IntroductoryVehicle Engineering

(2)Tyre

南台科技大學

機械系 先進車輛組 張崴縉

Circle Track Racing

• Problem:How to get the car to go around the track as

quickly as possible

Driving strategy

• Cornering 過彎– Go around the corner as fast as possible without

sliding sideways off the track.• Acceleration 加速

– Accelerate out of the corner as quickly as possible and continue accelerating down the straightway.

• Braking 煞車– At the last possible minute, hit the brakes to slow

down just enough to keep from sliding off the track in the next corner.

Problems Analysis• Speed in the corners is limited primarily by the amount of

traction between the tires and the road.• Acceleration is limited by

– the power the engine can provide– the efficiency– inertia of the drivetrain– The weight of the car– The aerodynamic drag– Traction between the tires and the road

• Braking is limited by– the performance of the braking system– traction between the tires and the road

Cornering

• Size and characteristics of tires • Downward aerodynamic force on tires• Suspension geometry

– The keep the tires on the road and prevent excessive body roll

• Vehicle gross weight• Height of the vehicle center of gravity

Top speed

• Net power at the driving wheels• Aerodynamics drag• Rolling resistance

Controllability and Response• Center of gravity height• Load transfer characteristics• Suspension geometry and alignment• Polar moment of inertia• Chassis and suspension link rigidity• Differential characteristics• Slip angle versus coefficient of friction curves of

the tires• Aerodynamic balance

Vertical load on tire

• The potion of total vehicle weight and aerodynamic downforce.

• Vehicle weight is constantly being transferred from one tire to another.

• Downforce varies with the square of road speed.

• The vertical load on any given tire is subject to continuous change.

Coefficient of friction• The racing tire does not follow Newton’s Laws of

Friction – which are for friction between smooth bodies.• The ratio of the force that the tire is capable of

generating to the vertical load applied to it is termed that tire’s “coefficient of friction”– 800 pounds force/500 pounds vertical load = 1.6 g– Under ideal and steady conditions the tire could accelerate or

decelerate at the rate of 1.6g or could develop a corning force of 1.6g

– The coefficient of friction is dimensionless– It is an indication of the maximum force which can be developed

by one tire when compared to another tire under the same conditions.

Each section of small print on a tire's sidewall means something:

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What All the Numbers Mean

• Tire TypeThe P designates that the tire is a passenger vehicle tire. Some other designations are LT for light truck, and T for temporary, or spare tires.

• Tire WidthThe 235 is the width of the tire in millimeters (mm), measured from sidewall to sidewall. Since this measure is affected by the width of the rim, the measurement is for the tire when it is on its intended rim size.

Aspect Ratio• This number tells you the height of the tire, from

the bead to the top of the tread. • This is described as a percentage of the tire

width. • For example, 235/75

– The aspect ratio is 75– The tire's height is 75 percent of its width, or 176.25

mm ( .75 x 235 = 176.25 mm, or 6.94 in). • The smaller the aspect ratio, the wider the tire in

relation to its height.

Calculating the Tire Diameter

• Multiply the tire width by the aspect ratio to get the height of the tire. Tire height = 235 x 75 percent = 176.25 mm

(6.94 in)Then we add twice the tire height to the rim

diameter. 2 x 6.94 in + 15 inches = 28.9 in (733.8 mm)This is the unloaded diameter; as soon as any

weight is put on the tire, the diameter will decrease.

High performance tires usually have a lower aspect ratio than other tires. This is because tires with a lower aspect ratio provide better lateral stability. When a car goes around a turn lateral forces are generated and the tire must resist these forces. Tires with a lower profile have shorter, stiffer sidewalls so they resist cornering forces better.

• Tire ConstructionThe R designates that the tire was made using radial (幅射) construction. This is the most common type of tire construction. Older tires were made using diagonal bias (D, 為正向交織線層型) or bias belted (B, 斜向交織帶層型) construction. A separate note indicates how many plies make up the sidewall of the tire and the tread.

• Rim DiameterThis number specifies, in inches, the wheel rim diameter the tire is designed for.

Uniform Tire Quality Grading• Passenger car tires also have a grade on them

as part of the uniform tire quality grading(UTQG) system. – Tread Wear: The higher the number, the longer you

can expect the tread to last. – Traction: Tire traction is rated AA, A, B or C, with AA

at the top of the scale. It does not indicate the tire's cornering ability.

– Temperature: The tire temperature ratings are A, Bor C. The rating is a measure of how well the tire dissipates heat and how well it handles the buildup of heat.

各線層種類輪胎

Service Description

• Load Ratings: – The load rating is a number that correlates to

the maximum rated load for that tire. • Speed Rating:

– The letter that follows the load rating indicates the maximum speed allowable for this tire (as long as the weight is at or below the rated load).

16503638125

16003528124

15503410123

15003308122

14503197121

14003080120

13602999119

13202911118

12852833117

12502750116

12152679115

11802601114

11502535113

11202469112

10902403111

10602337110

10302271109

10002205108

9752149107

9502095106

9252039105

9001984104

8751929103

8501874102

8251819101

462101881

45099080

43796479

42593778

41290877

40088276

38785375

37582774

36580573

35578372

34576171

33573970

32571769

31569568

30767767

30066266

29063965

28061764

27260063

26558462

25756761

25055160

Kilograms (kgs)Pounds (lbs)Load Index

8001764100

775170899

750165398

730160997

710156596

690152195

670147794

650143393

630138992

615135691

600132390

580127889

560123488

545120187

530116886

515113585

500110284

487107483

475104782

Traction • All-Season Tires with Mud and Snow

DesignationIf a tire has MS, M+S, M/S or M&S on it, then it meets the Rubber Manufacturers Association(RMA) guidelines for a mud and snow tire.

• Hydroplaning– when the car drives through puddles of standing

water, if the water cannot squirt out from under the tire quickly enough, the tire will lift off the ground and be supported by only the water.

– Tires have deep grooves running in the same direction as the tread, giving the water an extra channel to escape from under the tire.

Coefficient of rolling friction (CRF)

• The CRF has nothing to do with how much traction the tire has; it is used to calculate the amount of drag or rolling resistance caused by the tires.

0.001Train wheel

0.006 - 0.01Truck tire

0.015Ordinary car tire

0.006 - 0.01Low rolling resistance car tire

Coefficient of Rolling FrictionTire Type

Power consumption• Car weighs: 4,000 pounds (1814.369 kg• Tire CRF: 0.015.

– The force is equal to 4,000 x 0.015, which equals 60 pounds (27.215 kg).

• How much power will be consumed?– Power = force x speed. – The amount of power used by the tires depends on how fast the

car is going. – At 75 mph (120.7 kph), the tires are using 12 horsepower, and at

55 mph (88.513 kph) they use 8.8 horsepower. (1 hp = 33000 lb-ft/min=745.7W, 1 mile = 1760 yd.)

• All of that power is turning into heat. Most of it goes into the tires, but some of it goes into the road (the road actually bends a little when the car drives over it).

A properly inflated tire and an underinflated or overloaded tire

Problems With Tires• Underinflation can cause tires to wear more on the

outside than the inside. It also causes reduced fuel efficiency and increased heat buildup in the tires. It is important to check the tire pressure with a gauge at least once a month.

• Overinflation– causes tires to wear more in the center of the tread. The tire

pressure should never exceed the maximum that is listed on the side of the tire.

– Car manufacturers often suggest a lower pressure than the maximum because the tires will give a softer ride. But running the tires at a higher pressure will improve mileage.

• Misalignment– causes either the inside or the outside to wear unevenly, or to

have a rough, slightly torn appearance.

The wear patterns of an underinflated, properly inflated and overinflated tire

How Tires Support a CarHow a car tire with 30 pounds per square inch (psi) of pressure can support a car.This flat spot is called the contact patch, as illustrated below.

A tire showing the side and bottom of the contact patch

Quiz

• 一輛 Ford Mondeo, 車重 1800公斤, 使用P195/60 R15 輪胎, 胎壓若皆為 30psi, 試問若胎寬不變且四輪所受重力相等時, 輪胎的contact patch 之長度 l 為何?1800 / 0.454 = 3964.76 lbArea of contact patch = (195/25.4) x l 3964.76 = 4 x 30 x [(195/25.4)x l ]l = 4.3 in

另解

30 psi = 30/14.2 kgf/cm2= 2.11 kgf/cm2

Area of contact patch = 195 x l mm2

1800 = 4 x 2.11 x [(195x l )x10-2]l = 109.37 mm

Elevation drop of tire center

• a = length of contact patch / 2 = l /2

• c = tire diameter / 2• b = √(c2-a2)• Offset of tire center

= c - babc

l

• Tire outside diameter 15x25.4 + 2x(195x0.6) =615 mmLength of contact patch = 4.3 x 25.4 = 109.22 mm

• Offset of tire center = 2 2615 615 109.22 307.5 302.61 4.89

2 2 2mm⎛ ⎞ ⎛ ⎞− − = − =⎜ ⎟ ⎜ ⎟

⎝ ⎠ ⎝ ⎠

Why don't they use normal air in race car tires?

• Nitrogen has a much more consistent rate of expansion and contraction compared to the usual air

• Air typically contains varying amounts of water vapor due to changes in the relative humidity on race day. Water causes the usual air to be inconsistent in its rate of expansion and contraction Air density = 1.2kg/m3; specific heat = 1.4 kJ/kg℃Nitrogen density = 1.25 kg/m3 ; specific heat = 1.04 kJ/kg℃

Why do we need self-inflating tires • Lots of consumer vehicles are equipped with a tire-

pressure monitoring system.• About 80 percent of the cars on the road are driving with

one or more tires underinflated. • Because tires are flexible, they flatten at the bottom

when they roll. This contact patch rebounds to its original shape once it is no longer in contact with the ground. This rebound creates a wave of motion along with some friction. When there is less air in the tire, that wave is larger and the friction created is greater -- and friction creates heat. If enough heat is generated, the rubber that holds the tire's cords together begin to melt and the tire fails.

New type tyres

Michelin Tweel

Slip

• Two distinct tire slip– Transverse

• “Slip angle”• Affects the generation of the tire’s cornering forces.

– Longitudinal • “Slip ratio” or “percentage slip”• Affects acceleration and braking

Slip Angle 側滑角• Definition

– The angular displacement between the plane of rotation of the wheel (the direction in which the rim is pointing) and the path that the rolling tire will follow on the road surface.

– The angular difference between the direction the contact is pointing and that of the wheel itself is called its slip angle.

• It is not uncommon for this slip angle to be as large as 6 to 10 degrees on the race track.

The relationship between slip angle, coefficient of friction and cornering force

• Coefficient of friction varies with slip angle• Cornering force varies with slip angle• The coefficient – and the cornering force –

increases with increasing slip angle until, at some given slip angle, it reaches its maximum value.

Tire temperature

• Most road racing car are designed to produce maximum traction with tread temperatures between 190 and 220 degrees Fahrenheit.

• Rain tires, with softer compounds, reach their maximums at 140 to 160 degrees.

•

Weight : 23.25 lbs Weight : 17.25 lbs Weight : 33 lbs Weight : 33.25 lbs

Size : 17*7 Size : 15*6.5 Size : 18*8.5 Size : 19*8.5

Model : 500 SS Model : RS6 Model : Design 2/5 Model : Design 1/6 Evo

Manufacturer : Fittipaldi Design

Manufacturer : Enkei

Manufacturer : Carlsson

Manufacturer : Carlsson

Spade (Silver)Very popular...We all know.

Silver425x100/114.318x7.5A9975810H42S

Silver424x100/114.318x7.5A997588H42S

Silver405x100/114.317x7A997710H40S

Silver404x100/114.317x7A99778H40S

FinishOffsetPCDSizePart #

a. 外徑b. 寬度c. 胎唇座d. 凸起e. 凸緣形狀f. 總寬g. 螺絲孔徑h. 螺絲孔中心直徑i. 輪軸孔直徑j. 才部座k. 輪胎組裝後中心l. 氣門嘴孔m. 輪胎中心與輪圈才部座距離（offset）

輪圈 Wheel

Offset• The offset of a wheel is the distance from the

mounting surface of the wheel to the true centerline of the rim.

• A positive offset means the mounting surface of the wheel is positioned in front of the true centerline of the rim / tire assembly. This in effect brings the tire in to the fender well more.

• A negative offset means the mounting surface of the wheel is behind the true centerline of the rim / tire assembly. This will cause the tire to stick out away from the vehicle.

Wheel Offset Calculation • Current Wheel Specs

– Width 7 inches; Offset 45 mm• New Wheel Specs

– Width 8 inches; Offset mm• Inner Clearance:

– (the inside of the wheel to the strut housing)

• Outer Position:– (position of the outside edge of the wheel)

32

- The same

– EXTEND an extra 26mm

Bolt Patterns• Each wheel has a different bolt pattern, and some wheels even have

2 different bolt patterns which allow it to be mounted on a wider range of vehicles.

Most Bolt Patterns are represented in the following manner:4/100

• The "4" indicates the number of holes in the wheel for the bolts to enter and mount the wheel onto the car.

• The "100" indicates the diameter of the bolt circle measured in millimeters or inches. – 4 & 6 bolt wheels are measured from the center of one bolt hole to the

center of the bolt hole directly across from it. – On a 5 bolt pattern, it is a bit trickier to measure without special tools.

Imagine a circle running through the centers of each bolt hole. You would measure from the center of one bolt hole to the imaginary circle that lays between the opposite two bolt holes.

Plus Sizing• Plus sizing your wheel & tire combination was designed to enhance

vehicle performance and looks by allowing fitment of larger diameter rims and lower profile tires.

• Keep the overall tire diameter within 3% of the original equipment tires. Because larger variances can cause problems with transmission shift points which can decrease fuel mileage. It can also confuse braking system computers which can even lead to brake failure.

• Here's the rule of thumb for "plus sizing": – Plus 1:

Increase section width by 10mmDecrease aspect ratio by 10 pointsIncrease rim diameter by 1 inch

Plus 2:Increase section width by 20mmDecrease aspect ratio by 20 pointsIncrease rim diameter by 2 inches.

Diameter Difference: 2.08%Diameter Difference: -

Speedometer Difference: 2.120% too slowSpeedometer Difference: -

Tire 1 - 215/50R20 >Search TiresStock Tire - 205/55R19 >Search Tires

205 mm8.07 inSection Width: 215 mm8.46 inSection Width:

482.6 mm19 inRim Diameter: 508 mm20 inRim Diameter:

Unrecognized tire size.Rim Width Range: Unrecognized tire size.Rim Width Range:

707.89 mm27.87 inOverall Diameter: 722.88 mm28.46 inOverall Diameter:

112.52 mm4.43 inSidewall Height: 107.44 mm4.23 inSidewall Height:

353.82 mm13.93 inRadius: 361.44 mm14.23 inRadius:

2223.7 mm87.55 inCircumference: 2270.7 mm89.40 inCircumference:

746.3Revs per Mile: 730.8Revs per Mile:

100 km/h60 mphActual Speed: 97.9 km/h58.7 mphSpeedometer1: