INTRODUCTION TO AERODYNAMIC

What do u think what is aerodynamics …

Aerodynamics (aero mean something involved to air or atmosphere, dynamic means characterized by constant change) 

As for aerodynamics means something involved with air with  the constant change in its properties so here in the introduction to aerodynamics we look at the different types of flow, how does pressure, density and speed of the air changes the property of the flow, we will also drive the following equations Continuity, Momentum (Euler’s, Bernoulli’s ), Energy equations.

DIFFERENT TYPES OF FLOW

    TYPES OF FLOW ON THE BASES OF PRESSURE

                   I.  COMPRESSIBLE FLOW:  compressible flow is a flow in which we don’t assume density (density₁≠density₂) of the flow to be constant, such type of flow is particularly important at high speed, such as for high-performance subsonic aircraft, all supersonic aircraft vehicles and rocket engine.

                 II.  INCOMPRESSIBLE FLOW:  incompressible flow is the flow in which the density of the flow is assumed to be constant(r₁=r₂), it is only a theoretical type of flow we assume density to be constant to simplify the calculations it is done in the flow in which the actual variation of r is negligibly small, otherwise, such type of doesn’t exist in reality  

TYPES OF FLOW ON THE BASES OF FRICTION

       I.        VISCOUS FLOW: it is a type of flow with friction. Types of viscous flow.

           a)   LAMINAR FLOW: in this type of flow Reynolds number is less than 2100. The streamline lines are smooth and regular and a fluid element moves smoothly along a streamline.

           b)  TURBULENT FLOW: in this type of flow Reynolds number is greater than 4000. The streamlines break up and fluid element moving in a random, irregular, and tortuous fashion

  II. INVISCID FLOW : in this flow velocity of the fluid is 0  in this flow we neglected viscosity

CONTINUITY EQUATION 

We will apply the basic physics principle in flowing gases to get the laws of aerodynamics.

Physics principle: mass can be neither be created nor be destroyed.

To apply this principle on flowing gases we will consider an imaginary circle drawn perpendicular to the flow direction as shown in the figure 1

    figure 1

The cross-section area of the stream tube (streamlines that go through the circumference of the circle, these streamlines form stream tube) may change with from point 1 to 2 as shown in figure 1

As the flow is steady the mass flow will remain constant throughout steam tube i.e. mass at point 1 =mass at point 2 because of the mass flowing through the stream tube is confined by the streamlines of the boundary much as the flow of water through a flexible garden hose is confined by the wall  

Consider all the fluid elements that are momentarily in the plane of A₁. After a lapse of time dt, these same fluid elements all moving a distance , as shown in figure. The elements have a swept out volume A₁ V₁ dt downstream at point 1.

The mass of the gas dm in this volume is equal to the density times of the volume

                                

         

This is the mass of the gas that as a swept through area A1 during time interval dt.        (Definition: the mass flow through an area A is the mass crossing A per unit time)

From equation 1, for area A_{1
Mass flow is} 

                                     

This is the continuity equation for steady fluid flow.

It gives us

1.       the algebraic equation that relates the value of r& V& area at one section of the stream tube to be the same quantities at any other point.

2.       There is a caveat in the equation

      I.   V₁&V₂ are assumed to be uniform over the entire area A₁&A₂ respectively.

      II.   Density1&dnsity₂ are assumed to be uniform over the entire area A₁&A₂ respectively.

     III.   In real life, it is an approximation, in real life V&r vary across cross-section area.

3.       The continuity equation is a workhorse in the calculation of the flow through all type of ducts and tube, such as wind tunnel and rocket moto 

   

figure 2

4.       Consider the streamline of flow over an airfoil, as shown in the figure. The space between two adjacent streamlines, such as the shaded space is a stream tube in figure 2  applies to the stream tube in the figure, is a stream tube. Equation 2 applies to the stream tube in where r₁&V1 are appropriate mean values over A1&r1 are appropriate mean value over A₁&r₂&V₂ are appropriate value over A₂.

   INCOMPRESSIBLE AND COMPRESSIBLE FLOW

1.        COMPRESSIBLE FOW:  compressible flow is a flow in which we don’t assume density (density₁≠density₂) of the flow to be constant, such type of flow is particularly important at high speed, such as for high-performance subsonic aircraft, all supersonic aircraft vehicles and rocket engine.

2.         INCOMPRESSIBLE FLOW:  incompressible flow is the flow in which the density of the flow is assumed to be constant(density₁=density₂), it is only a theoretical type of flow we assume density to be constant to simplify the calculations it is done in the flow in which the actual variation of r is negligibly small, otherwise, such type of doesn’t exist in reality  

                   A₁ V₁ = A₂ V₂

                      V₂= V1 (A₁/A₂)

This explains why all common garden hose nozzle is convergent shape.

This same principle is used in the nozzle for a subsonic wind tunnel. Built for aerodynamics testing.

MOMENTUM EQUATION

The continuity equation says nothing about pressure in the flow

From intuition, that the pressure is an important flow variable, the difference in pressure creates a force that acts on the fluid element and causes them to move.so the relation between pressure and velocity is given by  Euler’s, Bernoulli’s equation

EULER’S EQUATION

We will apply the basic physics law in flowing gases to get the laws of aerodynamics.

We will use newton’s second law of motion

\       Force= mass ×acceleration

                                 F=ma

To apply this physic law inflowing gas consider an infinitesimally small fluid element moving along a streamline with velocity V, as shown in the figure3

figure 3 

At some given instant, the element is located at point P. the element is moving in the x-direction, where the x-axis is oriented parallel to the streamline at point P, Y&Z axis are mutually perpendicular to X-axis

Force on the fluid element is given by

     1.  The pressure acting in a normal direction on all the six faces

     2.  Frictional shear is acting tangentially on all the 6 faces of the element

     3.  Gravity is acting on the mass inside the element  

Here we will ignore the presence of friction forces, the gravity force is generally a small contribution to the total force.

We will assume the only force acting on the fluid element is pressure.

How to calculate the pressure acting on a fluid element

      a)  Dimensions of the fluid element are dx dy dz  

      b )  Consider the faces which are perpendicular to x-axis (in x-direction because of the pressure on  the faces parallel to the streamline doesn’t affect the motion of the element along the streamline.)

     c)   Pressure on the left face is P

The area on the left face is dy dz

       Force is p(dydz)                                          it is in a positive X direction

     d)   We know that pressure varies from point to point in the flow, \ there is a change in pressure per          unit length, symbolized by the derivative dp/dx

     e)   If we move away from the left face by a distance dx along the x-axis , the change in pressure is           (dp/dx)dx

     f)      Pressure on the right face is p+(dp/dx)d
             The area on the right face is  dy d
            Force on the right face is [p+(dp/dx)dx](dydz)                    is in negative x direction

From newton’s 2^nd law of motion

      F=ma
combine equation 3,4&5

 The above equation is Euler’s equation

Point to be taken into consideration when dealing with Euler’s equation

1.  It is a rate of change of momentum   

2.  We neglected friction and gravity

3.  It can also be said as a momentum equation of inviscid flow.

4.  Assumed to be steady, invariant w.r.t to time

5.  The equation is valid for both compressible and incompressible flow

6.   It gives us change in pressure dp to change in velocity

7.   A differential equation, it describes the phenomena in an infinitesimally small neighbourhood around the given point

To obtain Bernoulli’s equation

We will take 2 points, far removed from each other in the flow but on the same streamline p&v at point 1&2 as shown in figure 4

figure 4

We will consider the case of incompressible flow.

These are the following points about Bernoulli’s equation

1. This equation hold for inviscid & incompressible flow

2.  Properties between different points along a streamline

ISENTROPIC FLOW

 There is neither heat exchange nor any defect due to friction (adiabatic process, reversible)

By using thermodynamics law’s and the appropriate calculation we get

Derivation of this equation will be there in a future blog 

LIFT/ DRAG

Aircraft, what is the first thing that comes to your mind?....
How does it manage to fly at such high altitude? What is the aerodynamic centre,  well, u guys are at the right place, yes, we will answer to all your question let's see what makes an aircraft fly.
let's start with what kind of forces acts on an aircraft. Four types of forces act on an aircraft
1. Lift
2. Drag
3. Thrust
4. Weight

1. LIFT (L)

The component of Aerodynamic force perpendicular to the relative wind

                                                          Or

It is an upward force which acts opposite to the weight of an aircraft

 Lift is denoted by L


2. DRAG (D)

Component of aerodynamics forces parallel to the relative wind is called a drag

                                                              Or

Drag is an aerodynamics force which acts opposite to the thrust and restricts the aircraft’s the motion through the air

Drag is produced through

1 Wing

2 Vertical and Horizontal Tail

3 Fuselage

4 Thrust

5 landing Gear

TYPES OF DRAG

1 Induce Drag:  Is the drag created by the vortices at the tip of an aircraft's wing. It is the drag due to lift. Induce Drag is direct proportion to the angle of attack i.e. Angle of Attack increase Induce Drag increase, Angle of Attack decrease Induce Drag decrease.

2 Skin friction Drag: It is caused by the actual contact of the air particles against the surface of the aircraft. Skin friction drag is an interaction between a solid (the aeroplane surface) and a gas (the air), the magnitude of skin friction drag depends on the properties of both the solid and the gas. For the solid aeroplane, skin friction drag can be reduced, and airspeed can be increased somewhat, by keeping an aircraft's surface highly polished and clean

3 Form or Pressure Drag:  A drag which is caused by the air that is flowing over the aircraft or airfoil. The separation of air creates turbulence and results in pockets of low and high pressure that leave a wake behind the aeroplane or airfoil (thus the name pressure drag). This opposes forward motion and is a component of the total drag. Since this drag is due to the shape or form of the aircraft, it is also called form drag. Streamlining the aircraft will reduce form drag

4 Parasite Drag:  it is the sum of Skin Friction, Form, and Interference Drag

   

5 Interference Drag: It comes from the intersection of air streams that create turbulence,  For example, the intersection of the wing and the fuselage at the wing root has significant interference drag. It is also very high when two surfaces meet at perpendicular angles.

6 Wave Drag: Wave Drag is a drag that retards the forward movement of an aeroplane in both supersonic and transonic flight, as a consequence of the formation of shock waves.

HOW IS LIFT PRODUCE

When the aerodynamic flow is passed over an airfoil it follows the law of nature, namely continuity equation and newton's second law of motion (Bernoulli's and Euler's equation)

As we can see in the figure the upper portion of an airfoil has an obstruction, because of this stream tube is squashed to a smaller cross-sectional area, according to continuity equation ( ρAV =constant ), velocity must be increased in the stream tube.where the tube is been squeezed on the lower portion, there is no obstruction, so the cross-section area increases and according to the continuity equation velocity tends to decrease

We can say that

Flow velocity increase over the top surface of an airfoil is more than the bottom surface.

For incompressible flow, from Bernoulli's equation, we can say if velocity increase so, static pressure decrease this tend is valid for compressible flow from Euler's equation we can say dv is positive so dp has to be negative

so we can say this if velocity increases pressure tends to decrease

from this, we can state that,

On the top surface of the airfoil, there is low pressure and on the bottom surface we have high pressure

This pressure difference creates in a force in an upwards direction called a lift

WHY MOST OF THE LIFT IS PRODUCED BY THE FIRST 20 TO 30%?

 The most to the lift are produced by the first 20 to 30% because the largest difference in pressure on the top and bottom surface is on the front part of the airfoil. as shown in figure

The main function of the back part is for streamline shape to avoid flow separation.

Factories affecting lift 

1. Free stream velocity
2. Free stream density. (altitude)
3. Wing area
4. Angle of attack
5. Shape of airfoil
6. Viscosity coefficient
7. Compressibility of airflow 

QUESTION AND ANSWER

Q1. Explain different types of aerodynamic forces?

 Ans. there are 4 different types of aerodynamic forces 

1. Lift(L): The component of Aerodynamic force perpendicular to the relative wind .we can also say It is an upward force which acts opposite to the weight of an aircraft.

2. Drag(D): Component of aerodynamics forces parallel to the relative wind is called a drag or we can say, Drag is an aerodynamics force which acts opposite to the thrust and restricts the aircraft’s the motion through the air.

3. Weight(W): Weight is a gravitational force which acts opposite to lift force. In steady-state flight W=L

4. Thrust(T): Thrust is a propulsion force it makes the aircraft moves in a forward direction.

Q2.  What is the aerodynamic centre? Which is the most preferred location for an aerodynamic centre

Ans. Aerodynamic centre is a point where submission of all the aerodynamic forces is equal to zero.

The aerodynamic centre should lie before the centre of gravity because these types of configuration give a stable effect to the aircraft.

Q3. What is the difference between the conventional tail configuration and canard configuration?

Ans. When the horizontal stabilizer is behind the wing it is called conventional tail configuration. In the conventional tail configuration, the lift on the tail is generally in the downward direction. This can be avoided if a control surface is located ahead of the wing. Such a configuration is called canard (see Wright flyer)It may be added that a canard, being ahead of c.g., has a destabilizing contribution to.

Q4. What is the lift coefficient?

  

As u can see in the picture lift is directly propositional to lift coefficient, dynamic pressure, wing area, that means if we want to increase lift or lift coefficient we have to increase wing area and dynamic pressure (square of velocity)
the lift coefficient is derived using dimensional analysis

Q5. Why aircraft fly at such a high speed?

Ans. As u can see in the above formula lift is directly propositional to dynamic pressure
and as we can see in the equation no.1 that dynamic pressure is directly propositional to the square of velocity i.e. if we want to increase lift, velocity will be increased by its square.

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/