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Work Smarter With Procedures, Measurement And Accountability

You’re working harder and faster today to stay ahead of the competition and boost profitability in a challenging business environment. You’re providing the highest quality repairs and top-notch customer service so that your shop’s car count...

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Are You Ready For Some Auto Repair?

A game is being played every day that doesn’t have many fans filling the bleachers. It’s a battle between man and machine. Yes, on playing fields across the country — whether it be one-bay garages, 12-bay shops or maybe just some far-off...

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Radiator Specialty Shop Hits 100 Years In The Business

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Step-by-Step Lexus Fuel Pump Replacement

We will use a third-generation 2006 Lexus LS430 as our case study for this fuel pump assembly replacement. First, discharge the fuel system pressure, disconnect the negative battery terminal and drain the fuel. Be sure to remove the rear seat cushion...

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Nissan: Squeak From Fuel Pump

Customer may report a squeak noise that is: • Coming from inside the vehicle; • Happens after driving for 30 minutes; • Is coming from under the vehicle or from the left rear area of the vehicle. If you confirm that a “squeak” noise...

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BMW Group to Develop Inductive Charging System For Hybrid Cars

BMW believes systems for the inductive charging of high-voltage batteries are the next step forward for energy supply. The development objective is to put reliable, non-wearing and user-friendly solutions for inductive charging into production that...

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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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How Ford's New Grille Shutters Control Airflow

Some new Ford vehicles feature active grille shutters — a new system that optimizes aerodynamics by using vents to control airflow through the grille to the cooling system and engine compartment. If air is required to cool the engine, the vents...

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How Engine Coolant Temperature Sensors Influence The Modern Powertrain

  Considering that roughly 1,500 or more ­different vehicle models are introduced into our domestic market each year, it’s becoming more difficult to predict how a powertrain control module (PCM) will utilize data from a particular sensor or...

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Diagnosing Power Steering Loss on a 2008 Ford Escape

The vehicle in question is a 2008 Ford Escape with a 3.0-L engine. The customer complaints are as follows: The steering wheel will turn by itself; at times, usually when turning, the vehicle will lose all power steering assist; and occasionally, while...

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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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