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No More Free Tire ­Rotations!

Tire rotation is a cornerstone of vehicle preventive maintenance and tire longevity. It is a well-proven fact that tire tread life can be greatly enhanced by regular and timely tire rotation. During rotation, each tire and wheel is ­removed from...

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ASE G1: How To Measure Cold Cranking Amps, Reserve Capacity

The ASE G1 test contains 55 scored, job-related questions, 15% of which will concern electrical maintenance and repairs. From the ASE G1 study guide, you will need to know how to: • Perform battery tests (load and capacitance); ­determine needed...

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ASE A5: Brake Fluid And Bleeding Sequence

The ASE A5 Test includes a portion on brake fluid, bleeding, flushing and leak testing. You must know how to: • Diagnose poor stopping, pulling, dragging, or incorrect pedal travel caused by problems in the brake fluid; determine needed repairs. •...

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When Timing Is Everything: A Look At The 2.5L, 2.0L Powerplants

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Modern Charging Systems: Cover All The Bases During the Diagnostic Process

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Audi Fuel System: MIL On/Multiple Low Fuel Pressure DTCs

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Redline Detection Seeks Nominations for 2nd Annual Redline Rock Star Performance Award

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Automotive Lift Institute (ALI) Elects 2015 Board

Jerome Lentz of Challenger Lifts (Louisville, Ky.) has been elected chairman of the Automotive Lift Institute (ALI) Board of Directors for 2015. Voting took place at ALI’s annual membership meeting Nov. 3 in Las Vegas. Lentz’s 2015 term will be...

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Top 5 Tools: John Forro, AST, Automotive Service Technology in Hinckley, OH

John Forro AST, Automotive Service Technology Hinckley, OH ALLDATA Information System: I use this system daily for researching labor pricing, wiring schematics, circuit descriptions, torque specs, etc. One doesn’t need to memorize all the information...

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Must-Read TPMS Technical Service Bulletins

Here’s a rundown of the top technical service bulletins related to TPMS. These TSBs should be analyzed by every technician that services TPMS. Audi TSB Number: 4413382034445/1 Models: 2010-’14 A4/S4, A5/S5 and Q5 Summary: This TSB addresses TPMS...

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Ford Reflash: Setting Up Your PC

You’ve just finished up a job on a Ford vehicle, and you’re about to try and start it up. However, it needs programmed first. You’ve decided to use a J2534 tool, but there are certain things you’ll need to consider ­before purchasing that subscription...

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Fuel Line Replacement: The Why and How

If you live in a state that doesn’t get snow, you can stop reading right now. If you live in the Snow Belt, you are about a month away from snow and ice. It’s not the adverse driving conditions that should scare you or your customers, it’s...

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Home Brakes BRAKE MATH: CALCULATING THE FORCE NEEDED TO STOP A CAR

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I made a mistake probably because of my distaste of math, now it is time to learn from it. In a three-part series, we will look at the math of brakes. We will start with the driver pushing the brake pedal and end with the pad contacting the rotor and bringing the car to a stop. Along the way, we will explore the math of boosters, quick take-up master cylinders and caliper sizing. 
 
On a mechanical level, it is easy to understand how brakes work. We all understand that brake fluid transfers force from one hydraulic component to another. But, how does this apply to how a brake pedal feels? This is where math is required.
 
You need only two simple math equations to commit to memory. First, the equation for calculating the surface area of a circle (caliper or master cylinder piston) is p(3.14) x radius2. Second, pressure is equal to the force divide by the area or pounds per square inch.  The rest of the math is just multiplication, division and addition/subtraction.

Pedal Ratio
Lets start with the driver. In a sitting position, the average driver can comfortably generate 70 lbs. of force on the rubber pad at the end of the brake pedal. The brake pedal is nothing more than a 
mechanical lever that amplifies the force of the driver. This is where the pedal ratio comes into play.
 
Pedal ratio is the overall pedal length or distance from the pedal pivot to the center of the pedal pad divided by the distance from to the pivot point to where the push rod connects.
 
The optimal pedal ratio is 6.2:1 on a disc/drum vehicle without vacuum or other assist method. This means that the 70 lbs. the driver has applied now is amplified to 434 lbs. (6.2 x 70 lbs.) of output force. The problem is that the travel of the pedal is rather long due to the placement pivot point and master cylinder connection.
Brake Boosters
A booster increases the force of the pedal so lower mechanical pedal ratio can be used. A lower ratio can give shortened pedal travel and better modulation. Most vacuum boosted vehicles will have a 3.2:1 to 4:1 mechanical pedal ratio.
 
The size of the booster’s diaphragm and amount of vacuum generated by the engine, will determine how much force can be generated. Most engines will generate around -8 psi of vacuum (do not confuse with inches of HG or Mercury). If a hypothetical booster with 7-inch diaphragm is subjected to -8 psi of engine vacuum, it will produce more than 300 lbs. of addition force. Here is the math:
 π(3.14) X radius(3.5)2 = 38.46 sq/inches of diaphragm surface area X 8 psi (negative pressure becomes positive force)= 307.72 lbs of output force
To keep things simple, let’s return to our manual brake example. The rod coming from the firewall has 434 lbs. of output force. When the force is applied to the back of the master cylinder, the force is transferred into the brake fluid.
The formula for pressure is force divided by the surface area.  
If the master cylinder has a 1-inch bore, the piston’s surface area is .78 square inches. If you divide the output force of 434 lbs. by the surface area of the piston, you would get 556 psi(434 lbs. divided by .78 inches) at the ports of the master cylinder. Not bad for a 70 lbs. of human effort.
If you reduce the surface area of the piston you, will get more pressure.
 
This is because the surface area is smaller, but the output force from the pedal stays the same. If you used a master cylinder with a bore of .75 inches that has a piston that has .44 inches of piston surface area, you would get 986 psi at the ports for the master cylinder (434 lbs. divided by .44 inches).
 
But, how is this force transferred to the calipers? How does the size of the caliper piston change the force needed to push the brake pad to the rotor? We will explore this next month. 
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Andrew Markel

Andrew Markel is an ASE Certified Technician and former service writer, and he brings this practical knowledge to the Brake & Front End team as editor.

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