A wing is a surface used to produce an aerodynamic force normal to the direction of motion by travelling in air or another gaseous medium, facilitating flight. For a wing to produce "lift", it must be oriented at a suitable angle of attack relative to the flow of air past the wing. When this occurs the wing deflects the airflow downwards, "turning" the air as it passes the wing. Since the wing exerts a force on the air to change its direction, the air must exert a force on the wing, equal in size but opposite in direction. This force manifests itself as differing air pressures at different points on the surface of the wing.

A region of lower-than-normal air pressure is generated over the top surface of the wing, with a higher pressure existing on the bottom of the wing. These air pressure differences can be either measured directly using instrumentation or they can be calculated from the airspeed distribution using basicphysical principles, including Bernoulli’s Principle which relates changes in air speed to changes in air pressure.

The lower air pressure on the top of the wing generates a smaller downward force on the top of the wing than the upward force generated by the higher air pressure on the bottom of the wing. Hence, a net upward force acts on the wing. This force is called the "lift" generated by the wing. A schematic representation of air flow over an airfoil is shown below in Fig. 1.

Fig: 1

**Wing Design****:**

Wing construction is basically the same in all types of aircraft. Most modern aircraft have all metal wings, but many older aircraft had wood and fabric wings.

To maintain its all-important aerodynamic shape, a wing must be designed and built to hold its shape even under extreme stress. Basically, the wing is a framework composed chiefly of spars, ribs, and (possibly) stringers.

**Problem Statement:**

Design the wing configuration of a high subsonic trainer aircraft and do the structural substantiation for the front and rear spar assembly.

- Identify types of aircraft wing structure, types of wing configuration, wing skeleton, wing cross section, NACA 4 & 5 series airfoils, super critical airfoils and its performance parameters and identify the correct airfoil for atypical high subsonic aircraft.
- Carryout the conceptual design, identify the overall wing dimension and part dimensions. Sketch the skeleton structure; identify the parts, subassemblies and assembly. Generate CAD Model of parts and assembly.
- Carry out the Static Structural Analysis & Modal Analysis to evaluate the stress and displacement under the limited load.

**Input Parametrs:**

- Aircraft type – high subsonic, trainer aircraft
- Fuel Storing: wing & fuselage
- Engine Thrust: 17000N
- Range – 900 km
- Service ceiling – 9000 m
- Endurance – 2.5 hours
- Maximum Dive Speed – 950 km/h
- Design Factor – 1.5
- Maximum Load Factor - +7.0/-2.5g
- 2 hard points with up to 1000 kg on each wing.

**Conceptual Parameters to Know:**

AR Aspect Ratio

b Span

c chord

C_{L } lift coefficient

c_{l } section lift coefficient

C_{mac} Pitching moment coefficient about the aerodynamic center

c_{r} root chord

c_{t} tip chord

c_{avg } mean geometric chord

D Drag

D_{i } induced drag

h_{wlet} height of winglet

L lift

l length

M_{b } bending moment

n Load Factor

q dynamic pressure

S wing area

t thickness

t/c thickness to chord ratio

V_{∞} free-stream velocity

V_{s} stall speed

W Weight

Ʌ Quarter chord sweep

λ taper ratio

ϕ dihedral angle

ρ density

σ bending stress

**Numerical Calculation****:**

General design procedure:

The general steps involved in the conceptual design calculations are:

- Finding maximum Lift co efficient C
_{L MAX} - Finding Reynold’s no
- Selection of airfoil
- Wing selection

- chord at the root section(c
_{ROOT}) - chord at tip (c
_{TIP}) - mean aerodynamic center (ĉ)
- Aerodynamic center
- distance from mean aerodynamic center chord from fuselage (Ŷ)
- selection of dihedral angle and wing incidence
- wet area calculation
- Finding drag co efficient (C
_{D})

**Step1**: **Finding maximum Lift co efficient C _{L MAX}**

In order to find Lift force,

L = C _{l max }×.5 × ρ × s × (V _{stall})^{2 }---- (1)

Where,

ρ – Density

s – wing area

V _{stall }– stalling speed

And C _{l max }– maximum lift coefficient.

But for steady for flight condition,

L=W ------- (2)

Therefore the equation becomes:

W=C _{l max }×0.5×ρ×s× (V _{stall})^{2}

Therefore, To find C _{l max}

C _{l max}= 2(w/s) / (ρ×V_{stall}^{2})

Where,

The wing loading, W/S= 270kg/m^{2}

At an altitude of 9000m,

Density, ρ =0.4663kg/m^{3}, Stalling speed,

The stalling speed shall not exceed beyond 50knots for trainer aircrafts (Reference from the book aircraft design by raymer)

(i.e) V _{stall} = 31.1m/s

Now substituting V_{stall} on C_{lmax, }we get,

C _{l max }= (270×2) / (0.4663×31.1^{2})

**C _{l max = 1.197}**

**Step2**: **Reynold Number Calculation:**

We know that,

R_{e }= (ρ×v×l)/µ -------- (3)

Where, Density ρ = 0.4663

V = 31.1 m/s

Chord, I = Span / Aspect ratio = 12.65 / 9 = 1.4m

Dynamic viscosity, µ= 14.35 × 10 ^{-6 }Kg/ms

Thus, R_{e} = (0.4663×31.1×1.4) / (14.35×10^{-6})

R_{e }= 1.41×10^{6}

**Step3**: **Airfoil Selection:**

From the obtained values of coefficient of lift and Reynold’s number, we can determine the type of airfoil for the design.

From the book **THEORY OF WING SECTIONS BY ABBOT**, Using the graph the airfoil can be selected. Thus the selection of airfoil is,

**NACA 4412**

**WING SELECTION**

Wing is the part of the aircraft, which produces lift force to the aircraft and in trainer aircrafts it provide for fuel storage and landing gear alignments. Generally the tapered wing the chord length of the airfoil is not the same in root and tip.

**Step1****: Chord at the Root Selection (C _{root})**

C _{root }= (2s) / [b×(1+λ)] -------- (4)

Where,

b - wing span

λ – taper ratio

S = W_{TO} / (W/S) (W_{TO} = Takeoff weight)

S = 4800 / 270 = 17.8 m^{2}

b = (Aspect ratio × span)^{1/2}

b = (9* 17.8)^{.5 }= 12.65 m

λ = 0.5 (For trainer aircrafts)

Therefore, C _{root }= (2×17.8) / [12.65× (1+0.5)]

C_{ROOT }= 2.63 m

**Step2****: Chord at Tip** (**C _{tip})**

C _{tip }= c _{root} × λ ------ (5)

C _{tip }= 2.63 × 0.5

C _{tip }= 1.315 m

**Step3****: Mean Aerodynamic Center** (**Ĉ**)

Ĉ = (2/3) × C _{root }× (1+λ +λ^{2}) / (1+λ) -------- (6)

Ĉ = (2/3) × 2.63 × (1+0.5+0.25) / (1+0.5)

Ĉ = 2.04 m

** Step 4****: Aerodynamic Center**

A/D center = 0.25 × Ĉ --------- (7)

A/D center = 0.25 × 2.04m

A/D center = 0.51m

** Step 5****: Distance from mean Aerodynamic center Chord from fuselage ****(ŷ)**

Ŷ = [b × (1+2λ) × (1+ λ)] / 6 ------- (8)

Ŷ = [12.65× (1+ (2×0.5)) × (1+0.5)] / 6

Ŷ = 6.325m

**Step6****: Selection of Dihedral Angle and Wing Incidence**

- The dihedral angle = 5 degrees. (
**Dihedral angle**is the upward angle from horizontal of the wings or tail plane of afixed-wing aircraft.) - Wing incidence = 1 degree.

The above parameters can be assumed. (Reference from the book aircraft design by raymer)

**Step7****: ****Wet Area Calculation**

S_{ wet }= S – S _{ref }---------- (9)

Where, S = 17.8 m^{2}

S _{ref }= Root Chord × Fuselage Diameter = 2.63 × 1.4

S _{ref }= 3.682 m^{2}

Thus, S _{wet} = 17.8 – 3.682 = 14.118 m^{2}

Where, (C_{L}) ^{2 }/ × (π ×e× AR) ----------- (10)

Where,

Efficiency e = 0.8

AR = 9

C_{L} = 1.197

Therefore,

(C_{L})^{2}/ × (π ×e× AR) = (1.197)^{2} / (π ×0.8×9)

= 0. 0633

Thus,

C_{D} = C_{DO }+ [(C_{L})^{2} / (π ×e× AR)] ----------- (11)

= 0.0091 + 0.0633

C_{D }= 0.0724

Thus the drag is calculated now,

D = (1/2) × ρ × V^{2 }× S × C_{D} ----------- (12)

D = (1/2) × .4663 × 31.1^{2 }× 17.8 × 0.0724

Therefore the total drag, D = 290.61 N

Winglet length is 20% of the wing semi-span.

**Pressure load****:**

During flight, the wing is subjected to a pressure load which acts in the upward direction, this pressure load is determined by calculating the load factor (n).

Since,

n = L/W

& n = 1/ Arccosine 15°

n = 1.03

Therefore,

L = n × W

= 1.03 × 4800 = 4944 Kg

L = 48.484 KN

This is the total lift which has to be generated by the sets of its wing. Thus the force developed by each wing is 24.242 KN.

This force is converted into the pressure load, which is in the form of uniformly distributed load by dividing this force by the semi wing area. Therefore, the total pressure load applied from the bottom of the surface is 1322 Pa.

**Specification of the wing****:**

WING SPAN |
12.65 m |

WING AREA |
17.8m^{2} |

C_{ L MAX } |
1.197 |

WING PLANFORM |
Tapered-slight swept wing |

STALLING SPEED |
31.1m/s |

AIRFOIL TYPE |
NACA 4412 |

ASPECT RATIO |
5.12 |

SWEEP ANGLE |
5 DEGREES |

Table: 1

By using the above derivatives, wing is modeled in CATIA V5R21. Firstly the coordinates of the airfoil (NACA 4412) is imported into CATIA through Excel then wing is modeled in “wireframe and surface design” workbench. Some of the tools used in the CATIA to create the CAD model are:

- Sketcher tool
- Extrude Surfaces
- Constraints & multi-section surfaces.
- Sketch based features
- Swept Surface Definition
- Transformation Surfaces.
- Split Surfaces etc.

**Geometry & Details****:**

** **

**Material Properties****:**The material assigned for wing is ‘Aluminum Alloy’ with given material properties:

Density (ρ) | 2770 kg/m^{3} |

Modulus of Elasticity (E) | 7.1E10 Pa |

Poisson’s Ratio (ʋ) | 0.33 |

Tensile Yield Strength | 280 MPa |

Shear Yield Stress (K) | 201.5 N/mm^{2} |

Maximum Allowable Stress | 300 N/mm^{2} |

Table: 2

**Methodology Adopted****:**This analysis was carried out by using Static Structural module in ANSYS Workbench. As the wing geometry is the assembly of different parts, all the parts are “Bonded” to each other.

**Meshed Model****:**

After setting up the boundary conditions the problem was solved to find out the equivalent stress and maximum deformation of the wing in Z- Direction without any shear.

**Results****:**

**Directional Deformation****:**

**Equivalent Stress****:**

**Conclusion****: **

After analyzing the above results for deformation and Von-Mises Stress of the wing, it is observed that the wing can maximum deform till 319 mm which is in the safer zone and the maximum Von-Mises Stress is reached up to 162.04 MPa which is well below than the tensile yield strength of the prescribed material i.e. 280 MPa.

**Modal Analysis****:**

Modal analysis is the study of the dynamic properties of structures under vibrational excitation. In aircraft due to the lift load and the load due to mounting engine on the wing leads to vibration. The modal analysis uses the overall mass and stiffness property of the structure to find the various periods at which it will naturally resonate.

Computation of natural frequencies and natural mode shapes of a structure could be of great significance. They tell us at what frequencies the structure can be excited into resonant motion. In many cases, this information is sufficient for modifying the structural design in order to reduce noise and vibration. In addition, a dynamic interaction between a component and its supporting structure is very important because the component could cause structural damage or failure if its operating frequency is close to one of the natural frequencies of the structure.

So we proceed further and analyze the wing structure for different frequency modes. The mesh parameters and the boundary conditions for the problem would be same as of above. The analysis was performed to find the total deformation under 5 modes.

**Total Deformation Mode 1****:**

**Total Deformation Mode 2****:**

** **

**Total Deformation Mode 3****:**

** **

**Total Deformation Mode 4****:**

**Total Deformation Mode 5****:**

** **

**Natural Mode shapes and Frequencies****:**

S.No. |
Mode Shape |
Frequencies (Hz.) |

1. | 1 | 1.8002 |

2. | 2 | 7.9148 |

3. | 3 | 11.165 |

4. | 4 | 18.249 |

5. | 5 | 24.117 |

** **Table: 3

**Conclusion****:**

The natural frequencies and the natural mode shapes of five modes are obtained by the Computational Modal Analysis and they are presented in Table 3. All the natural mode shapes are shown from fig.5 to fig.9.

These results will be used in dynamic interaction between the wing and its supporting structures.

**Final Deduction****:**

Static Structural and Modal analysis for the aircraft wing was carried out successfully, and it is observed that the wing structure is safe under the above loading conditions. Hence the design of the wing structure is validated.

Thus, the Design of the aircraft wing and its structural validation is done successfully.