LEVEL TURN / V-n DIAGRAM

Which is the maximum speed at which an aircraft fly?  Well, it is defined at the time of manufacturing only. We will see how to obtain maximum speed of aircraft at the maximum lift with the help of V-n diagram. It is a very important diagram, and every aircraft has its own V-n diagram. We will first derive the formula for angular velocity and radius required for a turning flight.

Case 1.  A-LEVEL TURN FLIGHT

As u can see in the figure

A

Φ Is bank angle

L is lift

R is radius

W is weight

 From figure

Components figure will be made

B

We can say from the figure  

A plane is at a constant altitude and horizontal plane

From the force diagram in figure B.The magnitude of the resultant force is

We will now introduce a new term “load factor”

n=L/W…1

The load factor is usually quoted in terms of “g’s”; for example, an aeroplane with lift equal to 10 times the weight is said to be experiencing a load factor of 10 g’s.

Hence, the equation can be written as,

From newton’s law of motion

Combining 2 and 3

The angular velocity is denoted by w=V∞/R called a turn rate.

 For both the civil aircraft and jet aircraft we required, The highest possible load factor, The lowest possible velocity.

Case 2.  PULL – UP MANOEUVRE

In this case the initially L=W then there is a sudden increase in the lift, L>W Airplane will begin  to turn upwards in the vertical plane.

The resultant force is, from figure

Combine equation 6 and 3

         

      

Case3. PULL-UP MANEUVER.

In this case, initially L=W, suddenly flight rolls to invert position in such a manner Land W both are in downwards direction as shown in figure

Cobine 9 and 3 equations

High-performance aircraft are  designed in such a way that they have high load factor and low turn radius,n+1 ≅  n and n-1 ≅ n, the equation  will be reduced to

We know that lift is

Substituting equation 14 and 1 into 12 and 13

From the above Equation, it clearly shows that lower the wing loading smaller the turn radius and larger the turn rate everything else is constant

Designing of the wing loading is done by the following points

1. Payload
2.  Range
3.  Maximum velocity 

V-n DIAGRAM

At high speed, n is limited because of structural designed. V-n Diagram is a graph of load factor versus velocity of a given aircraft

  

The plane is at velocity V₁ and at an angle of attack where C_l<C_lmax, is point 1 in the diagram. Velocity remains the same V₁, angle of attack is increased to get max lift and max load factor that can be obtained at velocity V₁ is point 2 in the diagram. 

With the same velocity, we will again increase the angle of attack, wing stalls and load factor drops at point 3, it is called a stall region, is unobtained in flight. 

Now, we will increase the velocity to V₄ and max possible load factor also increases, is the point is 4.

Beyond a certain value of load factor, defined as the positive limit load factor and showed by the horizontal line in the diagram. Velocity corresponding to point B is V*. We will again increase the velocity to V₅, is the velocity where we fly at Cl<C_lmax, so that +limit load factor is not exceeding. Point 5 is a point where we get c_lmax at velocity V₅ with structural damage in aircraft. 

Vertical line CD is the high-speed limit, the velocity greater than this, the dynamic pressure becomes so large that again structure damage may occur to the aeroplane. AE&ED they are negative absolute angles of attack that is a negative load factor

Point B is called a manoeuvre point. At this point lift and load factor both simultaneously at the highest possible values, velocity corresponding to pint B is called the corner velocity V*