AfterMarketNews Auto Care Pro AutoProJobs Auto-Video.com Brake&Frontend BodyShopBusiness Counterman EngineBuilder Fleet Equipment ImportCar Motorcycle & Powersports News Servicio Automotriz Shop Owner Tire Review Tech Shop Tomorrow's Tech Underhood Service

The Problem With Living In The 'Now'

I once had a shop manager who concentrated on the “now.” Every day was a mad dash to complete the jobs at hand. He wanted to know who was working on what, where the parts were and when everything would be done. He was constantly reacting to a customer’s...

Read more...

ASE G1: Drive Belt Inspection, Replacement

The ASE G1 Certification test contains 55 scored questions, plus 10 unscored ­research questions, that cover a range of skills and knowledge related to maintenance and light repairs in engine systems, automatic transmission/transaxle, manual drivetrain...

Read more...

Amateurs and Hacks Provide Job Security For Automotive Service Professionals

Two cars pull up in front of my shop. The drivers didn’t come in, but I heard the commotion from my office window. The boyfriend opens the hood of his girlfriend’s car. They both stare at the engine; she tells the boyfriend that she was supposed...

Read more...

Audi Engine Timing Chain Failure Due to Lack of Maintenance

If you’ve been working on cars as long as me, you’ll remember the first timing belt you did and thought, “what was wrong with timing chains?” It was only a year ago, when I was working on a 2005 Audi A6 Quattro with a 3.2L engine with a broken...

Read more...

Acura: Clunk Noise While Turning

Model: Acura RSX 2005-’06 Symptom: The front suspension makes a ­clunking noise while turning. Probable Cause: The front springs are moving on the spring seats. Corrective Action: Replace both front springs and do a four­-wheel alignment. Diagnosis:...

Read more...

Inside Import Car Collision Warning, Automatic Braking Systems

Anything that moves under its own power also has to stop, so brakes have been a safety feature on cars since day one. Over the years, technical innovations such as antilock brakes (ABS) have ­improved the ability to stop with minimal skidding on...

Read more...

Bendpak Breaks Ground On New Warehouse and Shipping Complex

    BendPak, Inc. announced the recent groundbreaking to celebrate beginning construction of a 67,000 square-foot multipurpose warehouse and shipping center located on 3.7 acres of land in Santa Paula, CA. The new 67,000 square-foot...

Read more...

Pulling Codes: 7 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...

Read more...

Analyzing the Cylinder Pressure Waveform from a Running Engine, Part 3

By Vasyl Postolovskyi and Olle Gladso Contributing Writers and Instructors at Riverland Technical and Community College in Albert Lea, MN   In Part 1 of this Maximizing Tools series, we discussed an alternative approach to diagnosing an engine...

Read more...

‘Green’ Bullets: Tips for Servicing Hybrid Vehicles

Newsflash: Hybrids are here to stay. The oldest Toyota Prius models are now 14 years old and many other hybrids from other manufacturers are crossing the 100,000-mile mark every day. Here are a few of my Silver Bullets, — or in this case “Green...

Read more...

Legendary Spark Plugs: The Six Toughest Vintage Spark Plug Replacements

1. AMC Pacer: The Pacer was supposed to get a GM Wankel rotary engine. If this were the case, the four plugs would have been easy to access. But thanks to emissions problems, the Pacer would get the regular AMC straight six. This forced the engineers...

Read more...

Battery Service and Diagnosis

A good battery with an adequate charge is absolutely essential for reliable cold starting. A weak battery, or one that is rundown, may not deliver enough amps to crank the engine when temperatures plunge and the oil thickens. Cold weather can be hard...

Read more...

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

Print Print Email Email

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. 
The following two tabs change content below.

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.
Latest articles from our other sites:

Timken Launches New Training Material Resources For Automotive Technicians


The Timken Company announces the launch of four new training videos and multiple TechTips focusing on light vehicles during Automotive Aftermarket Week. Timken will reveal all of its new technical training...More

Expanded Walker Direct-Fit Catalytic Converter Line Helping Shops Return To Emissions Segment

A growing number of automotive service providers that have historically outsourced catalytic converter replacement and other emissions control services are returning to the category due in part to the...More

Audi Engine Timing Chain Failure Due to Lack of Maintenance

If you’ve been working on cars as long as me, you’ll remember the first timing belt you did and thought, “what was wrong with timing chains?” It was only a year ago, when I was working on a 2005...More

Acura: Clunk Noise While Turning

Model: Acura RSX 2005-’06 Symptom: The front suspension makes a ­clunking noise while turning. Probable Cause: The front springs are moving on the spring seats. Corrective Action: Replace both...More

Rotary Lift To Showcase Updated Four-Post Car Lifts At SEMA Show 2014

Vehicle service professionals will have the first opportunity to see Rotary Lift’s updated 14,000-lb. capacity four-post general service and alignment lifts at the SEMA Show. The enhanced lifts will...More

Bendpak Breaks Ground On New Warehouse and Shipping Complex

    BendPak, Inc. announced the recent groundbreaking to celebrate beginning construction of a 67,000 square-foot multipurpose warehouse and shipping center located on 3.7 acres of...More

‘Green’ Bullets: Tips for Servicing Hybrid Vehicles

Newsflash: Hybrids are here to stay. The oldest Toyota Prius models are now 14 years old and many other hybrids from other manufacturers are crossing the 100,000-mile mark every day. Here are a few...More

Legendary Spark Plugs: The Six Toughest Vintage Spark Plug Replacements

1. AMC Pacer: The Pacer was supposed to get a GM Wankel rotary engine. If this were the case, the four plugs would have been easy to access. But thanks to emissions problems, the Pacer would get the regular...More