2.2 Platform

A wind-tunnel contains 3 significant parts: the powering section, an accelerating section, and a testing section.

2.2.1 Powering Section

The powering section normally contains air fans to produce air flows. In lab wind-tunnels, the power of the fan is usually high. In home, however, fans and hair driers are approximately the only devices to produce air flows. Driers usually have larger speed; however, the diameter of the flow produced by driers are usually too narrow to cover the whole model. Fans, however, produce flow with less speed but with larger cross-sectional area. The cross-sectional area of 1 fan, however, is not enough to be increased to a significant speed. 2 fans, therefore, has to be used. To increase the speed of the flow and cover the edge area between the two fans in which no flow is generated, a third fan is used. They are placed in the following configuration:

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2.2.2 Accelerating Section

Since most of the fans are usually not high enough in power to produce an air flow with a significant speed or are costing too much power to do so, an accelerating section is usually necessary.

The construct of this section is similar to a Venturi tube, tubes whose diameter changes throughout its body to accelerate the flow inside it. Venturi tube is used in the chassis of modern F1 cars. In the bottom of a F1 car, however, Venturi tube is not an open-ended tube, but rather wings to accelerate the air flowing through the bottom of the car. A Venturi tube can also measure the speed of a flow using difference in pressure at different locations.

Mass of conservation is crucial in understanding how a Venturi tube increases the speed of a fluid. The mass entering the Venturi tube should be equal to that leaving the tube according to law of conservation of mass, which states that matter can be neither created nor destroyed. Therefore:

Where ?is mass of fluid entering the tube; ?is mass leaving the tube.

Where ?is density of fluid, ?is cross-sectional area of the tube, and T is thickness of the cross-sectional area.

The equation could be written as:

Therefore, speed of flow at one point of a Venturi tube is inversely proportional to the cross-sectional area at that location. To increase the speed exiting the tube, the area of Departure of the tube, the cross-sectional area where the flow leaves the Venturi tube, must be smaller than that of the area of Entrance, the cross-sectional area where the flow enters the tube.

Since the Venturi tube compresses the air, this should lessen the problem created by the uneven distribution of fan at each location of the Entrance of the wind-tunnel.

In order to have a more uniform flow, paper tubes are staked between the Venturi tube and the testing section. They will regulate the air flow so that the flow blowing onto the model would be parallel to the tube instead of going at various directions. They will act as flow straighteners.

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2.2.3 Testing Section

The testing section measures the forces exerted on the model. An actual wind-tunnel in labs contain intricate balances to measure the force exerted on the car by air in each direction, therefore to determine the side force, drag force, and downforce a car experiences at a given speed. However, it is hard to construct a wind-tunnel balance at home; therefore, a normal balance measuring objects’ weights will be used. The model car will be put on the balance, which is in the wind tunnel, and as downforce is created when wind flows through the model, the weight of the car, or the normal force the car exerts on the balance, will increase.

Actual wind-tunnels also have designs in order to keep the wheels of the car turning while the car remains stationary to the outside. Whether or not the wheels are turning makes a significant difference to open-wheel racecars such as F1 racecars since the wheels would produce a turbulence. Modern F1 cars have come up with various solutions to keep this turbulence from creating drag. However, since this design is hard to be constructed especially for a 1:20 scale model car, the wheels will remain stationary during the test.

The best configuration of cross-sectional shape of the testing section of a wind-tunnel built to test performance of cars is closer to semi-circles since they most accurately mimic the flow of air around the actual car in actual conditions; however, due to limitations of materials used in constructing the wind-tunnel, a rectangular shape is applied since it is easier to be applied.

It is worth noticing that in actual conditions, the ground is moving with respect to the car, and the air is stationary with respect to the ground; in a wind-tunnel, the ground is stationary with respect to the car and the air is moving with respect to the ground and car. This affects the ground-effect of a car since with moving ground, larger downforce would be created. But just as the turning of wheels and shape of cross-sections, such effects have to be ignored given the limitations of building a wind-tunnel using the simplest materials.

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?????? Since the tube’s cross-section has a limited width and height, unlike the actual condition when the space beside the car and above the car is nearly infinite, the air flowing through the car will be compressed because of the model and the limited edges, which is known as the Blockage Effect. Also, flow around the edges of the tube tends to be slower than that around the middle. Both of these conditions means that the model car has to be significantly smaller than the cross-section of the tube both in width and in height.

Therefore, it is stated by the Society of Automotive Engineers that the front projection width and height must be smaller than 30% of the cross-sectional width and height, respectively.

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2.2.4 Variables

A pitot tube will be used prior to measurement to measure the speed of flow generated by the wind-tunnel. This speed is important in calculating the downforce a car produces at different speeds in the actual condition.

A Pitot tube is a commonly used device in fluid mechanics to measure the speed of a flow. A pitot tube has a part which intercepts no air directly and measures the static pressure of the fluid. It also has a part that intercepts some of the air which measures the stagnation pressure. The tube has two holes on the other end, the pressure difference could be obtained by measuring the pressure in each of the holes. A U-tube will be used to measure the speed.

The Bernoulli equation is important in calculating speed of fluid from pressure difference in a Pitot tube. The Bernoulli equation is as follows:

Where P is the pressure inside the fluid, ?is the density of the fluid, v is speed of the fluid, g is gravitational constant, and h is height of the fluid.

Since height involved in a Pitot tube is normally small, the gravitational potential energy of the fluid is often ignored. Therefore, the equation can be simplified as follows:

Static pressure measures the pressure of the fluid with speed. Therefore, static pressure is equal to:

Stagnation pressure measures the pressure of the fluid after all the kinetic energy is transferred into pressure. Stagnation pressure is equal to:

Therefore, by combining these two equations, there is:

v could then be derived from pressure difference, which is equal to :

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Reynolds number is a characteristic of a fluid. However, different fluids with different velocities, densities, and viscosities could have the same Reynolds number. Reynolds number is given by , where ?is the density of the fluid, which is taken as 1.29kg/m^3 for air in this experiment; v is its velocity; l is the characteristic of length, which, in this experiment, is length of the car; and ?is viscosity of the fluid, taken as 1.83*10^-5kg/m*s in this experiment. The same car performs differently under fluids of different Reynolds numbers. Therefore, ideally, when performing a wind-tunnel test on a model car, the velocity of the air should increase inversely proportional to the minification; however, that means if a wind-tunnel test is to be performed on a 1:20 scale model car to test the downforce the actual car receives, so as this experiment intends to do, the speed of the wind tunnel of this experiment would be too high. The problem of this is not just the inability of a home-made wind-tunnel to reach this speed, but also that the air might no longer be approximated to an incompressible fluid after the air speed exceeds an insurance speed of 92 m/s, meaning that the density of the fluid would be inconsistent throughout the tube. This would pose problems on the calculations of the lift force. Exceeding the limit of incompressibility is not an usual question to be considered by car engineers, but rather exist as a problem in building jets. Therefore, as long as the Reynolds number is larger than 10^5, where the lift coefficient is approximately constant, the experiment will proceed.

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From the velocity obtained from the Pitot tube, it is possible to calculate the downforce on the actual car with a different speed. Lift force is calculated as follows:

?????? Where ?is lift force, which, in this occasion of cars that generate downforce, takes vertical downward as the positive direction; ?is the lift coefficient, which is a constant associated with Reynolds number; ?is area of horizontal projection area of the wing; v is speed of the air flow.

?????? Therefore,

?????? And since the model is of 1:20 scale, that is, the length of the model is 1/20 of the actual car, ?should be 20*20 = 400 times of

?????? Therefore,