3.1 Transient model
3.1.10 Simulation results
3.1.10.1 Accelerating and braking
Figure 3-12 – Plot of longitudinal acceleration (top), with detail for accelerating (middle) and braking (bottom)
The response plots show that Concept 4 is the one with the highest longitudinal acceleration at all phases of the Concept 4 event. The average relative difference from the best to the worst solutions, for this case, is 3.3% while accelerating and 5.6% while braking.
3.1.10.2 Skid-pad
Figure 3-13 – Plot of lateral acceleration in the Skid-pad scenario, with detail of the beginning of the left corner
The response plots show that Concept 4 is the one with the highest lateral acceleration at all phases of the simulated event. The average relative difference from the best to the worst solutions, for this case, is 0.6% while turning left and 0.8% while turning right, in the transient phase, and 0.4% in steady-state.
3.1.10.3 Chicane
Figure 3-14 – Plot of lateral acceleration in the Chicane scenario (top), with detail of corner-entry
Observing the lateral acceleration response, Concept 5 is the best at corner-entry, but in the rest of the simulation Concept 4 remains the one with higher performance. A chicane manoeuvre never reaches a steady-state phase, as, while in corner-entry the speed is decreasing and the steering input is increasing, in corner-exit the opposite happens. This explains why there is such a significant variation of lateral acceleration over time. The average relative difference from the best to the worst solutions, for this case, is 5.1% at corner-entry and 2.2% at corner-exit.
3.1.10.4 Hairpin
Figure 3-15 – Plot of lateral acceleration in the Hairpin scenario (top), with detail of corner-entry (middle) and corner-exit (bottom)
Observing the lateral acceleration plot, it’s clear that Concept 5 has greater lateral acceleration at corner-entry, during the transient phase. After that, when the acceleration progresses into the steady state phase, Concept 4 becomes the best solution. The average relative difference from the best to the worst solutions, for this case, is 1.2% at corner-entry, 8.3% in steady-state and 2.1% at corner-exit.
3.1.10.5 Slalom
The response plots show that Concept 4 is the one with highest lateral acceleration. The average relative difference from the best to the worst solutions, for this situation, is 0.9%.
Figure 3-16 – Plot of lateral acceleration in the Slalom scenario, with detail of one corner (bottom)
3.1.10.6 Simulation conclusions
From the acceleration plots presented, Concept 4 is the one that shows the highest performance overall. Concept 5 shows higher lateral acceleration while braking and turning, which is when the steering wheels have a higher vertical load. The car has a complex suspension system, similar to the one shown in Figure 3-7, so any kind of input somewhere on the system will affect the response of the entire system. From the response plots, it’s clear that at corner-entry, having a higher un-sprung mass, and therefore lower natural frequency (as it happens with Concept 5 relative to the others), means there is less variance in the vertical response of the wheels and consequently in the vertical load on the tire, which, in turn, means a smaller variance in the total produced lateral force. This only happens in this phase of the corner (while the car is under braking and turning), since when the response progresses towards the steady state phase, a lower mass will mean a higher lateral acceleration. This effect is not seen in the Skid-pad and slalom scenarios, as they are simulated at constant speed, so there isn’t any braking while cornering situation.
The effect of performance difference at corner-entry is very small when looking at an entire lap of a track, because the car will only be in that state in an extremely small fraction of the track’s length. For that reason, this effect will be neglected and the chosen solution for the system is the one of Concept 4.
3.2 Steady state model
3.2.1 Software overview
Optimum Lap is a commercial software created by Optimum G, a motorsport consulting company.
It’s a steady state simulator, that uses a point-mass representation of the car, as shown in Figure 3-17.
It has an accuracy higher than 90% [25], which means it’s suitable for the required analyses.
𝑭 𝒅𝒓𝒂𝒈 𝑭 𝑿 𝒔 𝑭 𝒀 𝒔
𝑭 𝒁 𝒔
Figure 3-17 – Illustration of the point-mass model
A steady state model shows the absolute peak performance of the car, as it considers the car is always performing at its limits, being them the tires or the motors. It doesn’t account for any transient effects or driver inconsistencies. For these reasons, the results extracted from this simulator represent an upper limit for the performance of the car.
3.2.2 Software inputs
As a simplified model, it requires a small amount of inputs: overall mass, aerodynamic coefficients (𝐶𝑑and 𝐶𝑙), transmission ratio and efficiency, tire friction coefficients and motor torque vs speed curve and track layout.
Table 3-1 – Car characteristics used in Optimum Lap simulations
Unlike in section 3.1.2, this software only uses the tire friction coefficients and load sensitivities.
The equations from the Magic Formula of Pacejka were used to find these constants.
1Accounts for the efficiency of Concept 4 and the average efficiency of the battery and inverters.
General data
Vehicle Type FSAE
Mass 281,8 kg
Driven Type AWD
Aero Data
Type Drag-Lift
Drag Coefficient 1,375
Downforce Coefficient 2,875
Frontal Area 1,35 m2
Air Density 1,24 kg/m3
Tire Data
Tire Radius 0,228 m
Rolling Resistance 0,03
Longitudinal Friction 1,6 at 0 kg Longitudinal Load Sensitivity 0,001
Lateral Friction 1,3 at 0 kg Lateral Load Sensitivity 0,001
Transmission Data
Transmission Type Sequential Gearbox
Gear Ratio 14,96
Final Drive Ratio 1
Drive Efficiency1 92 %
3.2.2.1 Motor
Since the software considers the car as a simple point-mass, the motor curve associated to that point must represent all set of the motors existing in the real car. Also, it doesn’t have a way of limiting the maximum available power in the car, as required by the competition rules. Efficiency is also simplified and represented by a single efficiency value. So, to consider the real efficiency map shown in Figure 3-18, which was provided by the motor manufacturer, as well as the maximum power requirements and the amount of motors, an equivalent motor curve was obtained.
The provided efficiency map is quite over-simplified, as there is no information between speed or torque intervals. To expand this map, a 4th degree polynomial interpolation was used, resulting in the new map of Figure C-1, presented in Appendix E.
A similar map can be created, showing power instead of efficiency, representing the output power Figure 3-20 – Example of the 4th degree approximation, of the first row of the
efficiency map, of Figure 3-18
Figure 3-19 – Efficiency map provided by the motor manufacturer [19]
corresponding entry of the efficiency map, results in the map of Figure C-3, that represents the power that the battery supplies to the motor (through the inverters).
Figure C-2 and Figure C-3 are relative to a single motor, but the car is an all-wheel drive, so all the four motors must be considered. In testing, previous FST Lisboa teams have concluded that to have a good balance between lateral and longitudinal performance, the maximum torque on the front motors must be 50% of the maximum torque on the rear ones. This occurs because a tire cannot produce the maximum longitudinal force and lateral force at the same time. The combined map of total input power to the motors, accounting for the 50% limit at the front wheels is shown in Figure C-4.
It’s clear that there are torque/speed combinations where the total power is higher than the 80kW limit defined by the competition rules. After removing those combinations, it becomes possible to find the equivalent motor curve, by multiplying the entries from the map in Figure C-4 by the efficiencies in Figure C-1, and then selecting the speed/torque combinations with higher power, Figure 3-21.
3.2.2.2 Track layout
The track layout represents the trajectory the car takes around the track. Twelve different layouts were inserted in the software, two corresponding to the acceleration and skid-pad events and the others corresponding to autocross and endurance events. FST Lisboa only participates in European competitions, therefore the defined track layouts correspond to the ones of those competitions. Figure 3-22 shows an illustration of how the track layout of Formula Student Spain was obtained, both the autocross layout as well as the endurance. The other track layouts used in the simulations are presented in Appendix E.
Figure 3-21 – Output torque and power curves of the equivalent motor
3.2.3 Results conversion
Since the software uses a point-mass model, some calculations must be performed using its outputs, like the one in Figure 3-23, to find the loads on each wheel. From the car’s longitudinal, lateral and yaw accelerations, and aerodynamic forces, the total longitudinal, lateral and vertical forces, and yaw moment, 𝐹𝑋𝑠, 𝐹𝑌𝑠, 𝐹𝑍𝑠 and 𝑀𝜓𝑠, respectively, can be computed as:
𝐹𝑋𝑠= 𝑀𝑎𝑥 (3.23)
Track limit
Inward offset, to account for the width of the car Car trajectory
Figure 3-22 – Illustration of how the track of Formula Student Spain was obtained (Background from Google Maps)
Figure 3-23 – Speed plot of an autocross lap in Formula Student Spain. Example of an output from the simulation in Optimum Lap
𝐹𝑌𝑠= 𝑀𝑎𝑦 (3.24)
𝐹𝑍𝑠= 𝑀𝑔 + 𝐹𝑑𝑜𝑤𝑛𝑓𝑜𝑟𝑐𝑒 (3.25)
𝑀𝜓𝑠 = 𝐼𝜓𝜓̈ (3.26)
The model as a point-mass doesn’t consider any steering input. The lateral friction coefficient used in the simulation was obtained with the assumption that each tire is always operating at a slip angle 𝛼 that corresponds to the highest lateral load. Knowing the value of 𝛼, equation (3.15) can be used to estimate the steering angles, with beta being calculated with equation (3.27).
𝛽1= tan−1(𝑎 + 𝑅𝑐𝑜𝑟𝑛𝑒𝑟sin 𝛽 𝑅𝑐𝑜𝑟𝑛𝑒𝑟cos 𝛽 − 𝑐) 𝛽2= tan−1(𝑎 + 𝑅𝑐𝑜𝑟𝑛𝑒𝑟sin 𝛽
𝑅𝑐𝑜𝑟𝑛𝑒𝑟cos 𝛽 + 𝑑) 𝛽3= tan−1(𝑏 − 𝑅𝑐𝑜𝑟𝑛𝑒𝑟sin 𝛽
𝑅𝑐𝑜𝑟𝑛𝑒𝑟cos 𝛽 − 𝑐) 𝛽4= tan−1(𝑏 − 𝑅𝑐𝑜𝑟𝑛𝑒𝑟sin 𝛽
𝑅𝑐𝑜𝑟𝑛𝑒𝑟cos 𝛽 + 𝑑)
(3.27)
To be able to calculate the longitudinal and lateral forces on the tires, first the vertical forces must be calculated.
𝐹𝑧1= 𝐹𝑍𝑠 𝑑 (𝑐 + 𝑑)
𝑏
(𝑎 + 𝑏)− 𝐹𝑋𝑠 ℎ𝐶𝑜𝐺 (𝑎 + 𝑏)
𝑑
(𝑐 + 𝑑)− 𝐹𝑌𝑠 ℎ𝐶𝑜𝐺 (𝑐 + 𝑑)
𝑏 (𝑎 + 𝑏) 𝐹𝑧2= 𝐹𝑍𝑠 𝑐
(𝑐 + 𝑑) 𝑏
(𝑎 + 𝑏)− 𝐹𝑋𝑠 ℎ𝐶𝑜𝐺
(𝑎 + 𝑏) 𝑐
(𝑐 + 𝑑)+ 𝐹𝑌𝑠 ℎ𝐶𝑜𝐺
(𝑐 + 𝑑) 𝑏 (𝑎 + 𝑏) 𝐹𝑧3= 𝐹𝑍𝑠 𝑑
(𝑐 + 𝑑) 𝑎
(𝑎 + 𝑏)+ 𝐹𝑋𝑠 ℎ𝐶𝑜𝐺 (𝑎 + 𝑏)
𝑑
(𝑐 + 𝑑)− 𝐹𝑌𝑠 ℎ𝐶𝑜𝐺 (𝑐 + 𝑑)
𝑎 (𝑎 + 𝑏) 𝐹𝑧4= 𝐹𝑍𝑠 𝑐
(𝑐 + 𝑑) 𝑎
(𝑎 + 𝑏)+ 𝐹𝑋𝑠 ℎ𝐶𝑜𝐺
(𝑎 + 𝑏) 𝑐
(𝑐 + 𝑑)+ 𝐹𝑌𝑠 ℎ𝐶𝑜𝐺
(𝑐 + 𝑑) 𝑎 (𝑎 + 𝑏)
(3.28)
The lateral forces 𝐹𝑦𝑖 can be calculated with the vertical forces 𝐹𝑧𝑖 and the tire’s lateral friction coefficient and load sensitivity. Those lateral forces, together with the diagram presented in Figure 3-8, the results from equations (3.23), (3.24) and (3.26), and the 50% limit on the front wheels, presented in section 3.2.2, can be used to calculate the longitudinal forces on each wheel.
𝐹𝑦𝑖 = 𝜇(𝐹𝑧𝑖) × 𝐹𝑧𝑖 (3.29)
𝐹𝑥1cos 𝛿1− 𝐹𝑦1sin 𝛿1+ 𝐹𝑥2cos 𝛿2− 𝐹𝑦2sin 𝛿2+ 𝐹𝑥3+ 𝐹𝑥4− 𝐹𝑑𝑟𝑎𝑔= 𝐹𝑋𝑠 (3.30) 𝐹𝑥1sin 𝛿1+ 𝐹𝑦1cos 𝛿1+ 𝐹𝑥2sin 𝛿2+ 𝐹𝑦2cos 𝛿2+ 𝐹𝑦3+ 𝐹𝑦4 = 𝐹𝑌𝑠
(3.31)
𝐹𝑥1(sin 𝛿1𝑎 − cos 𝛿1𝑐) + 𝐹𝑥2(sin 𝛿2𝑎 + cos 𝛿2𝑑) − 𝐹𝑥3𝑐 + 𝐹𝑥4𝑑
+𝐹𝑦1(cos 𝛿1𝑎 + sin 𝛿1𝑐) + 𝐹𝑦2(cos 𝛿2𝑎 − sin 𝛿2𝑑) − 𝐹𝑦3𝑏 − 𝐹𝑦4𝑏 = 𝑀𝜓𝑠 (3.32)
Wheel travel ℎ𝑖𝑠 can be estimated using the vertical loads 𝐹𝑧𝑖 on each wheel and the respective wheel-rate (𝐾𝑖), as shown in equation (3.33).
ℎ𝑖𝑠=𝐹𝑧𝑖 𝐾𝑖
(3.33)
Knowing the magnitude of 𝐹𝑥𝑖, the torque on each wheel, 𝑇𝑖, can be calculated by multiplying the forces by the tire radius r. The speed of each wheel, 𝑣𝑖, can be estimated with equation (3.35), aided by Figure 3-8.
𝑇𝑖= 𝐹𝑥𝑖× 𝑟 (3.34)
𝑣𝑖= 𝜓̇𝐿𝑖cos 𝛼𝑖 (3.35)
With torque and speed, the output power on each wheel can be calculated. In a braking event, the power will be negative. Using the limitation imposed by FST Lisboa, regarding the battery, a maximum of 15kW can be regenerated under braking. Therefore, when the magnitude of braking power is higher than 15kW, it is considered that the remaining power above those 15kW will come from the mechanical braking system, Figure 3-24.
There’s always power loss in any type of mechanism. The dissipated power in the motors can be calculated applying the efficiency map shown in Figure C-1, to the power response plot. This dissipated power, together with the power dissipated in the drive train parts 𝐻𝐷𝑇 and the power dissipated in the
Figure 3-24 – Plot of total braking power, electrical regeneration and mechanical braking
braking system 𝐻𝑏𝑟𝑎𝑘𝑒, represents the total dissipated power 𝐻𝑡𝑜𝑡𝑎𝑙, which is useful for estimating the temperatures of all parts of the system.
3.2.4 Operating temperature estimation
One of the main factors that influences the mechanical properties of materials is temperature. To assure the proper stiffness and resistance of all components, their operating temperatures must be estimated. A purpose-developed thermal model was used, created in Simulink, where the dissipated power losses are the input and the temperatures of the various components are the output.
The model is made of interconnected thermal resistances and masses, which are used to estimate the temperatures variation over time. These resistances were obtained by making a thermal finite element analysis of the Concept 4, to which heat powers were applied in different places. In that FEA model, the applied heat power 𝐻 and the temperature differences between components ∆𝑇𝑖→𝑗 were used to calculate the resistance 𝑅𝑖→𝑗, with equation (3.36) [26].
𝑅𝑖→𝑗=∆𝑇𝑖→𝑗
𝐻 (3.36)
Faramarz and Salman [27] analysed the temperature distribution and forced convection effect on brake discs and pads. They concluded that the amount of braking power dissipated through the disc and pads is:
Figure 3-25 – Diagram of the thermal model in Simulink
𝐻𝑑𝑖𝑠𝑐= 𝐻𝑏𝑟𝑎𝑘𝑒× 𝑝ℎ𝑒𝑎𝑡 (3.37)
𝐻𝑝𝑎𝑑𝑠= 𝐻𝑏𝑟𝑎𝑘𝑒× (1 − 𝑝ℎ𝑒𝑎𝑡) (3.38)
𝑝ℎ𝑒𝑎𝑡= √𝑘𝑑𝑖𝑠𝑐𝜌𝑑𝑖𝑠𝑐𝑐𝑑𝑖𝑠𝑐
√𝑘𝑑𝑖𝑠𝑐𝜌𝑑𝑖𝑠𝑐𝑐𝑑𝑖𝑠𝑐+ √𝑘𝑝𝑎𝑑𝜌𝑝𝑎𝑑𝑐𝑝𝑎𝑑 (3.39)
Where pheat is the heat partition coefficient and the term √𝑘𝑖𝜌𝑖𝑐𝑖 is the thermal effusivity of the material.
Vidiya and Singh[28] analysed the typical air flow characteristics in regular Formula Student cars, through CFD analysis, obtaining a linear forced-convection coefficient ℎ𝑓𝑜𝑟𝑐𝑒𝑑, dependent on the car’s speed 𝑣:
ℎ𝑓𝑜𝑟𝑐𝑒𝑑= 17𝑣 + ℎ𝑛𝑎𝑡𝑢𝑟𝑎𝑙 (3.40)
To validate the model, the thermal constants were modified to correspond to the ones of the most recent car from FST Lisboa, using the same approach as before to fin the thermal resistances. For the same test session as the one already presented in section 3.1.9, sensors were mounted on the car to measure the temperature of the brake disk, pads and calliper, and the upright, in positions shown in Figure D-1, in Appendix D.
While the car is running, the brake disc is rotating, an infrared sensor (ZTP-135SR) was used to measure its temperature, as it doesn’t require any contact with the surface. This type of sensor is made of a thermopile (which are several thermocouples connected in series), and an NTC resistor, which is used to calculate the reference temperature 𝑇𝑟𝑒𝑓. Using equations (3.41) and (3.42), the measured surface temperature can be calculated.
𝑇𝑟𝑒𝑓= 1
ln ( 𝑈𝑁𝑇𝐶
𝑈𝑖𝑛𝐼𝑅− 𝑈𝑁𝑇𝐶)
3920 + 1
298.15
(3.41)
𝑇𝑑𝑖𝑠𝑐= (𝑈𝐼𝑅
𝑆 + (𝑇𝑟𝑒𝑓+ 273.15)4)
1ൗ4
− 273.15 (3.42)
where 𝑈𝑖𝑛𝐼𝑅 is the input voltage supplied to the sensor (5V), 𝑈𝑁𝑇𝐶 is the measured voltage of the NTC and 𝑈𝐼𝑅 is the measured voltage of the infra-red sensor, both in volt [V]. Temperature values in Celsius [ºC].
𝑆 is a constant that represents the sensor’s field of view, the emissivity of the disc surface, the Stefan-Boltzman constant and the sensor sensitivity, and was defined experimentally, as shown on Figure 3-26. After heating up a sample brake disc to a temperature of 100ºC, it was placed on 3 supports with minimum contact over the infra-red sensor, which was used to measure the temperature variation over time. 𝑆 = 5x10-11 was obtained by comparing the measured values of the infra-red sensor with those of an external temperature sensor, measuring the surface temperature.
With the voltage measured in the NTC and the surface temperature 𝑇𝑠𝑢𝑟𝑓, measured in the external temperature sensor, equation (3.41) can be used to calculate the temperature 𝑇𝑟𝑒𝑓, and equation (3.42) can be manipulated into equation (3.43), to find the value of K. The measured 𝑇𝑠𝑢𝑟𝑓 and 𝑇𝑟𝑒𝑓 are presented in Figure 3-28.
𝑆 = 𝑈𝐼𝑅
(𝑇𝑠𝑢𝑟𝑓+ 273.15)4− (𝑇𝑟𝑒𝑓+ 273.15)4 (3.43)
For the remaining measurement points, NTC resistors (NTCLE100E3) were used. Their temperatures, 𝑇𝑁𝑇𝐶𝑖 can be estimated with equation (3.44), where 𝑈𝑖𝑛 is 3.3V and 𝑈𝑖 is the voltage measured in each sensor.
NTC voltage
Thermopile voltage
External temperature sensor
Infra-red sensor Power supply
Figure 3-26 – Setup to obtain the value of K. The infra-red sensor is underneath the brake disc
𝑇𝑁𝑇𝐶𝑖= 1 ln ( 𝑈𝑖
𝑈𝑖𝑛− 𝑈𝑖)
3977 + 1
298.15
(3.44)
Figure 3-27 shows the acquired data overlaid with the simulation results. Comparison between measured and simulated temperatures for other components are presented in Figure 3-27. It’s clear that the simulation is well designed as the presented result is within an error margin of 6%.
Figure 3-27 – Comparison between measured and simulated temperature of the brake disc
Figure 3-28 – Measured temperature variation of 𝑇𝑠𝑢𝑟𝑓 and 𝑇𝑟𝑒𝑓
3.2.5 Simulation results
3.2.5.1 Converted results
Using equations (3.23) through (3.32), for the track shown in Figure 3-22, the forces on each wheel are obtained.
Figure 3-29 – Forces Fx, Fy and Fz on each wheel, for an autocross lap in Formula Student Spain
3.2.5.2 Temperature
With the thermal constants corresponding to Concept 4 (Appendix E), the following results were obtained from the thermal model, assuming an ambient temperature of 25ºC.
Figure 3-30 – Temperatures at the front-left (top) and rear-left (bottom) wheels, during an autocross lap in Formula Student Spain. It represents the fourth lap in a row, which justifies the high temperatures at the beginning of the plot
4 Load cases for structural analysis
The car will be subjected to different types of loading throughout its life. In the earlier days it will be subjected to mild testing, at low speed and low power, since there are multiple electrical and mechanical systems that must be checked. After that, the car will be tested at racing speeds, to find the ideal suspension setup and tune the control systems. Then the car will be subjected to the same types of loadings, but in the competition environment. Finally, there is a testing phase after the competitions, to help in the development of the following year’s car.
To simplify the simulations, the initial phase of testing was neglected, as the expected loads are very small. For the remaining phases, it was assumed that the performed tests represented the dynamic events of the competitions. For the entire life of the car, the expected number of times each event is tested is:
• Acceleration: 84 times, 4 laps each time;
• Skid-pad: 70 times, 4 laps each time;
• Autocross: 14 times, 4 laps each time;
• Endurance: 28 times, 22 laps each time.
With this information, together with the results from the steady state simulations, it is possible to estimate the total expected travelled distance about 760Km, with a total expected operating time about 55h.
4.1 Drive train load cases
The structural design of the gears was performed in KISSsoft (section 5.1.2). The software accepts a full load spectrum, with relative torque, speed and time, the latter representing the percentage of time the system is experiencing the specific torque and speed combination. Table 4-1 shows the first four entries of the spectrum, as an example.
Table 4-1 – First four entries of the drive train load spectrum for a rear wheel
Ner [%] Time [%] Torque [%] Speed
1 0.00241 80.95 45
2 0.00011 80.95 40
3 0.02804 76.19 50
4 0.20479 76.19 45
The load spectrum is the same between the front wheels and between the rear wheels, as
which apart from time, are different in each stage of the transmission system. In the first stage, the reference torque and speed are 21 Nm and 20000rpm, corresponding to the limits of the motor. The references for the second stage depend on the transmission ratio of the first stage. The software uses this spectrum to apply the Palmgren-Miner rule during the analysis.
4.2 Suspension load cases
All components, except for gears, were analysed using FEA (Finite Element Analysis). Those analyses require the definition of load cases and constraints applied to the components. From the calculations made and the results obtained in section 3.2, a load spectrum can be defined, with all the information regarding the car’s performance throughout its life. This spectrum has 877080 load cases, each representing a single set of longitudinal, lateral and vertical forces and accelerations, wheel positions, steering angles and temperatures for each wheel. Naturally this amount of information is too high to be inserted into a FEA software, therefore only the most significant points of the spectrum were considered in those analyses.
To find those reference points, the G-G diagram of the car, shown in Figure 4-1, was observed.
Each grey dot represents a point of the spectrum, with a certain longitudinal and lateral acceleration.
Figure 4-1 – G-G diagram of the car (with Concept 4), with concentric inner and outer rings
The diagram is divided into 2 concentric rings, each divided into 16 areas. These areas represent specific states of the car, such as pure accelerating or braking (areas 1 and 9), pure cornering (areas 5 and 13) and combinations of the two (remaining areas). The outer ring (Oi) represents the absolute peak performance of the car, so from a structural point of view they correspond to the critical points in terms of stress, whereas the inner circle (Ii) represents the load cases that the system will experience more often. Each yellow dot is the selected reference point the respective area, corresponding to a single set of reference loads. The car is considered to be symmetrical, so both wheels on each axle must have
O1
O2
O3
O4
O5
O6
O7
O8
O9
O10
O11
O12
O13
O14
O15
O16
I15
I1
I2
I3
I4
I5
I6
I7
I8
I9
I10
I11
I12
I13
I14
I16