Aerofoils - What Speed Increase do Aerofoils Give to an F1 Car - Assignment Example

Name Course Tutor Date Computer Lab Assignment Two: Aerofoils - What Speed Increase do Aerofoils Give to an F1 Car? Introduction The concentration on straight-line speed in F1 cars has drastically reduced over years due to an invention that aerofoils could probably increase the grip against the track considering such conditions as tyre and negotiation of sharp corners by drivers. This development has had its share of criticism in that preceding cars skid the oncoming ones off the tracks in cases where the range is not close enough to receive the oncoming stream without turbulence. By introducing aerofoils on an F1 car, the innovators were however motivated by the fact that this aids in virtual increase of weight thus giving it the required stability while considerably increasing the speed on the track. According to Hornsey (2011), aerodynamics in F1 has continued to elicit controversial studies with most of the stakeholders engaging in various simulation exercises as part of education meant for demystification of existing challenges. Due to the importance that aerodynamics possesses towards the survival of F1 racing, this report has given importance to the concepts involved in aerodynamics such as coefficient of friction, centripetal force, angular acceleration, unit conversion, aerofoil lift, moments of forces, Newton’s laws, scaling and dimensioning. The major aims of this study is to establish the speeds of an F1 car around the corner without the foils on, speed of an F1 car for each of the new conditions introduced by both the tyre conditions and introduction of aerofoils and lastly plotting of the summarizing characteristic graphs. Discussion In order to determine the speed improvements that aerofoils impart on an F1 car, there was need to calculate speeds of both conditions i.e. when the aerofoils are mounted and when they are not mounted. The software that was applied in coming up with simulations for speed calculations when the aerofoils were mounted is called FoilSim III Student Version 1.4d. The chord and the span of the chosen F1 car (Ferrari F1-2000) searched through Google image were imposed on the Foilsimu for analysis and subsequent simulation. These measurements were taken through the use of pixel count method and scaling in order to establish the unknown dimensions now that the width is a mandatory standard of 1.8m. Assumptions Determination of the objectives identified above was based on the following assumptions the car will be travelling around a bend of fixed radius of 50 m, 100m, 200m or 500m. Secondly the standard weight of the car was maintained at a constant 620kg as per the Formula one racing conventions. Thirdly, the centre of gravity was assumed to be 2/3rds of the way back between the wheels, and 1/3rd of the height up from the ground. As defined by the F1 regulations, the maximum width of the car was maintained at a normal 1.8m. It was also assumed that the maximum height of the car is 0.95m; which defines its stability. The following coefficients were assumed for the friction coefficients between the tyres and the road: i. Intermediate tyres in the dry: 0.7 ii. Intermediate tyres in the wet: 0.4 iii. Slicks in the dry: 0.9 iv. Slicks in the wet: 0.1 This analysis was done through the help of the equations enlisted below as per the tutorial videos offered for this study. Also the definitions to the terms provided in the introductory part would serve a huge purpose in aiding understand the direction that this study would take. Establishing the maximum speed around the specified bends (50m / 100m / 200m / 500m) would need absolutely no involvement of any other formula other than the Newton’s laws of motion. The first consideration made was that centripetal force and frictional force are related to each other by equation (1) below; (1) Secondly, the frictional component for an object considered to be travelling in a straight line is calculated using equation (2) below: (2) Where m represents the car’s mass, r represents the radius of the bend and v represents the velocity of the car. In order to come up with the force that is required for the purpose of maximum friction that is exerted by the car on the track, a coefficient of friction is introduced. This is meant to represent the prevailing conditions between the existing weight of the car and the type of contact created. Therefore, this force is represented by equation (3) shown below: (3) Where is the coefficient of friction while N is the normal force acting down on the road surface. It is however important to keep in mind that the F1 car weight is given in kilograms, therefore; (4) Substituting (2) and (4) in equation (1) gives equation number (5) shown below for the calculation of the maximum bend velocity as calculated for in the table below. (5) These tables give evidence that speed of an F1 car differs around the radii for different conditions that are provided. Increasing the coefficient of friction for example raises the car stability thus increase in speed is recorded. An increase in radius of the bend seems to straighten the road thus the car no longer banks as compared to smaller radiuses whose banking occurs at a very low speed thus veering the cars off the track. A solution meant to square out this problem is thus designed through the use of aerofoils that are studied in the next objective. Maximum Speed of F1 Car in m/s   Bend Radius (m) μ 50 100 200 500 0.1 7.00 9.90 14.01 22.15 0.4 14.01 19.81 28.01 44.29 0.7 18.53 26.20 37.06 58.60 0.9 21.01 29.71 42.02 66.44 Table 1: Maximum speed of F1 car in m/s Maximum Speed of F1 Car in mph   Bend Radius (m) μ 50.00 100.00 200.00 500.00 0.1 15.76 22.29 31.52 49.83 0.4 31.52 44.57 63.03 99.66 0.7 41.69 58.96 83.38 131.84 0.9 47.27 66.86 94.55 149.49 Table 2: Maximum speed of F1 car in mph Speed (mph) Speed (m/s) Fc (N) Ff N 0 0.00 0.00 608.22 1 0.44 1.22 608.22 2 0.89 4.90 608.22 3 1.33 11.02 608.22 4 1.78 19.60 608.22 5 2.22 30.62 608.22 6 2.67 44.09 608.22 7 3.11 60.01 608.22 8 3.56 78.38 608.22 9 4.00 99.20 608.22 10 4.44 122.47 608.22 11 4.89 148.19 608.22 12 5.33 176.36 608.22 13 5.78 206.97 608.22 14 6.22 240.04 608.22 15 6.67 275.56 608.22 16 7.11 313.52 608.22 17 7.56 353.94 608.22 18 8.00 396.80 608.22 19 8.44 442.11 608.22 20 8.89 489.88 608.22 21 9.33 540.09 608.22 22 9.78 592.75 608.22 23 10.22 647.86 608.22 24 10.67 705.42 608.22 25 11.11 765.43 608.22 26 11.56 827.89 608.22 27 12.00 892.80 608.22 28 12.44 960.16 608.22 29 12.89 1029.97 608.22 30 13.33 1102.22 608.22 Table 3: Maximum frictional force and centripetal forces involved in the above condition Graph 1: Formula One car cornering forces without aerofoils. This section gives a breakdown of how the rear and front aerofoils were designed in order to achieve the desired results. Figure 1 shows an F1 racing car marked ready for carrying out dimensioning. Figure 1: Ferrari F1-2000 marked for carrying out measurements The pixilation for each of the dimensions in the model above is as shown below and each of them is represented by the scale of 1 pixel = 0.008955m. These dimensions are further broken down in the calculations carried out in figure 2 below. i. Front aerofoil = 57x162 pixels ii. Rear Aerofoil = 37x114 pixels iii. Between rear and front tyres = 346 pixels iv. Between rear aerofoil and rear tyre =55 pixels v. Between front aerofoil and front tyre = 198 To find out the dimensions, the following calculations were carried out: The length of the car as per the set standards = 1.8m (201 Pixels) 1 pixel = 0.008955m Taking this as the standard of our calculations then: i. Front aerofoil = (162 x 57) 0.008955m = 1.45m x 0.51m ii. Rear aerofoil = (37x114) 0.008955 = 1.02m x 0.33m iii. The distance between the rear and front tyres = 346 x 0.008955m = 3.10m iv. The distance between the rear aerofoil and rear tyres = 55 x 0.008955m = 0.49m v. The distance between the front aerofoil and front tyres = 55 x 0.008955m = 1.77m Figure 2: Dimensional calculations for a Ferrari F1-2000 Applying the above dimensions in the design of front and rear aerofoils the following data and graphs are successfully generated in the FoilSim III Student Version 1.4d as the main design and analysis software. Following a successful analysis and design of the aerofoils based on the information provided in the above photograph, the resulting graphs rather the aerofoil designs were imported as shown in graph 2 and 3 below. The differences that are seen in the aerofoil designs are based on the differences between the dimensions such as the chords and the spans. The angles of attacks also differ from each other for the betterment of the aerodynamic conditions i.e. downforce required to manoeuvre the car through a corner without any problems. Design of front aerofoil Joukowski Airfoil Camber = 15.0 % chord , Thickness = 12.5 % chord Chord = 0.5 m , Span = 1.45 m Angle of attack = 9.0 degrees Standard Earth Atmosphere Ambient Pressure = 101.261kPa, Ambient Velocity = 160 km/hr X/c Y/c P V -0.497 0.112 97.601 322 -0.475 0.137 97.381 329 -0.443 0.16 97.271 333 -0.401 0.182 97.194 335 -0.35 0.201 97.159 336 -0.293 0.214 97.183 336 -0.229 0.222 97.279 333 -0.161 0.224 97.452 327 -0.09 0.219 97.7 319 -0.017 0.206 98.018 308 0.054 0.187 98.392 295 0.125 0.161 98.807 280 0.193 0.131 99.245 263 0.257 0.096 99.688 244 0.316 0.059 100.119 225 0.369 0.022 100.522 205 0.414 -0.012 100.887 186 0.451 -0.042 101.206 166 0.477 -0.064 101.475 148 0.477 -0.064 101.475 148 0.492 -0.076 101.695 132 0.491 -0.076 101.867 117 0.472 -0.062 101.997 105 0.431 -0.037 102.09 95 0.366 -0.005 102.153 88 0.276 0.026 102.19 83 0.168 0.052 102.206 81 0.05 0.067 102.205 82 -0.067 0.07 102.19 83 -0.177 0.065 102.169 86 -0.273 0.056 102.152 88 -0.352 0.048 102.162 87 -0.414 0.044 102.236 77 -0.459 0.047 102.411 48 -0.489 0.055 102.484 28 -0.505 0.07 101.001 179 -0.507 0.09 98.465 293 -0.497 0.112 97.601 322 Table 4: Data utilized in coming up with the front aerofoil design. Plotting the above data into a graph as per the video tutorials provided result in the front aerofoil design shown in graph 2 below. It is evident from the above data table that the angle of attack shall have to be set at 9 degrees in order to achieve a maximum downforce at a camber of 15.0 % chord and thickness of 12.5 % chord. Graph 2: Front aerofoil design Design of Rear Aerofoil Joukowski Airfoil Camber = 15.0 % chord , Thickness = 12.5 % chord , Chord = 0.33 m , Span = 1.02 m Angle of attack = 9.0 degrees Standard Earth Atmosphere Ambient Pressure = 101.261kPa Ambient Velocity = 160 km/hr X/c Y/c P V -0.497 0.112 97.601 322 -0.475 0.137 97.381 329 -0.443 0.16 97.271 333 -0.401 0.182 97.194 335 -0.35 0.201 97.159 336 -0.293 0.214 97.183 336 -0.229 0.222 97.279 333 -0.161 0.224 97.452 327 -0.09 0.219 97.7 319 -0.017 0.206 98.018 308 0.054 0.187 98.392 295 0.125 0.161 98.807 280 0.193 0.131 99.245 263 0.257 0.096 99.688 244 0.316 0.059 100.119 225 0.369 0.022 100.522 205 0.414 -0.012 100.887 186 0.451 -0.042 101.206 166 0.477 -0.064 101.475 148 0.477 -0.064 101.475 148 0.492 -0.076 101.695 132 0.491 -0.076 101.867 117 0.472 -0.062 101.997 105 0.431 -0.037 102.09 95 0.366 -0.005 102.153 88 0.276 0.026 102.19 83 0.168 0.052 102.206 81 0.05 0.067 102.205 82 -0.067 0.07 102.19 83 -0.177 0.065 102.169 86 -0.273 0.056 102.152 88 -0.352 0.048 102.162 87 -0.414 0.044 102.236 77 -0.459 0.047 102.411 48 -0.489 0.055 102.484 28 -0.505 0.07 101.001 179 -0.507 0.09 98.465 293 -0.497 0.112 97.601 322 Table 5: Data utilized in coming up with the rear aerofoil design. Transforming the data in columns X/c and Y/c into a graph gives results shown in graph 3 below. This is the desired shape of the rear aerofoil design. Graph 3: Rear aerofoil design When the above aerofoils are employed in Formula One car design, the effective friction coefficient tends to one. This is because the relative weight of the car is increased by a huge margin thereby imparting stability on it. The graph of such a car shall appear as shown below in graph 4. Graph 1: Formula One car cornering forces without aerofoils. Conclusion The aerofoil effect on an F1 car is tremendously felt as observed in the discussion section above. The graphs 1 and 4 indicate the deviation in the force required to veer the car of the track with a considerable reduction in the F1 car with aerofoils. This is attributed to the downforce brought about by the presence of the rear a front aerofoils as designed by the Foilsimu application. The Foilsimu application on the other side is successfully deployed in the design of the rightful aerofoils desired for the Ferrari F1-2000. Works Cited Hornsey, David. Race & Track Day Driving Techniques. Dorchester: Veloce Publishing Ltd, 2011. Lux. Ferrari F1-2000 - 2000 . 2000. 12 January 2014 . Read More

Intermediate tyres in the dry: 0.7 ii. Intermediate tyres in the wet: 0.4 iii. Slicks in the dry: 0.9 iv. Slicks in the wet: 0.1 This analysis was done through the help of the equations enlisted below as per the tutorial videos offered for this study. Also the definitions to the terms provided in the introductory part would serve a huge purpose in aiding understand the direction that this study would take. Establishing the maximum speed around the specified bends (50m / 100m / 200m / 500m) would need absolutely no involvement of any other formula other than the Newton’s laws of motion.

The first consideration made was that centripetal force and frictional force are related to each other by equation (1) below; (1) Secondly, the frictional component for an object considered to be travelling in a straight line is calculated using equation (2) below: (2) Where m represents the car’s mass, r represents the radius of the bend and v represents the velocity of the car. In order to come up with the force that is required for the purpose of maximum friction that is exerted by the car on the track, a coefficient of friction is introduced.

This is meant to represent the prevailing conditions between the existing weight of the car and the type of contact created. Therefore, this force is represented by equation (3) shown below: (3) Where is the coefficient of friction while N is the normal force acting down on the road surface. It is however important to keep in mind that the F1 car weight is given in kilograms, therefore; (4) Substituting (2) and (4) in equation (1) gives equation number (5) shown below for the calculation of the maximum bend velocity as calculated for in the table below.

(5) These tables give evidence that speed of an F1 car differs around the radii for different conditions that are provided. Increasing the coefficient of friction for example raises the car stability thus increase in speed is recorded. An increase in radius of the bend seems to straighten the road thus the car no longer banks as compared to smaller radiuses whose banking occurs at a very low speed thus veering the cars off the track. A solution meant to square out this problem is thus designed through the use of aerofoils that are studied in the next objective.

Maximum Speed of F1 Car in m/s   Bend Radius (m) μ 50 100 200 500 0.1 7.00 9.90 14.01 22.15 0.4 14.01 19.81 28.01 44.29 0.7 18.53 26.20 37.06 58.60 0.9 21.01 29.71 42.02 66.44 Table 1: Maximum speed of F1 car in m/s Maximum Speed of F1 Car in mph   Bend Radius (m) μ 50.00 100.00 200.00 500.00 0.1 15.76 22.29 31.52 49.83 0.4 31.52 44.57 63.03 99.66 0.7 41.69 58.96 83.38 131.84 0.9 47.27 66.86 94.55 149.49 Table 2: Maximum speed of F1 car in mph Speed (mph) Speed (m/s) Fc (N) Ff N 0 0.00 0.00 608.22 1 0.44 1.22 608.22 2 0.89 4.90 608.22 3 1.33 11.02 608.22 4 1.78 19.60 608.22 5 2.22 30.62 608.22 6 2.67 44.09 608.22 7 3.11 60.01 608.22 8 3.56 78.38 608.22 9 4.00 99.20 608.22 10 4.44 122.47 608.22 11 4.89 148.19 608.22 12 5.33 176.36 608.22 13 5.78 206.97 608.22 14 6.22 240.04 608.22 15 6.67 275.56 608.22 16 7.11 313.52 608.22 17 7.56 353.94 608.22 18 8.00 396.80 608.22 19 8.44 442.11 608.22 20 8.89 489.88 608.22 21 9.33 540.09 608.22 22 9.78 592.75 608.22 23 10.22 647.86 608.22 24 10.67 705.42 608.22 25 11.11 765.43 608.22 26 11.56 827.89 608.22 27 12.00 892.80 608.22 28 12.44 960.16 608.22 29 12.89 1029.97 608.22 30 13.33 1102.22 608.22 Table 3: Maximum frictional force and centripetal forces involved in the above condition Graph 1: Formula One car cornering forces without aerofoils.

This section gives a breakdown of how the rear and front aerofoils were designed in order to achieve the desired results. Figure 1 shows an F1 racing car marked ready for carrying out dimensioning. Figure 1: Ferrari F1-2000 marked for carrying out measurements The pixilation for each of the dimensions in the model above is as shown below and each of them is represented by the scale of 1 pixel = 0.008955m.

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