Airfoils in the Speed of F1 Cars - Book Report/Review Example

Airfoils in the Speed of F1 Cars Thermodynamics Introduction This project aims at evaluating various measurements that influencethe movement of Formula One (F1) vehicles. These properties include angular acceleration, centripetal force, coefficient of friction and moments of forces (McBeath 2000, p23). It also uses various unit conversions, problem solving, dimensioning and scaling. The whole concept of this study is to analyze the increase and decrease of the car speed depending on the frictions and other forces applied. Figure 1 below shows a typical design of a formula 1 car. Figure 1: Typical Formula 1 Car, Ferari F 310 2. Objective of this Study The main objective of this project is to analyze the properties and demonstrate the effects aerofoils on the speed improvement a F1 cars. The study also aims at presenting the information obtained in a systematic manner, making it easy to interpret. The first task requires the use of Foilsim software to perform calculation of the maximum speed the aerofoils as well as without aerofoils. The second task requires the use of Foilsim Software to perform the calculation of the new maximum speed for each of the bend radii for the four tyre conditions. The third task is to plot a set of graphs to concisely summarize the findings with the aerofoils and without the aerofoil, the bend radius and the coefficient tyre friction. The final task requires the use of Foilsim to calculate the forces for a specific corner radius when there is no aerofoil and the tyre combination to determine whether it is the front tyres or the back tyres that slip first. 3. Assumptions In the calculations, it is assumed that the car travels around a bend of specific radius of 50m, 100m, 200m and 500m. Secondly, it is assumed that the mass of the formula 1 car is 620kg. The Centre of gravity is assumed to be 2 / 3 of the way back horizontally between the wheels, and 1 / 3 of the height vertically up from the ground. Additionally, it is assumed that the maximum width of car is 1.8 m as defined by the F1 regulations, and that the Maximum height is 0.95 m. Further assumption is that the coefficient of friction between the tyres and the road Intermediate tyres in the dry is 0.7, when immediate tyre is in wet is 0.4, when slicks are in the dry is 0.9 and when slicks are in the wet is 0.1. 4. Calculations The calculations in this study are dependent on the assumptions presented above, among other factors. 4.1. Task 1: Maximum Speed Without Airfoil This is the calculation of the maximum speed of the Formula one car around the four bend radii without the aerofoils for each of the four tyre conditions. First, the question for consideration in this calculation is the connection between the normal force and the frictional force on the car. Being a static problem, we apply the inequality between fs,  s and N. Since N is a constant and is equivalent to the weight of the car, the friction has to increase. Thus, at the maximum speed, the car experiences maximum frictional force. Therefore, the maximum speed will be calculated as follows: f max / N =  s 4.1.1. Intermediate tyres in the dry: 0.7 Calculation of the maximum speed Maximum radius = 500m f max / N =  s = 0.7. Thus 0.7 = v2 / (r g) v2 = (0.7) (r g) v2 = (0.7) (500) (9.8) vmax = √3430 m / sec vmax = 58.566 m / sec 4.1.2. Intermediate tyres in the wet: 0.4 Calculation of the maximum speed Maximum radius = 500m f max / N =  s = 0.4 Thus 0.4 = v2/(r g) v2 = (0.4) (r g) v2 = (0.4) (500) (9.8) vmax = √1960 m / sec vmax = 44.27 m / sec 4.1.3. Slicks in the dry: 0.9 Calculation of the maximum speed Maximum radius = 500m f max / N =  s = 0.9 Thus 0.9 = v2/(r g) v2 = (0.9) (r g) v2 = (0.9) (500) (9.80) v2 = 4410 v = 66.41 m/sec 4.1.4. Slicks in the wet: 0.1 Calculation of the maximum speed Maximum radius = 500m f max / N =  s = 0.1 Thus 0.1 = v2/(r g) v2 = (0.1) (r g) v2 = (0.1) (500) (9.80) v2 = 490 v = 22.136 m/sec Figure 2: F1 Car Dimensioning Figure 3: Height and Weight 4.2. Task 2: New Maximum Speed for each bend Radius 4.2.1. Intermediate tyres in the dry: 0.7 Calculation of the maximum speed Maximum radius = 500m f max / N =  s = 0.7. Thus 0.7 = v2 / (r g) v2 = (0.7) (r g) v2 = (0.7) (500) (9.8) vmax = √3430 m / sec vmax = 58.566 m / sec 4.2.2. Intermediate tyres in the wet: 0.4 Calculation of the maximum speed Maximum radius = 50m f max / N =  s = 0.4 Thus 0.4 = v2/(r g) v2 = (0.4) (r g) v2 = (0.4) (50) (9.8) vmax = √196 m / sec vmax = 14 m / sec 4.2.3. Slicks in the dry: 0.9 Calculation of the maximum speed Maximum radius = 100m f max / N =  s = 0.4 Thus 0.9 = v2/(r g) v2 = (0.9) (r g) v2 = (0.9) (100) (9.80) v2 = 882 v = 29.698 m/sec 4.2.4. Slicks in the wet: 0.1 Calculation of the maximum speed Maximum radius = 200m f max / N =  s = 0.4 Thus 0.1 = v2/(r g) v2 = (0.1) (r g) v2 = (0.1) (200) (9.80) v2 = 196 v = 14 m/sec 4.2.5. Calculations With Aerofoil The racing cars go round the bend with radii of 50m, 100m, 200m and 500m and at different coefficients of friction of 0.1, 0.4, 0.7 and 0.9. Because of the aerofoil, the maximum velocities of the racing cars round the bends will change. The mass of the car is 620kg. In this calculation, we take Ff to represent the friction force and Fn to represent the net normal force. Take Bend Radius = 50 and Friction Force = 0.1 Ff = Fn * μ μ = 1.00. Ff / Fn = 1.00. Fn = m * a m = 620 kg a = 9.81 ms¯². Ff = 1.00 * Fn Fn = ma = 620 * 9.81 = 6082.2 Thus Ff = 1.00 * 6082.2 Ff = 6082.2N Ff represents the centripetal force Ff = Fc. Fc = m * v² / r m = 620 kg, r = 50m Therefore v² = ((Ff * r) / m) v = √ ((Ff * r) / m). Thus, v = √ ((6082.2N * 50m) / 620 kg). v = 22.15 ms¯¹ Take Bend Radius = 100 and Friction Force = 0.4 Ff = Fn * μ μ = 0.40. Ff / Fn = 4.40. Fn = m * a m = 620 kg a = 9.81 ms¯². Ff = 0.40 * Fn Fn = ma = 620 * 9.81 = 6082.2 Thus Ff = 0.40 * 6082.2 Ff = 2,432.88N Ff represents the centripetal force Ff = Fc. Fc = m * v² / r m = 620 kg, r = 100m Therefore v² = ((Ff * r) / m) v = √ ((Ff * r) / m). Thus, v = √ ((2,432.88 * 100m) / 620 kg). v = 19.81 ms¯¹ Take Bend Radius = 200 and Friction Force = 0.7 Ff = Fn * μ μ = 0.70. Ff / Fn = 0.70. Fn = m * a m = 620 kg a = 9.81 ms¯². Ff = 0.70 * Fn Fn = ma = 620 * 9.81 = 6082.2 Thus Ff = 0.70 * 6082.2 Ff = 4258.54N Ff represents the centripetal force Ff = Fc. Fc = m * v² / r m = 620 kg, r = 200m Therefore v² = ((Ff * r) / m) v = √ ((Ff * r) / m). Thus, v = √ ((4258.54N * 200m) / 620 kg). v = 37.06 ms¯¹ Take Bend Radius = 500 and Friction Force = 0.9 Ff = Fn * μ μ = 0.90. Ff / Fn = 0.90. Fn = m * a m = 620 kg a = 9.81 ms¯². Ff = 0.90 * Fn Fn = ma = 620 * 9.81 = 6082.2 Thus Ff = 0.90 * 6082.2 Ff = 5,473.98 N Ff represents the centripetal force Ff = Fc. Fc = m * v² / r m = 620 kg, r = 500m Therefore v² = ((Ff * r) / m) v = √ ((Ff * r) / m). Thus, v = √ ((5,473.98 N * 500m) / 620 kg). v = 66.44 ms¯¹ 4.3. Task 3: Plotting of Graphs 4.3.1. Without Aerofoil BEND RADIUS R V MAX 50 14 100 29.698 200 14 500 58.566 Table 1: Maximum Velocity against Bend Radius without Aerofoil Figure 4: Maximum Velocity against Bend Radius without Aerofoil Coefficient Of Friction V MAX 0.1 22.36 0.9 66.41 0.4 44.27 0.7 58.566 Table 2: Maximum Velocity against the Coefficient of Friction Figure 5: Maximum Velocity against the Coefficient of Friction without Aerofoil Coefficient Of Friction V MAX 0.1 22.15 0.4 19.81 0.7 37.06 0.9 66.44 Table 3: Velocity against Coefficient of Friction with Aerofoil Figure 6: Maximum Velocity against Coefficient of Friction with Aerofoil RADIUS R V MAX 50 22.15 100 19.81 200 37.06 500 66.44 Table 4: Maximum Velocity against Bend Radius with Aerofoil Figure 7: Maximum Velocity against Bend Radius with Aerofoil 4.4. Task 4: Calculation of Forces Assuming that the car is without aerofoils, this section covers calculations of the forces for one particular combination of corner radius and tyre to determine whether the front or the back tyres slip first. 4.4.1. Calculation of the Forces against the Bend Radius For the racing car going round the bends of radius of 50 m, 100 m, 200m and 500m, the maximum speed at each radius is already calculated as 14, 29.698, 14 and 58.566 respectively. The mass of the car is 620 kg. The centripetal Force acting on the car is calculated using the following formula: Force = mv2 / r Taking radius to be 50m Force = 620 * 14^2 / 50 Force = 2430.4N Taking radius to be 100m Force = 620 * 29.698^2 / 100 Force = 5468.221465N Taking radius to be 200m Force = 620 * 14^2 / 200 Force =607.2N Taking radius to be 500m Force = 620 * 58.566^2 / 500 Force = 4253.170681N 4.4.2. Plotting the Forces against Bend Radius without Aerofoil Table 5 below shows the results of the calculation of the forces against the bend radius. In these calculations, the car does not have aerofoils. RADIUS R V MAX Force 50 14 2430.4 100 29.698 5468.221465 200 14 607.6 500 58.566 4253.170681 Table 5: Forces against Bend Radius without Aerofoils Figure 8: Plotting of Forces against Bend Radius without Aerofoils 4.4.3. Determining Whether the Front or the back tyre slips first The point at which the tyre slips depend on the amount of centripetal force applied on the car (Williams 2005, p32). Greater Centripetal force quickens the slipping of the tyre. In this regard, the tyre with greater Centripetal Force force slips before the tyre with less centripetal force (Benson 2011, p47). RADIUS R V MAX Force in the Back Tyre Force in the Front Tyre Results 50 14 2430.4 6,082.20 Front Tyre Slips first 100 29.698 5468.221465 2,432.88 Back Tyre Slips first 200 14 607.6 4258.54 Front Tyre Slips first 500 58.566 4253.170681 5,473.98 Front Tyre Slips first Table 6: Determination of the tyre that slips first Figure 9 below shows the plotting of the forces for the two tyres on the same plane. Figure 8: Comparison of Forces in Tyre 1 and tyre 2 5. Discussion The observation of the racing car behavior demonstrates the effects of the friction force on the bending and changing of speed of the car. The clear observation is that when the coefficient of friction drops, it also decreases the maximum velocity of the car at which it can take a bend. In the same manner, as the coefficient of friction increases, it increases the maximum velocity at which the racing car takes the bend (McBeath 2006, p43). Moving further in consideration of the down force, it has remarkable impacts on the behaviors of the racing car. When the car has designed aerofoil is installed in the car, it creates a down force in the direction of the ground. This enables the racing formula one car to take a bend at reduced velocities (Henry 1985, p56). Another remarkable observation is that no matter the mass of the racing car, the maximum velocity at which the racing car takes the bend does not change, but remains constant. 6. Conclusion The conclusion of this project is that adding aerofoil to the racing car racing car provided a down force. The aerofoil is an improvement to the racing car speed as it goes round the corners. The question that every driver of the racing formula 1 car asks is on the maximum speed which the car requires, which is ensured by adding the aerofoil. Indeed, aerofoils grant the driver control of the car against the effects of gravitational pull and centripetal force. References McBeath, S. 2000. Competition Car Down force: A Practical Handbook, SAE International. Henry, A. 1985. Brabham, the Grand Prix Cars, Osprey. Benson, A. 2011. "BBC Sport - Formula 1 bosses confirm engines will not change until 2014". BBC News. McBeath, S. 2006. Competition Car Aerodynamics, Sparkford, Haynes, p43. Williams, R. 2005. "No change as formula one goes on making fools of rule-makers". The Guardian (Guardian Media Group). Read More