Fig. 14   The velocity of the air flowing past the wing has different value at different points on the wing. This creates a difference in pressure which results in a net upward force (lift) on the wing.

How do the wings of a plane generate the lift? Fig. 14 shows the cross-section of a typical wing. The upper and lower parts of the wing are not symmetrical, and the wings are tilted at a small angle to the horizontal. As such, when the plane is moving forward, the velocity of the air flowing past the wing has different values at different points on the wing. Using the principles in fluid mechanics, one can relate the pressure to the velocity of the air at different points on the wing. Adding up (integrating) the pressure variation times the area around the entire wing gives the total (aerodynamic) force on the wing. Hence, the special shape and the tilt of the wing are important factors affecting the aerodynamic force acting perpendicular to the flow direction of the air. This is lift.

Drag is essentially the force due to air resistance. According to Newton's first law, the thrust generated by the plane engines must counterbalance the drag so that the plane can maintain its uniform forward motion. During a long journey, the energy generated by the plane's engines is mainly dissipated in counteracting the drag.

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How rockets work

 Fig. 15   As a rocket launches, the force exerted on the hot gas and the force exerted on the rocket form a pair of action and reaction forces.

You probably have seen rockets launched on television. When a rocket launches, burning gas is expelled from the rocket and the rocket moves upwards. In fact, the upward movement of a rocket has to do with a basic law of physics, the Newton's third law of motion, which says,

"To every action there is an equal and opposite reaction."

A rocket works by burning fuel to produce hot gas. The hot gas rushes out from the nozzles at the bottom of the rocket at high speed. There is a downward force that expels the hot gas out of the rocket. According to Newton's third law, an equal and opposite force must exist. This force propels the rocket upwards. The force exerted on the hot gas and the force exerted on the rocket are a pair of action and reaction forces.

Another way of looking at the launch involves another fundamental physics principle, the conversation of momentum. Initially, the rocket (with the fuel) is at rest and has zero momentum. When the fuel is burnt, the hot gas rushes out of the rocket due to the great heat and pressure produced by the release of chemical energy in burning. The hot gas moves downwards at a high speed, and thus carries a downward momentum. By conservation of momentum, the rocket will acquire an upward momentum of equal magnitude, so that the total momentum of the gas and the rocket remains zero. Hence the rocket moves upward with an increasing velocity (acceleration) as more hot gas is expelled.

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Shape and energy efficiency

 Fig. 16   The Concord was designed with a streamline shape to minimize air resistance.

Have you noticed that rockets, aeroplanes and MagLev trains are all long and thin in shape, and have small and pointed or sloping frontal areas? The shapes of these modes of transportation are specially designed to reduce the air resistance when they are travelling at high speeds. The effect of air resistance becomes more and more important as speed increases. Scientists have found that for a certain range of speeds, the air resistance (force) experienced by an object is given by the equation:

where Cd is called the coefficient of drag which depends on the shape of the object only, r is the density of air, A is the reference area related to the frontal area of the object and v is the speed of the object. Shapes that are long with a sloping or pointed front have a lower coefficient of drag. This partly explains the shapes of high-speed trains and aeroplanes. A lower drag means lower energy loss in moving the object forwards, and therefore better energy efficiency can be achieved.

 [1] KCRC Official Corporate Homepage (History): http://www.kcrc.com.hk/html/eng/corporate/about_kcrc/history/index.asp [2] Transrapid International web site > English > Projects > China