What Additional Cornering Speed Can Aerofoils Provide to a Formula One Car - Coursework Example

Introduction In the design of F1 cars the aim is creating a down force which is a thrust force that is generated as a result of the aerodynamics of F1 car. The FI cars are to negotiate corners are very high speeds in comparison to the ordinary cars due to increased vertical force that is subjected to tires ensuring there is tight grip on the road. The creating of forces is very similar to the forces that are created in aircrafts enabling it to rise from the ground but as opposed to the case in aircrafts in FI cars the force is in the downward direction (American flyers, 2013). The down force that is created in F1 cars is referred to as aerodynamic grip which is different from mechanical grip that is dependent on the mass of the car, the tires and suspension of the car. The passive devices being added to the car there will also be some creation of drag force in addition to the down force and a good design is a compromise between the two. The aerodynamics to be exhibited by F1 cars will vary greatly in conformation to the race tracks that the cars are to race on. The flow of air over and under the car is responsible for creation of the down force where the force created is proportional to the square of the speed at which the car is moving, meaning that the down force will increase up to four times when the speed of an F1 car is doubled. A minimum speed that the car should travel is important for there to be any substantial creation of a down force (Clancy,1975). In some cases airfoils have been reported to create instability in the car aerodynamics where minor changes in the angle of attack or a change in the car height results to great variation in the down force in some incidences the car may be lifted from the ground. Such incidences are reported when the car moves over a bump or the car strip streams over a crest, and such incidences may lead to a disastrous situation. The spectacular flipping of a Mercedez –Benz CLR that was being driven by Peter Dumbreck when being chased by a competitor closely on a rump in the 1999 Le Mans 24 hours is a typical case. The body shape and the incorporation of airfoils are the two major components that are responsible for the a down force being created when the car is at a high speed. In car racing the change or adjustment of aerodynamic devices is only allowed at pit stops but not in the course of the race. car airfoil down force is given by : Where: D = downforce ( Newtons) WS =wingspan (metres) H = height (metres) = angle of attack F = i lift coefficient ρ = air density ( kg/m³) V = velocity ( m/s) In designing the F1 car the top usually has a tapered shape enabling the car to easily cut through the air keeping the level of wind resistance low. Spoilers and underbody tunnels are some of the additional features incorporated in the cars which serve to ensure that the flow of air is smooth and that the air will be directed to the airfoils. For an ordinary car, the shape is similar to that of airplane where the air flow on the upper side is much faster than under a result of which is the car experiencing a lift. Air fouls with large surface will translate to high down force but this will also mean drag force will also be high. The aspect ratio is very an important parameter in describing the air foil and it is given by Aspect ratio AR =b squard/s where, b = span squared and s is the area of the airfoil. Increasing the angle of attack of the airfoil results to production of a higher down force meaning higher level of pressure on tires more so the rear ones and also this result to increased level of drag Front aerofoil In addition to the front airfoils being responsible for creating down force for the font tire, these air foils are also important in channeling the air flow so as to ensure the air flow is optimal on the entire F1 car body. In F1 cars which have an open wheel design, the cars will be modified constantly depending on the data gathered for each of the races which ensures that the adjustment are made to conform to the needs a particular circuit. Usually the design of the wings is such that it is easy to make adjustment in the course of the race. Rear aerofoil The flow of air on the from airfoil and other components such as the front wheels, drivers helment, side mirrors , side pods and exhausts greatly affects the air flow on the rear airfoil. These consequently lowers the lowers the performance of this airfoil in comparison to that of the front airfoil. But more down force is required to be generated by this airfoil. This usually is achieved by designing the airfoil with a high aspect ratio and having two or more elements just like the in the case of front airfoils , the rear airfoils may be adjusted at point of service when the race is in progress or before the start of the race Discussion The standard maximum width of F1 car is taken as 1.8m as can be seen from the image. The length of 1.8m is equal to 157 pixels. 1m = 157/1.8 = 87.22pi By use of this relationship the dimension of the F1 car can be calculated Front airfoil length= 123pi=123/87.22=1.41 Width of front airfoil is approximated to be 35pi= 35/87.22= 0.4m Front airfoil area = 0.4 x 1.41 = 0.564m2 Back airfoil length = 73pi = 73/87.22= 0.84 Back airfoil width = 53pi = 53/87.22 = 0.61 Back airfoil area = 0.84 x 0.61 = 0.512 The downforce D can be expressed as D = C Calculation of maximum speed for various conditions without airfoils The maximum velocity is attained at the point where the side force (centrifugal force) will just go beyond the friction force between the racing track and the tires. Friction force can be expressed as =  Side force expression is =  Where m is mass of the car, v is velocity at which the car is moving while are is the radius of the corner being negotiated For maximum velocity =  Simplifying =  At  r=50  = 12.13 Applying the same formula for the other conditions the results is as summarized in the table. Table 3 Radius of corner µ 50 100 200 0.1 7.003571 9.904544 14.00714 0.3 12.13054 17.15517 24.26108 0.6 17.15517 24.26108 34.31035 0.95 21.58645 30.52786 43.17291 Graphical results Graphical approach can also be used in obtaining the maximum speed that can be safely negotiated. In the graphs the lines named series 4, series 5 and series 6 represents the total friction force, the frictional force on the front tires and the frictional force on the rear tires respectively. While series 1, series 2 and series 3 represents total lateral force, lateral force on the front tires and lateral force on the rear tires respectively. In the graphs the maximum speed is the value on the x-axis where the total friction line crosses with the total lateral force line. Maximum speed for =0.3 and r=50m From the figure the maximum speed is 12.2 Figure 1 Maximum speed for =0.6 and r=50m From the graph maximum speed is 17.5m/s Figure 2 Maximum speed for =0.95 and r=50m From the graph maximum speed is 21.5m/s Figure 3 Calculating maximum velocity after adding airfoil As a result of airfoil the car will be subjected to a downforce and this will be factored in the calculation D = C =  =  The areas A1 and A2 have been calculated as 0.564 and 0.512 The coefficients for the airfoils are 2.13 and 2.82 respectively as obtained from foilsim =  =  =  =  =  At  r=50 Applying this formula to the other racing conditions the results will be as summarized in the table 2. Table 2 radius of corner µ $50 100 200 0.1 7.60357 10.16469 14.77355 0.3 13.16977 18.62487 29.06378 0.6 18.62487 29.06378 54.68696 0.95 23.43578 42.33643 216.118 Graphical results for maximum speed after adding airfoils Graphical approach can also be used in obtaining the maximum speed that can be safely negotiated. In the graphs the lines named series 4, series 5 and series 6 represents friction force on front tires , the frictional force on the rear tires and the total friction respectively. While series 1, series 2 and series 3 represents total lateral force, lateral force on the front tires and lateral force on the rear tires respectively. In the graphs the maximum speed is the value on the x-axis where the total friction line crosses with the total lateral force line. Some of the sample graphs are as in the following section Maximum speed for =0.95 and r=50m when airfoils included From the figure it can be seen that the maximum speed is about 23.7 Maximum speed for =0.95 and r=100m when airfoils included From the figure it can be seen that the maximum speed is about 35m/s Maximum speed for =0.95 and r=200m when airfoils included Conclusion The results clearly illustrates the principals that govern formula 1 cars. The results indicated that when sharp corners are to be negotiated the practical speed of negotiation of the corners is lower. As the radius increases so do the possible speed increases. The results confirmed that airfoils can only have significant effect when dealing with high speed. This is clearly seen in the case when a small radius is being used putting the maximum speed to be low. In this case it was found that the maximum speed for the case of excluding airfoils and that of including airfoils were almost equal. With no airfoils for 50m radius speed was 21.5 and with inclusion of airfoils the possible speed increased to 23.4. On the other hand increasing the corner radius to 100m the possible speed 30.2 for the case of no airfoils and inclusion of air foils at this radius increased the possible speed of negotiation of the corner to 42.33m/s. From the results it has also be seen that slipping in F1 does not occur simultaneously in the rear and the front tires. Whether the rear or the front tires will slip first will be subject to the fraction of the weight acting on the tires (this being dependant on the location of centre of gravity of car) and the magnitude of downforce generated by each of the two air foils. References American flyers (2013). Different types of flaps, Anderson, John D. (2004), Introduction to Flight (5th ed.), McGraw-Hill, pp. 352–361, §5.19, ISBN 0-07-282569-3 Bertin, J. J.; Smith, M. L. (2001). Aerodynamics for Engineers (4th ed.). Prentice Hall. Clancy, L.J. (1975), Aerodynamics, Pitman Publishing Limited, London ISBN 0-273-01120-0 Houghton, E.L. and Carpenter, P.W.-2006- Fifth Edition Aerodynamics for Engineering Students Read More

Spoilers and underbody tunnels are some of the additional features incorporated in the cars which serve to ensure that the flow of air is smooth and that the air will be directed to the airfoils. For an ordinary car, the shape is similar to that of airplane where the air flow on the upper side is much faster than under a result of which is the car experiencing a lift. Air fouls with large surface will translate to high down force but this will also mean drag force will also be high. The aspect ratio is very an important parameter in describing the air foil and it is given by Aspect ratio AR =b squard/s where, b = span squared and s is the area of the airfoil.

Increasing the angle of attack of the airfoil results to production of a higher down force meaning higher level of pressure on tires more so the rear ones and also this result to increased level of drag Front aerofoil In addition to the front airfoils being responsible for creating down force for the font tire, these air foils are also important in channeling the air flow so as to ensure the air flow is optimal on the entire F1 car body. In F1 cars which have an open wheel design, the cars will be modified constantly depending on the data gathered for each of the races which ensures that the adjustment are made to conform to the needs a particular circuit.

Usually the design of the wings is such that it is easy to make adjustment in the course of the race. Rear aerofoil The flow of air on the from airfoil and other components such as the front wheels, drivers helment, side mirrors , side pods and exhausts greatly affects the air flow on the rear airfoil. These consequently lowers the lowers the performance of this airfoil in comparison to that of the front airfoil. But more down force is required to be generated by this airfoil. This usually is achieved by designing the airfoil with a high aspect ratio and having two or more elements just like the in the case of front airfoils , the rear airfoils may be adjusted at point of service when the race is in progress or before the start of the race Discussion The standard maximum width of F1 car is taken as 1.

8m as can be seen from the image. The length of 1.8m is equal to 157 pixels. 1m = 157/1.8 = 87.22pi By use of this relationship the dimension of the F1 car can be calculated Front airfoil length= 123pi=123/87.22=1.41 Width of front airfoil is approximated to be 35pi= 35/87.22= 0.4m Front airfoil area = 0.4 x 1.41 = 0.564m2 Back airfoil length = 73pi = 73/87.22= 0.84 Back airfoil width = 53pi = 53/87.22 = 0.61 Back airfoil area = 0.84 x 0.61 = 0.512 The downforce D can be expressed as D = C Calculation of maximum speed for various conditions without airfoils The maximum velocity is attained at the point where the side force (centrifugal force) will just go beyond the friction force between the racing track and the tires.

Friction force can be expressed as =  Side force expression is =  Where m is mass of the car, v is velocity at which the car is moving while are is the radius of the corner being negotiated For maximum velocity =  Simplifying =  At  r=50  = 12.13 Applying the same formula for the other conditions the results is as summarized in the table. Table 3 Radius of corner µ 50 100 200 0.1 7.003571 9.904544 14.00714 0.3 12.13054 17.15517 24.26108 0.6 17.15517 24.26108 34.31035 0.95 21.58645 30.52786 43.17291 Graphical results Graphical approach can also be used in obtaining the maximum speed that can be safely negotiated.

In the graphs the lines named series 4, series 5 and series 6 represents the total friction force, the frictional force on the front tires and the frictional force on the rear tires respectively. While series 1, series 2 and series 3 represents total lateral force, lateral force on the front tires and lateral force on the rear tires respectively. In the graphs the maximum speed is the value on the x-axis where the total friction line crosses with the total lateral force line.

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