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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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North Dakota Woman Goes From Daycare To Auto Repair

Everyone reading this, raise your hand if you ran a daycare before working in or owning an auto repair shop. Anyone? Well, that’s the story for Elyzabeth Goerger, who was recently profiled in North Dakota’s Prairie Business. Georger is the...

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South Dakota Tech Program Graduates In High Demand

The automotive repair industry, in certain pockets of the country, has a labor force problem. There either isn’t enough technicians to go around, or not enough properly trained technicians to go around. This isn’t the case in Sioux Falls, SD. What...

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Honda: Easy Fix for Engine Noise

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Toyota: Rough idle, surging between 500 to 800 RPM

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Volkswagen: Engine Does Not Start

Vehicle: 2001 Volkswagen Passat GLX, 2.8L Complaint: The customer says the vehicle will not start. Cause: Confirmed the customer’s complaint and found the vehicle did not start. Connected a scan tool and found the following codes: • 17978...

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Midtronics Launches Informational Microsite

  Midtronics, Inc. has launched an informational microsite — or mini website — to provide customers with detailed information about the company’s newest diagnostic platform — the DSS-7000 Battery Service Diagnostic System. The microsite...

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German Tool Specialist KC Tool Announces Addition of Gedore Tools

As of August 1 KC Tool became the first certified reseller of Gedore Tools in the United States already adding more than 2,500 Gedore tools to its selection of German made tools. KC Tool plans to add an additional 6,000 Gedore Tools over the next few...

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United Stationers Expands Into Auto Aftermarket

United Stationers announced Sept. 11 that its wholly owned subsidiary, United Stationers Supply Co., signed an agreement to acquire MEDCO, a U.S. wholesaler of automotive aftermarket tools and supplies, and its affiliates including G2S Equipment de Fabrication...

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Chevrolet: Navigation Information Not Displaying Accurate Location

Customers may complain the navigation radio is not displaying the correct vehicle location icon on the map accurately after a radio or battery has been replaced or after battery power has been removed from the radio. The vehicle location icon accuracy...

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What’s a Battery?

  The first documented battery that used two dissimilar metals with an electrolyte between them was invented in 1800. Known as the voltaic pile after its ­inventor, Volta, this early battery consisted of copper and zinc discs piled on top of...

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Installing Spark Plugs: Torque and Gap Are Critical

When installing spark plugs, a technician must be aware of the torque specifications for that particular plug. Remember that either overtorquing or undertorquing a spark plug will affect the quality of the installation and the performance of the vehicle’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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