBJECTIVE

CAD



To generate the CAD model of wing using the available data and

prepare the assembly of all components

CAE



Determine the Spar locations with respect to chord length.



_{Determine the dimensions for flange and web of the spars.}

SCOPE OF THE PROJECT

Estimation of spar position.

Dimension calculations of front and rear spars.

Calculations for number of ribs and their positions.

CAD

Profile creation of the wing using the given NACA standards.

Creation of the wing geometry

Use available data to develop CAD models for each individual component

Prepare an assembly of all components using CATIA

Root chord

:

2400 mm

Tip chord

:

700 mm

Semi Span length

:

5500 mm

Exposed Span

:

4750 mm

Airfoil (root)

:

NACA 64A

₁

215

(tip)

:

NACA 64A

₁

210

Aircraft weight

:

14000 N

Lift Load

:

6g

Design Factor

:

1.5

Given Spar Position(in % of chord length)

Front Spar :

18-25

Rear Spar :

62-70

DERIVED INPUT

●

Limit load

: 14000 * 6=

84000 N

●

Design Load

: 84000 * 1.5=

126000 N

●

Load on semi-span

: 126000 / 2=

63000 N

●

Exposed wing area

:

7.3625 E6 mm

2

WING GEOMETRY

R

O

O

T

C

H

O

R

D

_{SWEEP AT ¼ CHORD}

4750

70

0

24

00

T

IP

C

H

O

R

D

LEADING EDGE

TRAILING EDGE

Top View [RH]

AIRFOIL

Generate the aerofoil section using the Coordinates of

NACA 64A

₁

215 and NACA 64A

₁

210.

[source : http://www.pdas.com/sections6a.htm]

DESIGN PROCEDURE

Calculation of the Shear force, Bending moment & Torsion for the

given load.

Calculation of load distribution between the front and rear spar.

Estimation of spar positions.

DESIGN PROCEDURE

Divide the wing area into number of divisions.

Calculate the chord length at each section.

Determine the C.G of each area.

Calculate the shear force, bending moment and Torque at the respective

sections.

Shear force =pressure*area.

Bending moment=shear force*CG distance.

METHODS AND METHODOLOGY

A

₁₀

A

₉

A

₈

A

₇

A

₆

A

₅

A

₄

A

₃

A

₂

A

₁

475

2400

700

L

₁

L

₂

L

₉

Chord Length, L

₁

= L

_root

-((L

_root

-L

_tip

) / S) * x

At section 2, L

₁

= 2400-((2400-700)/4750)*4275

L

₁

= 870 mm

Area of Trapezium, A

₁

= 0.5*(L

₁

+L

_tip

)*h

A

₁

= 0.5*(870+700)*475

A

₁

= 373 E3 mm

2

CG of Trapezoid Section = h/3*((L

_tip

+2L

₁

)/(L

_tip

+L

₁

))

CG=475/3*((700+2*870)/(700+870))

CG = 246 mm

from L

_tip

DESIGN PROCEDURE

S

x

L

_root

L

tip

L

₁

A

₁

h

DESIGN PROCEDURE

Limit load = 84000 N

Design Load = Limit Load*Design factor

Design load on wing, = 84000*1.5

= 1,26,000 N

Design load on semi-span wing, =

₆₃₀₀₀

_N

pressure load on wing [P]

=

8556.87 E-6 N/mm

2

Load At Section 2, = P

₂

+P

₁

= P*A

₂

+P

₁

= 8557 E-6 * 453625 + 3190.65

=

3881.6 + 3190.65 =

7072.25 N

Bending Moment At Section 2, M

₂

= P

₂

* CG

₂

+ P

₁

* (CG

₁

+ L

₂

)

M

= 3881.6 * 230 + 3190.65 * (229 + 475)

SHEAR FORCE

Root 475 950 1425 1900 2375 2850 3325 3800 4275 TIP 0.00 10000.00 20000.00 30000.00 40000.00 50000.00 60000.00 70000.00 63000.00 53590.65 44872.25 36844.85 29508.40 22862.90 16908.39 11644.85 7072.25 3190.653190.65

Shear force diagram for the wing

S

h

e

a

r

fo

rc

e

[

N

]

BENDING MOMENT

40000000

60000000

80000000

100000000

120000000

140000000

123020000 95259000 71809000 52341000 36527000 24039000

Bending moment diagram for the wing span

di

ng

m

om

en

t

[N

-m

m

]

LOAD DISTRIBUTION

Centre of Pressure, CP = 45% of Chord Length (C) from LE [870mm]

[1]

Front Spar Position

= 25% of C from LE

[217.5mm]

Rear Spar Position

= 62% of C from LE

[539.4mm]

Chord Length 'C'

45% of C

25% of C

a

b

c

62% of C

R

_A

R

_B

FS

RS

Chord

CP

a=174mm

b=148mm

c=322mm

C=870mm

Shear Force Distribution:

Shear Force on Front Spar, = Load * b/c

At Section 1, SF

_FS

= 3190.65 * (148/322)

SF

_FS

= 1465.974 N

Shear Force on Rear Spar SF

_RS

= 3190.65 - 1465.974

SF

_RS

= 1724.676 N

SF on Front Spar

= 45.9% of total load

SF on Rear Spar = 54.1% of total load

Bending Moment Distribution:

Moment is distributed in same ratio as that of the Shear force.

Bending Moment on Front Spar,

M

_FS

= 0.459 * 781700

M

_FS

= 359159 N-mm

Bending Moment on Rear Spar,

M

_RS

= 781700 - 359159

M

_RS

= 422541N-mm

Front Spar

Rear Spar

MATERIAL

Material

: AA 2024-T6

Ultimate tensile strength, σ

: 427 MPa

Shear strength

: 283MPa

Density

: 2.79 E-6 kg/mm

3

Young's Modulus, E

: 72400 Mpa

Poisson's Ratio

: 0.33

Moment of Inertia:

I = M*y/σ

Where, I

= Moment of Inertia, in mm

4

M = Bending Moment, in N-mm

y

= distance b/w neutral axis to top surface, in mm

σ = Tensile strength, in MPa

Moment of Inertia on Front Spar, I

_FS

= 359159 * 52.8

/

427

I

_FS

= 44412 mm

4

Moment of Inertia on Rear Spar, I

_RS

= 422541 * 43.44

/

427

I

_RS

= 42987 mm

4

MOMENT OF INERTIA

Front Spar

TORSION

Area of Torque Box, A

₁

= 30980.3 mm

2

CG of Torque Box

= 165 mm From Rear spar

Distance Between CG & CP

= 18.268 mm

Torque, T = Load*d

= 3190.65 * 18.268

Torque

TORQUE DIAGRAM

ROOT 0 475 950 1425 1900 2375 2850 3325 3800 4275 TIP 4750

0

2000000

4000000

6000000

8000000

10000000

12000000

11857039.54 8689789.08 6187429.48 4252608.34 2795550.39 1734041.9 992888.78 506210.31_{212789.9958285.91} 0

Torque diagram for the wing span

Wing span [root to tip] [mm]

T

or

qu

e

[N

-m

m

]

Shear force (SF) on Front Spar

SF

_FS

= q * h

_FS

SF

_FS

= 0.941*105.6 =

99.34 N

Total SF on FS

= 1465.974+99.34

=

1565.313 N

On Rear Spar

SF

_RS

= q*h

_RS

SF

_RS

= 0.941*86.88

SF

_RS

= 81.729 N

Total SF on RS = 1724.676+81.729

SHEAR FORCE DUE TO TORSION

Front Spar

TOTAL SHEAR FORCE

Front Spar

WEB THICKNESS

Thickness of the Web can be calculated from the following formula,

ح

_{shear strength}

=

SF

_FS

/ A

_web

Where,

ح

_{shear strength}

= Shear strength of the material AA 2024-T6 in MPa

A

_web

= Area of the web = (height * thickness) in mm

283 = 1565.313 / (105.602 * t

_web

)

t

_web

= 0.052 mm

Area of the web = height * thickness

=

105.602 * 0.052

A

_web

= 5.531 mm

2

Moment of Inertia of Web:

Moment of Inertia of a rectangular section web is given by,

I

_web

= t

_web

* (h

_FS

)

3

_{/ 12}

Front Spar

Rear Spar

FLANGE

MOI

_flange

= MOI

_{Front Spar}

- MOI

_Web

I

_flange

= I

_FS

- I

_web

= 44411 - 5140.175

I

_flange

= 39270.825 mm

4

Also Moment of Inertia of the flange is given by,

I

_flange

= A

_flange

* (y

_FS

)

2

Where, I

_flange

= Moment of Inertia of flange in mm

4

y

_FS

= height from neutral axis to top surface of the flange in mm

Hence, A

_flange

= I

_flange

/ (y

_FS

)

2

= 39270.825 / (52.801)

2

FLANGE

Front Spar

MASS CALCULATIONS

A

_FS

= A

_flange

+ A

_web

A

_FS

= 14.09 + 5.53 =

19.62 mm

2

V

_FS

= A

_FS

* 475 = 19.62 * 475

V

_FS

= 9318.3 mm

3

Mass = Density * Total Volume

= 2.78 E-6 * 4218551.12

62

63

64

65

66

67

68

69

70

11.50

12.00

12.50

13.00

13.50

14.00

12.50 12.62 12.75 12.88 13.02 13.17 13.32 13.49 13.67 12.39 12.50 12.62 12.74 12.88 13.02 13.17 13.33 13.50 12.27 12.38 12.49 12.61 12.74 12.88 13.02 13.18 13.34 12.16 12.26 12.37 12.49 12.61 12.74 12.88 13.02 13.18 12.05 12.15 12.25 12.36 12.48 12.60 12.73 12.87 13.02 11.95 12.03 12.13 12.23 12.34 12.46 12.59 12.72 12.87 11.84 11.92 12.01 12.11 12.21 12.33 12.45 12.59 12.77

11.73

11.81 11.89 11.98 12.08 12.19 12.34 12.51 12.68

18

19

20

21

22

23

24

25

Rear spar position in %

M

as

s

[k

g]

MASS CALCULATIONS

F

ro

n

t

sp

ar

p

o

si

ti

o

n

BUCKLING

To Check whether the web fails under shear

buckling.

Condition: Shear stress

_induced

< Buckling stress (safe design)

●

The thickness calculation is based on iterations,

F

_induced

= q

/

t

_web

F

_critical

= k*E*(t

_web

/ b)

2

where

,

q = shear flow, in N/mm

E = Young's Modulus, in MPa

_{b = height of spar, in mm}

t

_web

= web thickness, in mm

[4]

BUCKLING CALCULATIONS

ITERATION 1.

RIB SPACING

FOR EQUAL DISTANCE OF 475mm

Web thickness's of front spar at section 1 is as follows,

F

_induced

= q

₁

/ t

_web

--- (1)

= 0.941

/ 0.052

F

_induced

= 18.09 N/mm

2

F

_allowable

= K * E * (t

_web

/ b)

2

_---(2)

18.09 = 5 * 72400 * (t

_web

/ 105.602)

2

The value calculated for t

_web

is re substituted in Eqn.(1) and this loop will

continue till we get equal consecutive thickness.

Hence, the thickness of the web is

0.30 mm

at section 1. Same calculations were

repeated for all sections of front spar to optimize the web thickness

Front Spar

MASS CALCULATION

●

Web design is safe under buckling.

●

From buckling calculation the total mass of the spars is 16.14 kg.

●

By this, mass of the spars got increased by 4.41 kg.

ITERATION-2

●

_{For optimum Rib spacing, (a/b) ratio >= 1}

Rib no.

Rib dist. From root

Spar heights

(a/b) ratio

K from graph

Web thickness

Web volume

FS

RS

FS

RS

FS

RS

FS

RS

[mm]

[mm]

[mm]

[mm]

[mm]

0

TIP4750

64.49

54.05

0

0.00

-

-

-

-1

4440

81.97

68.4

3.78

4.53

5.10 5.00

0.22

0.2

5590.56

4240.8

2

4110

100.58

83.67

3.28

3.94

5.17 5.08

0.34

0.3

11285.3

8283.53

3

3780

119.19

98.94

2.77

3.34

5.30 5.15

0.44

0.39

17306.53

12734.09

4

3450

137.8

114.22

2.39

2.89

5.50 5.20

0.53

0.48

24101.05

18091.81

5

3120

156.41

129.49

2.11

2.55

5.75 5.40

0.64

0.57

33033.37

24356.69

6

2790

175.02

144.76

1.89

2.28

6.00 5.60

0.74

0.67

42739.15

32006.44

7

2470

193.06

159.57

1.66

2.01

6.30 5.80

0.84

0.76

51894.8

38807.18

8

2150

211.11

174.38

1.52

1.84

6.55 6.20

0.94

0.84

63500.68

46872.81

9

1830

229.15

189.19

1.40

1.69

6.90 6.25

1.03

0.94

75528.17

56907.75

10

1520

246.63

203.53

1.26

1.52

7.25 6.55

1.12

1.02

85630.63

64357.45

11

1210

264.11

217.88

1.17

1.42

7.60 6.80

1.2

1.1

98250.04

74297.42

12

900

281.59

232.23

1.10

1.33

7.80 7.00

1.31

1.19

114355.32

85668.54

13

600

298.51

246.11

1.00

1.22

8.20 7.35

1.39

1.26

124479.09

93029.96

14

300

315.43

259.99

1.05

1.15

8.00 7.60

1.51

1.35

142888.88 105297.57

15

Root 0

332.35

273.88

1.11

1.10

7.80 7.80

1.63

1.43

162519.15 117494.52

Total volume

1053102.72 782446.56

Web volume

1835549.28

[mm

3

] [mm

3

]

FS

RS

WEIGHT CALCULATION

●

Finally mass of the

spars reduced by 0.89 kg when compared to 1

_st

iteration.

RESULTS AND DISCUSSION

Root 0 300 600 900 1210 1520 1830 2150 2470 2790 3120 3450 3780 4110 4440 4750

-0.40

0.00

0.40

0.80

1.20

1.60

2.00

0.39 0.36 0.34 0.32

0.29 0.27 0.25 0.22

0.20 0.17 0.15 0.12

_{0.10 0.07 0.04}

1.63

1.51

1.39

1.31

1.20

1.12

1.03

0.94

0.84

0.74

0.64

0.53

0.44

0.34

0.22

WEB THICKNESS FOR FRONT SPAR

ACTUAL

FROM BUCKLING

FROM ROOT TO TIP [mm]

T

H

IC

K

N

E

S

S

O

F

W

E

B

[m

m

]

0.00

0.40

0.80

1.20

1.60

2.00

0.52 0.49 0.46

0.43 0.39 0.36

0.33 0.30 0.26

_{0.23 0.20}

0.16 0.13 0.10

_0.06

1.43

1.35

1.26

1.19

1.10

1.02

0.94

0.84

0.76

0.67

0.57

0.48

0.39

0.30

0.20

WEB THICKNESS FOR REAR SPAR

ACTUAL

FROM BUCKLING

T

H

IC

K

N

E

S

S

O

F

W

E

B

[m

m

]

CONCLUSION

●

Front Spar positioning is estimated to 25% and Rear Spar to 62% of the

Chord Length.

●

Flange and web dimensions are calculated and suitable changes in

dimensions are incorporated from manufacturing point of view.

●

Number of Ribs and their positioning for the prevention of bending and

buckling of Spars is calculated.

●

Mass of the spars calculated from iterations is 15.25 kg.

SCOPE FOR FURTHER WORK

●

Spar position can be optimized based on buckling calculations.

●

Further optimization of Rib is possible.

--Varying number of Ribs and spacing of Ribs.

●

Use of other materials for the design of spars can be thought of.

●

Detail stress analysis of individual components and its validation with

Taking values from NACA Standards

At Root: Profile: NACA 64A

₁

215.

Leading Edge radius = 1.556% c.

Slope of mean line at leading edge = 0.0842.

At Tip: Profile: NACA 64A

₁

210.

Leading Edge radius = 0.701% c.

Slope of mean line at leading edge = 0.0842.

●

INCORPORATING THE LEADING EDGE RADIUS AS

SPECIFIED IN THE PROFILE STANDARD.

1.Giving the slope in the

sketcher

mode

2.Creating the arc of the

required

dimension coming

out of sketcher.

●

Using the connect curve option to join the leading edge radius

and the aerofoil profile.

●

Create the surface using multi section

INTERSECTION OF THE PROFILES

●

Creating the planes at the four sections at ½, ¼, ¾ of the span of the wing.

ANGLE OF ATTACK

●

Create a point at the quarter chord and draw a line for reference.

●

Rotate the intersected profiles as 0.6

0

at the quarter, 1.1

0

at mid span, 1.6

0

at three

By considering the profiles generated with angle of attack at different sections,

the wing surface is created using multi-section surface option.

CREATE THE SURFACE USING MULTI SECTION

SURFACE OPTION

CREATION OF REFERENCE AEROFOIL SECTIONS

●

15 planes are created at rib positions along the wing span.

CONSIDERATIONS MADE

DURING THE DESIGN OF SPAR

ELEMENTS

●

The maintenance of the nose box is made easy.

●

The front spar is I – section.

●

The rear spar is C – section.

DESIGNING OF SPAR ON

MANUFACTURING BASIS

➢

The front spar is placed at 25% of chord length from leading edge.

➢

The rear spar is placed at 62% of chord length from leading edge.

➢

Thicknesses of the flanges and webs are different.

➢

The flanges are made of T-sections and L- sections.

➢

The webs are made with sheet metal.

➢

The thicknesses are optimized based on the availability of the standard gages of sheet metal.

➢

The final assembly of elements can be fastened with rivets.

CROSS SECTION SPAR

Skin area, A

_s

= (b +2*20*t

_s

) mm

2

Rib no.

Dist. From root Flange Width Skin Area Available area Flange Thickness Effective Flange areaWeb thickness

From root

(mm)

(mm)

(mm)

(mm)

1

Root 0

70

220

266.94

3.81

266.94

1.63

2

300

70

220

215

3.07

215

1.63

3

600

70

220

175

2.5

175

1.63

4

900

65

210

150

2.31

150

1.29

5

1210

65

155.2

144.9

2.23

144.9

1.29

6

1520

60

147.2

116.4

2

120

1.29

7

1830

60

147.2

86.4

2

120

1.29

8

2150

55

139.2

60.4

2

110

0.91

9

2470

50

88.8

55.6

2

100

0.91

10

2790

45

82.8

36.1

2

90

0.91

11

3120

40

76.8

16.6

2

80

0.64

12

3450

35

70.8

-0.4

2

70

0.64

13

3780

30

64.8

-12.4

2

60

0.64

14

4110

30

64.8

-19.9

2

60

0.64

15

4440

30

64.8

-24.9

2

60

0.64

16

NO RIB 4750

(mm

2

₎

_(mm

2

₎

_(mm

2

₎

REAR SPAR DIMENSIONS

Rib no. Dis t. F rom root

F lange W idthS k in A rea A vailable areaF lange Thic k nes s

E ffec tive F lange area

W eb thic k nes s

F rom root

(m m )

(m m )

(m m )

(m m )

1

Root 0

90

260

415.01

4.61

415.01

1.45

2

300

90

260

340

3.78

340

1.45

3

600

80

240

295

3.69

295

1.45

4

900

75

230

257.5

3.43

257.5

1.15

5

1210

70

204

223

3.19

223

1.15

6

1520

65

194

180.5

2.78

180.5

1.15

7

1830

60

184

138

2.3

138

1.15

8

2150

55

174

100.5

2

110

0.91

9

2470

50

148

73.5

2

100

0.91

10

2790

45

138

48.5

2

90

0.91

11

3120

40

128

21

2

80

0.64

12

3450

35

118

4

2

70

0.64

13

3780

30

108

-19

2

60

0.64

14

4110

30

108

-36.5

2

60

0.64

(m m

2

₎

_{(m m}

2

₎

_{(m m}

2

₎

CREATION OF THE SPAR SECTIONS

1. Two T sections for the flange, and web section for the front spar.

2. Two L sections for the flange, and web section for the rear spar.

GENERATING SPAR USING

DIFFERENT SECTIONS

CRIMP HOLES OR LIGHTENING HOLES

The lightening holes are made in the element in order to reduce the weight of the

element. the crimp holes are made to the web element of the spar. These holes

provided in between the two successive rib locations.

BIBLIOGRAPHY

1] Abbot & Albert,'Theory of wing sections',Dover publication,1949.

2] David J. Perry,'Aircraft structures',Mc-Graw Hill publication,1950.

3] E. F. Bruhn,'Analysis and design of flight vehicle structures',1973.

4] Michael C. Y. Niu, 'Airframe Stress Analysis and Sizing', 2001.

5] Michael C. Y. Niu, 'Airframe structural design', Conmilit press Ltd., 1989.

6] Kuethe and Schetzer, 'Foundations of Aerodynamics', 2nd Edition, John Wiley

and Sons, New York, 1959.

7] ASM Material Data Sheet

8] MIL Handbook.

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