Design of a Hydraulic Housed Within a for Increased Aerodynamics

Shawn Phillip Gravois Spring 2010 Magna Cum Laude Bachelor of Science in Mechanical Engineering

Introduction

The purpose of this design project is to design an original front brake for a time trial bicycle. A time trial is an individual cycling event, where each rider is timed on their completion of a set course. Typically, specialized bikes are used for time trialing, which are more aerodynamic than standard road bikes. Figure 1 below shows an example of a typical road bike (left) and a typical time trial bike (right).

http://www.roadcycling.com/reviews/Cervelo.shtml Figure 1: Road bike (left) and time trial bike (right).

A rider is limited to how much power they can produce, thus the increased aerodynamics of a time trial bike allows the rider to complete the course more quickly, without having to produce more power. Time trialists usually use aero wheels, handlebar extensions, streamlined helmets, and tighter clothing to reduce the total drag on them when riding. Any further increases to the aerodynamics of a time trial bike help to further reduce the course time of the rider, so companies are continually working to streamline their bikes. Typically, the front brake is a dual pivoting caliper mounted to the front of the front fork as shown in the above Figure 1, but many companies have looked into changing the brake locations in order to streamline the bike and reduce drag. Companies have recently mounted the front brake behind the front fork and most recently Trek has mounted a mechanical cable operated brake in the front fork. The objective of this design project is to design a hydraulically actuated cam driven brake that is integrated into the front fork of a time trial bike. The part count should also be reduced to decrease the brake complexity and to reduce the total cost. The purpose is to reduce the drag on the bike as well as to reduce the amount of force needed to squeeze the brake lever by the rider to apply the brake.

Constraints

There are limitations put on bicycle by the Union Cycliste Internationale (UCI). The UCI is the main governing body of bicycle racing and they have a few regulations regarding brakes, component shape, and fairings. The following regulations were found in the UCI’s Technical Regulations for : A Practical Guide to Implementation.

2

o Article 1.3.006: “Bicycles used in road events must be fitted with an efficient braking system that acts on both wheels (either simultaneously or independently) operated by two brake levers.” Pg.2

o Article 1.3.021: “For time trials on the road…the elements making up the frame are not restricted provided they fit freely inside a defined template and comply with the 1:3 ratio described above (Article 1.3.020)” Pg. 6.

o Article 1.3.021: “For offset fork designs, the pivoting part must be contained within the template of the .” Pg. 6.

o Article 1.3.024: “Protective screens, aerodynamic shapes, fairings or any other device that is added or forms part of the structure, and that is destined or has the effect of reducing wind resistance, are prohibited.” Pg. 9.

For the design, size and weight should be minimized, although weight is not crucial for time trial applications. Aerodynamic advantages outweigh weight savings in time trials as most time trials are relatively flat, so gravity is not as impactful as drag force. The cost of the should also be minimized within reason, as this brake is being designed for high-end race bikes that are quite costly to start with.

Functionality

The functional requirements of the hydraulic brake are to transfer a brake lever input from a rider to an actuation of the brakes onto a rotating rim in order to slow or stop a bicycle. The hydraulic brake must provide a similar clamping force to that of conventional cable driven brakes and require a similar gripping force input from the rider. The brake need to hold up to environmental factors without failing or corroding.

The brake actuation is accomplished through the use of hydraulic cylinders and cams. First, the rider squeezes the brake lever, which depresses the plunger in the brake piston. The brake piston forces hydraulic fluid from the brake piston, through tubing, into the cam bracket piston. The cam bracket piston moves based on the relation of the piston areas and stroke lengths. The cam bracket piston extends from the input from the brake piston, which moves the cam bracket down. The downward movement of the cam bracket causes the wedge shaped cams to move down as well. The cams widen as they move down, thus pushing on the bearings on the guides. The brake shoe guides are oriented and supported by the guide posts. The cams force the brake shoe guides to slide along the guide posts, which causes the brakes to move together. The pistons spring return to their naturally retracted positions due to their spring return, thus lifting cams. The brake shoe guides are returned by the springs attached to the bearing support arms. Figure 2, below, shows the brake open (left) and compressed (right)

3

Figure 2: Brake open (left) and compressed (right).

Design

The design calls for the brake to be integrated into the front fork of a time trial bicycle. To save space and reduce the force needed to actuate the brake, a brake lever and hydraulic piston are used to depress a set of cams, via a cam bracket, to compress the brakes against the wheel rim. Hydraulics were used because they use incompressible fluid, so braking power is directly transferred without fade. The cams provide a large mechanical advantage, and the use of hydraulics eliminates the stretching of cables found in traditional bicycle brakes. The proposed design of the hydraulic brake is pictured below in Figure 3 with a close-up view of the area. Detailed and dimensioned drawings can be found in Appendix D.

Figure 3: Hydraulic brake assembly.

4 The design is broken down into three subassemblies. These subassemblies are the piston subassembly, the brake subassembly, and the guide subassembly. These subassemblies are pictured below in Figures 4, 5, and 6.

Piston Piston Support

Cam Bracket

Cam

Cam Screw (hidden)

Figure 4: Piston subassembly.

Brake Shoe Guide Brake Shoe Bearing

Bearing Screw

Spring Brake Shoe Screw (hidden)

Figure 5: Brake subassembly.

5 Guide Post Plate

Guide Post

Figure 6: Guide subassembly.

The brake assembly will be completely housed within the front fork, although a custom fork will be needed to house the design. The fork will need an enclosure that passes in front of the head tube of the bike frame and connects the fork crown to the handlebar . The protrusion will also increase the length to thickness ratio of the front end of the bicycle, allowing for a more aerodynamic profile, thus reducing drag. An example of the typical dual pivot front brake caliper setup (left) and the proposed design setup (right) are pictured below in Figure 7.

Figure 7: Conventional front brake (left) and proposed brake design (right). An example of the general shape of this fork protrusion is pictured below in Figure 8.

6 http://www.velonews.com/photo/91773 Figure 8: Brake housing fork protrusion.

The functional requirements and design specifications for each part are presented in the following section.

Cam Bracket

The cam bracket is a curved aluminum piece that connects the piston rod to the cams, as well as orients the cams. Aluminum was chosen for its light weight and corrosion resistance. The FEA justification of aluminum can be found in the Analysis section. The piston rod threads into the 10-32 UNF threaded hole in the top of the cam bracket. The bottom of each leg of the cam bracket has a 1-72 UNF threaded hole for the cams to screw into. The cam bracket was designed with curved segments to strengthen the member and reduce distortion. The cam bracket is shaped so that it fits in the crown of a fork and can move through its full range of motion. The cam bracket would be cast as the surface finish is not critical and casting is relatively quick and inexpensive.

7 Cam

The cams are wedge shaped pieces that transfer the vertical motion of the piston and cam bracket to the brake shoe guide. The cam has a countersunk hole through the top for the cam screws. The sides of the brake shoe guide fit in the notch that is in the middle of the cam. The bearings on the brake shoe guide roll along the faces of the prongs on either side of the cam to achieve their horizontal motion. The back surface of the cam is Teflon coated to reduce the between the cam and the guide post plate. Aluminum was chosen for the cam for its light weight and corrosion resistance. The cams will be cast and surface finished yielding smooth surfaces to slide on. The cam profile can be adjusted to fit the preference of the rider, which makes the braking characteristics of the system adjustable.

Cam Screws

The cam screws are ½ inch long with 1-72 UNF threading. The screws are stainless steel to prevent rusting. Stainless steel also has a high yield strength and is an industry standard for bicycle hardware.

Piston

8 The piston is a nose-mount single acting cylinder with a spring return. The cylinder is naturally retracted with a one inch stroke length. The piston diameter is 7/16 inch. The cylinder is stainless steel to prevent rusting in the event of water entering the fork. The piston rod has a 10-32 UNF threading to mesh with the cam bracket. The piston transfers the hydraulic pressure generated by the squeezing of the brake lever to move the cam bracket. The hydraulic fluid is incompressible, thus the braking power is directly transferred without fade. The piston will be supported by the piston support and will be housed within a support fairing in the front fork.

Piston Support

The piston support is an aluminum tab that will be bonded to the inside of the support fairing of the custom fork. The piston support will align the piston with the brake shoe guides, so that the cams move perpendicular to the brake shoe guides. The piston support has a hole in the center for the piston to nose mount in. The piston support will be manufactured by metal stamping.

Brake Shoe Guide

The brake shoe guide is a rectangular titanium part with rectangular protrusions on either side. These protrusions are rounded on the top back edge and have a 1-64 UNF hole tapped in their centers. These protrusions hold the bearings and provide extra material for the bearing screws to thread into. The back side of the brake shoe guide has a rectangular cavity with rounded edges. This cavity fits over the guide post, which supports the brake shoe guide, and constrains it to slide along one axis without rotating. The front of the brake shoe guide has a slot machined out, where the brake shoe is mounted. The slot provides adjustability in the height of the brake shoes as wheel diameters vary slightly. The brake shoe guide will be cast and finish milled to yield smooth surfaces for sliding. Titanium was chosen, because it can support the required loading and will not rust. The material justification for titanium is presented in the following analysis section.

9 Bearings

The roller bearings chosen for the design have a 0.197 inch diameter, 0.079 inch thickness, and a 0.039 inch central hole. The bearings would be stainless steel, though chrome steel is harder, the stainless steel is chosen to prevent rusting. The bearings reduce friction between the cams and the brake shoe guides.

Bearing Screw

The bearing screws are ¼ inch long with 1-64 UNF threading. The screws are stainless steel to prevent rusting. Stainless steel also has a high yield strength and is an industry standard for bicycle hardware.

Spring

The springs are made of HBMC spring steel. This steel has a high carbon content making it stronger to be able to handle high and infrequent stresses. The spring will have a length of 3.20 inches, a diameter of .142 inches, and eight coils.

10 Brake Shoe

The brake shoe is a commercial style brake shoe. A standard brake shoe was chosen so that commercial brake pads will fit and be readily available. The brake shoes would be purchased from a manufacturer and installed during assembly.

Brake Shoe Screw

The brake shoe screw fastens the brake shoe to the brake shoe guide through the slot in the face of the brake shoe guide. The brake shoe screw would also be made of stainless steel, so it would not rust if exposed to water.

Guide Post

The guide post is a rectangular aluminum piece of metal with a profile that matches that of the cavity of the brake shoe guide. The guide post orients and constrains the brake shoe guide to move in only one axis and prevent any rotation of the brake shoe guide. The guide post would be machined from rectangular bar stock as a smooth surface is required to reduce wear with the brake shoe guide. The guide post is press fit and adhered onto an elliptical peg on the guide post plate. The elliptical peg orients the guide post and prevents it from rotating.

11 Guide Post Plate

The guide post plate is an aluminum plate that is adhered to the inside of the outermost wall of the fork. This plate provides a surface for the cam to rub on, so as not to damage the carbon fiber of the fork. This plate also supports and aligns the guide post.

Assembly

To assemble the brake in the fork a set of subassemblies are first made and then the parts are inserted into the fork.

1) First, the guide posts are pressed on and adhered to the guide post plates.

12 2) The cams are then screwed onto the cam bracket using the cam screws.

3) The bearings are screwed onto the brake shoe guides with the bearing screws.

4) Then, the brake shoes are screwed onto the brake shoe guides with the brake shoe screws.

13 5) The guide post subassembly is then inserted through the top of the fork and bonded to the inner wall of the fork.

6) Once the guide post assembly epoxy has dried, the brake shoe guide subassembly is inserted trough an opening in the inner walls of the fork.

7) The springs are positioned and fastened to the brake shoe guides and a retaining plate is fastened to the inside fork wall. This plate supports the end of the brake shoe guide and provides a surface to compress the springs.

14

8) The cam bracket subassembly is then inserted through the back side of the fork protrusion over the brake shoe guide.

9) The piston is then inserted into the piston support, which was adhered to the fork during the production of the fork. The nut that nose mounts the piston to the support is slipped over the piston rod. The piston is then screwed into the cam bracket, and once secure the piston nut is tightened.

15

10) The remaining hydraulic connections are attached and the lines are bled, thus completing the brake assembly.

Analysis

Braking Force Calculations

The required force on the brake pads was determined based on the energy dissipated in stopping a 165 lb rider and bicycle moving at 36.45 ft/s. The braking distances were found in a test preformed by the Velonews magazine, where thirteen different cable brakes were tested on the same flat course with minimal winds at the same initial speed. The braking distances can be found in Appendix A. The rider would ride at a constant 36.45 ft/s then apply the brakes as hard as they could without locking up the tires, also known as “panic braking”. It is assumed that the front brake did all of the braking to determine the worst case scenario for design. The average stopping distance was found to be 27.14 ft and the friction coefficient of the bicycle brake pads on aluminum rims is 0.6. The following were found in the Vector Mechanics for Engineers textbook by Beer et al. The kinetic energy Equation 1, below was used to determine the initial energy of the rider and bike before the brakes were applied. A reference of all symbols used can be found in Appendix B.

1 1 (1) KE  mv2  5.13lbm 36.45 ft / s2  3407.48lbft 2 2

16 The normal force required on the brake based on the coefficient of friction was found using Equation 2 below, from Shigley’s text by Budynas and Nisbett. Figure 9, below shows the brake diagram with the forces indicated.

. rim brake v

Fn Fn

FF FF

Figure 9: Brake force diagram.

E  2FF d (2) F  F  F n E 3407.48lbft  F    174.36lbf n 2 2 d 2  0.62  27.14 ft .

Since there are two brake pads, the normal force on each pad is half of the above normal force. The normal force required on each brake is 87.18 lb.

Cam Piston Force Calculations

The cam piston force required to move the cam bracket was calculated using the following cam geometry. The forces were summed in the x and y directions and the reactions R1 and R2 can be neglected as they do not affect FP or Fn. The force diagrams of the cam and brake shoe are presented below in Figure #5. The force required by the piston was found using the following Equation 3.

17

FP/2 x F R1 Fn F y

Brake Shoe Guide 76 Cam R 2 R1 F FP/2 Fn

F R2 14 76

Figure 10: Cam force diagram.

  F  Fn cos(14 )  87.18lb cos(14 )  84.59lb (3)   F / 2  F cos(76 )  84.59lb cos(76 )  21.75lb P FP  43.5lbf

Brake Lever Force Calculations

The force on the brake lever needed to be determined to ensure that the rider could apply enough force to stop the bike. The brake lever piston was sized from a hydraulic brake and the cam piston was chosen to minimize weight, while providing enough force to satisfy the earlier brake force calculations. An iterative process was used to finally determine the industrial standard piston sizes. The brake lever and piston specifications are presented below in Table 1.

Table 1 – Piston Specifications Brake Lever Piston Cam Piston Diameter (in) 0.625 0.438 Area (in2) 0.307 0.150

Knowing that the piston stroke length must be 0.80 in to move the cam through its entire range, the stroke length of the brake lever could then be determined using the hydraulic volume relation presented below in Equation 4. The hydraulic calculations were found in Basics of Hydraulics by Zhang.

18

V  S  A (4) V  V  S A  S A B P B B P P 0.800in 2  0.150in 2 S   0.392in B 0.307in 2

The stroke length of the brake lever piston is 0.392 in. To determine the grip force applied to the brake lever, the force on the brake piston needed to be calculated using the pressure Equation 5, below.

F P  A (5)

FB FP PB  PP   AB AP 43.50lbf  0.307in 2 F   88.78lbf B 0.150in 2

The force needed on the brake lever piston is 88.78 lbf. To determine the grip force applied, it is assumed that the grip force is applied to the brake lever 2.50 in from the pivot and the brake lever piston is mounted 0.50 in from the pivot. The grip force is found by finding the moments about the brake lever pivot using Equation 6.

M  r  F (6) M  M  r  F  r  F G B G G B B 0.50in  88.78lbf FG   17.756lbf 2.50in

The calculated grip force of 17.76 lbf is acceptable, because it is lower than the average grip strength of men, which is 98.7 lb, and women, which is 58.4 lb. The average grip strengths were found in an exercise test entitled Grip and Pinch Strength: Normative Data for Adults.

Material Selection

The materials used in the design all needed to be lightweight, corrosion resistant, and able to support the applied loads. To determine the appropriate materials for the parts, a FEA analysis was preformed in Autodesk Inventor 2009. The cam bracket was the first part analyzed. To save weight 6061-T6 aluminum was tested with the loading calculated above. The material properties were found in Shigley’s Mechanical Engineering Design textbook. Table 2 below shows the properties of 6061-T6 aluminum and Table 3 summarizes the results of the Autodesk analysis. Figure 11, below, shows the principle stresses on the cam bracket under the 43.5 lb load. Figure 12 shows the

19 deformation of the cam bracket under the applied load. The minimum safety factor was found by dividing the maximum ultimate stress by the maximum principle stress.

Table 2 – 6061-T6 Aluminum Properties Cam Piston Ultimate Strength (psi) 45,000 Yield Strength (psi) 40,000

Table 3 – Aluminum Analysis Results Cam Piston Maximum Principle Stress (psi) 2,607 Maximum Deformation (in) 7.05x10-4 Minimum Safety Factor 14.17

Figure 11: Principle stresses on the aluminum cam bracket.

20

Figure 12: Deformation the aluminum cam bracket.

The brake shoe guide was then analyzed. To save weight 6061-T6 aluminum was tested with the previously calculated load. Table 4 summarizes the results of the Autodesk analysis. Figure 13, below, shows the principle stresses on the brake shoe guide under the 88.78 lb load. Figure 14 shows the deformation of the cam bracket under the applied load.

Table 4 – Aluminum Analysis Results Cam Piston Maximum Principle Stress (psi) 15,120 Maximum Deformation (in) 3.27x10-4 Minimum Safety Factor 4.01

21

Figure 13: Principle stresses on the aluminum brake shoe guide.

Figure 14: Deformation the aluminum brake shoe guide.

According to the article Engineering and Applications Factor of Safety Review in Engineers Edge, “when the whole load, or nearly the whole load, is likely to be alternately put on then taken off, the factor of safety should be 5 or 6.” Based on the alternating loading on the brake shoe guide, aluminum would not provide a high enough factor of safety to be used. A stronger light weight metal would have to be used, so titanium was analyzed. Table 5 below shows the properties of Ti-6Al-4V and Table 6 summarizes the results of the Autodesk analysis. Figure 15, below, shows the principle stresses on the brake shoe guide under the 88.78 lb load. Figure 16 shows the

22 deformation of the cam bracket under the applied load. The minimum safety factor was found by dividing the maximum ultimate stress by the maximum principle stress.

Table 5 – Ti-6Al-4V Properties Cam Piston Ultimate Strength (psi) 130,000 Yield Strength (psi) 120,000

Table 6 – Titanium Analysis Results Cam Piston Maximum Principle Stress (psi) 15,620 Maximum Deformation (in) 2.20x10-4 Minimum Safety Factor 7.68

Figure 15: Principle stresses on the titanium cam bracket.

23

Figure 16: Deformation of the titanium cam bracket.

Titanium should be used for the brake shoe guide, as it meets the required factor of safety and is a strong lightweight metal. The limiting factor for the brake shoe guide is its size. The brake shoe guide must be as narrow as possible to fit within the fork legs; this is why titanium needed to be used to support the load without yielding.

Weight

The weight of the proposed hydraulic brake is calculated below. The material properties are found in the Aerospace Metals website. The weight of the brake shoe was found at the Shimano website. The weight of each part is calculated using Equation 7 below and the results are presented in Table 7. The volumes of each part were found using the part models in Autodesk Inventor 2009. The total weight column in Table 7 is the weight of that component multiplied by the number of components, equaling the combined weight of all of that particular component.

w   V (7)

24 Table 7 – Part Weights Number Part Material Density Volume Total Weight (lb/in3) (in3) (lb) 4 Bearing Stainless 0.284 0.0014 0.006 Steel 4 Bearing Screw Stainless 0.284 0.0017 0.002 Steel 2 Brake Shoe 6061-T6 Al - - 0.088 2 Brake Shoe Ti-6AL-4V 0.160 0.1740 0.057 Guide 2 Cam 6061-T6 Al 0.098 0.1648 0.330 1 Cam Bracket 6061-T6 Al 0.098 0.6999 0.069 2 Cam Screw Steel 0.284 0.0040 0.002 1 Fairing Piston Stainless - - 0.142 Steel 2 Guide Post 6061-T6 Al 0.098 0.1052 0.021 2 Guide Post 6061-T6 Al 0.098 0.0916 0.018 Plate 1 Mounting 6061-T6 Al 0.098 0.0701 0.007 Bracket 4 Spring Spring Steel 0.280 0.0006 0.003 Total 0.746

The total weight of just the internal fork mounted brake components with brake shoe assemblies was calculated to be 0.746 lb. The standard weight of a Shimano dual pivot brake caliper is 0.375 lb as found on the Shimano website. The designed hydraulic brake is 0.371 lb heavier, which is reasonable. Increased aerodynamics was the major design goal and keeping weight reasonable was a secondary goal, as drag reduction should outweigh weight gain in a relatively flat time trial.

Aerodynamics

The main force that must be overcome in a time trial is drag force from the wind. The drag force is mainly composed of skin friction and pressure drag. The proposed design lessens the frontal area, because the internal hydraulic brake does not have any protrusions that add to the total frontal area of the fork. A conventional brake caliper has brake arms that stick out to the side of the fork. The additional frontal area of the traditional brake caliper is measured to be 1.4 in2. The conventional cabled brake also has an external brake cable that reaches from the brake caliper to the handlebars. This also adds drag to the bicycle. The proposed internal hydraulic brake has internal hydraulic lines which are housed within the fork, thus they do not add any drag to the bicycle. The protrusion of the external brake will be modeled as a hemispherical body, as the arms and cable tension adjusting cam have curved frontal profiles and flat rear faces. The drag coefficient (CD) is found to be 0.4 from table in the Fluid Mechanics Fundamentals and Applications textbook by Cengel and Cimbala. The drag force at 30

25 mph on this area is calculated using the following Equation 8. The density of air at 80 F is 0.07350 lbm/ft3 as found in Table A-9E of the Fluid Mechanics Fundamentals and Applications textbook.

2 2 V 2 3 44 ft / s FD  CD A  0.4 0.0097 ft  0.07350lbm / ft  0.28lb (8) 2 2

The conventional cabled brake creates a flow separation off of its trailing edge. This flow separation causes an area of low pressure behind the external brake. This flow separation creates a wake that disrupts the airflow over the crown of the fork and head tube of the bike. Theoretically, the internal hydraulic brake would reduce the drag on the front of the bike by smoothing the leading edge of the fork and allowing for a less turbulent flow over the fork and head tube. Wind tunnel testing of a scaled prototype fork would be required to fully justify the design, but based on the streamlining of the front end of the bicycle by integrating the brake in the fork, it is expected that the drag force would be reduced.

Conclusions

The purpose of this design project was to design an original front brake for a time trial bicycle. Traditional brake calipers mount to the outside front of a bicycle fork, where as the proposed design is housed within the fork. The integrated brake should streamline the front end of the bicycle, thus reducing the drag force. A rider can only produce a limited amount of power, so any reductions in drag yield faster time trial times. Though the proposed design should be more aerodynamic than conventional brakes, it is slightly heavier and due to internal components, it would be harder to maintain. The designed hydraulic brake can produce an equivalent braking force to that of a conventional brake. The hydraulic power transfer from the brake lever to the braking piston has less friction than a conventional cable driven brake. When the hydraulics are used with cams to actuate the brake shoes, a large mechanical advantage is obtained, thus reducing the required input force by the rider to apply the brakes. The light weight materials for the brake were selected according to the loads applied to them as well as to hold up to environmental factors. Most of the components were chosen to be 6061-T6 aluminum as it has a relatively high strength to weight ratio, is inexpensive, and is corrosion resistant. The brake shoe guide had to be titanium to handle the applied loading and space requirements. The rest of the hardware was stainless steel as it has high yield strength, is corrosion resistant, and is commonly used in bicycle applications. To fully accept the design additional testing would be required. The additional tests are presented in the following section.

26 Further Project Design and Testing

Further research and design work for this project could be preformed. Due to time constraints and limited resources, certain areas were not able to be addressed. A wind tunnel test of the two brake configurations should be preformed to determine the reduction of drag for the integrated brake design over the conventional brake. A fork that will house the brake also needs to be designed. A fully functioning prototype should also be constructed to test the workings of the brake on a bicycle. Currently, there are no hydraulic brake levers integrated into time trial handlebars, so an integrated hydraulic brake lever should also be designed. This brake lever should satisfy the specifications laid out in the Analysis section.

Acknowledgments

The author thanks David Mikolaitis. PhD. for consultation. Bobby Sweeting for assistance in analysis and design collaboration.

27 Appendix A

Panic braking distances from 24.85 mph averaged 36.45 ft/s.

Trial Distance (ft) 1 32.87 2 28.54 3 26.61 4 23.75 5 23.29 6 33.40 7 24.87 8 36.19 9 27.43 10 21.13 11 23.56 12 25.30 13 25.92 Velonews Tech Report: Brake Check

28 Appendix B

Symbol Reference

KE – kinetic energy m - mass v – velocity Fn – normal force FF – frictional force E - energy μ – coefficient of friction d – distance Fp – piston force R – reaction force V – volume S – stroke length A – area P – pressure F – force M – moment r – radius FD – drag force CD – coefficient of drag ρ - density w - weight

29 Appendix C

Works Cited

Beer, F., Johnston, E., & Eisenberg, E. (2007). Vector Mechanics for Engineers: Statics & Dynamics Eighth Edition. Ney York, New York: McGraw Hill.

Budynas, R., & Nisbett, J.(2008). Shigley’s Mechanical Engineering Design. New York, New York: McGraw Hill.

Cengel, Y., & Cimbala, J. (2006). Fluid Mechanics: Fundamentals and Applications. New York, New York: McGraw Hill.

Pococha, M. (2009, June). Tech Report: Brake Check. Velonews,107, 116.

Engineering and Applications Factor of Safety Review. (2009). Engineers Edge. Retrieved October, 10, 2009, from http://www.engineersedge.com/analysis/factor- of-safety-review.htm.

Technical Regulations for Bicycles: A Practical Guide to Implementation. (2009). Union Cycliste International. Retrieved October, 5, 2009, from http://www.uci.ch/Modules/BUILTIN/getObject.asp?MenuId=MTkzNg&ObjTyp eCode=FILE&type=FILE&id=NTI0MDY&LangId=1

Ultegra 6700 Specifications. (2009). Shimano\ North America. Retrieved November, 2, 2009, from http://bike.shimano.com/publish/content/global_cycle/en/us/index/ products/road/ultegra_6700/product.-code-BR-6700.-type-.html

Virgil Mathiowetz, MS, et al. (1985). Grip and Pinch Strength : Normative Data for Adults (Arch Phys Med Rehabil 66:69-72). Milwaukee, WI: Occupational Therapy Program.

30 Appendix D Drawing Package

31 PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT 2 1 PRODUCED BYANAUTODESKEDUCATIONALPRODUCT

B B

SCALE 1 / 2

DRAWN Shawn Gravois 11/28/2009 A CHECKED University of Florida - EML4905 A

QA PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT EDUCATIONAL AUTODESK AN BY PRODUCED TITLE MFG

APPROVED Hydraulic Brake Assembly

SIZE DWG NO REV A 1 SCALE SHEET 1 OF 1

2 1 PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT EDUCATIONAL AUTODESK AN BY PRODUCED PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT 2 1

SCALE 2 : 1

R.050 .001 R.138 .001 PRODUCED BYANAUTODESKEDUCATIONALPRODUCT

B B

.500 .003 .415 .002 .105 .001

.585 .003 .059 .001 .895 .005 .329 .002 1.000 .005 .210 .001 .210 .001 .414 .002 .499 .002 .559 .003

.159 .001

DRAWN .106 .001 Shawn Gravois 11/28/2009 A CHECKED University of Florida - EML4905 A .460 .003 QA PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT EDUCATIONAL AUTODESK AN BY PRODUCED .565 .003 TITLE MFG

.724 .004 APPROVED Brake Shoe Guide

SIZE DWG NO REV A 2 SCALE SHEET 1 OF 1

2 1 PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT EDUCATIONAL AUTODESK AN BY PRODUCED PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT 2 1

.300 .002 PRODUCED BYANAUTODESKEDUCATIONALPRODUCT

B R.050 .001 .225 .002 B

.300 .002

1.500 .008

.215 .001

.785 .004 1.000 .005

DRAWN .175 .001 Shawn Gravois 11/28/2009 A CHECKED University of Florida - EML4905 A

QA PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT EDUCATIONAL AUTODESK AN BY PRODUCED TITLE MFG

APPROVED Cam R.05 SIZE DWG NO REV A 3 SCALE SHEET 1 OF 1

2 1 PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT EDUCATIONAL AUTODESK AN BY PRODUCED PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT 2 1

10-32 UNF 1.725 .009 PRODUCED BYANAUTODESKEDUCATIONALPRODUCT 1.325 .007 B B

SCALE 1 : 1 .225 .002 2.825 .014

3.050 .015 DRAWN Shawn Gravois 11/28/2009 A CHECKED University of Florida - EML4905 A

QA PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT EDUCATIONAL AUTODESK AN BY PRODUCED .40 TITLE MFG

APPROVED Cam Bracket

SIZE DWG NO REV 1-72 UNF 1-72 UNF A 4 SCALE SHEET 1 OF 1

2 1 PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT EDUCATIONAL AUTODESK AN BY PRODUCED PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT 2 1 PRODUCED BYANAUTODESKEDUCATIONALPRODUCT

B B

1.000 .005

.620 .003 .380 .002

SCALE 1 10-32 UNF 2.000 .010

DRAWN Shawn 12/6/2009 A CHECKED University of Florida - EML4905 A

QA PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT EDUCATIONAL AUTODESK AN BY PRODUCED TITLE MFG

APPROVED Piston

SIZE DWG NO REV A 5 SCALE SHEET 1 OF 1

2 1 PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT EDUCATIONAL AUTODESK AN BY PRODUCED PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT 2 1

.550 .003 .100 .001 PRODUCED BYANAUTODESKEDUCATIONALPRODUCT

B B

.437 .003 1.571 .006

R.570 .003 SCALE 2 : 1

DRAWN Shawn 12/1/2009 A CHECKED University of Florida - EML 4905 A

QA PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT EDUCATIONAL AUTODESK AN BY PRODUCED TITLE MFG

APPROVED Piston Support

SIZE DWG NO REV A 6 SCALE SHEET 1 OF 1

2 1 PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT EDUCATIONAL AUTODESK AN BY PRODUCED PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT 2 1

1.000 .005 PRODUCED BYANAUTODESKEDUCATIONALPRODUCT 1.565 .008 B B 1.754 .008

3.000 .015

SCALE 1 : 1 .030 .001

.200 .001

.526 .004 .474 .003 DRAWN Shawn Gravois 11/28/2009 A CHECKED University of Florida - EML4905 A

QA PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT EDUCATIONAL AUTODESK AN BY PRODUCED TITLE MFG

APPROVED Guide Post Plate

SIZE DWG NO REV A 7 SCALE SHEET 1 OF 1

2 1 PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT EDUCATIONAL AUTODESK AN BY PRODUCED PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT 2 1

.350 .002 .200 .001 PRODUCED BYANAUTODESKEDUCATIONALPRODUCT

B B

.750 .004 .469 .002

.281 .002

SCALE 3 : 1 R.050 .001

.201 .001 .149 .001

DRAWN Shawn Gravois 11/28/2009 A CHECKED University of Florida - EML 4905 A

QA PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT EDUCATIONAL AUTODESK AN BY PRODUCED TITLE MFG

APPROVED Guide Post

SIZE DWG NO REV A 8 SCALE SHEET 1 OF 1

2 1 PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT EDUCATIONAL AUTODESK AN BY PRODUCED PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT 2 1 PRODUCED BYANAUTODESKEDUCATIONALPRODUCT

B B

.320 .002

R.072 .001

SCALE 10 : 1

DRAWN Shawn Gravois 11/28/2009 A CHECKED University of Florida - EML4905 A

QA PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT EDUCATIONAL AUTODESK AN BY PRODUCED TITLE MFG

APPROVED Return Spring

SIZE DWG NO REV A 9 SCALE SHEET 1 OF 1

2 1 PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT EDUCATIONAL AUTODESK AN BY PRODUCED PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT 2 1

.098 .001 .200 .001 PRODUCED BYANAUTODESKEDUCATIONALPRODUCT

B B

SCALE 13 : 1 .059 .001

DRAWN Shawn 12/6/2009 A CHECKED University of Florida - 4905 A

QA PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT EDUCATIONAL AUTODESK AN BY PRODUCED TITLE MFG

APPROVED Bearing

SIZE DWG NO REV A 10 SCALE SHEET 1 OF 1

2 1 PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT EDUCATIONAL AUTODESK AN BY PRODUCED PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT 2 1 PRODUCED BYANAUTODESKEDUCATIONALPRODUCT

B B .140 .001

.210 .001

SCALE 5 : 1 1-64 UNF

DRAWN Shawn 12/6/2009 A CHECKED University of Florida - EML4905 A

QA PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT EDUCATIONAL AUTODESK AN BY PRODUCED TITLE MFG

APPROVED Bearing Screw

SIZE DWG NO REV A 11 SCALE SHEET 1 OF 1

2 1 PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT EDUCATIONAL AUTODESK AN BY PRODUCED PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT 2 1 PRODUCED BYANAUTODESKEDUCATIONALPRODUCT

B B .175 .001

.500 .003

SCALE 5 : 1 1-72 UNF

DRAWN Shawn 12/6/2009 A CHECKED University of Florida - EML4905 A

QA PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT EDUCATIONAL AUTODESK AN BY PRODUCED TITLE MFG

APPROVED Cam Screw

SIZE DWG NO REV A 12 SCALE SHEET 1 OF 1

2 1 PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT EDUCATIONAL AUTODESK AN BY PRODUCED