F1 Car and more Powerful Cornering Capability Rounded Way - Coursework Example

F1 car and dоwnfоrсе Name: Course: Lecturer: Institution: City & State: Date: Table of Contents Table of Contents 2 Introduction 3 Angular motion 4 Uniform circular motion 4 Non-uniform circular motion 4 Friction 6 Objectives 6 Results and discussion 7 The data that provided (Assumptions): 7 The F1 Car dimension 8 The maximum speed without airfoil: 9 Foil sim 18 Designing front airfoil 18 Conclusion 29 References 29 Introduction When a car is negotiating a corner of certain radius, it experiences different forces on its body. Considering F1 car, it is an open cockpit design car with substantial wings in the rear and the front, with the engine behind the driver. These cars are designed for racing in formula one competition racing events. Therefore, design of the wings will depend on the aerodynamics of the wing. Thus, development of the wings will concern the aerodynamic designer on downforce creation, which help in pushing the tyres of the car onto the track. In addition, creating the downforce helps in cornering the forces. Secondly, the aerodynamic designer will be concerned with the need to minimize the drag. Drag in the F 1 car is caused by turbulence when the car is moving and as a result, this slows and reduces the speed of the car. Thus, it is ideal to focus on the aerodynamics of the wing to improve on the car speed and developing stable forces to push the car to stability. F 1 car is designed such that it has higher cornering force, which is about 6 g, which means it has a downforce of six times its own weight (Pater & Lissauer 22). Ground effect aerodynamics is regulated by the F 1 regulations. Despite the regulations, ground effect aerodynamics is the easier means that the car develops efficient means to create downforce. Thus, for the car to have proper aerodynamics, the underside of the car must have a flat under tray between the axles. A rear diffuser located at the under tray, which is at the rear body of the car provides the car with a substantial downforce (Gron 231). Due to limited wing size there are limitations that the F 1 car has and this requires for the car to have high angle of attack used to create enough downforce to hold the car In order to increase the downforce and decrease the drag the airflow is manipulated by the car’s small winglets and on the parts excluding the front and rear wing. The front wing of the car is designed such that it can push air to the bargeboards and the winglets thus smoothing the airflow. Angular motion Bodies moving along a circular at a uniform speed must experience a force, which enables them to follow the curved path. This direction is always orthogonal to the body’s velocity, which is always directed towards an instantaneous center of the curvature of a fixed point. This force is centripetal force, and it generally causes the circular motion to occur. Centripetal force draws or impels bodies to the direction that tends to the centre point of a given path bend. Uniform circular motion A body moving at a constant rate of rotation along a given curve has a uniform circular motion. The body must follow a given path at a given position and magnitude and an angle that will help the body to maintain its trajectory movement along the curved path. Non-uniform circular motion When a body is moving at along a curved path at an angular rate that is not constant it usually has non-uniform angular motion. Therefore, the body experiences changing forces at different points along the path. The changing forces at different points along the path are accounted for the changing angular speed of the body at these different points thus it develops changing angular acceleration. Thus, for changing radius along the curved path has an inverse effect on the angular acceleration of the body along that curve. Thus for a given car along a given curve Where, =angular velocity = Time = Rotation angle  =Angular acceleration Moreover, when the car corners at a higher angular acceleration it changes the torque on the body which in turn affects the moment of inertia of the car along that curve. Thus,  Where,= torque =Moment of inertia =Angular acceleration Friction When a body is moving on another fixed body, it experiences a resistive force, which is a frictional force between the surfaces. When a car is moving it has different frictional forces acting on it. Dry friction: this is when two solids are in relative lateral motion and are in contact, this is mostly experienced on the tyres when the car is moving. Fluid friction: it describes the frictional force between viscous fluids that are in relative motion to each other. Skin friction: this is a drag component and it is usually a force that resists the body to have motion in a fluid When a body is moving a long a given path, the frictional force acts on the opposing direction. Thus, for a car, moving along a curved path the frictional force is exerted on the tyres and acts on two dimensions; one is towards the center of the curve and the other is parallel to the directional path. Objectives This report aims at studying on how to analyze information and present the information to be meaningful. In addition, it helps in gathering important information in analyzing the F 1 sporting and effects on the design of the car as well the driving areas. Moreover, this assessment helps one to understand the effect of the forces involved in driving along a bend at a given radius. Results and discussion Considering the dimensional analysis of F 1 car for the data analysis of the forces acting at a given curve, the F 1 car best fits the analysis since it is used for racing. Moreover, different radii paths are used and thus this would help determine the speed at which the car can move along a curved path at different radius curved path. Speeds at which the car can move were determined with the airfoil absent and when the airfoil in position at different radius along a curved path. The data that provided (Assumptions): The F1 car will be travelling around a bend four different of fixed radius (50m / 100m / 200m / 500m ) F1 car Mass = 620kg. Centre of gravity is 2/3rds of the way back between the wheels, and 1/3rd of the height up from the ground. Maximum width of car = 1.8m Maximum height = 0.95m Coefficient 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 F1 Car dimension There are several steps to be used to find the measurement of the F1 Car: 1- Find a F1 car picture from Google web site 2- Import the picture on the Microsoft Paint 3- By using the 1.8m as the maximum width of F1 car, select a straight line shape then draw it on the rear of the F1 car. 4- Then measure the straight line length by pixels , by using the formula that’s convert the lengths from pixels to meters 1.8m = 317px , for example if the span is 77 px then 5- Using themaximum width of the car1.8m = 317px as a reference point to get all other needed dimensions for the F1 car (Front (Span, chord),rear (Span, chord) and the total car length). 6- The dimension is : Front span = 1.70 m Front chord = 0.488 m Rear span = 0.800 m Rear chord = 0.54 m F1 car length = 2.611 m The maximum speed without airfoil: Using the data provided, analysis was done on the car speed with the airfoil absent, which as tabulated The equation can be used to get the maximum frictional force is: Centripetal force =  frictional force =  m = mass g = gravity v = velocity r = radius  = coefficient friction Therefore: The centripetal force (Fc) is ≤ maximum frictional force (Ff).  ≤  v2 =  v =  To calculate maximum speed of the four types of tires with different coefficient friction by using the pervious formula (v  ) and with bend four different of fixed radius . Table 1: speed analysis without the airfoil in M/S Table 2: speed analysis without the airfoil in Mph From tables 1 and 2, it is clear that as the coefficient of friction increases so does the speed increase at any given radius of the curved path. Consequently, it is clear that as the radius of the curved path increases so does the speed, which therefore mean at higher raidius the car can move at higher speeds. This proves the relation v2 =  to be true for the speed analysis for any given curved path. To calculate frictional force () m = 620 Kg g = 9.81 Intermediate tires in the dry Frictional force  Frictional force  Intermediate tires in the wet  Frictional force  Frictional force  Slicks in the dry  Frictional force  Frictional force  Slicks in the wet  Frictional force  Frictional force  To calculate centripetal force () without airfoil: Where:  = mass = velocity  = bending radius By using the excel we can find () This graph shows the relation between the frictional force () and centripetal force () with different speeds. From the force-velocity graph above, at a given frictional force the car is always at a different velocity with a different centripetal force. For instant, at frictional force 5500N, and in a 50m radius path, the car is at low velocity and higher centripetal force than at a radius of 200m. THE FIGURES ARE AT 50M BEND RADIUS WITHOUT AIR FOIL Speed FC (50 m ) FF (µ=0.1) FF (µ=0.4) FF (µ=0.7) FF (µ=0.9) (MPH) m N N N N 16 634.3872 608.22 2432.88 4257.54 5473.98 32 2537.549 608.22 2432.88 4257.54 5473.98 42 4371.324 608.22 2432.88 4257.54 5473.98 48 5709.485 608.22 2432.88 4257.54 5473.98 Table 3: frictional force at 50m radius without airfoil From the force-velocity graph, velocity is directly proportional to the change in frictional and centripetal forces. This is further depicted in table 3, where as the speed increase so does the frictional force and the centripetal force. In addition, as the coefficient of friction increases so does the frictional force, this also increases with increasing speed of the car at increasing centripetal force. THE FIGURES ARE AT 100M BEND RADIUS WITHOUT AIR FOIL Speed FC (100 m) FF (µ=0.1) FF (µ=0.4) FF (µ=0.7) FF (µ=0.9) (MPH) m N N N N 22 599.6941338 608.22 2432.88 4257.54 5473.98 44 2398.776535 608.22 2432.88 4257.54 5473.98 58 4168.122037 608.22 2432.88 4257.54 5473.98 66 5397.247204 608.22 2432.88 4257.54 5473.98 Table 4: frictional force at 100m radius without airfoil At 100m radius, the car moves at higher velocity than at 50m radius. Consequently, this changes the centripetal force exerted on the car as it increases its speed maintaining the frictional force equal to that of the car at 50m radius (table 4). THE FIGURES ARE AT 150m BEND RADIUS WITHOUT AIR FOIL Speed FC (150) FF (µ=0.1) FF(µ=0.4) FF (µ=0.7) FF (µ=0.9) (MPH) m N N N N 22 399.7961 608.22 2432.88 4257.54 5473.98 44 1599.184 608.22 2432.88 4257.54 5473.98 56 2590.414 608.22 2432.88 4257.54 5473.98 64 3383.398 608.22 2432.88 4257.54 5473.98 Table 5: frictional force at 150m radius without airfoil As the bend radius increases so does the speed of the car, which in turn result to a decrease in the centripetal force. Compared to 100m and 50m radii, the centripetal force at 150m radius is lower, which means the car can corner the curve with ease. THE FIGURES ARE AT 200m BEND RADIUS WITHOUT AIR FOIL Speed FC (200) FF (µ=0.1) FF(µ=0.4) FF (µ=0.7) FF (µ=0.9) (MPH) m N N N N 32 634.3872 608.22 2432.88 4257.54 5473.98 62 2381.43 608.22 2432.88 4257.54 5473.98 84 4371.324 608.22 2432.88 4257.54 5473.98 94 5474.068 608.22 2432.88 4257.54 5473.98 Table 6: frictional force at 200m radius without airfoil With the increasing radius of the curve, the speed at which the car can corner the curve increases which in turn require an increased centripetal force to prevent the car from reaching the traction force and topple over (Shipman 62). Thus, maintaining the frictional force the car can manage to corner 200m radius curve at higher speeds, since it has higher centripetal force to control the car. Foil sim When designing the F 1 car, it is necessary to consider the aerodynamics of the car in relation to expected racing speed. Therefore, the front of the car must have airfoil that will help in lowering the static pressure at the bottom while increasing the velocity at the lower section. Thus, a air foil located at the front of the car helps to reduce resistive forces exerted on the car by wind. Moreover, other points that have airfoil are, rear and the sides of the car. This in turn helps in increasing the downnforce to propel the car at high speed without toppling over (Robert 165). Designing front airfoil Front Airfoil chord 0.488 m span 1.7 m Angle -deg -8.48 Camber-% -16.64 Thick-%crd 8.391 When designing the airfoil for the F 1 car front side, the airfoil must develop low pressure and a higher velocity on lower section (Steven 123). This stabilizes the car by applying higher pressure on the tyres thus increasing the frictional force on the tyres (figure 1 and 2). Joukowski Airfoil Camber = -16.64 % chord , Thickness = 8.391 % chord , Chord = 0.488 m , Span = 1.7 m , Angle of attack = -8.48 degrees , Standard Earth Atmosphere Ambient Pressure = 101.261kPa, Ambient Velocity = 160 km/hr , Speed Speed Down Force Mph Km/h N 0 0 0 20 32.179 97 50 80.448 606 100 160.897 2425 200 321.795 9700 Designing rear air foil Rear Air foil chord 0.54 m span 0.800 m Angle -deg -10 Camber-% -15.28 Thick-%crd 11.602 FoilSim III 1.4d beta - 21 Mar 11 Joukowski Airfoil Camber = -16.64 % chord , Thickness = 8.391 % chord , Chord = 0.488 m , Span = 1.7 m , Angle of attack = -8.48 degrees , Standard Earth Atmosphere Ambient Pressure = 101.261kPa, Ambient Velocity = 160 km/hr , Designing the rear airfoil it also uses the same dimensions as that in the front, this further helps stabilizing the car and increasing the downforce on the tyres. Consequently, as indicated in table 7 and figure, an increase in speed leads to an increased downforce of the car. Total Down Force: Table 7:effect of increasing speed on the downforce Speed Speed Total Down Force Mph Km/h N 0 0 0 20 32.179 136 50 80.448 851 100 160.897 3405 200 321.795 13621 THE FIGURES ARE 4 BEND RADIUS WITH AIR FOIL Figure 6: force-velocity curve with airfoil THE FIGURES ARE 50m BEND RADIUS WITH AIR FOIL Table 8: 50 m radius bend with airfoil Speed FC (50 m ) FF (µ=0.1) FF (µ=0.4) FF (µ=0.7) FF (µ=0.9) (MPH) N N N N N 16 634.3871828 695.3272 2519.9872 4344.6472 5561.0872 34 2864.654623 1001.77 2826.43 4651.09 5867.53 44 4797.55307 1267.384 3092.044 4916.704 6133.144 50 6195.187332 1459.45 3284.11 5108.77 6325.21 From table 8, and the graph when the car has airfoil in place in a 50 m radius bend has higher speed compared to 50 m radius without airfoil. In addition, the ca has a higher centripetal and frictional force than when airfoil is absent. Therefore, is it means that when airfoil is place the car is more stable and hence it can move at higher speeds. THE FIGURES ARE 100m BEND RADIUS WITH AIR FOIL Graph 8: 100m bend radius with air foil Speed FC (100 m) FF (µ=0.1) FF (µ=0.4) FF (µ=0.7) FF (µ=0.9) (MPH) N N N N N 26 837.5893 838.3252 2662.9852 4487.6452 5704.0852 52 3350.357 1528.9216 3353.5816 5178.2416 6394.6816 68 5729.309 2182.7872 4007.4472 5832.1072 7048.5472 78 7538.304 2680.0092 4504.6692 6329.3292 7545.7692 Table 9: 100m bend radius with airfoil Consequently, increasing the radius to 100m bend the car can corner the bend at higher speeds and the respective frictional and centripetal forces increase. This is due to an increase in the car’s down force when the airfoil is in place (table 9). THE FIGURES ARE 150m BEND RADIUS WITH AIR FOIL Graph 9: 150m bend radius with airfoil graph Table 10: 150m bend radius with air foil Speed FC (150) FF (µ=0.1) FF (µ=0.4) FF (µ=0.7) FF (µ=0.9) (MPH) N N N N N 34 954.8849 1001.77 2826.43 4651.09 5867.53 70 4047.522 2276.782 4101.442 5926.102 7142.542 94 7298.757 3617.254 5441.914 7266.574 8483.014 106 9281.217 4434.6292 6259.2892 8083.9492 9300.3892 Further, table 10 clearly shows how varying the bend radius to higher levels enable the car to corner the bend with increased speeds, which consequently increases the frictional and centripetal forces of the car. Moreover, comparing the car when the airfoil is absent and with airfoil in position, the car has a higher downforce with the airfoil in position than when absent (graph 9 and table 10). THE FIGURES ARE 200m BEND RADIUS WITH AIR FOIL Graph 10: 200m bend radius with airfoil graph Table 11: 200m bend radius with airfoil Speed FC (200) FF (µ=0.1) FF (µ=0.4) FF (µ=0.7) FF (µ=0.9) (MPH) N N N N N 46 1310.90164 1328.6812 3153.3412 4978.0012 6194.4412 92 5243.606558 3490.5616 5315.2216 7139.8816 8356.3216 122 9220.916826 5677.0516 7501.7116 9326.3716 10542.8116 140 12142.56717 7283.224 9107.884 10932.544 12148.984 From table 11 and graph 10, justifies that an increase in speed and downforce of the F 1 car will depend on the airfoil presence in the car. Further, this increases the centripetal and frictional forces in the car. This increase and change on forces determines the F 1 car stability and thus increases its racing speeds along curved bends. Combining the two calculations with and without airfoil Table 12: combining the two calculations with and without airfoil Speed FC (50 m ) FF (µ=0.1) FF (µ=0.4) FF (µ=0.7) FF (µ=0.9) FF (with AIR FOIL) (µ=0.1) FF (with AIR FOIL) (µ=0.4) FF (with AIR FOIL) (µ=0.7) FF (with AIR FOIL) (µ=0.9) (MPH) m N N N N N N N N 16 634.387 608.22 695.327 30 2230.27 2432.88 34 2864.65 2826.43 42 4371.32 4257.54 44 4797.55 4916.7 46 5243.61 5473.98 50 6195.19 6325.21 Combining the two calculations with and without airfoil further shows that when the airfoil is in place the car has higher speeds and subsequent frictional and centripetal forces (table 12) Table 13 the two calculations with and without airfoil in 100m radius bend Speed FC (100 m) FF (µ=0.1) FF (µ=0.4) FF (µ=0.7) FF (µ=0.9) FF (with AIR FOIL) (µ=0.1) FF (with AIR FOIL) (µ=0.4) FF (with AIR FOIL) (µ=0.7) FF (with AIR FOIL) (µ=0.9) (MPH) m N N N N N N N N 22 599.6941 608.22 26 837.5893 838.3252 44 2398.777 2432.88 52 3350.357 3353.582 58 4168.122 4257.54 66 5397.247 5473.98 68 5729.309 5832.11 78 7538.304 7545.769 When the airfoil is in place and the car is at a 100m radius bend further justifies the relation, that an increase in radius has a subsequent increase in speed, and frictional and centripetal forces, which increase with the increasing coefficient of friction. Table 14: the two calculations with and without airfoil at 150m radius bend Speed FC (150) FF (µ=0.1) FF (µ=0.4) FF (µ=0.7) FF (µ=0.9) FF (with AIR FOIL) (µ=0.1) FF (with AIR FOIL) (µ=0.4) FF (with AIR FOIL) (µ=0.7) FF (with AIR FOIL) (µ=0.9) (MPH) m N N N N N N N N 26 558.3929 608.22 34 954.8849 1001.77 54 2408.689 2432.88 70 4047.522 4101.442 72 4282.113 4257.54 82 5554.192 5473.98 94 7298.757 7266.57 106 9281.217 9300.39 At 150m radius, the speed and the related forces acting on the car further proves the airfoil-downforce relationship as valid since, this increases the cetripetal and frictional forces on the car. Table 15: the two calculations with and without airfoil at 200m radius bend `Speed FC (200) FF (µ=0.1) FF (µ=0.4) FF (µ=0.7) FF (µ=0.9) FF (with AIR FOIL) (µ=0.1) FF (with AIR FOIL) (µ=0.4) FF (with AIR FOIL) (µ=0.7) FF (with AIR FOIL) (µ=0.9) (MPH) m N N N N N N N N 32 634.3872 608.22 46 1310.902 1328.681 62 2381.43 2432.88 84 4371.324 4257.54 92 5243.607 5315.2216 94 5474.068 5473.98 122 9220.917 9326.37 140 12142.57 12149 Lastly, at 200m it is a further justification that when the car has airfoil in place has a positive impact on the F 1 car speed as well as its downforce. This leads to an increase in centripeteal and frictional forces that result to increased stability of the car at higher speeds (Shipman, 58). Conclusion Essentially, studying forces that act on a moving body helps one to develop the aerodynamics of the cars that are designed for racing. Therefore, this analysis gives one ideal case that is used to improve on the development of the racing F 1 cars. Moreover, changing the speed of the car at a given curve with a given radius affects the centripetal force acting on the car. Further, changing the aerodynamics of the rear and front of the car increases stability as well as the downforce of the car (Rusty 57). For the graphs when the airfoil is in place, the car develops a high frictional force, which consequently leads to high speeds. These higher speeds calls for the car to dev develop higher centripetal forces that will manage to hold the car along the path taking care of the traction force. Thus, starting from 50m speed increases to higher speeds when the radius is at 200m. Consequently, this increases the stability and the speed of the car (McBain 87). Therefore, it is recommendable to use airfoil in a F 1 car since, it increases downforce of the car increasing the centripetal and the frictional forces. References Rusty, L. M. 2006, The basics of physics, Greenwood Publishing Group, New York. McBain , G. D.2012, Theory of Lift: Introductory Computational Aerodynamics, John Wiley & Sons, New York. Steven, H. 2011, Physics I For Dummies, John Wiley & Sons, New York. Robert, A. P.& Joshua, F. 2007, Barron's AP Physics C 2008, Barron's Educational Series, New York. Shipman, J. T. et al, 2012, An Introduction to Physical Science, Cengage Learning, New York. Pater, I. & Lissauer, J. J. 2010, Planetary Sciences, Cambridge University press, Cambridge. 22 Gron, O. 2012, Einstein's theory, Sringer, New York. 230-234 Read More