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Bicycle Model Analysis Assignment Sample

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Bicycle Model Analysis Assignment Sample


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The race vehicle (as well as the cutting-edge Sport scar) is an evolution of post-World War II racing automobiles. The designs progressed from street sports cars to the racing car seen in road racing today and the 24 Hours of Le Mans. Modern professional race vehicles use unique single or double seat constructions, a mid-engine back wheel arrangement, and a densely packed aerodynamic framework. Many sports racers use wings and rear sub frame recirculation tunnels to generate down force, which allows them to turn at much quicker speeds.
The technical constraints set by the event organizers substantially impact the aerodynamic design of the vehicles. In this report, the handling of student are cars are analyzed, and considering transient and steady-state characteristics stability characteristics of the race car are also analyzed. Then Considering appropriate ARB and spring stiffness, tyre properties, suspension geometry, damping rates, and geometry of vehicles recommendations are provided for the handling and stability of the race car.

Main body

Handling of Race Car

The Fundamental behavior of the vehicle is driven by the term Handling. Handling often describes the response of a car input. A race car's handling characteristics are determined by the interaction of several variables. If a setup performs well on one track, it does not mean it will perform well on another track or in a different event. Engineers change the architecture of vehicles to increase reaction times. This is done manually through a series of adjustments that can be time-consuming and are regularly changed on the fly, decreasing the overall quality of the design process. A race car's handling characteristics are determined by the interaction of several variables. Many of them appear to be pre-determined during the design process, and they cannot be changed once the car is finished (Yu and Gao, 2021). The position of the vehicle's center of mass, its mass, and the connection sites of the rear and front suspension systems on the chassis are among the "fixed" factors. The vehicle's responsiveness and overall efficiency can be fine-tuned by modifying several characteristics such as roll and suspension stiffness, tyre inflation pressure, braking ratio, and tyre camber angle. The parameters that can be changed to manage the handling characteristics are referred to as the car's "set-up." Finding a specific optimal set-up for a race car that gives the highest level of efficiency in every race circuit and competition event is exceedingly difficult, if not impossible to achieve.

Weight distribution

How the weights of a race car will be distributed is determined by the position of various components of the vehicle when it is in the static position. This Static Weight Distribution will also affect how the car performs on the track. The tyres that connect the car to the track cause friction with the track surface and transfer braking, turning, and accelerating forces to the racing car's chassis (if any) and suspension. The Weight Distribution induced by these forces is mostly responsible for whether or not the vehicle acts as intended.

Track width
The distance between the centers of the tyre contact zones determines an automobile's track width. The track width is important because it affects how much weight the car's mass transmits when turning. Figure 1 below shows the track width of a race car.

The length between the rear and front wheels measured from the wheel centers is referred to as a car's wheelbase. The wheelbase is important because it affects the weight distribution by the vehicle's mass during braking and acceleration, as well as the torque characteristics during turning. Figure 1 below shows the wheelbase of a race car.

Distribution of static weight

Each part of a car contains mass, and the amount of mass on each tyre is determined by where the mass is positioned about the tyres.
Two ratios define the distribution of the static weight of the race car, these are

  • The ratio of the net weight on the right and left tyres of the car.
  • The ratio of the net weight on the rear and front tyres of the car.

Because of the huge equipment and their needed locations, most cars' static weights are never completely balanced.

Location of CG
Understanding the distribution of weight from front to rear and right to left allows for the identification of the CG (Center of gravity) throughout the length (Linear) and width (Lateral) of a vehicle. The CG represents the location at which the car may be in balance if one jack it up under that point. To stabilize the vehicle during turning, the car's center of gravity should be as close to the center of the wheelbase as possible in a lateral motion.

Height of CG
When the distance from the ground of the identical components listed above is taken into account, the static distribution of weight is just a two-dimensional concept. The vertical placement of the mass of the mechanical elements defines the CG level.
The CG point is very important for the race car as it is always driven at high speed. To increase the performance of a race car the design of the car should be such as way that

  • The CG height should be reduced
  • Equilibrium should be maintained by keeping the distribution of static weight balanced as possible (left/right and rear/front). It will make it easier to work properly if there will be any future imbalance.
  • If the surface is quite slippery, reduced track width and a higher CG will help to transfer weight outside the wheel to provide more bite. In this situation, narrow tyres also help.
  • The Packaging component as near as the CG can optimize the polar moment of inertia of the car.

Weight Transfer
All of the aforementioned characteristics are mixed while an automobile is turning, speeding, and decelerating. Each of these driving duties necessitates the racing vehicle adjusting its velocity in some way. The driver directs the automobile to accelerate in order to increase its forward pace. The driver orders the automobile to limit forward momentum by slowing down. The driver orders the vehicle to change its momentum from the direction it has been traveling by turning. Each change is caused by the tyres making contact with the ground. The tyres initiate the shift (by spinning faster, twisting, or slowing down), and the rest of the automobile reacts to it. It also helps the tyre to increase its grip and here the weight transfer is used.

Stability characteristics

To take advantage of the benefits of ground effect as well as the comparatively large floor plan area of these autos, low ground tolerances must be employed (Preda et al. 2019). To achieve optimum turning and straight-line efficiency, chassis features are regularly changed to aerodynamic effects in order to minimize pitch and hence friction at high speeds while keeping relatively significant downward force when turning.

Steady State characteristics

The wheelbase of a car must be at least 1525 mm. Because a longer wheelbase adds weight to the automobile and needs more room while turning in a curve. To provide stability, the rear wheel track must be wider than the front wheel track, at the penalty of slightly under steering and taking up more lane space while entering a curve.
The offset frequency is the undammed natural frequency of the sprung mass. The offset frequency has a great effect on the effect of the suspension. Increasing the offset frequency will strengthen the suspension and improve the performance and rigidity of the suspension system (Zinnet al. 2018). If the offset frequency is low, the suspension will be soft and the ride quality will be smooth. In some cases, some ride quality may be sacrificed. The offset frequency of the car is determined by the following equation (1)
= 1/2 … (1)
Where offset frequency is, is also the optimum stiffness, and m is the mass of the shaft.
The car is in static stability when the slip angle of both rear and front is equal. The equation of slip angle is given by the following equation (2) and equation (3)
= (b.r -)/ … (2)
= - (a.r +)/ … (3)
Where a is the acceleration of the car, V is the velocity of the car, and is the steering angle of the wheel.

Transient characteristics

If the speed of the car is greater than the critical speed then the car will be unstable.
For stability, the car has to be in the under steer. For the under steer condition, the speed of the car has to be V =
The stability index of the car is given by the effective measurement of the moment arms among the CG and lateral force (Xia et al. 2018). If the value of the stability index is less than zero, then the car will be in stable condition, If the value of the stability index is greater than zero, then the car will be in an unstable condition.

Vehicle geometry

The measurement of the vehicle geometry becomes convenient by choosing the two coordinate systems and the origin of the coordinate system. The vectors x, y, z define the ground coordinate system which is fixed for the vehicle. The vehicle geometry is consists of several other components of the car. This is known as the subsystem.

Chassis subsystem - It is the single rigid body and defines the location of the various parts of the car which are fixed and non-rotating relative to the coordinate system of the car such

as bodywork, frame, radiator, frame, driver, wiring, and ballast, etc (Anderson et al. 2019). different parts of the chassis system such as Rear and front suspension, power train, steering, rear and front wheels/tyres, brake, rear and front antiroll bars together develop th full vehicle.

Ackermann Steering geometry
Steering geometry is an important tool of the race car to ensure the maximum performance by all four tyres of the car (Asuelinmen et al. 2020). When a car travels along a circular path (Considered that the car turning at a low speed and all four tyres are in rolling condition, there is no sliding in the car) all four tyres follow a specific trajectory around a turned center as shown in the below figure. The different radii of curvatures ensure no sliding by the steering geometry. It can be achieved if the front tyres move at a greater angle than the outside tyre. The angles at which the tyres can avoid sliding is called steering angle and defined by the following equation (4)
= and = … (4)
Where L is the wheelbase, the turning radius is R, the track width is T.

Suspension geometry, ABR, and spring stiffness

The damper is essential for the suspension of the race vehicle. Suspension travel must be at least 50mm to provide the ability to meet the car's stability and competitive maneuverability needs (Wirawanet al. 2018). The race vehicle suspension must meet the following requirements:

It should be able to dampen vibrations. It must guarantee that the vehicle is extremely stable and maneuverable. It must be both light and sturdy. It should make the driver's control more comfortable. It should be simple to install and configure.

When the roll angle stiffness is raised, the stability and handling improve while the ride comfort suffers. The automobile will instead travel in the direction of its roll axis. The roll angle should be controlled between 2° and 5° as a result of the 0.5g horizontal rigidity. Because roll angle stiffness affects stability and handling, the rear suspension roll angle stiffness is regarded lower than the front to reduce rolling over. When the roll center is higher, the roll torque decreases, and the body-roll angle increases. As a result, when the vehicle tilts, an elevated roll center may pressurize the wheel raceway, reducing tyre service life. For competition, the roll center is set as low as feasible so that the spring-mass does not roll very much, resulting in effective stability and handling. The simultaneous double fixed support's roll center is the same as the cross arm viewed from the vertical direction perpendicular to the vehicle axis from the center of the tyre contact patch. The center roll is dynamically positioned on the ground as a result of the suspension design.

Damping rates

The damping ratio value has a major influence on the dynamic movement of the automobile as well as the vertical load of the car when considering the rebounding and compression of suspension in response to street shocks (Herrmann et al. 2020). When a vehicle meets a speed breaker, the suspension compresses and bounces with little oscillation, as in the case of an automotive shock absorber. This scenario is very damped (damping ratio, (ζ= 1), which indicates that if there is more oscillation between rebonding and compression, it is overdamped ((ζ> 1), however, if there is no oscillation as the system recovers instantaneously after compressing, it is under-damped (ζ < 1). A system with high damping is recommended for a good car suspension system. This is because structures with too much damping will vibrate significantly during road impacts (this is not recommended), and structures with insufficient damping will not absorb the impact and will cause road impacts (Ipilakyaa et al. 2018). Decelerating because it is transmitted directly to other parts of the car, so if the increased torque in this particular part is too large, it will crack or burst, and if it is small, the road shock can also be transmitted directly. Damage will occur to the driver in the car.

Tyre properties

Slip Angle
Slip angle is the first idea you must understand in order to fully understand tyre mechanics. This is defined as the angle (degrees) formed between the wheel's true direction of travel and its 'bearing' location (perpendicular to the axis of rotation) (Luthfie et al. 2020). There is always an angle between the two when a race car encounters lateral acceleration.

The above figure 3 demonstrates how the contact area components have been shifted in the direction of motion. As the force acting lessons, these components at the rear of the contact patch restore to normal. When a slip angle is applied to the tyre, horizontal forces occur on it, causing the contacting patch to alter its form. This deformation results in strain (modulus of elasticity) inside the tyre's molecular structure of rubber. Additionally, the elasticity of the tyre structure opposes the strain, resulting in a force normal to the rotating axis (Ozerem and Morrey, 2019). The compression cycle that the tyre goes through with each round develops interfacial tension and hence temperature within the rubber, which increases the grip of tyre. This builds up to the point when the rubber tyre is overused and traction is significantly diminished, which is commonly referred to as the cliff.

Slip ratio
The slip angle is only used to describe the creation of lateral force. In the longitudinal value, this is referred to as the slip ratio. The slip ratio is as same as the slip angle in that it shows the amount of slip the tyres experience when compared to a skidding condition, however, it is stated in angular movement rather than degrees of slip (Chindamo and Gadola, 2018). The longitudinal force maximum at a slip ratio of about 0.3 – 0.4 is a frequent tyre propensity.

Cornering stiffness
The tyre's turning stiffness is an important parameter for determining its lateral grip capabilities. Newtons per degree of slip angle (N/°) is the unit of measurement. A tyre with a higher turning stiffness will generate more lateral acceleration for a given slip angle, and this is an essential efficiency parameter for all tyres.

Friction circle
The g-g graph or friction circle graphically displays the constraints of a tyre that creates both lateral and longitudinal acceleration at the same time, as well as how the automobile moves in proportion to this (Swamy et al. 2020). The g-g graph appears more like an ellipse than a complete circle, but the lesson here is that a motorist cannot predict the type of lateral acceleration caused in proper turning while necessitating braking/acceleration and vice versa.

Coefficient of friction
It is crucial to recognize that the Coefficient of friction (CoF) does not grow proportionally to the reaction force (vertical load of tyre). Or, double the reacative force does not double the CoF, and hence the tyre gripping level does not double (Chaitanya et al. 2021). This is critical in understanding grip levels in racing car mechanics when the reaction force is not uniformly distributed throughout the vehicle's right and left, or rear and front, due to load transfer.
MATLAB Codes to analyse speed

This result defines that the speed can vary with the specific direction. Normal fluctuations can be observed by this graph.

How the grip of the vehicle changes by changing the damping ratio and the cornering stability

Constant radius Cornering test
In this case the overall validity of the bicycle model is normally examined by the proper comparison and calculation of the value of coefficient of cornering. In this case this value is represented by the K. This value is calculated by the several experiments of the model which is designed. The overall test is performed below 3 km per hour. This factor is changed due to the several Coefficients like tires, lateral force, aligning torque value, roll steer. 

Cornering stiffness
The actual motion of the tire is normally affected by the different factors like size of tire, material which are used to make the tire, structure of the road surface and the quality of the hour. During the experiment it is observed that there are three types of tires used to check the cornering stiffness and in the main type the stiffness value becomes 71687 (Firman et al.2021). This overall Coefficient value changed due to the impact of lateral force which is created by the surface of the road and applied on the cornering. 

Constant radius cornering test
In the simulation result 20 are performed with the help of the highest speed of 20 to 80 km per hour and in this case three different types of values are used for the proper measurement of radius cornering test. In this case for every cornering performance the understeer coefficient is fixed which is represented by K and for this region the proposed method is applied with a different velocity. After the implementation it is observed that if the stiffness of cornering is decreased with the time, then the overall tyre slip angle normally increases with the time. In this case these are applied to maintain the proper turning radius of the difference tyre and for this reason the steering wheel should be at maximum angle to achieve the maximum stiffness of the different corner of the tire. 

Yaw rate gain of steady state response
In this case the maximum value of Yaw rate gain can be obtained from the high speed of the bicycle. Yaw Gain is normally simulated in the MATLAB design for the proper observation of the fluctuation of vehicle speed within a specific range. This value is measured for the different type of cornering stiffness ratio. During the simulation time it is observed that the lateral force which affects the tyre is the main reason for the fluctuation of different types of speed of the bicycle. This Yaw gain rate normally fluctuates for the different types of tires and for this reason the speed also varies for the material of rubber (Hu e al. 2021). In this case it is observed that this rate normally helps to improve the overall steering sensitivity with the lower slip angle of the tyre and also increase the handling and the stability of steering. 

According to the result it is observed that the model becomes oversteer then the original bicycle simulation and for this reason the cornering stiffness value becomes higher in the simulation model. In this simulation the result is observed that the stability factor becomes decreased than the original value. In this case the Yaw rate gain is normally described as the mole ratio of the angle of the steering wheel and the Yaw rate of the tire. It can be stated that if the angle of steering will become reduced then the cornering stiffness will be increased than the normal value and this will impact on the Yaw rate. On the other hand, the natural frequency is a proper relationship between the angle of the steering wheel and the proper value of Yaw of rate. In this case if the cornering stiffness becomes reduced then the angle of the steering should be 0.4 g which helps to increase the overall acceleration. 

In this analysis paper different types of semis active and proper active Suspension systems are evaluated and investigated for the different types of control strategy by the proper optimisation of different gripping in bicycles. In the result it is observed that the particle suspension normally impacts Grips at the different four corners of bicycles. This phenomenon can be easily controlled by the proper suspension of differences for variations (Peer, S., 2019). For the proper declaration a model is designed in this analytical paper and the overall performance is generated in MATLAB to observe the overall performance of the gripping system by the different variation of roads. For the proper analysis at first lag type controller is adopted for the observation of sprung mass acceleration and the different type of unsprang mass which help to decrease the effect of vertical acceleration in the wheel. It will help to guide the overall damping Force for the different types of semis active and inactive type suspension systems. In this case two different ways are considered for the evaluation of break Optimisation (Kabzan et al. 2020). One is the proper minimization of vertical acceleration and the other one is the proper comparison of braking distance in the different wheels of a bicycle. The result declares that the properly developed controller normally helps to control the vertical acceleration rather than the soft suspension. The LQG type controller normally applied on the semi-active suspension to perform the overall braking process in the wheel of a bicycle. This controller helped you optimize the road gripping process with the help of reduction of braking   distance for the specific road condition. In this model different corners are focused for the proper observation of the gripping mechanism in the bicycle. Grip of the vehicle is normally controlled by the damping ratio because in this case it is observed that the lower value of damping ratio normally represents the dynamic performance of the vehicle and the higher damping ratio represents the magnificence vibration of the overall bicycle (Firman et al. 2020).  This factor influences the overall performance of the vehicle because if the damping ratio changes slightly then the overall grip of the vehicle is completely lost and the motion of the vehicle becomes unpredictable. In this case the design model can easily track the cornering stability during the staff corner and for those cases it implements a small amount of braking force on every wheel to maintain the overall speed of a bicycle. In this way the overall speed can be easily optimized and the Braking System can be evaluated on the bicycle. 

Grip of vehicle changes with the changing of damping ratio
In this case the main role of the shock absorber is to control the body rules and the suspension movement in the bicycle. When the model is running on the bumpy road then the shock absorber normally observes the high bumps pressure and controls the overall body of the system. In this case it is observed that the shock absorber normally decreases the overall movement of the spring and on the other hand the soft shock absorber climbs to faster movement of the spring. In this case the damping ratio is the main concern for the proper vehicle movement. If the damping ratio becomes 0, then the overall control becomes easier (Liniger, A. (2018). On the other hand, if the damping ratio is increased from 0 to 1 then the overall system becomes over them and, in this case, the proper breaking aur dripping cannot be possible. For this reason, the vehicle becomes out of control and different types of accidents can be   introduced. In normal cases it is observed that the rebound type damping normally controls the proper reduction of weight in the fastest way on the other hand bums normally control how the weight can be transferred to the other tyre of the vehicle (Hosseinpour et al. 2021). In different cases it is the most effective factor to control the overall vehicle in a higher roughness area. 

Grip of vehicle changes with the the cornering stability
In result it is clearly visible that the corner and stability normally helps the tire to grip the road during the critical turning point. It is observed that during any kind of turning the tyre changes in shape. It enabled the higher power to grip the surface of the Road. This overall phenomenon normally happens when the actual steering angle of the system becomes successful to produce a proper amount of lateral Force for the vehicle (Wang et al. 2021). The right amount of weight in the tyre also impacts on the greeting and it also enables the traction of the tyre. In the corner stability changes then the overall grip becomes changed because if stability becomes zero, then the tyre becomes out of control during any kind of turning and it becomes out of track due to the higher acceleration. The suspension factor normally helps to leave the tire according to the surface and for this reason the car becomes steady during turning. This overall phenomenon is also observed in the results which are derived by the MATLAB. In this case it declared how the cornering stability normally controls the grip of the vehicle (Kelarestaghi et al. 2019). This controls the kids during the sharp corner. Generate the higher amount of braking force on every will to maintain the stability in the vehicle.


After the analysis of the handling and stability characteristics of the race car, there are few recommendations, these are

  • The race car should have a good static distribution of weight.
  • Good suspension geometry can be provided by increasing the contact patch of tyres.
  • The car should have good aerodynamics.
  • The handling response can be consistent by maximizing the torsional rigidity of the chassis.


A race car`s handling characteristics are determined by the interaction of several variables. Finding a specific optimal setup for a race car that gives the highest level of efficiency in every race circuit and competition event is exceedingly difficult, if not impossible to achieve. The Weight Distribution induced by these forces is mostly responsible for whether or not the vehicle acts as intended. To stabilize the vehicle during turning, the car's center of gravity should be as close to the center of the wheelbase as possible in a lateral motion. For stability, the car has to be in the under steer. To meet the stability and maneuverability requirements of the vehicle during competition. The value of the damping ratio has a great influence on the dynamic movement of the car. The design and features of the race car should be according to the specific standards to avoid any rover or crash as the speed of the race car is comparatively high.

Reference List


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