Speed Improvement of Aerofoils to an F1 Car - Book Report/Review Example

Speed Improvement of Aerofoils to an F1 Car Affiliation Speed Improvement of Aerofoils to an F1 Car Introduction This research paper introduces concepts of angular acceleration, centripetal force, moments of forces, scaling and dimensioning, coefficient of friction, unit conversion, and problem solving. The research involves the calculation of the maximum speed with and also without aerofoils. ‘Foilsim’ software is used in the research to aid in solving the problem of what speed improvement do aerofoils give to an F1 car. Firstly, the maximum speed of the car around the four bend radii (of 50m, 100m, 200m and 500m) without the aerofoils, for each of the four tyre conditions is calculated. Next, in order to determine the chord and span of each aerofoil, a Google image search is performed to come up with a top view of an F1 car, and using the maximum width (approx. 1.8 m) as a scaling reference, the dimensions of the car are measured. Then the image is copied into the Ms-word programme and measured to obtain the positions of the wheels, wings and overall length. These measurements are used as the basis of further calculations. Thereafter, the new maximum speed for each bend radius is calculated for each of the four tyre conditions and a set of graphs plotted which concisely summarise all the findings (with / without aerofoils, bend radius, tyre friction coefficient). Finally, the forces for one particular corner radius / tyre combination are calculated when the car is without aerofoils and further determined whether if the front or the back tyres slip first. The task of the Research The following assumptions are made about the formula one car: 1. The car will be travelling around a bend of fixed radius: (50m / 100m / 200m / 500m) 2. The car’s mass is assumed to be 620kg 3. The centre of gravity is two thirds of the way back horizontally between the wheels and one third of the height vertically up from the ground 4. The maximum width of the car is also assumed to be 1.8 m (as defined by F1 regulations) and its maximum height to be 0.95m. The entire task shall be handled as outlined in the introduction above. Discussion Where; is the centripetal force, is the coefficient of friction, is the Normal force upon the car which is equal to the weight of the car., is equal to the mass of the car is the gravitational force upon the car, is equal to the weight of the car, is the velocity of the car, is the radius of the bend that the car shall be negotiating From the above derivation, it is apparent that velocity is affected by the radii of the bends, the frictional coefficients and the gravitational pull upon the car. Thus, the velocity of the car is to be calculated based on the magnitude of the frictional coefficients and the radii of the bends. 1. Calculation of the Maximum Speed of the car without the Aerofoils i. Velocity Calculation for the Intermediate tyres in the dry with Frictional Coefficient of 0.7 For the bend radius of 50m, For the bend of radius 100 m, For the bend of radius 200m, For the bend of radius 500 m, ii. Velocity Calculation for the Intermediate tyres in the wet with Frictional Coefficient of 0.4 For the bend radius of 50m, For the bend of radius 100 m, For the bend of radius 200m, For the bend of radius 500 m, iii. Velocity Calculation for Slicks in the dry with Frictional Coefficient of 0.9 For the bend radius of 50m, For the bend of radius 100 m, For the bend of radius 200m, For the bend of radius 500 m, iv. Velocity Calculation for Slicks in the wet with Frictional Coefficient of 0.1 For the bend radius of 50m, For the bend of radius 100 m, For the bend of radius 200m, For the bend of radius 500 m, 2. Calculation of the Maximum Speed of the car with the Aerofoils The primary function of the aerofoils is to create a down force, that aids in pushing the tyres of the car onto the track and consequently improve the cornering forces; and minimise the drag that is brought about by turbulence and finally act to slow the car down (Formula1, 2014). Using the aerofoil software, the lift force, equivalent to the down force in Formula 1 cars, is equal to for an aerofoil of span and chord of. Thus, the total down ward force is equal to the value of the weight of the car, , and the aerofoil down force of . In this case, the centripetal force, , is directly proportional to the resultant upward force on the car as a result of the two down ward forces, and not merely the weight of the car as earlier calculated. The use of the moment of forces can be utilised to come up with the resultant upward force. The turning point of the moments is taken to be at the front of the car. The down force is assumed to be acting at the rear of the car and the resultant upward force at the centre of gravity (COG) of the car. The diagram 1 in the appendix clearly shows the positions of the said forces, as the overall car length is assumed to be 4.5 m. The principle of the moment of forces states that when a system is “in equilibrium the total sum of the anti-clockwise moment is equal to the total sum of the clockwise moment”. Simply put, this principle implies that, at a point; In the case above, the clockwise moments are the ones comprising of the weight and down force, both acting at the centre of gravity and the rear part of the car respectively. The anticlockwise moment is composed of the resultant upward force on the car. Hence, the whole system becomes; Therefore, the resultant upward force is equal to; . From the previous formula, i. Velocity Calculation for the Intermediate tyres in the dry with Frictional Coefficient of 0.7 For the bend radius of 50m, For the bend of radius 100 m, For the bend of radius 200 m, For the bend of radius 500 m, ii. Velocity Calculation for the Intermediate tyres in the wet with Frictional Coefficient of 0.4 For the bend radius of 50m, For the bend of radius 100 m, For the bend of radius 200 m, For the bend of radius 500 m, iii. Velocity Calculation for Slicks in the dry with Frictional Coefficient of 0.9 For the bend radius of 50m, For the bend of radius 100 m, For the bend of radius 200 m, For the bend of radius 500 m, iv. Velocity Calculation for Slicks in the wet with Frictional Coefficient of 0.1 For the bend radius of 50m, For the bend of radius 100 m, For the bend of radius 200 m, For the bend of radius 500 m, Forces at a bend of radius 100 m for the various tyre conditions Therefore, the centripetal force,, for the intermediate tyres in the dry of the coefficient of friction, of 0.7 is; The centripetal force,, for the Intermediate tyres in the wet of the coefficient of friction, of 0.4 is; The centripetal force,, for the Slicks in the dry of the coefficient of friction, of 0.9 is; The centripetal force,, for the Slicks in the wet of the coefficient of friction, of 0.1 is; Since there is no net force in the vertical direction, N is assumed to W, weight of the car and it is given by the, (Waynes, 2014) The coefficient of friction can be calculated from the formula derived below. The coefficient of friction is the minimum value for any system. If is any smaller than this, then there won’t be adequate force towards the centre of the circle for the car to follow the curve and it will slip (Roylance, 2000). The coefficient of friction can be decreased by decreasing the speed of the car or increasing the radius of the bend (Rana & Kaushik, 2014). And since the centre of gravity is 2/3 rds way back horizontally between the wheels, the rear wheels will slip first as the centre of gravity is inclined to the rear part of the car. Conclusion In the first case (speed of the car without the aerofoils), the speed of the car is influenced by the radius of the bend, coefficient of friction and the gravitational acceleration. As either the radius of the bend or coefficient of friction increases, the speed of the car also increases. Hence, the speed of the car is directly proportional to the radius of the bend and the coefficient of friction. On the other hand, in the second case (speed of the car with the aerofoils), the speed of the car is influenced by the radius of the bend, coefficient of friction and the mass of the car. In this car the speed of the car is inversely proportional to its mass; as the mass increases, its speed decreases and vice versa. On the other hand, the car’s speed is directly proportional to the radius of the bend and the coefficient of friction; speed increases with an increase in the radius of the bend and coefficient of friction. References De Groote, S. (2009, May 14). Aerodynamics in racing - F1technical.net. Retrieved December 22, 2014, from http://www.f1technical.net/articles/10 Jim Clark Foundation. (1969). Aerofoil report: A study of the aerodynamic characteristics of racing cars fitted with aerofoils. London: Jim Clark Foundation. Leslie-Pelecky, Diandra L. 2008. The physics of NASCAR: how to make steel + gas + rubber = speed. New York: Dutton. Pelican Technical Article: Physics of Racing Series. (n.d.). Retrieved December 23, 2014, from http://www.pelicanparts.com/techarticles/physics_racing/ Rana, A & Kaushik, P, S. 2014. Increasing Down force in High- speed Motorcycle Specially during Cornering. International Journal of Applied Engineering Research, Volume 9, Number 5 (2014) pp. 559-566 Roylance, D. 2000. Statics of Bending: Shear and Bending Moment Diagrams. The US: Massachusetts Institute of Technology Waynes, 2014. Cars and Their “Cornering” Ability. Retrieved from < http://www.mrwaynesclass.com/circular/notes/corner/home.htm> Accessed on 24th Dec, 2014 Appendix Diagram 1 Up ward Force, 3m 4.5m Mg (Weight) Top View of the F1 Car Read More