- Leo Wang
Aeroplanes have become an increasingly popular method of transportation for human beings to travel all over the world. In this case, some people may consider why the aeroplanes drive faster or how these huge machines fly successfully in the air. This research is mainly to figure out this amazing ability for a specific shape to race through the air.
Forces: Basically, there are four forces acting on the plane when flying.
In this research, we are mainly trying to find out the reaction between the air and the plane.
In other to make a successful journey for the flight, there are two main keys to determine: Wings and Engines
Wings of a aeroplane can also be called an airfoil (aerofoil) with a curved upper surface and a flatter lower surface, making a cross-sectional shape.
In this case, when air meets the wings, it splits into two streams, top and bottom.
When the flight starts accelerating on the ground, the upper air travels the same time as the air underneath. But the upper air needs to travel a longer distance than the lower, therefore the former has a higher speed passing through the plane(wings).
According to the fluid dynamics of Bernoulli’s Principle, when the air moves faster, the pressure will decrease. Therefore the pressure at the top is lower than the bottom, which causes a force on the wing, lifting the plane upwards.(as shown below)
Figure 1 Different pressure exists on the wings
However, as what we can see in Fig 1 above, the lines on the top are moving faster than the bottom, though the position of the air starts at the same vertical line before it hits the wings. As we can see more clearer on Fig 2, the air at the top gets considerably earlier than the bottom. It is because the air beneath is affected by the free stream air and get slowed down. As the result of it, the separated air does not have the same time at the trailing edge, in which case the Bernoulli’s Principle can not be used in this situation.
Fig 2 the acceleration and deceleration of the different streams
Therefore we need another cause of lift wings.
According to Newton’s Law:
Newton’s first Law: Any object must maintain uniform linear motion or rest until an external force acts on it to change the state of motion
Newton’s second Law: The total force of an object equals to the mass of the object multiplied by the acceleration of the object.
Newton’s third Law: The interaction between the two objects and the reaction force is always equal in magnitude and opposite in direction , acting on the same straight line.
From the Newton’s first Law, if the air is originally at rest, and it starts to accelerate or move, then there will be a force acting on it.
From the Newton’s third Law, if there is a reaction from the wings acting to the air, then there will be a lift acting on the wings to lift it up in the opposite direction.
Fig 3 There is no lift acting on the wings
Fig 4 Wings with a certain angle can cause the lift
In Fig 4, the air passes over the wings and bent down. Therefore the bending air causes the downward force acting on the air and the reaction to the wings is the lift.
According to Newton’s second Law, F=ma, the lift force is always equal to the mass of aeroplane multiply by the downward acceleration.
which can also be expressed as the rate of change of momentum of the air downward.
This can also be rearranged to .The quantity is called the impulse.
And because of Newton’s Third Law, momentum is always conserved.
Comparing the two figures above, we can see that the plane is heading at an angle to produce a lift. If not, there will be no force acting on the plane.
Angle of the attack to the air
As shown on Fig 5, the greater angle of attack, the greater lift can act on the wings.
There is a lift coefficient related to the angle of attack. When angle of attack is increasing, the lift coefficient will increase up to the maximum lift coefficient, after which it starts to decrease.(as shown in figure 6)
In fluid dynamics, a stall is the term to explain the reduction of the lift after normally 10-20 degrees of attack angle(as shown in the graph above).From Figure 7, after the stall point, it is noticeable that the gap between the air flowing and the wing is increasing and as a result of it, the drag increases while lift starts decreasing.
Lift and Lift Coefficient
In reality, there are a few conditions affecting the lift acting on the plane. As what we can think of, the air density and the size of the wing can have an influence on the amount of lift force.
The relationship between lift force and coefficient of lift is shown below:
L is lift force
ρ is the air density
v is true airspeed (is the speed of aircraft relative to the air mass or density)
A is wing area
is the lift coefficient
The equation above comes from the ThePrandtl lifting-line theory used to predict the lift distribution, in this case to measure out the lift force for a particular plane in the air.
Flaps and Slats
In reality for the plane to fly, the pilots need to change the angle of attack in different conditions and height. There are a few ways to achieve this. The most common method is to extend flaps and slats.
By altering the position of flaps and slats, the angle of attack is changed as the lift characteristics of a wing is improved. Therefore it can reduce the speed and aircraft can be flown safely and increase the angle of landing. As the drag can be increased during these changes, then the takeoff and landing distances can be shortened effectively.
When the plane is coming down towards to the ground, landing gear comes out to give the plane keep driving on the ground for a distance until it finally comes to rest. In this case the friction should be the only force existing to slow down the plane. The acceleration is at the highest value when it first reaches the ground.
1. If the ground friction increases, f=-ma, then the acceleration will decrease more quickly.
2. If the shape of plane increases, the area of air contacting increases, which means the air resistance will increase. Using the same idea, then the acceleration will decrease more obviously.
Therefore, as the ground friction or the shape of plane increases, the quicker the plane will stop.
Engine: (Fueling flight)
When it comes to propelling an aircraft through the sky, different types of engines are taken in account, which can depend on the amount of thrust needed for each flight.
In a typical propulsion system, fuel is burnt and releases plenty of energy, which can generate mechanical power.
Turbo engine from the front of the intake air flows in the booster compressor, upcoming oil mixed with gas and ignited in the combustion chamber. High-temperature exhaust gas flowing through the turbine combustor after the rotation force generated , this force through the drive shaft to drive the compressor. At this point the exhaust still contains even more energy, namely via high-speed spray nozzle to produce thrust reaction according to Newton’s third law .
As the development of technology, there are increasingly various ways to speed up the plane in the air, but the basic of flying aeroplane is related to the change of momentum of the planes. Meanwhile, Bernoulli’s effect is not the key effect for lift as the lift generated is very small in terms of flying the aeroplane.
- http://www.allstar.fiu.edu/aero/airflylvl3.htm How Airplanes Fly: A Physical Description of Lift Level 3
The preceding is an article byDavid Anderson, Fermi National Accelerator Laboratory, andScott Eberhardt, formerly of the Department of Aeronautics and Astronautics, University of Washington, now at the Boeing Company.
- http://science.howstuffworks.com/transport/flight/modern/airplanes.htm How Airplanes Work by Marshall Brain, Robert Lamb and Brian Adkins
- http://en.wikipedia.org/wiki/Lift_(force)#Increased_flow_speed_and_Bernoulli.27s_principle Lift (Force), From Wikipedia, the free encyclopedia
- http://en.wikipedia.org/wiki/Stall_(fluid_mechanics) Stall (fluid mechanics), From Wikipedia, the free encyclopedia
 Influid dynamics,Bernoulli’s principlestates that for aninviscid flowof anonconductingfluid, an increase in the speed of the fluid occurs simultaneously with a decrease inpressureor a decrease in thefluid‘spotential energy.
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