How brakes stop a vehicle

It is late October and the first snow of the season has already come and gone twice. Kiran Dhaliwal is six months into her apprenticeship at Ridgeline Auto Service, and Marty Kowalchuk has promised her that this is the month she starts on brakes. On Monday morning Hal Osei, the fleet manager for Front Range Parcel, calls Simone Tremblay at the service desk. Van 2 of his three delivery vans has started making a grinding noise when it stops, and its driver says the pedal feels different. It is the second set of front brakes on that van in eleven months.

“Courier vans eat brakes,” Marty says when Simone puts the repair order on the board. “They weigh almost four tons loaded, they stop a hundred times a day, and the drivers are always in a hurry. Before you touch one, you need to understand what a brake actually does.” He sends Kiran to the whiteboard in the training room and draws a van, a hill and a stop sign.

This lesson explains the physics of stopping: what a brake does with the vehicle's energy, why heavier and faster vehicles are so much harder to stop, how the tires limit every stop, how weight shifts to the front wheels during braking, and how stopping distance is made up of reaction distance and braking distance. It ends with an overview of the brake system's parts and of the standards every new vehicle's brakes must meet. The rest of the course takes each part in turn.

A brake is a heat machine

A moving vehicle has kinetic energy, the energy of motion. To stop it, that energy has to go somewhere. In almost every car and truck on the road, the service brakes turn it into heat: brake pads or shoes are pressed against a rotor or drum that turns with the wheel, and friction between them converts the motion into heat in the rotor, the drum and the pads. The heat then passes to the air flowing around the brakes. Hybrids and electric vehicles also recover part of the energy as electricity, which Lesson 11 covers, but they still carry friction brakes for hard stops and emergencies.

Kinetic energy depends on mass and on the square of speed. Doubling the mass doubles the energy; doubling the speed multiplies it by four. That square is the single most important fact about brakes. A van stopping from 60 mph must get rid of almost twice as much energy as the same van stopping from 45 mph, even though the speed is only about 40 percent higher.

In this formula, E is the kinetic energy in joules, m is the mass in kilograms, and v is the speed in meters per second. To convert kilometers per hour to meters per second, divide by 3.6. In US units the same relation can be used with mass in slugs and speed in feet per second to give foot-pounds, but it is easier to convert to metric, calculate, and convert the answer back, which is what the code in this lesson does.

# Kinetic energy of the shop's vehicles at highway and city speeds
UNITS = "US"                       # "metric" or "US"
vehicles = [("courier van, loaded", 3900), ("courier van, empty", 2700), ("Gord's pickup", 2220), ("Dr. Singh's EV", 1690)]   # mass in kg
speeds_kmh = [50, 100] if UNITS == "metric" else [48.3, 96.6]                                                            # 30 and 60 mph
for name, m in vehicles:
    for v_kmh in speeds_kmh:
        v = v_kmh / 3.6                       # m/s
        e = 0.5 * m * v ** 2                  # joules
        if UNITS == "metric":
            print(f"{name:<22} at {v_kmh:5.0f} km/h: {e / 1000:6.0f} kJ")
        else:
            print(f"{name:<22} at {v_kmh / 1.609:5.0f} mph: {e * 0.7376 / 1000:6.0f} thousand ft lb ({e / 1055:5.0f} BTU)")

courier van, loaded    at    30 mph:    259 thousand ft lb (  333 BTU)
courier van, loaded    at    60 mph:   1036 thousand ft lb ( 1331 BTU)
courier van, empty     at    30 mph:    179 thousand ft lb (  230 BTU)
courier van, empty     at    60 mph:    717 thousand ft lb (  921 BTU)
Gord's pickup          at    30 mph:    147 thousand ft lb (  189 BTU)
Gord's pickup          at    60 mph:    590 thousand ft lb (  758 BTU)
Dr. Singh's EV         at    30 mph:    112 thousand ft lb (  144 BTU)
Dr. Singh's EV         at    60 mph:    449 thousand ft lb (  577 BTU)

The loaded van at highway speed carries about four times as much energy as it does at city speed, and almost twice as much as the empty van. All of that energy ends up as heat in four rotors and eight pads, most of it in the front ones, every time the driver stops from highway speed. Do that a few times in a row coming down a long hill and the rotors can reach several hundred degrees.

Heat, fade and why brakes are sized the way they are

Brake parts are designed to absorb and shed heat. A rotor is a heavy disc of cast iron because cast iron stores a lot of heat for its cost, resists wear, and keeps its strength when hot. Many rotors are vented, with cooling vanes between their two friction faces, so that air is pumped through them as they turn. Pads and shoes are made of friction materials whose grip stays fairly steady over a wide range of temperatures.

When brakes get too hot, they lose effectiveness, a condition called fade. There are three kinds. In friction fade, the pad material overheats and its friction falls, so the driver has to push harder for the same deceleration; the pedal stays firm but the vehicle does not slow as it should. In fluid fade, the brake fluid near the calipers boils, forming vapor bubbles that compress, so the pedal goes soft and sinks toward the floor; Lesson 4 explains why old, wet fluid boils sooner. In mechanical fade, a drum expands away from its shoes as it heats, so the pedal travel increases; Lesson 8 covers drums. Fade on a long downhill is why drivers of heavy vehicles are taught to use a lower gear.

# Temperature rise of the front rotors in one stop (all energy into the rotors, no cooling during the stop)
UNITS = "US"
m_vehicle = 3900          # kg, loaded van
front_share = 0.70        # fraction of braking done by the front axle
rotor_mass = 10.5         # kg, each front rotor
c_iron = 460              # J/(kg K), specific heat of cast iron
for v_kmh in (50, 80, 100):
    v = v_kmh / 3.6
    e_front = 0.5 * m_vehicle * v ** 2 * front_share
    rise = e_front / (2 * rotor_mass * c_iron)
    if UNITS == "metric":
        print(f"stop from {v_kmh:3d} km/h: each front rotor warms by about {rise:4.0f} C")
    else:
        print(f"stop from {v_kmh / 1.609:3.0f} mph: each front rotor warms by about {rise * 1.8:4.0f} F")
print("ten hard stops close together, with little time to cool, can add several hundred degrees")

stop from  31 mph: each front rotor warms by about   49 F
stop from  50 mph: each front rotor warms by about  126 F
stop from  62 mph: each front rotor warms by about  196 F
ten hard stops close together, with little time to cool, can add several hundred degrees

The real rise is somewhat lower, because some heat goes into the pads and hubs and some is carried away during the stop. Even so, the calculation shows why delivery vans and towing pickups wear their brakes quickly, and why Hal's drivers are told to avoid repeated hard stops and to let the brakes cool before parking with the parking brake set after a long downhill.

The tires decide

A brake can only stop the wheel. What stops the vehicle is the grip between the tires and the road. The largest braking force a tire can produce is the load on that tire multiplied by the coefficient of friction between the tire and the road, written with the Greek letter mu. On dry asphalt mu is about 0.8 to 0.9 for a good tire; on wet asphalt about 0.5 to 0.7; on packed snow about 0.2 to 0.3; and on glare ice it can fall to 0.1 or less. These values are typical, and real ones vary with the tire, its tread depth, its temperature and the road surface.

The maximum possible deceleration is mu times the acceleration of gravity, 32.2 ft/s². On dry pavement, a well-equipped car can therefore decelerate at about 0.8 to 0.9 g. If the brakes apply more force than the tire can transmit, the wheel slows faster than the vehicle and begins to skid. A skidding tire has less grip than one that is still rolling with a little slip, and it cannot steer. Preventing that is the job of anti-lock brakes, described in Lesson 10. Winter tires, which Ridgeline fits every fall, have softer rubber and many small slits called sipes that improve grip in the cold, and they shorten stopping distances on snow and ice more than any change to the brakes could.

Weight transfer

When a vehicle brakes, its mass continues to push forward at the center of gravity, which sits above the road. That pushes the front of the vehicle down and lifts the rear, moving load from the rear wheels to the front wheels. The amount moved depends on the deceleration, the height of the center of gravity and the wheelbase. A high van with a heavy load transfers a great deal of weight; a low sports car much less.

Because the front tires carry more of the load during a stop, they can produce more braking force, and so the front brakes are made larger than the rear ones. On most cars and light trucks the front brakes do roughly 60 to 75 percent of the work in a hard stop. If the rear brakes were as strong as the front, the lightly loaded rear wheels would lock first and the vehicle could spin. Brake systems therefore use smaller rear calipers or drums, and valves or electronic controls that limit rear pressure, to keep the rear wheels from locking before the front ones; Lesson 3 explains the valves and Lesson 10 the electronic method.

Here delta W is the weight moved from the rear axle to the front, W is the vehicle's weight, a is the deceleration, h is the height of the center of gravity, g is the acceleration of gravity and L is the wheelbase. The ratio a over g is simply the deceleration in g.

# Weight transfer during braking for the loaded van and Gord's pickup
UNITS = "US"
def transfer(front_kg, rear_kg, cg_height_m, wheelbase_m, decel_g):
    total = front_kg + rear_kg
    moved = total * decel_g * cg_height_m / wheelbase_m
    return front_kg + moved, rear_kg - moved
for name, f, r, h, l in [("loaded van", 1750, 2150, 0.95, 3.75), ("Gord's pickup", 1290, 930, 0.72, 3.66)]:
    for g in (0.3, 0.8):
        nf, nr = transfer(f, r, h, l, g)
        share = nf / (nf + nr) * 100
        if UNITS == "metric":
            print(f"{name:<14} at {g} g: front {nf:5.0f} kg, rear {nr:5.0f} kg -> front carries {share:3.0f} %")
        else:
            print(f"{name:<14} at {g} g: front {nf * 2.205:5.0f} lb, rear {nr * 2.205:5.0f} lb -> front carries {share:3.0f} %")

loaded van     at 0.3 g: front  4512 lb, rear  4087 lb -> front carries  52 %
loaded van     at 0.8 g: front  5602 lb, rear  2998 lb -> front carries  65 %
Gord's pickup  at 0.3 g: front  3133 lb, rear  1762 lb -> front carries  64 %
Gord's pickup  at 0.8 g: front  3615 lb, rear  1280 lb -> front carries  74 %

At rest the loaded van carries more weight on its rear axle than on its front, but in a hard stop the balance swings to the front. That is why its front pads wear out two or three times as fast as its rears, and why van 2 is in for front brakes again.

Stopping distance

A driver's stopping distance has two parts. The reaction distance is how far the vehicle travels between the moment the driver sees a hazard and the moment the brakes begin to act. It includes the time to notice, decide, move the foot to the pedal and take up the slack in the system, typically about 1 to 1.5 seconds for an alert driver, and much more for a distracted one. During that time the vehicle is still traveling at full speed. The braking distance is the distance covered while decelerating to a stop.

In this formula, d is the total stopping distance, v the starting speed, t sub r the reaction time, and a the average deceleration. The braking part grows with the square of speed, so stopping distances grow much faster than speed. Worn brakes, glazed pads, old fluid and worn tires all reduce the deceleration a driver can achieve and lengthen the second part; nothing a technician does can shorten the first.

# Stopping distance: reaction distance plus braking distance
UNITS = "US"
t_react = 1.5                                   # seconds
surfaces = [("dry asphalt", 0.80), ("wet asphalt", 0.55), ("packed snow", 0.25), ("ice", 0.10)]
speeds = [50, 100] if UNITS == "metric" else [30, 60]
for spd in speeds:
    v = spd / 3.6 if UNITS == "metric" else spd * 0.44704      # m/s
    for road, mu in surfaces:
        a = mu * 9.81
        react = v * t_react
        brake = v ** 2 / (2 * a)
        if UNITS == "metric":
            print(f"{spd:3d} km/h on {road:<12}: reaction {react:5.1f} m + braking {brake:6.1f} m = {react + brake:6.1f} m")
        else:
            print(f"{spd:3d} mph on {road:<12}: reaction {react * 3.281:5.0f} ft + braking {brake * 3.281:6.0f} ft = {(react + brake) * 3.281:6.0f} ft")

 30 mph on dry asphalt : reaction    66 ft + braking     38 ft =    104 ft
 30 mph on wet asphalt : reaction    66 ft + braking     55 ft =    121 ft
 30 mph on packed snow : reaction    66 ft + braking    120 ft =    186 ft
 30 mph on ice         : reaction    66 ft + braking    301 ft =    367 ft
 60 mph on dry asphalt : reaction   132 ft + braking    150 ft =    282 ft
 60 mph on wet asphalt : reaction   132 ft + braking    219 ft =    351 ft
 60 mph on packed snow : reaction   132 ft + braking    481 ft =    613 ft
 60 mph on ice         : reaction   132 ft + braking   1203 ft =   1335 ft

The parts of a brake system

Every modern car and light truck has two independent braking systems. The service brakes are the ones the driver uses with the pedal. The parking brake, applied by a lever, a pedal or an electric switch, holds the parked vehicle and can be used to slow it if the service brakes fail. Lesson 9 covers parking brakes.

The service brake system is hydraulic. The pedal pushes a rod into the master cylinder, usually with help from a power booster. The master cylinder turns the driver's push into fluid pressure, which travels through steel lines and flexible hoses to a caliper or wheel cylinder at each wheel. There, the pressure pushes pistons that press friction material against a rotor or drum. Electronic systems, anti-lock brakes and stability control, sit between the master cylinder and the wheels and can reduce, hold or even build pressure at each wheel on their own.

Brakes are safety-critical, and the rules reflect that. In the United States, every new passenger vehicle must meet Federal Motor Vehicle Safety Standard 135, which sets stopping distances, fade and recovery tests, parking brake performance and warning lamp requirements for light vehicles, and FMVSS 126, which has required electronic stability control on new light vehicles since the 2012 model year. A shop does not certify brakes against those standards, but it must restore them to the manufacturer's specifications, using parts that meet them, and it must never leave a vehicle less safe than it arrived. Colorado has no periodic safety inspection, so a shop's own inspection is often the only check a vehicle's brakes get; Ridgeline measures and records them in a set way on every brake job.

Marty's first rule of brake work

Before Kiran starts on van 2, Marty gives her the rules he gives every apprentice. A brake job always starts with a road test, if the vehicle is safe to drive, and with a conversation with the customer or driver about exactly what they notice and when. Brakes are inspected and measured, not guessed at. Parts on the same axle are replaced in pairs, so that both sides brake equally. The vehicle is road tested again before delivery, and the pedal is pumped up before the vehicle moves at all, because a freshly serviced caliper needs several strokes to push its pistons back against the pads.

And brake dust is treated with respect. Older brake linings contained asbestos, and although asbestos has been phased out of new brake parts in the United States, though not completely banned in every product until recently, old parts and some imported parts may still contain it. Brakes are never blown off with compressed air. They are cleaned with a low-pressure wet method or an approved enclosure, and the shop's procedures for dust, which Kiran learned in AUTO-110, apply to every brake job.