Aerodynamic: Formula 1 - Report Example

F1 CAR DOWNFORCE By Student’s name Course code and name Professor’s name University name City, State Date of submission Introduction Aerodynamics has over years been considered as the key to success within the Formula 1 sporting industry. The most important concerns to the modern aerodynamic designers have always been identified as minimization of drag through streamlining and creation of downforce to ensure the car does not veer off the track. The F1 evolution has therefore seen tremendous improvements on the ground effect as brought about by downforce optimization in as much as challenges have faced the F1 fraternity during the experimentation processes. According to Formula 1 (2014) Aerodynamic downforce is identified as the force that is developed when air pressure acting at the car top is greater than that generated by air pressure at the bottom. In other words, when the air pressure at the top is less than that at the bottom, a formula 1 car is likely to generate a lift. Aerodynamic enthusiasts have developed aerofoils as part of the F1 cars in order to aid in speed improvements especially when negotiating corners considering the fact that vehicles lose a lot of time in the race due to the fact that they have to decelerate. Downforce in Formula 1 is therefore realized due to the massive increment in pressure as a result of aerofoil inversion (Adams, 1993). This laboratory assignment therefore sought to investigate the speed increments that come with the introduction of aerofoils by utilizing such concepts as coefficient of friction, centripetal force, angular acceleration, unit conversion, aerofoil lift, moments of forces, Newton’s laws, scaling and dimensioning, estimation and problem solving. The main objective of this laboratory report was to learn how to analyse and present information in a meaningful way and write a report suitable for presentation. Discussion In order to solve the problem on speed improvements brought about by the aerofoils mounted on Formula 1 cars, the following assumptions were put into consideration: 1. The car will be travelling around a bend of fixed radius of 50m, 100m, 200m and 500m. 2. Car mass is 620kg. 3. The centre of gravity is 2/3rds of the way back between the wheels, and 1/3rd of the height up from the ground. 4. The maximum width of car = 1.8 m (this is defined by F1 regulations). 5. The maximum height = 0.95m. 6. The coefficients of friction between the tyres and the road were assumed as follows: 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 According to the laboratory manual, the first problem was aimed at calculating the maximum speed of the car around the four bends radii without the aerofoils, i.e. with no downforce for each of the four tyre conditions mentioned in the assumptions section above. The equations below were derived with the aid of the video tutorials provided as part of the learning process involved. The first derivation is the centripetal force Fc which is defined as the force that keeps an object in circular motion (Georgia State University, 2014). This component is usually directed towards the centre of a circular path on which the motion is taking place. It is calculated by equation 1 below: 1 (1) Where Fc = centripetal force r = radius of the bend m = mass of the car v = velocity of the car Secondly, the maximum friction which is required to ensure that the downforce is sufficient for the F1 car to move around the track is required. Friction is the force that opposes motion on a surface and is dependent on the texture or conditions of both surfaces. Friction is said to be dependent of the normal force which is usually the measure of exerting against each of the surfaces involved. The maximum force is therefore relevant for this study since the F1 rubber tyres and the track are considered to be in relative motion with each other. Equation (2) below shall be used to calculate the maximum friction force Ff: Where Ff = Maximum friction force N = Normal force acting down on the road surface = coefficient of friction But Where m = mass of the car g = acceleration due to gravity. Therefore (2) For the car to remain in friction with the road surface around the bend, the centripetal force has to be less or equal to the maximum frictional force generated by the tyre. In order to calculate the velocity, centripetal force and frictional force are equated to give the equation (3) below: (3) Rearranging the equation above yields to the equation for maximum velocity around the bend shown in (4) below: (4) Using equation (4) in excel to find the maximum speed of the car around the radii 50m, 100m, 200m and 500m without the aerofoils results to the figures shown in table 1 below: 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: The maximum speed of a Formula 1 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: The maximum speed of a Formula 1 car in mph Table 3: An excel sheet showing maximum speed of the F1 car in both m/s and mph without aerofoils. Tables 1 and 2 above show simple variation calculations for maximum speed of F1 car in m/s and mph respectively as derived in excel. The variance comes in a due to the parameters involved such as coefficient of friction, radius of the bend and downforce which in this instance is the weight of the car since the F1 car is without aerofoils. An increase in friction coefficient also labelled as a shift in track conditions leads to an increase in speed at = 0.9. The downforce is therefore meant to achieve the highest friction coefficient in order to aid in achieving the highest velocities that are required in case of a race. Graph 1: A graph of centripetal force against velocity ms-1 for F1 car without aerofoils. Figure 1: Top view of a Renault 2010 F1 car whose aerofoils are to be designed (F1wolf, 2010). In designing the rear and forward aerofoil the Renault 2010 Formula 1 car above obtained through a Google search, the scaling process was applied. The basic fact that the maximum width of an F1 car is set at a 1.8m standard was utilized with respect to the number of pixels that make up this distance. These two variables (pixels and metres) were scaled against each other as shown in the calculations below through the aid of Microsoft Paint program which was utilized in obtaining the all the desired distances for this assignment’s success. The photographic presentation of this process is shown in figure 2 below. The chord and span of the existing aerofoils were then applied in the “FoilSim III Student Version 1.4d” application to obtain the desired design of aerofoil for the Renault 2010 F1 car. Figure 2: Anatomy of an airfoil. Calculations 288 - 127 Pixels = 1.8m 1 Pixel = = 0.0112 m/ pixel Front aerofoil = 77 x 40 pixels = 0.86 x 0.45 m Rear aerofoil = 161 x 40 pixels = 1.8 x 0.45 m Distance between rear and front tyre = 520 – 220 pixels = 300 x 0.0112 m = 3.36m Distance between rear tyre and extreme end of rear aerofoil = 607 – 520 pixels = 87 x 0.0112 m = 0.97m Distance between front tyre and extreme end of front aerofoil = 219 – 171 pixels = 48 x 0.0112 m = 0.54m Figure 3: Dimensioning of Renault 2010 F1 car through use of pixel standard width scaling Design of aerofoils for Renault 2010 F1 Car Graph 2: Aerofoil design appropriate for the rear section. The “FoilSim III Student Version 1.4d” online software was used to analyse the data obtained in the calculation section above as a means of coming up with effective aerofoils for the Renault 2010 F1 car. The instructions provided in the video tutorials were followed to achieve the dimensional data in table 4 and 5 which were then applied in coming up with the graphical presentation whose nature shows the typical cross sections of the aerofoils. Smoothening of the graphs was however carried out to ensure that the aerofoils designed were true representation of what is expected for the Renault 2010 F1 car. The resulting aerofoil designs are therefore presented for in graph 2 and 3 for rear and front sections respectively. Basically, their shapes differed due to notable differences in their cambers and thicknesses as seen below in table 4 and 5 for rear and front respectively. Table 4: “FoilSim III Student Version 1.4d” data used to obtain the design of the rear aerofoil. Table 5: “FoilSim III Student Version 1.4d” data used to obtain the design of the front aerofoil. Graph 3: Aerofoil design appropriate for the front section. Deploying the rear and front aerofoils designed above in the Renault 2010 F1 the downforce is significantly increased thus the effective friction coefficient tends to one. The speed is observed to reduce significantly as drag sets in at around 2000N. This is however 1400N above the expected downforce which aids in the maintenance of maximum frictional force required for the car to maintain on the track. A graph of frictional conditions plotted against the velocity achieved further gives evidence that with increased downforce the speed eventually starts to decline. This means that the aerofoils must be customised for each car type depending on the size of the front and rear parts. The table below shows the data obtained for the sake of coming up with graph 4 below. Table 6: Data generated for F1 car with aerofoils installed. Graph 4: A graph of centripetal force against velocity ms-1 for F1 car with aerofoils. Conclusion F1 sporting has tremendously improved its approach towards the straight line speed by introducing the aerofoils as part of their technology in countering the cornering speed losses. This is well understood in this report as analysis is carried out through the online educational software “FoilSim III Student Version 1.4d” sponsored by NASA. The outcomes of this report are clearly achieved since it is established for objective number one that the velocity around a bend differs with the frictional conditions and radii of the bend. These results are further indicated in terms of easy translational graphs that are shown in the sections above. List of References Adams, H. (1993) Chassis Engineering, New York: Penguin. F1wolf (2010) 2010 F1 Cars – Renault goes black and yellow (and confirms Petrov), [Online], Available: http://www.f1wolf.com/2010/02/2010-f1-cars-renault-goes-black-and-yellow- and-confirms-petrov.html [22 January 2014]. Formula 1 (2014) Aerodynamics, [Online], Available: http://www.formula1.com/inside_f1/understanding_the_sport/5281.html [23 January 2014]. Georgia State University (2014) Centripetal Force, [Online], Available: http://hyperphysics.phy- astr.gsu.edu/hbase/cf.html [23 January 2014]. Read More