TYPES OF WING

The wing is one of the most important part of an aircraft as is produces the majority of the lift and keep fuel intact in it. In this blog, we will see different types of the wing we usually use like the infinite wing, finite wing, high wing, low wing,mid-wing, elliptical wing, tapered wing, rectangular wing. 

INFINITE WING 

 Model of infinite wingspan in the test section of the wind tunnel is through and through. The flow about infinite wing is 2 dimensional i.e. in X & Y direction, as it is ±∞ in the Z direction. Lift, Drag, Moment coefficient for the infinite wing is represented as C_L, C_D, C_M, (capital letters).

FINITE WING   

The finite wing is defined wingspan (distance between two wingtips, denoted as b)

Which means the flow about finite wing is 3 dimensional i.e. the flow over the wing is in  X & Y & Z direction. Lift, Drag, Moment coefficient are represented as C_l, C_d, C_m, (small letters).

HIGH WING

The wing is placed on the top of the fuselage i.e. the centre of gravity (Cg). It is a negative distance w.r.t. aerodynamic centre (ag) in the Z direction as shown in the figure. Aerodynamic centre is a point where the sum of all aerodynamic forces is equal to 0. This is called a high wing. It is more stable as compared to the mid and low wing.

 MID WING  

 The wing is placed where the centre of gravity and aerodynamic centre have 0 distance in the Z direction. It is less stable than a high wing and more stable than the low wing

LOW WING

 The wing is placed on the bottom of the fuselage i.e. centre of gravity is a positive distance w.r.t. aerodynamic centre in Z direction it is called a low wing. It is very less stable as compared to the mid and high wing

TYPES OF WING ON THE BASES OF ASPECT RATIO

Aspect ratio:


        

Where C_d,i = induced drag

             C_L= lift coefficient

             AR= aspect ratio

As from the above equation, we can intuition that higher the aspect ratio less the induced drag

 Elliptic wing

        elliptic wing: this type of wing, it has a high aspect ratio. We don’t use this type of wing because it is expensive to manufacture

           Rectangular wing

         Rectangular wing: in this type of wing it has a low aspect ratio i.e. the lift distribution far from optimum.  
  

   Tapered wing

        Tapered wing: in this type of wing the aspect ratio is lower than an elliptic wing and higher than a rectangular wing.  Commercial aircraft have tapered wing because it is easy to manufacture     

ALTITUDE AND DERIVATION OF THE HYDROSTATIC EQUATION

Atmosphere! study about basic of the atmosphere is important in aerodynamics as it will tell us about what is pressure, density, temperature, specific volume flow velocity and streamline with its most commonly used units in aerodynamics it will also brief us about which are the 6 different types of altitude, hydrostatic equation 

PRESSURE

 The pressure is a normal force per unit, area exerted on the surface due to the time rate of change of momentum of the gas molecules on that surface. It is usually defined at a point in the gas or a point on a surface and can vary from one to another.

Commonly used units of pressure are  

1. Newton per square meter (N/m²)
2. Dynes per square centimetre (Dyn/cm²)
3. Pounds per square foot (lb/ft²)
4.  Atmospheres (atm)

 DENSITY

  The density of a substance including gas is the mass of that substance per unit volume. Density will be designated by symbol r

Commonly used units of density are

1.  kilogram per cube meter (kg/m³) 
2.  slug per cube foot (slug/ft³)
3.  pound per cube foot (lb_m/ft³)     (1 slug=32.2Ib_m)

 TEMPERATURE

Temperature is the measure of the average kinetic energy of the particles in the gas.

Commonly used units of temperature are

1.  kelvin (K)
2.  degree Celsius (°C)
3.  degree Rankine (°R)
4.  degree Fahrenheit (°F)

SPECIFIC VOLUME

r is mass per unit volume. Inverse if r is called a specific volume i.e. volume per unit mass

Units

1.  m³/kg
2.  ft³/slug   

FLOW VELOCITY

  Velocity is the distance travelled by an object with respect to time, we all know what 40 m/s velocity of a vehicle means. When we talk about flow velocity it is more subtle as 40 m/s due to south in a horizontal plane. It is very important to designate both speed and direction of flow velocity. 

Each region of gas doesn't need to have the same velocity, it will vary point to point. Flow velocity varies, along with p (pressure), r(density), T (temperature) is a point property

   

The velocity at any fixed point in the flowing gas is the velocity of an infinitesimally a small fluid element as it sweeps through point.

STREAMLINES

 The path took by a moving fluid element is called as streamlines of the flow. There can be no flow across streamlines

DIFFERENT TYPES OF ALTITUDE

There are 6 types of altitude

1. Pressure altitude
2. Temperature altitude
3. Density altitude
4. Absolute altitude
5. Geometric altitude
6. Geopotential altitude

Absolute altitude (h_a): The distance measured from the centre of the earth

1

Geometric altitude: it is defined as the distance measured from the ground from the fig, we can say that

From fig 1 we can say that

....1

                

From newton’s law of gravitation (g varies inversely as the square of the distance from the centre of the earth)

                                              

  (From equation no 1)   

                                   


 Here

                     g= local acceleration of gravity

                     g₀= gravitational acceleration at sea level

                      r= radius of the earth

                      h_G=geometric altitude

                     h_a= absolute altitude

 We will take a model which will allow us to calculate the variation of r,p, T as the function of altitude      

Consider the small stationary fluid element in air as shown in fig 2.

2

We take rectangular faces where dh_G is the height of the side face of the rectangle which is infinitesimally small. 
We will take a model which will allow us to calculate the variation of r,p, T as the function of altitude      

Consider the small stationary fluid element in the air as shown in the fig.

We take rectangular faces where dh_G is the height of the side face of the rectangle which is infinitesimally small.

On the bottom face, the pressure p is felt which gives rise to upwards force of p×1×1 exerted on the fluid element & the top surface is slightly at higher altitude by the distance of dh_G,

 The pressure differs from the infinitesimal value of dp hence, the pressure felt by the top surface is p+dp. It gives rise to a downwards force of (p+dp)(1)(1)on the fluid element.

 The volume of the fluid element is (1)(1)dh_G = dh_G.

Mass of the fluid element is rdh_G. The weight of the fluid element is grdh_G.  

Pressure forces and weight must be balanced because the element is in the rest position

......2

The above equation is called as  HYDROSTATIC EQUATION

Equation number 2 is in a differential form we will integrate this equation to get the variation of pressure in terms of altitude assuming g is constant throughout the atmosphere which is equal to g₀

Altitude h in equation 3 must be different from h_G in equation 2 to compensate for the fact that g is slightly different from g₀. We have defined a new altitude h, which is geopotential altitude. In practical geopotential altitude is a "fictitious" altitude  

RELATION BETWEEN GEOPOTENTIAL AND GEOMETRIC ALTITUDES   

By convention, we will set both h and h_G equal to zero at sea level. Now, consider a given point in the atmosphere. This point is at a certain geometric altitude h_G , and associated with it is a certain value of h (different from h_G,) integrating equation 5 between the sea level and given point we get 

            

HISTORY OF AEROSPACE

SIR GEORGE CAYLEY (1773-1857)

SIR GEORGE CAYLEY (1773-1857)
Sir George Cayley introduced the concept of a fixed wing for generating lift, combined vertical &horizontal tail for stability and another separate mechanism for propulsion.
Sir George Cayley was born at Scarborough in Yorkshire, England on December 27/1773. He was educated at York and Nottingham and later studied chemistry and electricity under several noted tutors. He was a scholarly man of some rank, a portrait of Cayley is shown below. He lived a long life of 84 years.

He engraved his revolutionary fixed-wing the concept on the silver disk in 1799 (see Fig) in 1804, he built a whirling-arm apparatus, shown in Fig, for testing airfoils this was simply a lifting surface (airfoil) mounted on the end of a long rod, which was rotated at some speed to generate a flow of air over the airfoil. In modern aerospace engineering, wind tunnels now serve this function, but in his time the whirling arm was an important development, which allowed the measurement of aerodynamic forces and the centre of pressure on a lifting surface

 Cayley’s states that the basic principle of a flying machine is “to make a surface support a given weight by the application of power to the resistance of air.” He notes that a surface inclined at some angle to the direction of motion will generate lift (upwards force acting on an airfoil) and that a cambered (curved) surface will do this more efficiently than a flat surface. He also states that lift is generated by a region of low pressure on the upper surface of the wing. He was the first one to suggest such multiplanes (i.e. biplanes and triplanes).

  SIR OTTO LILIENTHANL

 Lilienthal was born on May 23, 1848, at Anklam, Prussia (Germany). He did his schooling in Potsdam and Berlin, the latter at the Berlin Technical Academy, graduating with a degree in mechanical engineering. Lilienthal designed and flew the first successful controlled gliders in history. He designed a glider in 1889, and another in 1890—both were unsuccessful. However, in 1891, Lilienthal’s first successful glider flew from a natural hill at Derwitz, Germany. He used cambered (curved) airfoil shapes on the wing and vertical and horizontal tail planes in the back for stability. He made over 2000 successful glider flights. On August 9, 1896, He was gliding from the Gollenberg hill near Stollen in Germany. A temporary gust of wind brought Lilienthal’s monoplane glider to a standstill, he stalled and crashed to the ground. Only the wing was crumpled; the rest of the glider was undamaged. However, Lilienthal was carried away with a broken spine. He died the next day in the Bergmann Clinic in Berlin. In 1893, he built a powered machine; the prime mover was a carbonic acid gas motor that twisted six slats at each wing tip. In 1895, he built a second, but larger, powered machine neither one of these aeroplanes was ever flown with the engine operating.

 WILBUR WRIGHT  & ORVILLE WRIGHT 

Wilbur Wright was born on April 16, 1867, in Millville, Indiana. Orville Wright was born on August 19, 1871, in Dayton, Indiana. Both the brothers have never officially received a high school diploma.  

Orville Wright was a prize-winning cyclist, and this prompted the brothers to set up a bicycle sales and repair shop in Dayton. Three years later they began to manufacture their own bicycle designs, using homemade tools. These enterprises were profitable and helped to provide the financial resources for their later work in aeronautics.

They built a wind tunnel in their bicycle shop in Dayton and tested more than different airfoil shapes. They designed a force balance to measure accurately the lift(a force acting opposite to weight)  and drag(a force acting opposite to thrust )They made a glider 3 glider was a classic. It was constructed in 1902. It was a biplane glider with a 32-ft 1-in wingspan. This number 3 glider is shown in Fig Note that, after several modifications, the Wrights added a vertical rudder behind the wings. This rudder was movable, and when connected to move in unison with the wing warping, it enabled the number 3 glider to make a smooth, banked turn. This combined use of rudder with wing warping (or later, ailerons) was another major contribution of the Wright brothers to flight control in particular, and aeronautics in general.

 References

1 introduction to flight by Jhon D Anderson Jr.

2http://www.wrightbrothers.org/History_Wing/History_of_the_Airplane/Century_Before/First_Airplanes/First_Airplanes.htm

3 https://www.century-of-flight.net/sir-george-cayley-paving-the-way-for-modern-aviation/

4 https://www.famousinventors.org/otto-lilienthal

5 https://airandspace.si.edu/exhibitions/wright-brothers/online/