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Thorough Brake Inspections Are Comeback Preventers And Profit Builders

How many times have you seen a hand-painted sign in a shop window that advertised a menu-priced brake pad replacement for “$XX.95 per axle.” Of course, a menu-priced brake replacement would be good if a simple brake pad replacement would cure all...

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Automotive Pet Peeves 2: Reader Feedback Is Overwhelming

How many auto repair pet peeves are out there? Well, enough of them that one article wouldn’t hold them all. I’ve received so many emails, texts and phone calls about my article in the February issue that I thought: why not put everyone’s pet peeve...

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Air Filter Show & Tell: Seeing Is Believing

Air filters are normal wear items that ­require regular checks and ­replacement. Their role is to trap dirt particles that can cause damage to engine cylinders, walls, pistons and piston rings. In fuel-injected vehicles, the air filter also plays...

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ZF 8-Speed Transmission Replacement

The ZF 8HP transmission made its debut in 2009, and since its introduction, has been one of the top choices for international car manufacturers. BMW, one of ZF’s largest customers, uses the 8HP across its entire product portfolio. BMWs featuring...

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Shop Folds After Shoddy Brake Work Endangers Woman

A Florida woman was thankful to walk away without injury after her vehicle’s brakes went out for the second time in as many months due to negligence on the part of her local repair shop, ABC Action News reported. Shelly Darling of Zephyr Hills, FL,...

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Air Ride Diagnostics: Reservoirs and Compressors

Just about every Asian and European luxury import nameplate manufacturer has a 7- to 10-year-old vehicle on the road with an air-ride suspension at all four corners. Chances are one of these vehicles will be coming to your shop sooner rather than later. Regardless...

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Can Cordless Power Tools Replace Pneumatic Tools?

I recently attended Milwaukee Tool’s annual media tool preview event where they unveiled over 80 new products that will be available later this year and early next year. Milwaukee Tool is known primarily as a leading supplier of professional-grade power...

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OTC's Technician Challenge Tour Will Award Ultimate Diagnostics for Life

The OTC Technician Challenge is going on tour with dates in six states, showcasing the Encore with new Bravo 2.0 software. Technicians nationwide will compete to win one of three Ultimate Diagnostics for Life packages. Ultimate Diagnostics for Life winners...

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New Productivity Features Added To Coverage In Snap-on Software Upgrade 15.2

Snap-on has increased its vehicle coverage in the new Software Upgrade 15.2 for the Auto-ID, One-Touch Full Vehicle Code Scan and the One-Touch Code Clear features to provide effective, accurate and fast diagnostics out of the box and miles down the road. The...

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BMW Recognized for Engine-Building Excellence

BMW Group’s engine-building prowess was recognized with four wins at the latest International Engine of the Year Awards. The drive unit in the BMW i8 earned two class wins as well as being declared overall winner, with a further class win being garnered...

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Diagnostic Dilemma: The Case of the Missing Code

When doing mobile diagnostic work, no-code stalling complaints are a major part of your agenda. In most cases, the client shop is simply too busy to duplicate the failure or, in some cases, a long test drive will yield nothing in the way of useful...

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Secondary Ignition: The Art of Spark

What is a coil? From the beginning of the internal combustion engine, several different ignition systems have been used to create a high-energy spark. The most popular system, and the one that’s in use today, is a step-up coil. A coil is nothing...

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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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