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Second-rate parts mean second-rate results

When it comes to diagnosing a problem, one of the biggest mistakes is thinking that the problem is gone after you’ve installed a new part. I’ve had vehicles brought in countless times with the same old story attached to them. The customer will say:...

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GearWrench Launches Street Team, a New Mobile Driver Program

GearWrench, a premier hand tool brand from Apex Tool Group, has announced Street Team, a new program that gives independent mobile distributors the support of an established tool brand without the restrictions of a franchise. "Response to the program...

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AUTO 7 Named Approved Vendor For Automotive Parts Associates

Steven Kruss, president of Auto 7, which supplies Korean-made, OEM-quality automotive parts to distributors across North America, announced that Auto 7 has been named an approved vendor of Automotive Parts Associates (APA), one of the nation’s...

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Internal Engine Oil Consumption Diagnostics

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Hyundai Fuel System, Emissions Diagnostics

Hyundai has done a good job of improving its ­offerings over the years from both an aesthetic and mechanical viewpoint. Complemented by a strong warranty and good value, the carmaker has been able to increase its market share year over year. If you aren’t...

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Curing Volvo Manual Transmission Rattle

In an effort to increase fuel efficiency, today’s engines produce more torque so they can be ­driven at extremely low rpm. ­Reduced viscosity engine and gearbox oils, less vehicle weight and improved aerodynamics also contribute to better fuel economy....

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AVI To Provide Technicians with $1 Million in Free Training

AVI (Automotive Video Innovations) is giving back to the automotive community that has given so much opportunity to the Florida-based video company. To carry out that mission, AVI reports that it is pledging to give away $1 million worth of training...

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GearWrench Launches Street Team, a New Mobile Driver Program

GearWrench, a premier hand tool brand from Apex Tool Group, has announced Street Team, a new program that gives independent mobile distributors the support of an established tool brand without the restrictions of a franchise. "Response to the program...

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Talk To All Available Modules With Autel's MaxiDiag Elite MD802

Derived from Autel’s Professional Series tool, the MaxiDAS DS708, the MaxiDiag Elite MD802 enables the user to not only get into the OE enhanced OBD II system with mode 6 access and live data graphing, but it also allows a technician to scan the...

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The Why, Where, When of TPMS Sensors

To understand any TPMS relearn procedure, you have to understand this: Sensors only transmit, they do not receive. No vehicle asks a sensor for information on how it is doing. I know you’re thinking a sensor does receive signals when the vehicle...

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Most Common Causes of Misfire Codes

A flashing check engine light and a P0301 to P0312 diagnostic trouble code (DTC) is a surefire indication that one or more cylinders are misfiring. Occasional misfires may pass unnoticed, but a steady misfire is hard to miss. The engine usually feels...

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Pattern Failures of MAF and MAP Sensors

Pattern failures are those failures that happen over and over again — and the same applies to how customers describe these failures. Customers might unknowingly give you the answer to their problem without needing to open the hood. In this article,...

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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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