Aerodynamics - 2

Aircraft's Rotations

An aircraft in flight is free to rotate in three dimensions. It is necessary to control the attitude or orientation of a flying aircraft in all three dimensions. In flight, any aircraft will rotate about its center of gravity, a point which is the average location of the mass of the aircraft. We can define a three dimensional coordinate system through the center of gravity with each axis of this coordinate system perpendicular to the other two axes. We can then define the orientation of the aircraft by the amount of rotation of the parts of the aircraft along these principal axes.

YAW

The yaw axis is defined to be perpendicular to the plane of the wings with its origin at the center of gravity and directed towards the bottom of the aircraft. A yaw motion is a movement of the nose of the aircraft from side to side. A positive yaw, or heading angle, moves the nose to the right.  The rudder is the primary control of yaw.
 
PITCH
 
The pitch axis is perpendicular to the yaw axis and is parallel to the plane of the wings with its origin at the center of gravity and directed towards the right wing tip. A pitch motion is an up or down movement of the nose of the aircraft. A positive pitch angle raises the nose and lowers the tail. The elevators are the primary control of pitch.
 
ROLL
 
The roll axis is perpendicular to the other two axes with its origin at the center of gravity, and is directed towards the nose of the aircraft. A rolling motion is an up and down movement of the wing tips of the aircraft. The angular displacement about this axis is called bank. The pilot changes bank angle by increasing the lift on one wing and decreasing it on the other. A positive roll angle lifts the left wing and lowers the right wing. The ailerons are the primary control of bank. The rudder also has a secondary effect on bank.
 
In flight, the control surfaces of an aircraft produce aerodynamic forces. These forces are applied at the center of pressure of the control surfaces which are some distance from the aircraft cg and produce torques (or moments) about the principal axes. The torques causes the aircraft to rotate. The ability to vary the amount of the force and the moment allows the pilot to maneuver or to trim the aircraft

HOW WINGS CREATE LIFT

                To understand the concept of lift we must be aware of two basic principles behind lift. that explained below

CONSERVATION OF MASS
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The theory of conservation of mass states that what goes in must come out at the same rate.
E.g. imagine if we send some air through a circular tube / wind tunnel in the front then the same amount of air must exit through the back. If we change the shape of the tube like narrowing the middle. So the air in the middle must converge because it has less space in middle so it must speed up in the middle to maintain same amount of airflow. After the middle part air slows down again. (Remember river flows fastly in narrow space)

BERNOULLI’S EQUATION

Bernoulli’s  equation states that, when a fluid is spread up the static pressure is lower compared to a slower moving fluid.( Air is also a fluid). Bernoulli’s equation applies only to subsonic speeds.

HOW THESE WORKING TOGETHER TO CREATE LIFT
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                Imagine an aircraft is travelling through air. The air molecules passes above & below of the wing. We know that the wing designed in an airfoil shape the air molecules in the upper part of the wing need to travel faster to cover a long distance relative to the lower part so the pressure in the upper part is lower than that of the lower part where the air molecules are moving slower than that of the upper part makes the lower part a higher pressure area.(imagine u r trying to push a wall while running and then do the same when in walk now u can feel that slower moving particles can apply more force ).
The speedy movement of air above the wing cause air to move downwards when leaving the trailing edge this is called down wash & also the air movement below the wing causes an upwards movement of air after leaving trailing edge this one is called up wash meanwhile we can see up wash & downwash in other parts of aircraft too. In wings up wash cancels out some of down wash but it results in overall down ward deflection of air. Here we can see Newton’s third law of motion this also contribute in lift.

SOME MORE EXPLANATIONS

There are many theories of how lift is generated. Unfortunately, many of the theories found in encyclopedias, on web sites, and even in some textbooks are incorrect, causing unnecessary Confusion. The theory can be labeled the "Longer Path" theory, or the "Equal Transit Time" theory.
The theory states that airfoils are shaped with the upper surface longer than the bottom. The air molecules have farther to travel over the top of the airfoil than along the bottom. In order to meet up at the trailing edge, the molecules going over the top of the wing must travel faster than the molecules moving under the wing. Because the upper flow is faster, then, from Bernoulli's equation, the pressure is lower. The difference in pressure across the airfoil produces the lift.

Lifting airfoils are designed to have the upper surface longer than the bottom. This is not always correct. The symmetric airfoil also generates plenty of lift and its upper surface is the same length as the lower surface. Think of a paper airplane. Its airfoil is a flat plate top and bottoms exactly the same length and shape and yet they fly just fine. This part of the theory probably got started because early airfoils were curved and shaped with a longer distance along the top. Such airfoils do produce a lot of lift and flow turning, but it is the turning that's important, not the distance. There are modern, low-drag airfoils which produce lift on which the bottom surface is actually longer than the top. This theory also does not explain how airplanes can fly upside-down which happens often at air shows and in air-to-air combat. The longer surface is then on the bottom!

Air molecules travel faster over the top to meet molecules moving underneath at the trailing edge-The flow over the top of a lifting airfoil does travel faster than the flow beneath the airfoil. But the flow is much faster than the speed required having the molecules meet up at the trailing edge. Two molecules near each other at the leading edge will not end up next to each other at the trailing edge. The lift predicted by the "Equal Transit" theory is much less than the observed lift, because the velocity is too low. The actual velocity over the top of an airfoil is much faster than that predicted by the "Longer Path" theory and particles moving over the top arrive at the trailing edge before particles moving under the airfoil.
The upper flow is faster and from Bernoulli's equation the pressure is lower. The difference in pressure across the airfoil produces the lift.-This part of the theory is correct. In fact, this theory is very appealing because many parts of the theory are correct.

In simple terms it’s not the velocity or distance but the turning of the air molecules makes pressure variations around the airfoil & that variation is the primary reason of lift.