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Lift

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Introduction

Lift is an interactive force. If there is no fluid, there will be no lift, as there is nothing to generate the force against the wing. It is not like gravitational or electric fields, which work in a vacuum, with no physical interactions. There needs to be physical contact between the wing and the air for lift to be generated.

Lift is also generated by a difference in velocity between the wings and the fluid. If there is no relative motion, there is no lift. It doesn’t even matter if the wing moves across stationary fluid, or the fluid moves across a stationary wing, the relative movement will create lift. Lift acts perpendicular to the motion, and drag acts in the opposite direction.

Lift and drag are both aerodynamic forces. Therefore, we take them both into account when we estimate the total aerodynamic efficiency of the plane. To do this, we use what is called the ‘lift-to-drag ratio’. If the amount of lift generated by an aircraft is large, and the amount of drag created is small, the aircraft has a high lift-to-drag ratio.

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Middle


The force created by lift (which we will give the notation,
image00.png) has a direct relationship, and is therefore directly proportion to a number of factors, stared below:

  • Density of air, image01.png: the density of a substance is the amount of mass it has per each unit of volume. The density relates to the viscosity and compressibility of the air.
  • The planform area, image08.png: as mentioned before, the amount of lift depends on the size and shape of the object. The planform area is the surface area of the fuselage and the wings.
  • The square of the velocity, image10.png: velocity is a factor of generated force, and it has a ‘square’ relationship with force.

As lift force is proportional to density, area and the square of velocity, we can derive the equation:

image11.png

Scientists have put the constant equal to half the coefficient of lift. So if we rearrange the equation, using image12.png as the lift coefficient, we get...

image13.png

...

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Conclusion

rder:0px solid #000000;width:13px;height:14px;">image08.png.The air pressure, image06.png.The normal unit vector pointing to the wing, image02.png, and the vertical vector that is perpendicular to the airflow, image03.png.

Forces and pressure have been experimented with, to show that the ratio between the difference in force, image04.png and the difference in surface area, image05.png is equal to the product of the pressure, image06.png and the vectors given above. Using this information, we can form a differential equation:

image07.png

We can now solve this to find the force, image00.png, by integrating the right hand side of the equation with respect to image08.png.

image09.png

This formula gives the value of the lift force, which can be used for many things, from determining the maximum weight of an aeroplane, to calculating the coefficient of lift.

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