The Speed Improvements that are Attached to the Introduction of Aerofoils on Formula One Cars - Example

Name Course Tutor Date What Speed Increase do Aerofoils give to an F1 Car? Introduction The ever growing need to remain technologically relevant saw the aerodynamics of the Formula One racing car change its physical configuration in the mid-1970s. Apart from adapting these cars for straight line speeds, the revolutionaries were also keen to design for negotiation of corners at gigantic speeds. The introduction of aerofoils was a move aimed at increasing the downforce which could in turn optimize the cars for cornering speeds. Further investigation into the aerodynamics indicated that introduction of aerofoils virtually increased the weight and the effective friction against the track also known as downforce. This report therefore seeks to analyse the speed improvements that are attached to the introduction of aerofoils on Formula One cars including their design through use of Foilsimu application. Discussion In carrying out the analysis on whether there are speed improvements due to the introduction of aerofoils to a Formula One car, the following assumptions were made: i. The car will be travelling around a bend of fixed radius: (50m / 100m / 200m / 500m) ii. Car mass is 620kg. iii. The centre of gravity is 2/3rds of the way back between the wheels, and 1/3rd of the height up from the ground. iv. The maximum width of car = 1.8 m (this is defined by F1 regulations). v. The maximum height = 0.95m. vi. The coefficients of friction between the tyres and the road: Intermediate tyres in the dry: 0.7 Intermediate tyres in the wet: 0.4 Slicks in the dry: 0.9 Slicks in the wet: 0.1 The first step was to calculate the maximum speed of the car around the four bend radii without the aerofoils, i.e. with no downforce (for each of the four tyre conditions). In order to carry out this task effectively, the following equations were derived keeping in mind the Newton’s Laws of Motion. An object travelling in a straight line is kept on track by force of inertia, but when it comes to negotiating a bend a force equivalent to centripetal force is introduced. This component is calculated by the equation (1) below: (1) Where m = mass of the car v = velocity of the car r = radius of the bend Another component required for this analysis to be successful is the maximum friction force. Coulomb friction also known as dry friction predicts a maximum friction when the contacting surfaces are dry. Further, whenever contacting surfaces are in relative motion they are assumed to be exerting maximum friction just like in the case of the F1 car being analysed. The equation used in calculating this force is shown in (2) below: (2) Where = coefficient of friction N = Normal force acting down on the road surface But Therefore (3) Another consideration to be made is that, for the car to remain in friction with the road surface around the bend, the centripetal force has to be less than the maximum frictional force available from the tyre. To find the velocity, we equate centripetal force and frictional force which results into the equation below: Rearranging the equation above results to equation for maximum velocity around the bend as shown in (4) below: (4) Applying equation (4) in excel aids in fulfilling objective one which is to find the maximum speed of the car around the four bend radii without the aerofoils. Table 1: An excel sheet showing maximum speed of the F1 car in both m/s and mph without aerofoils. The tables shown above give an indicator that the maximum speed of an F1 car differ from one condition to the other. These conditions are indicated by the difference in coefficient of friction between tyres and the track surface. It is noted that an increase in coefficient of friction is followed by an increase in speed which is evident as stability tends to increase too. The downforce usually acts in the same way by virtually increasing the weight of the car thereby rendering it stable. In a bid to analyse speed, maximum force and centripetal forces the following data is theoretically obtained and a relationship graph plotted to show exactly how these conditions affect the cornering speeds. Table 2: An excel sheet showing the analysis of speed, maximum force and centripetal forces involved in the above conditions. Graph 1: F1 car cornering forces without aerofoils. Aerofoil design The vehicle in consideration for this exercise was the “BMW F1.09 – 2009 F1.” Shown below: Photograph 1: BMW F1.09 – 2009 F1 In order to find the dimensions of the car shown in photograph 1 above, the Microsoft paint accessory is applied. The pixilation on each axis is depended upon in order to achieve the correct measurements given that the maximum width of the car as per the F1 regulations is kept at a constant 1.8m. These calculations are shown in photograph 2 below: Photograph 2: An analysis of the dimensions of the BMW F1.09 – 2009 F1 racing car. For this analysis the following anatomical figure of an aerofoil was used to ascertain some of the parameters required for the analysis to be successful. The chord and span were the most used especially in the design of the front aerofoil as part of the exercise of learning the Foilsimu application. Figure: The anatomy of an aerofoil. Keeping in mind that the maximum height at which the aerofoil is mounted is 0.95m the following data was are achieved using Foilsimu application for undergraduate. This data was further transformed into designs for rear and front aerofoils which shown in graph 2 and 3 respectively. The differences in the two aerosols can be clearly be seen right from the way they are shaped to the way the practical data that is contained in the beginning of tables 3 and four. For example, the angle of attack in the rear aerofoil is 8.44° while that of the forward aerofoil is 5.0°. Table 3: Geometry data obtained from “FoilSim III Student Version 1.4d” for the design of aerofoil. Graph 2: Design of rear aerofoil necessary for BMW F1.09 – 2009 F1. Graph 3: Design of forward aerofoil using data generated from generated by Foilsimu. Table 4: Geometry data obtained from “FoilSimu III Student Version 1.4d” for the design of forward aerofoil. Implementing the above aerofoils designed in the Foilsimu software as produces high friction coefficient of approximately 0.9. A graph of tyre friction and side force plotted against vehicle speed under downforce is shown below. There exists an observable difference in the cut-off force before and after mounting of the airfoil. Inasmuch as the speed is reduced by the airfoils, the cornering occurs safely since the downforce takes care of sliding thereby maintaining a high coefficient of friction. Graph 4: F1 car cornering forces with airfoils mounted. Conclusion This report successfully portrays the effects of the introducing aerofoils on an F1 sporting car. The Foilsimu application meant for the generation of geometry data to be employed in the design of the aerofoils is also well understood with the designs being shown in graph 3 and 4 in the discussion section. The differences between the two graphs (one with aerofoils and one without) is also noted as the speed during which skidding occurs. The increase in speed is also tabulated above accordingly and concluded that due to an increase in stability, the car seems to take off at a higher speed as tallied in tables 3 and 4. Works Cited Collantine, Keith. BMW F1.09 – 2009 F1 car. 20 January 2009. 9 January 2014 . Read More