eita giovanna

H. TYRES

Release 8.1 / 2012

INDEX

TYRES ............................................................................................................ 3 1. SAFETY NOTICE ....................................................................................... 4 1.1. Recommendations ................................................................................ 4 1.2. Valves ................................................................................................ 4 1.3. Tyre assembly and disassembly.............................................................. 4 1.4. Tyre regrooving ................................................................................... 5 1.5. Storage and Carriage ............................................................................ 5 1.6. Tyre aging ........................................................................................... 5 1.7. Monitoring and maintenance .................................................................. 5 1.8. Terms of use ....................................................................................... 6 2. RECOMMENDATIONS OF USE ................................................................... 6 2.1. Front Slick tyre .................................................................................... 6 2.2. Rear Slick tyre ..................................................................................... 6 2.3. Front Wet tyre ..................................................................................... 7 2.4. Rear Wet Tyre...................................................................................... 7 3. PROFILE MEASURMENT ........................................................................... 8 3.1. Front tyre ............................................................................................ 8 3.2. Rear tyre............................................................................................. 9 4. DEFLECTION AND DEFORMATION .......................................................... 10 4.1. Front tyre .......................................................................................... 10 4.2. Rear Tyre .......................................................................................... 15 5. TYRE MATHEMATICAL MODEL ................................................................ 20 5.1. Introduction ...................................................................................... 20 5.2. Front tyre graphics ............................................................................. 22 5.3. Rear tyre graphics .............................................................................. 30 5.3. Front tyre Pacejka coefficient ............................................................... 38 5.4. Rear tyre Pacejka model...................................................................... 39

H-2

Release 8.1 / 2012

TYRES

H-3

Release 8.1 / 2012

1. SAFETY NOTICE We recommend to all users to read the “safety guidelines” below. After a run, the delta of temperature between the inside shoulder and the outside shoulder has to be less than 20°C. Exceeding of some of these data levels (f.e. camber) may cause a tyre damage or a fall of performances : • higher tyre wear, • influence concerning balance problems (oversteer/understeer), • lap times will finally also drop (less constant). One stint is equivalent to the mileage indicated (including a maximum of 2 pit stops and/or driving under pace car). At this mileage and this speed limit, the integrity of the construction is guaranteed for endurance but not for wear potential or grip potential. Therefore, depending on the conditions of use, a tyre : • Could be worn before achieving the indicated mileage, • Could be only partially worn even though the indicated mileage has been achieved. In this case, the integrity of the construction cannot be guaranteed, the tyre must be replaced. These recommendations are valid unless the tyres have been damaged: for example puncture or flat spots. The recommendations regarding rain tyres are only for wet conditions and not intended for a drying racetrack. For any use apart from the defined recommendations, please contact Circuit Michelin technical department. Phone : +33(0)4 73 30 44 73.

1.1. Recommendations Before-use checklist • Make sure that all Tyres on the same axle are of the same type (brand, commercial name or industrial reference, dimensions, structure). Prior to mounting make sure that: • The rim is in good condition and does not present wear-and-tear (cracks, deformation, etc.) and the valves are in proper condition and if not, have them replaced. • The Tyres have not been repaired and the valves are in proper condition and if not, have them replaced.

1.2. Valves Routinely screw down the valve cap It protects the valve mechanism and ensures the complete sealing of the Tyre assembly. Make sure that the valve is in good condition (no ovalization, no impact trace, etc.). Regularly check torque settings of screwed-in valves.

1.3. Tyre assembly and disassembly Tyre assembly, disassembly, topping and balancing must be done on suitable goodcondition equipment entrusted with qualified and trained personnel that would ensure, H-4

Release 8.1 / 2012 among other things: • Compliance with the manufacturer and legal rules in the selection of Tyres. • Preliminary examination of the outside and inside aspect of the Tyre by the installer. • Compliance with Tyre assembly, disassembly, balancing and toping procedures. • Proper positioning of the Tyre on the vehicle (left, right, front, rear). • Proper working pressure.

1.4. Tyre regrooving Regrooving tyres is strictly forbidden.

1.5. Storage and Carriage In order to preserve the performance of Tyres, there are some important rules to be observed during the storage and the freight like : • Minimum temperature of freight and storage: 0°C • Direct and prolonged exposure to sunlight, sources of high heat (extended storage in container) and humidity. • Long-term storage in stacks. • The presence of solvents, lubricants, fuel and other chemical products. • Equipment causing ozone emission (transformers, welding units, electric motors, etc.). • The storage space must be dry, well-ventilated, without direct light and reserved for Tyres. Racks suitable for storing Tyres vertically should be used to avoid exercising pressure on the carcasses.

1.6. Tyre aging Tyres age even when not used or if they are only used occasionally; excessive aging of Tyres may lead to loss of grip. Remove from usage Tyres presenting clear signs of aging or fatigue (cracking of the rubber of the outer tread, of the shoulder, of the bead side, deformation, etc.). When in doubt, contact a Tyre professional.

1.7. Monitoring and maintenance Check Tyre pressure prior to any run and adjust pressure if it does not correspond to the recommended working pressure. Tyre pressure must be checked they are cold (the Tyres have not been driven, they have not been warmed) Inflating Tyres with nitrogen does not exempt you from having to check Tyre pressure routinely. In case of unusual loss of pressure, check the outside and inside condition of the Tyre as well as the condition of the wheel and of the valve. Any visible perforation, cut or deformation must be checked in-depth by a Tyre professional. Never use damaged Tyres or Tyres that have run flat without the help of a professional.

H-5

Release 8.1 / 2012

1.8. Terms of use • • •

•

Never treat the rubber of the outer tread chemically. Never use Tyres with unknown past. Make sure that the pressure, camber angle, speed and axle load values are those recommended by Michelin for the intended use (check recommendations depending on use). Standard terms of use are available at www.michelinsport.com or contact Circuit Michelin technical department phone : +33(0)4 73 30 44 73.

2. RECOMMENDATIONS OF USE 2.1. Front Slick tyre

2.2. Rear Slick tyre

H-6

Release 8.1 / 2012

2.3. Front Wet tyre

2.4. Rear Wet Tyre

H-7

Release 8.1 / 2012

3. PROFILE MEASURMENT 3.1. Front tyre Dimensions: Rim: Pressure: Weight:

26/64-13 12J13 1,5 bar 9,870 kg

H-8

Release 8.1 / 2012

3.2. Rear tyre Dimensions: Rim: Pressure: Weight:

32/66-13 13,7J13 1,5 bar 11,625 kg

H-9

Release 8.1 / 2012

4. DEFLECTION AND DEFORMATION 4.1. Front tyre

H-10

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H-11

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H-12

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H-13

Release 8.1 / 2012

H-14

Release 8.1 / 2012

4.2. Rear Tyre

H-15

Release 8.1 / 2012

H-16

Release 8.1 / 2012

H-17

Release 8.1 / 2012

H-18

Release 8.1 / 2012

H-19

Release 8.1 / 2012

5. TYRE MATHEMATICAL MODEL 5.1. Introduction

H-20

Release 8.1 / 2012

H-21

Release 8.1 / 2012

5.2. Front tyre graphics 1000 CORNERING FORCE daN

26/64-13 Camber: 0 degrees Pressure: 1,5 bar Speed: 100 kph

800

600

400

200

SLIP ANGLE

0 -8,0

-6,0

-4,0

-2,0

0,0

2,0

4,0

6,0

-200

LOAD (daN) -400

300

375

450

525

-600

600 -800

-1000

H-22

8,0

Release 8.1 / 2012

1200

26/64-13 Camber: -4 degrees Pressure: 1,5 bar Speed: 100 kph

2011

CORNERING FORCE daN

1000

800

600

400

200

SLIP ANGLE

0 -8,0

-6,0

-4,0

-2,0

0,0

2,0

4,0

6,0

-200

LOAD (daN) 300

375

450

525

-400

-600

-800

-1000

H-23

600

8,0

Release 8.1 / 2012

800,0

26/64-13 Camber: 0 degrees Pressure: 1,5 bar Speed:100 kph

SELF ALIGNING TORQUE m.N 600,0

400,0

200,0

SLIP ANGLE 0,0 -8,0 -7,0 -6,0 -5,0 -4,0 -3,0 -2,0 -1,0 0,0 1,0 2,0 3,0 4,0 5,0 6,0 7,0 8,0

-200,0

LOAD (daN) 300

375

450

525

600

-400,0

-600,0

-800,0

H-24

Release 8.1 / 2012

1000

26/64-13 Camber: 0 degrees 900 Pressure: 1,5bar Speed: 100 kph 800 CORNERING FORCE daN

700

600

500

400

300

Slip Angle (degrees)

200

1

2,25 3,5

100

4,75 6 0 0

100

200

300 Load (daN)

H-25

400

500

600

700

Release 8.1 / 2012

1200

26/64-13 Camber: -4 degrees Pressure: 1,5 bar Speed:100 kph

1000

CORNERING FORCE daN 800

600

400

Slip Angle (degrees) 1

200

2,25 3,5 4,75 6

0 0

100

200

300 Load (daN)

H-26

400

500

600

700

Release 8.1 / 2012

100,0

26/64-13 Camber: 0 degrees Pressure: 1,5bar 0,0 kph Speed: 0 100 100 200

300

400

(daN) 500 Load600

700

-100,0

-200,0

-300,0

SELF ALIGNING TORQUE m.N

-400,0

-500,0

Slip Angle (degrees) 1

2,25 3,5

-600,0

4,75 6 -700,0

H-27

Release 8.1 / 2012

300

26/64-13 Camber: 0 degrees Pressure:1,5 bar Speed:100 kph

250

Cornering Stiffness daN/deg 200

150

100

50

Load (daN) 0 0

100

Slip Angle (degrees)

200

300

1

400

2,25

H-28

500

3,5

600

700

Release 8.1 / 2012

300

26/64-13 Camber: -4 degrees Pressure:1,5 bar Speed: 100 kph

250

Cornering Stiffness daN/deg 200

150

100

50

0 0

100

Slip Angle (degrees)

200

300

1

400

Load (daN)

2,25

H-29

3,5

500

4,75

600

6

700

Release 8.1 / 2012

5.3. Rear tyre graphics 1500 CORNERING FORCE daN

32/66-13 Camber: 0 degrees Pressure: 1,5 bar Speed: 100 kph

1000

500

SLIP ANGLE

0 -8,0

-6,0

-4,0

-2,0

0,0

-500

-1000

-1500

H-30

2,0

4,0

6,0

LOAD (daN) 300

375

450

525

600

8,0

Release 8.1 / 2012

1500 CORNERING FORCE daN

32/66-13 Camber: -4 degrees Pressure: 1,5 bar Speed: 100 kph 1000

500 SLIP ANGLE

0 -8,0

-6,0

-4,0

-2,0

0,0

2,0

4,0

6,0

LOAD (daN)

-500

-1000

H-31

300

375

450

525

600

8,0

Release 8.1 / 2012

800,0 SELF ALIGNING TORQUE m.N

32/66-13 Camber: 0 degrees Pressure: 1,5bar Speed: 100 kph

600,0

400,0

200,0

SLIP ANGLE 0,0 -8,0 -7,0 -6,0 -5,0 -4,0 -3,0 -2,0 -1,0 0,0 1,0 2,0 3,0 4,0 5,0 6,0 7,0 8,0

-200,0

LOAD (daN) 300

375 -400,0

450

525

600 -600,0

-800,0

H-32

Release 8.1 / 2012

1000

32/66-13 Camber:0 degrees 900 Pressure:1,5 bar Speed:100 kph 800

CORNERING FORCE daN

700

600

500

400

300

Slip Angle (degrees)

200

1

2,25 3,5

100

4,75 6 0 0

100

200

300

400

Load (daN)

H-33

500

600

700

Release 8.1 / 2012

1200

32/66-13 Camber: -4 degrees Pressure: 1,5bar Speed:100 kph

1000

CORNERING FORCE daN 800

600

400

Slip Angle (degrees) 1

200

2,25 3,5 4,75 6

0 0

100

200

300 Load (daN)

H-34

400

500

600

700

Release 8.1 / 2012

0,0 0

100

200

300

32/66-13 Camber: 0 degrees Pressure: 1,5bar -100,0 Speed:100 kph

-200,0

400

500

600

700

Load (daN)

SELF ALIGNING TORQUE m.N

-300,0

-400,0

-500,0

Slip Angle (degrees) 1

2,25 -600,0

3,5 4,75 6

-700,0

H-35

Release 8.1 / 2012

350

32/66-13 Camber: 0 degrees Pressure:1,5 bar Speed:100 kph

300

Cornering Stiffness daN/deg 250

200

150

100

50

Load (daN) 0 0

100

Slip Angle (degrees)

200

300

1

400

2,25

H-36

500

3,5

600

700

Release 8.1 / 2012 300

32/66-13 Camber: -4 degrees Pressure:1,5 bar Speed:100 kph

250

Cornering Stiffness daN/deg

200

150

100

50

0

0

100

Slip Angle (degrees)

200

300 400 Load (daN)

1

2,25

H-37

500

3,5

600

700

Release 8.1 / 2012

5.3. Front tyre Pacejka coefficient Dimension 26/64-13 Formulation : MF5.2 Coefficients D(Z) & G(Z): Coefficient

Pky10 Pky11 Pky20 Pky21

D(Z) Value -23,5211 -16,4543 -0,5475 1,4382

Coefficient

Qdz10 Qdz11 Qdz20 Qdz21

G(Z) Value 0,2860 -0,1003 0,0304 -0,0150

Coefficients Fy0 & Mz0:

Coefficient

Pcy1 Pdy1 Pdy2 Pdy3 Pey1 Pey2 Pey3 Pey4 Pky1 Pky2 Pky3 Phy1 Phy2 Phy3 Pvy1 Pvy2 Pvy3 Pvy4

Modelisation Fy0 P=1.30 P=1.50 1,0000 1,0000 1,8717 1,7712 -0,5521 -0,4074 0,1000 0,1000 -0,4839 -0,6364 -1,7890 -1,9706 0,0414 -0,0019 -4,0493 -1,4293 -44,9116 -48,2025 1,3221 1,6098 0,2427 4,5480 -0,0013 -0,0022 0,0014 0,0017 0,0459 0,1517 -0,0249 -0,0523 0,0465 0,0673 -1,2911 0,9834 -1,6690 -2,7501

P=1.70 1,0000 1,7055 -0,3150 0,1000 -0,5328 -1,8496 -0,0013 -1,2890 -51,4933 1,8974 4,8489 -0,0029 0,0022 0,1757 -0,0764 0,0872 1,6279 -2,6949

Coefficient

Qbz1 Qbz2 Qbz3 Qbz4 Qbz5 Qbz9 Qbz10 Qcz1 Qdz1 Qdz2 Qdz3 Qdz4 Qdz6 Qdz7 Qdz8 Qdz9 Qez1 Qez2 Qez3 Qez4 Qez5 Qhz1 Qhz2 Qhz3 Qhz4

Modelisation Mz0 P=1.30 P=1.50 5,9591 4,1715 -8,3889 1,1969 7,9424 -1,3337 7,0193 0,0123 12,4708 5,6498 7,2924 6,2298 0,0000 0,0000 1,1156 3,0669 0,1557 0,1356 0,0108 0,0078 -1,8599 -5,5951 -57,8305 -59,4210 -0,0173 -0,0173 0,0008 -0,0010 -0,9872 -0,8725 -0,4438 -0,8600 -1,4992 0,0574 -4,5210 0,0896 -3,3295 -0,6546 50,3707 23,1364 -227,6028 395,1045 0,0097 0,0075 -0,0008 -0,0266 0,2549 0,2028 -0,1527 -0,2498

P=1.70 3,7834 0,2340 -0,6447 0,0114 2,0084 0,3505 0,0000 2,7248 0,1155 0,0048 -8,7048 -60,7722 -0,0157 0,0017 -0,7614 -0,8314 0,0315 -0,8568 -1,2126 14,8343 179,2389 0,0222 -0,0376 -0,1339 -0,6327

Coefficients Mx & Reff: Modelisation Mx Coefficient Qsx1 Qsx2 Qsx3

P=1.30 -0,4681 1,2977 0,0148

P=1.50 -0,4584 1,3556 0,0091

Modélisation Reff P=1.70 -0,4539 1,4968 0,0054

Coefficient B Cz D F

P=1.30 30,1108 210372,2416 0,2989 0,1215

Cz = Vertical stiffness (N/m)

H-38

P=1.50 24,3592 236541,6313 0,3425 0,1118

P=1.70 40,7193 261299,0161 0,3462 0,1457

Release 8.1 / 2012

5.4. Rear tyre Pacejka model Dimension 32/66-13 Formulation : MF5.2 Coefficients D(Z) et G(Z): Coefficient

Pky10 Pky11 Pky20 Pky21

D(Z) Value -31,0161 -17,7096 -0,4539 1,4822

Coefficient

Qdz10 Qdz11 Qdz20 Qdz21

G(Z) Value 0,2662 -0,0938 0,0530 -0,0246

Coefficients Fy0 & Mz0:

Coefficient

Pcy1 Pdy1 Pdy2 Pdy3 Pey1 Pey2 Pey3 Pey4 Pky1 Pky2 Pky3 Phy1 Phy2 Phy3 Pvy1 Pvy2 Pvy3 Pvy4

Modelisation Fy0 P=1.30 P=1.50 1,0000 1,0000 2,0281 1,8544 -0,6321 -0,3063 0,1000 0,1000 -0,1465 -0,3072 -1,1931 -1,5188 -0,0016 -0,0021 9,1923 1,5465 -54,0385 -57,5805 1,4729 1,7694 0,2132 5,2422 -0,0016 -0,0023 0,0010 0,0010 0,0317 0,1629 -0,0382 -0,0619 0,0445 0,0422 -1,7374 1,5101 -1,8594 -3,1906

P=1.70 1,0000 1,6565 -0,0438 0,1000 -0,2456 -1,4755 -0,0023 0,2014 -61,1224 2,0658 5,5850 -0,0029 0,0025 0,2135 -0,0793 0,0882 2,6556 -3,0803

Coefficient

Qbz1 Qbz2 Qbz3 Qbz4 Qbz5 Qbz9 Qbz10 Qcz1 Qdz1 Qdz2 Qdz3 Qdz4 Qdz6 Qdz7 Qdz8 Qdz9 Qez1 Qez2 Qez3 Qez4 Qez5 Qhz1 Qhz2 Qhz3 Qhz4

Modelisation Mz0 P=1.30 P=1.50 8,1433 8,3410 -9,0124 1,4002 6,7204 -10,1225 -0,0065 -0,0009 4,1527 6,0038 -10,3179 -5,0957 0,0000 0,0000 1,1065 1,6250 0,1443 0,1255 0,0211 0,0161 -5,3373 -2,1979 -133,1042 29,2378 -0,0100 -0,0119 -0,0053 0,0018 -0,9340 -1,2637 -0,5575 -1,0200 0,2448 0,0068 0,7453 -0,1264 0,5313 0,6360 -98,0406 -127,7246 12,5091 -930,2113 0,0121 0,0125 0,0079 -0,0008 0,0847 0,1660 0,1688 -0,1105

P=1.70 9,6125 1,1367 -10,5111 -0,0003 -3,1066 8,6430 0,0000 1,5895 0,1067 0,0112 0,3141 249,7538 -0,0123 0,0021 -1,4015 -1,4455 -0,0122 0,0124 0,2731 -128,1802 -604,8304 0,0066 0,0012 -1,0093 0,2223

Coefficients Mx & Reff: Modelisation Mx Coefficient Qsx1 Qsx2 Qsx3

P=1.30 -0,4703 1,7357 -0,0042

P=1.50 -0,4567 1,8487 -0,0087

Modelisation Reff P=1.70 -0,4433 1,9676 -0,0119

Coefficient B Cz D F

H-39

P=1.30 73,0921 215051,9007 0,2938 0,0995

P=1.50 70,8657 241781,8399 0,3291 0,1096

P=1.70 54,0922 267355,6577 0,3557 0,1146

Release 8.1 / 2012 Transitory Coefficients Coefficient

Kz Pty1 Pty2 Qtz1 Mbelt

P=1.30 500,0000 1,6232 1,4739 0,0000 0,0000

H-40

P=1.50 500,0000 1,7606 1,7694 0,0000 0,0000

P=1.70 500,0000 1,9225 2,0649 0,0000 0,0000