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

Oklahoma Shops Organize To Join Auto Care Association

The auto shops in Tulsa, Okla., are organizing an effort to all join the Automotive Service Association in order to improve the overall service levels of the city. ABC Channel 8 in Tulsa, Okla., has the details: Randy Calley of Same Day Auto Repair...

Read more...

Service Adviser Pay Program Tips That Work

If you are looking to drive up your profits, you need to ensure you have service advisers that have the right attitude, aptitude and ethics. They will need to have the natural talent to sell, they will need to be well trained, and they will need to have...

Read more...

Should Your Shop Be Open December 26th?

Merry Christmas! What? Christmas? Yup, it’s not that far away, and if you haven’t looked at the calendar it falls on Thursday this year. So what? Well, if you’re a shop owner you will probably give little thought about the Friday after Christmas...

Read more...

Mercedes-Benz: Installation guidelines for Smart Car front wheel bearing

The typical solution for replacing the front wheel hub on a 2008-‘13 Mercedes-Benz Smart Car is a front wheel hub assembly, including a front wheel hub and knuckle. However, with a wheel hub-only ­solution for the Mercedes Smart Car, like the one offered...

Read more...

Kia: Uncovering Unperformed Maintenance

While some vehicle problems will motivate the customer to make an appointment, an equal amount of Kia repair opportunities will be discovered as the vehicle is being serviced. If you’re not already doing so, always encourage your customers to keep...

Read more...

The Evolving Oil Change Market

The only constant in the oil change business is change itself, especially if you’re trying to maintain an inventory of engine oil for all makes and models of vehicles. Since Volkswagen began ­requiring application-specific engine oil in the mid-1990s,...

Read more...

Snap-on Franchisee Conference Introduces Latest Tool & Equipment Innovations

The Snap-on Tools Franchisee Conference (SFC), held in Orlando, FL, played host to more than 8,000 registered attendees this past weekend; including principals representing more than 3,000 North American routes as well as their families and guests. The...

Read more...

TPMS: Weighing The Options

By Sean Phillips, Contributing Writer As a former technician who has dealt with the incredibly wide range and variety of OE tire pressure sensors that shops need to cover, using one of the newest aftermarket systems that can cover the vast majority...

Read more...

Making Money Servicing TPMS

If a vehicle leaves your shop with the TPMS light on or flashing, you could be fined upwards of $10,000. Every vehicle since 2008 has been equipped with TPMS in accordance to new government regulations, so this monitoring system has grown rapidly in population...

Read more...

Cartridge Oil Filter Tips

Cartridge oil filters account for a large number of oil filter applications in the field. The chances of improperly installing a cartridge oil filter are greater than with a spin-on filter. The key is to take your time, inspect before installing and follow...

Read more...

The Case of the Missing Starter

I was called last fall by a client who owns a heavy-duty diesel shop to diagnose a no-cranking condition on his father-in-law’s 2006 Chevrolet Tahoe. Because his work is mainly with heavy-duty trucks, my client knew he was lacking both in tooling and...

Read more...

Spark Plug Replacement Do’s and Don’ts

Tooling has changed from the old 13/16-inch spark plug socket to a multiplicity of 5/8-inch long, short, intermediate and swivel, thin-wall sockets needed to ­replace spark plugs on many modern engines. Similarly, tightening spark plugs with the old...

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 posts by Andrew Markel (see all)

Latest articles from our other sites:

Oklahoma Shops Organize To Join Auto Care Association

The auto shops in Tulsa, Okla., are organizing an effort to all join the Automotive Service Association in order to improve the overall service levels of the city. ABC Channel 8 in Tulsa, Okla., has...More

Toyota Synergy Drive Hybrid Brake Job

Making its debut in 1997, Toyota’s Synergy Drive has been used in the Prius, Camry and offered on almost all Lexus models since 2006. Below are some of the basic rules of the road and some fixes...More

Mercedes-Benz: Installation guidelines for Smart Car front wheel bearing

The typical solution for replacing the front wheel hub on a 2008-‘13 Mercedes-Benz Smart Car is a front wheel hub assembly, including a front wheel hub and knuckle. However, with a wheel hub-only ­solution...More

Toyota: Fixing Prius HID Headlamp Problems

High Intensity Discharge (HID) bulbs are unlike halogen light bulbs, which simply stop working at the end of their useful life. HID bulbs nearing their service end-of-life may flicker or intermittently...More

Snap-on Franchisee Conference Introduces Latest Tool & Equipment Innovations

The Snap-on Tools Franchisee Conference (SFC), held in Orlando, FL, played host to more than 8,000 registered attendees this past weekend; including principals representing more than 3,000 North American...More

Patented EVAP Leak Detection from MotorVac

MotorVac’s patented Cool Smoke does not use a heat source to generate its UV dye-enhanced smoke. No heat source means the machine produces a high-density smoke immediately. Cool Smoke does not require...More

Cartridge Oil Filter Tips

Cartridge oil filters account for a large number of oil filter applications in the field. The chances of improperly installing a cartridge oil filter are greater than with a spin-on filter. The key is...More

The Case of the Missing Starter

I was called last fall by a client who owns a heavy-duty diesel shop to diagnose a no-cranking condition on his father-in-law’s 2006 Chevrolet Tahoe. Because his work is mainly with heavy-duty trucks,...More