2016 CU Boulder Baja Braking System & Pedal Assembly. Landis MacMillan. Bachelor of Science: Mechanical Engineering. Advisor: Peter Himpsel

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1 2016 CU Boulder Baja Braking System & Pedal Assembly Landis MacMillan Bachelor of Science: Mechanical Engineering Advisor: Peter Himpsel

2 2016 CU Boulder Baja Braking System Landis MacMillan The University of Colorado at Boulder Abstract The purpose of this project was to design a brake system for the CU Boulder Baja SAE vehicle that could adequately handle the given input forces, and produce braking forces that would stop the rotation (lock) of all for wheels. This system would need to abide by the competition rules and optimize weight and packaging characteristics. This report will record and state design intent, budget, proof of design and testing. Contents Abstract... 2 Introduction... 2 Applicable Rules... 2 Brake System... 2 Objective... 2 Design... 3 Purchased Components... 3 Master Cylinders... 3 Calipers... 4 Brake Rotors... 5 Bias-Bar... 5 Brake Pedal Assembly... 5 Calculations... 5 Design Intent... 6 Brake Pedal... 6 Pedal Brackets... 7 Configuration... 8 Throttle Pedal... 8 Assembly... 9 Budget... 9 Testing and Proof of Design Conclusion Recommendations Contact References Definitions, Acronyms, Abbreviations Appendix A Pedal System Design Lead Appendix B Appendix C Introduction The objective of the Baja SAE competition is to design and manufacture a four-wheel off-road vehicle that can be operated by one person and can compete with manufactured products in terms of safety, appearance, performance and cost. The University of Colorado at Boulder will be competing in the 2016 California Baja SAE competitions. The goal for the 2016 team was to design a vehicle that would pass tech inspection and finish all coinciding races and challenges. Being a first year team, this seems to be a realistic and appropriate goal considering the team has never had any prior experience in automotive design competitions. To achieve the presented goal, the brake system must be robust, but retaining a lightweight design and create a comfortable motion for the driver. Applicable Rules To see full wording of rules, see Appendix A. B11.1 Foot Brake B11.2 Independent Brake Circuits B11.3 Brake(s) Location B11.4 Cutting Brakes B11.5 Brake Lines Brake System Objective The brake system must be able to produce more than the required braking force designated by the SAE competition rules. The brakes must allow the driver to lock all for wheels at a comfortable input force. The brake system should also be robust enough to withstand larger 2

3 than anticipated forces and make it through all racing events, but light enough to reduce weight in the vehicle and weight at the wheels. Design The braking system was designed in sync with the rules, restrictions, and requirements provided by the SAE organization. Being a first year team, there was no set budget for cost or weight for the pedal system because no team member knew what would be an adequate budget. Recommendations for future teams and designs will be mentioned in the section Recommendations. Purchased Components There are certain components in the brake system that would be too costly and time consuming to design and manufacture. These components will be discussed in this section, along with reasons for selection and implementation. Master Cylinders The master cylinders (MC s) are the components that directly transfer the force of the pedal to pressurize the hydraulic braking circuit. In order to receive the proper amount of force needed to decelerate at 0.7g, the MC s needed to transfer the correct pressure to the brake caliper pistons. There are two types of master cylinders that can be chosen for this application. There is a single chamber master cylinder that acts like a plunger and cylinder. One plunger pressurizes one brake circuit. The other type of master cylinder is a dual chamber. One push of the plunger on this MC pressurizes two circuits at different or the same pressure. Figure 1 shows the basic mechanism of the dual chamber master cylinder below. To understand the general concept of this master cylinder, follow this reference [1. There are pros and cons to both of these master cylinders. The dual chamber MC allows for a simpler design of the pedal assembly. The pedal only needs to actuate one piston that will provided pressure to both brake circuits. Once again with one master cylinder, mounting becomes easier to design. However, the assembly itself is much more complicated than a single chamber MC. As one can see from Figure 1, there are many more part interfaces than the single chamber master cylinder in Figure 2. These part interfaces are areas susceptible to wear and potential failure. When designing separate brake circuits proportioning the pressure in each circuit is vital in order to prevent one set of wheels locking before the other, which causes unwanted handling characteristics (slide 32-33) [2; These effects are mitigated by adding a proportioning valve to the dual chamber MC brake circuit. The valve is simple and is easy to adjust. Figure 2: Single Chamber MC A single chamber MC has the opposite benefits of a dual chamber MC. It is a much simpler design, therefore there is less potential for failure. However, the single chamber only produces pressure for one circuit, which means that there needs to be two single chamber MC s in the final design to abide by SAE s rules. With two MC s, features need to be designed to mount and position both MC s. Along with added features, there needs to be a way to proportion the pressure of each circuit. This is done with the use of a mechanical mechanism called a bias-bar. The bias bar works as a simple lever. Depending where you position the pedal input (fulcrum), the proportion of the lever dimensions directly relates to the amount of force Figure 1: Dual Master Cylinder 3

4 distributed between the two brake circuits [3. An image of a bias-bar s basic operation can be seen in Figure 3. The bias-bar achieves what a proportioning valve would do on a dual chamber MC, but with added parts and features. Not only do you have to include the bias-bar in your design, but you must design features into the pedal to allow for a bias bar to slide. This sliding allows for the bar to proportion the two circuits accordingly. Figure 3: Bias-Bar Operation For the final design, two single chamber MC s were chosen. Reliability was the teams main concern, so the two single chamber MC s seemed like the better choice. Along with reliability, it was easy to find different bore sizes that would match the sizes produced by the brake system calculations. The master cylinders selected for use, were two Wilwood racing master cylinders (part number: & ). These master cylinders had a bore size of inches (front) and 0.75 inches (rear). These bore sizes were chosen based of the calculations performed, seen in Appendix B, and for a more centered brake bias-bar. maintaining braking performance, by switching to a dual chamber MC, then it could be worth the design change. But the decision should be based on the considerations listed above. However, please read my comments in Testing and Proof of Design, as well as the Recommendations section to understand some of my difficulties. Calipers The calipers were chosen based on packaging (ability to fit and operate within allotted space) requirements and other sub-teams decisions. They needed to be small enough to fit within the front wheel hubs but large enough to house the proper piston size to produce the needed braking force. Things to consider when choosing a caliper are cost, weight, packaging and most importantly its functionality with the designed system. Keep weight low to reduce the sprung weight of the vehicle. Cost is always nice to keep low because there will be unforeseen expenses. The shape and size of the caliper needs to be considered in order to fit properly in other sub-teams assemblies. Coordination with these teams is crucial in order to successfully integrate parts. Having an accurately modeled part in Solidworks will streamline this process. Lastly, will the caliper be able to produce the needed clamping force on the rotor? This needs to be analyzed in the braking system calculations. See section Calculations for more details. The Wilwood PS1 caliper with a 1.12-inch piston bore was chosen for the final design. This caliper was able to produce more than the needed force on the rotors, while still remaining small enough for packaging concerns. In terms of pros and cons, the decision between the dual and single chamber MC is a wash. They both have perks that could aid in design and implementation and they both have obstacles that make design a little difficult. The true deciding factor is how the MC will work in the vehicle. Analyze the packaging requirements, cost, weight, personal understanding MC operation, and its ability to produce enough pressure for the required braking force. If cost and weight can be reduced, while 4

5 Brake Rotors The brake rotors were chosen based on packaging requirements as well. The front rotors are from a Yamaha Banshee 300 because they came with the front hubs the suspension team chose to use. These are outboard brakes, so there needs to be individual calipers and lines routed to each rotor. Caliper Rotor and the rear wheels, as mentioned in the Master Cylinders section. Brake Pedal Assembly Given the bore sizes, rotor diameters of purchased equipment and other assumed values, the pedal assembly was designed to create the needed braking force from the driver input. Calculations The calculations to determine the pedal ratio and the required force will be recorded in the following section. Apart from the assumptions made, the calculations stayed very close to the calculations found through online research [4. The following spreadsheet can be found in the following server file location: cubaja->controls->resources->brake Data Sheet Figure 4: Front Hub & Brake Assembly The rear brake rotor was designated as an inboard rotor. Because packaging was limited on the rear uprights, the rotor was mounted to the final driveline coming from the Spicer gearbox. This meant that only one caliper was needed for the rear brake circuit. The rotor chosen was a Hammerhead Sportworks rotor sourced from BMI Karts and supplies. These rotors were produced for a two-person buggy, so it was assumed the design could handle the use in a Baja SAE vehicle. Figure 5:Rear Brake Location Bias-Bar The brake bias-bar allows for minor adjustment in the force allocated to each master cylinder. Depending the results seen in testing, the bias-bar can be adjusted to direct more force to the corresponding master cylinder in order to keep consistent lock-up between the front 5 There were assumptions that needed to be made in order to make these calculations. Without a completed Solidworks model, these values were estimated to the most accurate degree possible. The center of gravity was assumed to be 24 inches based on ride height of shocks and driver position. The wheelbase was determined through the suspension team s design. The total weight was assumed to be 600 pounds; with an average driver weight of 150 pounds and an anticipated vehicle weight of 450 pounds. From the preliminary solidworks model, the weight distribution was 40:60 (40% front, 60% rear). The assumed rate of deceleration was 0.7 g, based on the advice given by the team s advisor. With the given assumptions and the dimensions of the purchased parts, the calculations could be made. First the dynamic weight shift needed to be calculated. When the car begins to decelerate, the momentum of the vehicle causes the weight to transfer to the front. This weight shift applies more force to the front of the vehicle, essentially adding more weight. Using the equations found from the online sources [4, the amount of weight shifted to the front of the vehicle was 158 pounds. This then calculated the amount of weight on each axle during braking (dynamic mass). 434 pounds would be located on the front axle and 172 would be located on the rear. Once the dynamic weight was calculated, the clamping force (pressure) of the brake system could be calculated. Using 0.7 as the coefficient of friction for rubber on

6 asphalt [5, the wheel locking force was calculated. This value describes how much force the brake caliper needs to exert on the rotor to lock of the wheels. By multiplying this force by a factor of safety of 1.5, any unknown inefficiencies are mitigated and one can assume the brakes will lock the wheels. Once the lock-up force is found, the torque required to produce the force on the rotor was calculated by using the effective radius of contact between the rotors and the calipers. Then the clamping force could be determined by dividing the torque by the number of friction surfaces, effective radius and the coefficient of friction between the rotor and brake pads (0.35) [6. Knowing the needed clamping force, the required system pressure could be calculated by dividing the clamping force by the known caliper piston area. The force needed was calculated for each brake circuit (front and rear) by multiplying the required system pressure by the area of the master cylinder bore. These two forces were combined to find the total force needed from the pedal. Once this force was calculated (700 lbf), the pedal ratio was found by dividing the needed force by the minimum driver input (100 lbf). All calculations can be seen in Appendix B. Design Intent The pedal assembly s design was themed around stock material thickness. The design was never intended to be worked out of a large piece of material or billet. The parts in the assembly were kept to common plate and tube sizes. All of the parts were modeled to fit and be used on both the throttle and brake pedal assemblies. Once the material was sourced and ordered, the parts made from the plate would be sent to be cut by a water jet, while all the tube stock could be spun on a lathe. All the parts were based on simple production methods. acceptable, and they can be used in a floor or ceiling mounted set-up. What dictates whether one design is used over the other is the design of the foot-box. Depending where the steering rack is located and the Figure 7: Second-Class Lever Figure 7: First Class Lever overall shape and dimensions of the foot-box, one design will fit better than the others. Important: Before finalizing any designs, make a prototype of the foot box and seating position. Make prototype parts that represent the steering rack, frame tubes, and pedals out of foam, pvc, cardboard, etc. Set in the mock-up and analyze how the comfort of the set-up. Are the pedals operable? Could feet possibly get caught in the assembly? Could a driver operate these pedals for four hours? These are the questions that need to be asked. Do not forget about ergonomics, they can make or break a race, and the driver literally. Brake Pedal The brake pedal was designed as a second class lever, where the load is placed between the fulcrum (bearing) and the applied force (foot-plate). This means whichever way the foot-plate moves, the load moves in the same direction, like Figure 7. One can design a pedal as a first class lever as well. This is a lever where the fulcrum is placed between the load and the applied force. That means when the load moves in the opposite direction of the foot-plate. This can be seen in the Error! Reference source not found.. Both of these pedal designs are 6

7 Seen in Figure 9, the pedal was designed with two identical ribs that were spaced by the rib-spacer. This spacer was shouldered to provide proper rib spacing and bored in order to allow the bias-bar to slide inside the spacer. The bias bar needed approximately an inch of travel in order to proportion the brakes properly. The pedal could have been deigned from a billet, but that would have taken much more time and money to manufacture. pedal strength, a pedal must be able to withstand a 2000 newton force (450 lbf) [7. Considering that the brake pedal was designed with two ribs that would distribute the force evenly, the FEA was run on only one rib with a force of 1000 newtons. Bearing-Spacer Bearing Bearing Race Spacer Rib-Spacer Pedal-Rib Foot-Plate Figure 9: Labeled Brake Pedal The fulcrum at which the pedal rotates was surrounded by a bearing that could withstand massive radial forces. This bearing required two different spacers to work properly. Another alternative to this design would be a bronze bushing. The bushing would not have as smooth of a rotation, however, it would reduce the need for the bearing-race spacer and bearing-spacer seen in Figure 9. This should be considered for a future design. The brake pedal was designed with a pedal ratio of 7:1, calculated in Appendix B. With an assumed driver input force of 100 lbf, a total force of 700 lbf was needed in order lock all four wheels. However, one also needs to consider a panic scenario, where the driver produces forces far beyond the required force to lock the wheels. Based on the Formula SAE safety values for acceptable Figure 8:Brake Pedal FEA As seen in the Figure 8 above, the pedal rib only experienced approximately 17.8 ksi while the aluminum has the a 40 ksi yield strength. So the pedal has a factor of safety of approximately 2.2. The fatigue analysis produced results that stated the forces were below the S-N curve of the material and no damaged was produced. Concluding that the pedal can withstand the forces produced throughout the life of the car. Pedal Brackets The brackets were designed to be interchangeable with the throttle pedal brackets as well. The brackets needed to hold and position the pedal with the master cylinders, while keeping a small profile for easy packaging. The brackets would also need features to allow it to mount to the frame of the vehicle. With the given suspension and steering configuration, the pedals were designed to be floor mounted. This would leave sufficient room for the driver s feet and steering rack. These brackets needed to withstand the same forces as the pedals, so it was run through the same FEA scenario. With the previous input force of 450 pounds, the force on the bracket was calculated through the use of lever proportions, equaling to 2900 pounds. 7

8 Since the brackets act like the pedals and distribute the force between two ribs, the force was halved and applied to one bracket in the scenario. The resulting analysis can be seen in the Figure 11. Figure 11: Bracket FEA The brackets saw a maximum stress of 15 ksi and the yield strength is 40 ksi. This gives a factor of safety of 2.7, which is plenty sufficient for the vehicle. Configuration With the pedals and brackets designed, they needed a way to mount to the frame. This was done by creating 0.25 tabs that were welded to the steering rack support and the front foot-box tube. These had holes to allow the corresponding hardware to fasten the brackets and pedals. The tabs were made from 4130 steel plate and had sufficient strength to handle the forces produced by the driver. The configuration can be seen in Figure 13,Figure 10, and Figure 14. Figure 10: In-Car Location Throttle Pedal The throttle pedal was design much like the brake pedal. It used the exact same parts, besides the pedal-ribs. The pedal rib geometry was altered from the brake pedal because the throttle had no use for a bias-bar, but it still used the rib-spacer for proper spacing. The other difference with the throttle pedal was the cable linkage holes. Since the throttle needs to have a mechanical linkage (cable) to the pedal, there needs to be a feature that allows for the cable to fasten to the pedal. In the final design, the cable connects to the pedal via a 3/8 bolt. This bolt extends through and out the side of the pedal where the eyelet of the cable fastens. Figure 14: Throttle Linkage Figure 12: Pedal Configuration Figure 13: In-Car Location (Side) 8 The throttle cable needs to actuate the throttle mechanism on the engine. This mechanism has a certain amount of length in which it can travel before it is limited by the design. If this mechanism extends past its max travel, it can become permanently damaged, possible limiting throttle control and endangering the driver. The throttle assembly mitigates the chance of this occurrence by having two features: multiple throttle attachment holes, and an adjustable throttle stop. The throttle mechanism on the engine has approximately

9 1.25 of travel. This needs to be translated into pedal travel. Through basic tests conducted on each team member, comfortable foot travel for the driver was about three inches. Foot travel can then be converted into degrees of rotation by the arc length equation. Once the degree of rotation is calculated, this can help find what hole would be closest to the desired travel of 1.25 by using the arc length equation again. Once the proper hole is found, the adjustable throttle stop can be adjusted to allow for more or less travel depending on the situation. The throttle pedal also needs to have a feature that returns the throttle to idle. One of the simplest ways to do this is through and extension spring. It can be done with a torsional spring as well as a compression spring. When considering a return mechanism, make sure that it is clear from the driver s feet to mitigate any chance of snagging. Considering the driver s feet, a torsion spring might be the best option for the design. However, this was not chosen because the brackets had to be redesigned and manufactured within two weeks. With such a large time-crunch, an extension spring was still use. The throttle assembly had a few extra features. An aluminum tab was welded to the back of the brackets to allow for an adjustable throttle stop to be installed. In order to bias the throttle in its return position, another adjustable stop was created to position the pedal in a comfortable orientation for the driver. This return stop also prevents the engine from hitting its kill-switch. If the throttle returns completely on the engine, it hits a switch that automatically shuts down the engine. This feature along with a redundant feature on the engine bracket prevents this from happening. The two throttle stops can be seen in Figure 16 below. Assembly Both the throttle and brake pedals were very similarly designed. They used the same number of parts and were assembled in the same fashion. The pedals were assembled by press fitting the bearings and rib-spacers. The foot plate was then welded on the two ribs after all the bearings and spacers were press fit. An exploded view of the brake pedal assembly can be seen below in Figure 15. Figure 15: Brake Pedal Exploded View Figure 16: Throttle Assembly 9 Once the pedals were assembled, they were positioned in the correct orientation and then a bolt fastened them to the brackets. Once the adjustments were made to the throttle cable and bias bar, the pedals were ready for use. Budget Without a past team to compare budgets, the brake system had no gauge on how much it should cost or weigh. By the end of design, the whole system, including: brake pedals, throttle pedals, brackets, all the related hardware, calipers, rotors, lines, and fittings weighed approximately 21 pounds. The entire system including pieces for the throttle cost approximately 930 dollars.

10 The prices for individual components were calculated based on SAE Baja material cost tables. The tables along with the breakdown of weight and cost can be seen in Appendix C. Testing and Proof of Design Testing, as with any project, proved to be a vital learning experience. With the initial configuration of the brake pedal assembly, the bias-bar became bent from the massive force produced by the pedal ratio. When the bias-bar is bent, the brakes cannot be adjusted or proportioned properly. The points that the clevis pins connected to the bias-bar were too far from the center, which produced a bend in the rod stock, seen in Figure 17. Figure 17: Balance Bar Failure This meant that the MC s needed to moved closer to the center of the bias-bar to prevent bending. The brackets were kept, but they were moved to the center of the pedal as opposed to having the brackets on either side of the pedal. This can be seen in Figure 18. Conclusion The brake system was designed and implemented to withstand extreme driver input and allow the driver to safely control the vehicle. Through some design alterations, the pedal system did exactly what they were supposed to do. They can withstand loads much higher than SAE requires, and they effectively lock all four wheels and control the throttle. Recommendations After experiencing the design process and implementing a design into a vehicle, there are some recommendations and tips that I would make to the proceeding teams. First, I highly recommend understanding the geometry of the footbox. To understand how comfortable a driver will be with a certain design, one must create a prototype that resembles the final product. If the prototype can rotate, has the same general shape and dimensions as the proposed design, the team will be able to see how well the design works with the driver. Second, a bias-bar is not as simple of a feature to account for. As mentioned previously in the Testing and Proof of Design section, the balance bar was bent with the initial pedal configuration. Because the MC s were so far apart, the moment on the bias-bar bent it very easily. Knowing this, one could design a system that keeps the MC s much closer than they originally positioned on the first configuration. I cannot say that a proportioning valve would be simpler to implement, but I think it would be worth researching. Third, position the throttle cable so that it experiences the most linear travel possible. The throttle cable was mounted near the bottom of the pedal, near the fulcrum, to limit chances of driver entanglement. However, when the cable was mounted there, most of the pedal travel simply rotated the cable about the fulcrum; there was barely any throttle actuation when this happened. An additional bracket was made in order to provide a more linear route, which fixed the issue. Figure 18: Brackets Moved to the Center Fourth, when designing for the rear brakes, account for the force produced by the engine. The engine does not immediately cut the torque to the rear axle, the CVT must slowdown in order to allow the belt to slip. Since there is a delay in power transfer, this puts more torque 10

11 on the rear brakes than what was calculated in the spreadsheet. Luckily multiplying by a factor of safety allowed the system to lock the rear wheels. I am not sure how to measure the extra torque produced by the delayed power transfer but it should definitely be acknowledged in future designs. Lastly, use human resources. Do not try to do everything yourself, you have a good advisor who knows a lot about vehicle design, and your professors and peers know more than you think. Heck, feel free to contact me if you have any questions. Definitions, Acronyms, Abbreviations : inch MC: Master Cylinder FEA: Finite element analysis ft: feet in: inches kgs: kilograms ksi: kilopound per square inch lbf: pound force N: newton Psi: pound per square inch PS, remember to have fun with this project as well. It was one of the best things I have ever done. Contact Landis MacMillan, Pedal System Lead Roma9589@colorado.edu References [1 [2 [3 "The Brake Master Cylinder," [Online. Available: ml. [Accessed S. International, "Brake Systems 101," [Online. Available: [Accessed J. James Walker, "Brake Proportioning Valves," [Online. Available: [Accessed [4 " Engineering Inspiration - Brake System Design Calculations," [Online. Available: [5 [6 [7 [8 "Friction and Coefficients of Friction," [Online. Available: Friction and Coefficients of Friction. "The Brake Bible," Pirate 4x4, [Online. Available: [Accessed SAE International, "2016 FSAE Rules," [Online. Available: [Accessed "2016 Baja Rules Final," [Online. Available: 11

12 Appendix A B11.1 Foot Brake The vehicle must have hydraulic braking system that acts on all wheels and is operated by a single foot pedal. The pedal must directly actuate the master cylinder through a rigid link (i.e., cables are not allowed). The brake system must be capable of locking ALL FOUR wheels, both in a static condition as well as from speed on pavement AND on unpaved surfaces. B11.2 Independent Brake Circuits The braking system must be segregated into at least two (2) independent hydraulic circuits such that in case of a leak or failure at any point in the system, effective braking power shall be maintained on at least two wheels. Each hydraulic circuit must have its own fluid reserve either through separate reservoirs or by the use of a dammed, OEM-style reservoir. B11.3 Brake(s) Location The brake(s) on the driven axle must operate through the final drive. Inboard braking through universal joints is permitted. Braking on a jackshaft through an intermediate reduction stage is prohibited B11.4 Cutting Brakes Hand or feet operated cutting brakes are permitted provided the section (B11.1) on foot brakes is also satisfied. A primary brake must be able to lock all four wheels with a single foot. If using two separate pedals to lock 2 wheels apiece; the pedals must be close enough to use one foot to lock all four wheels. No brake, including cutting brakes, may operate without lighting the brake light B11.5 Brake Lines All brake lines must be securely mounted and not fall below any portion of the vehicle (frame, swing arm, A- arms, etc.) Ensure they do not rub on any sharp edges. Plastic brake lines are prohibited 12

13 Appendix B Front Assumed Values and Inputs Loaded Tire Diameter Front Caliper Bore Deceleration Loaded Tire Diameter Rear Caliper Bore 21 in 1.12 in 0.7 G 21 in 1.12 in m m Height of CG Wheelbase m m Pad-Rotor Outer Pad-Rotor Outer Contact Contact Diameter Front Caliper Area 24 in 64 in Diameter Rear Caliper Area 6 in in^ m m 8 in in^ m m^2 Total Mass (Car&Driver) m m^2 Pad-Rotor Inner Pad-Rotor Inner Contact Contact Diameter Master Cylinder Bore (D) 275 kg Diameter Master Cylinder Bore (D) 5 in in lbm 5 in in m m StaticWeight Distribution m m Master Cylinder Area Mass Front Mass Rear Master Cylinder Area in^2 125 kg 150 kg in^ m^ lbm lbm m^ % 54.55% Dynamic Mass Shift kg Dynamic Weight Distribution Dynamic Mass Front Dynamic Mass Rear kg kg 71.70% 28.30% Friction Between Tire & Road Number of Friction Surfaces 2 - Frinction Between Calipers&Pads Factor of Safety Rear Braking Force Braking Force F_b = g*a*m_df F_b = g*a*m_dr N N Braking Force Per Caliper Braking Force Per Caliper F_bc=F_b/2 F_bc=F_b N N Wheel Lock Force For Front Axel Wheel Lock Force For Rear Axel F_wl=m_df*9.81*friction F_wl=m_dr*9.81*friction N N After Factor of Safety After Factor of Safety F_bfos = fos*f_wl F_bfos = fos*f_wl N N Braking Torque per Front Wheel Braking Torque per Rear Axel T_b = F_bfos*R_tr T_b = 2*F_bfos*R_tr N-m N-m Effective Radius Effective Radius R_e = (Do_r+Di_r)/4 R_e = (Do_r+Di_r)/ in 3.75 in m m Clamping Force Clamping Force F_c = T_b/(R_e*friction*surfaces) F_c = T_b/(R_e*friction*surfaces) N N Required System Pressure Required System Pressure P_s = F_c/A_cal P_s = F_c/A_cal Pa Pa psi psi Needed Input Force into Master Cylinder Needed Input Force into Master Cylinder F_i = P_s*A_mc F_i = P_s*A_mc N N lbf lbf Total Needed Input Force Front Input Force + Rear Input Force N 711 lbf

14 Appendix C Weight Breakdown Part/Assembly Weight Quantity Total Brake Pedal Assem Throttle Pedal Assem Master Cylinders Calipers Rotors Misc lbs Cost Breakdown Cost Quantity Total Pedal Plate Brake Pedal Ribs Throttle Pedal Ribs 2 0 Pedal Spacers Bearing Spacers Bracket Spacers Bearing Spacers Pedal Brackets Front Tabs Rear Tabs Throttle stop Thrtottle stop tab Front Throttle Stop tab Bias Bar Master Cylinders Calipers Rotor Hardline Flexline Fittings Switches rod stock MC nut Fulcrum Bolt Fulcrum Nut Brake Pads Throttle cable Total $ Material Cost Table Density Mild Steel, e.g. 1010, 1025 $ 1.00 /lb lb/in³ Alloy Steel, e.g. 4130, ChroMoly $ 2.00 /lb lb/in³ Aluminum $ 5.00 /lb lb/in³ Mag $ 9.00 /lb lb/in³ Titanium $ /lb lb/in³ Non-graphite composites $ /lb - Graphite-based composites $ /lb - 14