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Numerical

Formulas and

Tables

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Table of Contents

Mathematical formulas………………………………………………………………….International System of Units (SI)……………………….................…….................Formulas of Dynamics……………………………………………..................…….....Table for Weight of Steel Bar………………………………………....……................List of Elements by Symbol and Specific Gravity………………………...............

Hardness Comparison Table......................................................................................Comparative Table of Gear Pitch...............................................................................Span Measurement Over k Teeth of Standard Spur Gear = 20° ...........................Span Measurement Over k Teeth of Standard Spur Gear = 14.5° ..........................Charts Indicating Span Measurement Over k Teeth of Spur and Helical Gears ..................Involute Function Table…………………………..............................…….................

34689

TABLE OF NUMBERS

NUMERICAL EXPRESSION, UNIT AND OTHER DATA

101112141617

56

3

Numerical Formulas and Tables

NUMERICAL EXPRESSION, UNIT AND OTHER DATA

Function y = f ( x ) and derivative y' = f ' ( x ) Trigonometric functions sin, cos, tan

cos θ = , sin θ = , tan θ =

sin2 θ + cos2 θ = 1, tan θ =

sin ( α ± β ) = sin α cos β ± cos α sin βcos ( α ± β ) = cos α cos β ± sin α sin β

The relationship between rectangular coordinates

(x, y)and polar coordinates (r, θ)

x = rcosθ , y = rsinθ ,

tan θ =

r 2 = x 2 + y 2

The equation for the straight line which passes the point (a, b), with an inclination m

( y − b ) = m ( x − a )

The equation for the circle, the center of which is the point (a, b) , with the radius r

( x − a ) 2 + ( y − b ) 2 = r 2

The root of the quadratic equation

y = ax 2 + bx + c = 0 (a 0)

x =

Function y = f ( x ) and derivative y' = f ' ( x )

1 Mathematical formulas

y = f ( x )

cos x

sin x

tan x

tan x − x NOTE 1.

y' = f ' ( x )

− sin x

cos x

tan2 x

y = f ( x )

sin2 x

sin3 x

y' = f ' ( x )

2 sin x cos x

3 sin2 x cos xNOTE 1. Involute function

An example of the application of the derivativeNewton's law

Introduced here is the method to obtain an approximate value of x 0 when the value of f (x0) is given in the involute function

f ( x ) = tan x − x

First, with an initial value x1

optionally chosen, obtain an approximate value x2 from:

x2 = x1 −

where f ' ( x1 ) = tan2 x1

Then, when the difference between the approximate value f ( x2 ) and the given f ( x0 ) is large, obtain an approximate value x3 using the same method.

x3 = x2 −

The more accurate value of x0 can be obtained by the repeated calculation using this method. The involute function, inv α, is frequently used in the calculation of gearing. Therefore, the Newton's law is really useful.

rx

ry

xy

cos θsin θ

xy

2a− b ± √ b2 − 4ac

tan2 x1

f ( x1 ) − f ( x0 )

tan2 x2

f ( x2 ) − f ( x0 )

cos2 x1

cos x1

sin x1

tan x1

cos xtan x

sin x tan x1

−

sin2 x1

−

x

yr

θ

x

y

rθ

P( x , y )

x

y

P( a , b )

x

y

P( a , b )

r

x

y

x1

y = f (x)

y

x

x

y

x0

x2 x10

f (x1)

f (x2)f (x0)

x2

f (x)

4


square metrecubic metremetre per secondmetre per second squaredreciprocal metrekilogram per cubic metreampere per square metreampere per metremole per cubic metrecubic metre per kilogramcandela per square metre

SI supplementary unitQuantum

Physical quantum

2 International System of Units (SI)

SI Base unit

Definition of SI base unit

Length

Mass

Time

Current

Temperature

Amount of substance

Luminous intensity

Base unit

Standard International unit

meter

kilogram

second

ampere

kelvin

mole

candela

Definition

The length equal to the length of the path traveled by light in vacuum during a time interval of 1/299,792,458 of a second.

The mass equal to the mass of the international prototype kilogram stored at Sèvres, France.

The fundamental unit of time equal to 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of an atom of cesium-133.

One coulomb of electrical charge (6.24 x 1018 charge carriers) moving past a specific point in one second.

A unit of absolute temperature equal to 1/273.16 of the absolute temperature of the triple point of water.

An mount of substance of a system which contains as many elementary units as there are atoms of carbon in 0.012 kilogram of the pure nuclide carbon-12.

The magnitude of an electromagnetic field, in a specified direction, that has a power level of 1/683 watt (1.46 x 10-3 W) per steradian at a frequency of 540 terahertz (540 THz or 5.40 x 1014 Hz).

SI supplementary unit

Angle

Solid angle

Name

radian

steradian

Symbol

rad

sr

Definition

The angle subtended at the center of a circle by an arc of circumference equal in length to the radius of the circle. The solid angle subtended at the center of a sphere of radius r by a portion of the surface of the sphere having an area r2.

SI derived unit

Quantum

AreaVolumeSpeedAccelerationWavenumberMass densityElectric current densityMagnetic field strengthAmount concentrationSpecific volumeLuminance

SI derived unit

Name Symbol

m2

m3

m/sm/s2

m-1

kg/m3

A/m2

A/mmol/m3

m3/kgcd/m2

5


1kW = 1.01972×10 2 kgf m/s1kgf m/s = 9.80665×10 − 3 kW

Prefix

Prefix (Symbol)

yotta (Y)

zetta (Z)

exa (E)

peta (P)

tera (T)

giga (G)

mega (M)

kilo (k)

hecto (h)

deca (da)

Factor

1024

1021

1018

1015

1012

1092

1062

1032

1022

1012

Prefix (Symbol)

desi (d)

centi (c)

milli (m)

micro (n)

nano (n)

pico (p)

femto (f)

atto (a)

zepto (z)

yocto (y)

Factor

10 − 10

10 − 20

10 − 30

10 − 60

10 − 90

10 − 12

10 − 15

10 − 18

10 − 21

10 − 24

Conversion factors for SI (International System of Units)

Name

Force

Stress

WorkEnergy

WorkPower

Equivalents

1N = 1.01972×10 − 1 kgf

1kgf = 9.80665N

1MPa or N/mm2 = 1.01972×10 − 1 kgf/mm2

1kgf/mm2 = 9.80665MPa or N/mm2

1J = 2.77778×10 − 7 kW h = 1.01972×10 − 1 kgf m

1kgf m = 9.80665J, 1kW h = 3.600×106 J

Newton: The unit of force in the meter-kilogram-second system, equal to the force which will impart an acceleration of 1 meter per second squared to the International Prototype kilogram mass.Kilogram force: A unit of force equal to the weight of a 1-kilogram mass at a point on the earth's surface where the acceleration of gravity is 9.80665 m/s22.

6


ω = = 2π n

Denomination

Denomination

Force

Moment of force (Torque)

Power (Dynamics)

Symbol and/or

formula

F

T = F r

P = FvLinear motion

P = TωRotational

motion

SI Conversion factors

1 kgf = 9.80665 N

1 kgf m = 9.80665 N m

When power is P ( kW ), force is F ( kgf ), velocity is v ( m/s ),

P = Fv ( kgf m /s) = 9.80665 Fv (W) = (kW)

When power is P ( kW ), torque is T ( kgf m ), rotational speed is n ( rpm ), P = Tω ( kgf m/s ) = 9.80665 T (W) = (kW)

Gravitational system of units

N (newton)

kgf

N m

kgf m

W

kgf m/s

W

kgf m/s

3 Formulas of Dynamics

Force, torque and dynamics

NOTE 1. Unit of dynamics 1W = 1 × 10−3 kW = 1J/S = 1N m/s

Comparison between linear and rotational motion

Displacement and angular displacementVelocity and angular velocityAcceleration and angular acceleration

Equation of motion

Work

Kinetic energy

Power(dynamics)

Linear motion

Symbol and/or formula

S

v =

α =

F = mα

E = Fs

E = mv2

P = Fv

Unit

m

m/s

m/s2

N

J

J

W

Rotational motion

Symbol and/or formula

θ

ω =

T = Iω

E = Tθ

E = Iω2

P = Tω

Unit

rad

rad/s

or 1/s

rad/s2

or 1/s2

kg m2/s2

or N m

J

J

W

NOTES 1. Radian (rad), the unit of plane angle θ, is dimesionless.

2. The unit of time( t) is second (s). 3. The unit of rotational speed (n) is 1/s (rps:

revolution per second) 4. The unit of mass(m) is kg.

5. 1N (newton) = 1kg m/s2

1N (newton) is the force which will impart an acceleration of 1 meter per second (1m/s2) squared to the International Prototype Kilogram mass (1kg).

6. The unit of "moment of inertia I = mk2" is kg m2. 7. The unit of work and kinetic energy is the same. 1J = 1N m

102Fv

30πn

974Tn

.

.

dtdS

dtdv

21

dtdω

dtdθ

21

NOTE 2 NOTE 3

NOTE 1

NOTE 6NOTE 5NOTE 4

NOTE 7

7


Gravitational system of units kgf ms2

Denomination

Moment of inertia mk2 (kg m2) or k2 (kgf ms2)

Mass point

Pole

Plate

Cylinder

Hollow cylinder

Shape Rotation axis

y — y

y 1 — y 1

y 2 — y 2

y — y

z — z

y — y

z — z

y — y

Moment of inertia Unit

SI kg m2

mr 2

m

m

m

m

m

m

m

r 2

NOTE 1. m : Mass W : Weight g : Acceleration of gravity = 9.80665m/s2

NOTE 2. GD2 = 4gI (kgf m2)

12l 2

3l 2

12a2 + b2

12a2

2r 2

4r 2

2r 1

2 + r 22

gW

gW

12l 2

gW

3l 2

gW

12a2 + b2

12a2

gW

2r 2

gW

4r 2

gW

2r 1

2 + r 22

gW

gW

y

y

r

y

yr1

r2

y

y

r

z

z

y

y

b

az

z

y2 y1

y2 y12l

2l

8


0.101.213.557.12

11.93

17.9625.2333.7343.4754.43

66.6380.0694.72

110.61127.73

146.09165.68186.50208.55231.84

256.36282.10309.08337.30366.74

397.42429.33462.47496.84532.45

569.28607.35646.65687.19728.95

771.95816.18861.64908.33956.25

1005.411055.801107.421160.271214.36

1269.671326.221384.001443.021503.26

1564.74

0.000.622.465.549.86

15.4022.1830.1839.4249.90

61.6074.5488.70

104.10120.74

138.60157.70178.02199.58222.38

246.40271.66298.14325.86354.82

385.00416.42449.06482.94518.06

554.40591.98630.78670.82712.10

754.60798.34843.30889.50936.94

985.601035.501086.621138.981192.58

1247.401303.461360.741419.261479.02

1540.00

Section

Round

Square

Hexagon

Dimension

(mm)

d

s

h

Weight of steel bar

for 1m (kgf/m)

0.00616d2

0.00785s2

0.00680h2

Material

Steel

Cast iron

Brass

Bronze

Specific gravity

(gf/cm3)

7.85

7.21

8.10

8.56

4 Table for Weight of Steel Bar

↑↓

↑↓

↑↓

Weight of round steel bar (kgf/m)

Dia.

0010203040

5060708090

100110120130140

150160170180190

200210220230240

250260270280290

300310320330340

350360370380390

400410420430440

450460470480490

500

0 1

0.010.752.725.92

10.36

16.0222.9231.0540.4251.01

62.8475.9090.19

105.71122.47

140.45159.67180.13201.81224.72

248.87274.25300.86328.70357.78

388.09419.63452.40486.40521.64

558.10595.80634.73674.90716.29

758.92802.78847.87894.19941.75

990.531040.551091.801144.291198.00

1252.951309.131366.541425.181485.06

1546.17

2

0.020.892.986.31

10.87

16.6623.6831.9341.4252.14

64.0977.2791.69

107.33124.21

142.32161.66182.24204.04227.08

251.35276.86303.59331.56360.75

391.19422.85455.74489.87525.23

561.82599.64638.69678.98720.50

763.25807.23852.45898.89946.57

995.481045.621097.001149.601203.44

1258.511314.821372.351431.121491.11

1552.34

3

0.061.043.266.71

11.39

17.3024.4532.8342.4453.28

65.3578.6693.19

108.96125.97

144.20163.67184.36206.29229.45

253.85279.47306.33334.42363.74

394.30426.08459.10493.35528.83

565.54603.49642.67683.08724.72

767.59811.70857.04903.60951.41

1000.441050.711102.201154.931208.89

1264.091320.511378.171437.061497.18

1558.54

4 5

0.151.393.857.55

12.47

18.6326.0334.6544.5155.59

67.9181.4796.25

112.27129.51

147.99167.71188.65210.83234.23

258.87284.75311.85340.19369.75

400.55432.59465.85500.35536.07

573.03611.23650.65691.31733.19

776.31820.67866.25913.07961.11

1010.391060.911112.651165.631219.83

1275.271331.951389.851448.991509.35

1570.95

6

0.221.584.167.98

13.03

19.3226.8335.5845.5656.77

69.2182.8997.80

113.94131.31

149.91169.75190.81213.11236.64

261.41287.40314.63343.09372.78

403.70435.86469.24503.86539.72

576.80615.11654.66695.44737.45

780.69825.17870.88917.82965.99

1015.391066.021117.891170.991225.32

1280.891337.681395.711454.971515.46

1577.18

7

0.301.784.498.43

13.61

20.0127.6536.5246.6357.96

70.5384.3299.35

115.62133.11

151.84171.80192.99215.41239.06

263.95290.07317.42346.00375.82

406.86439.14472.65507.39543.37

580.57619.01658.68699.59741.72

785.09829.68875.52922.58970.87

1020.401071.161123.151176.371230.82

1286.511343.431401.581460.961521.58

1583.42

8

0.392.004.838.90

14.19

20.7228.4837.4847.7059.16

71.8585.77

100.93117.31134.93

153.78173.86195.17217.72241.50

266.51292.75320.22348.93378.87

410.03442.44476.07510.94547.03

584.36622.92662.72703.74746.00

789.49834.21880.17927.35975.77

1025.421076.301128.411181.761236.34

1292.151349.191407.461466.971527.70

1589.67

9

0.502.225.189.37

14.79

21.4429.3338.4448.7960.37

73.1987.23

102.51119.02136.76

155.73175.94197.37220.04243.94

269.08295.44323.04351.87381.93

413.22445.74479.50514.49550.71

588.16626.85666.76707.91750.29

793.91828.75884.83932.14980.68

1030.451081.461133.691187.161241.86

1297.791354.961413.361472.991533.85

1595.94

EXAMPLE: Weight of round steel bar, diameter(128mm) and length(1m), is 100.93kgf.NOTE: Unit of diameter is millimeter (mm)

9


Name

ZincAluminiumAntimonySulfurYtterbiumYttriumIridiumIndiumUraniumChlorineCadmiumPotassiumCalciumGoldSilverChlorineSiliconGermaniumCobaltOxygen

NaPbNbNiPtVPdBaAsFPuBeB

MgMnMo

IRaLiP

Name

BromineZirconiumMercuryHydrogenTinStrontiumCaesiumCeriumSeleniumBismuthThalliumTungstenCarbonTantalumTitaniumNitrogenIronTelluriumCopperThorium

Name

SodiumLeadNiobiumNickelPlatinumVanadiumPalladiumBariumArsenicFluorinePlutoniumBerylliumBoronMagnesiumManganeseMolybdenumIodineRadiumLithiumPhosphorus

Symbol

ZnAlSbS

YbYIrInUClCdKCaAuAgCrSiGeCoO

Symbol

BrZrHgHSnSrCsCeSeBiTlWCTaTiNFeTeCuTh

SymbolSpecific gravity

(20 ) g/cm3

07.133 (25°)02.69906.6202.0706.9604.4722.507.3119.0703.214×10−3

08.6500.8601.5519.3210.4907.1902.33 (25°)05.323 (25°)08.8501.429×10−3

03.1206.48913.54600.0899×10−3

07.298402.6001.903 (0°)06.7704.7909.8011.8519.302.2516.604.50701.250×10−3

07.8706.2408.9611.66

00.971211.3608.5708.902 (25°)21.4506.112.0203.505.7201.696×10−3

19.00 19.7201.84802.3401.7407.4310.2204.9405.000.53401.83

5 List of Elements by Symbol and Specific Gravity

Specific gravity

(20 )g/cm3

Specific gravity

( 20 )g/cm3

10


10

1 Hardness Comparison Table

Approximate conversion values against Rockwell C hardness of steel materials

HRC

Rockwell

C

hardness

6867666564

6362616059

5857565554

5352515049

4847464544

4342414039

3837363534

3332313029

2827262524

23222120

(18)

(16)(14)(12)(10)(8)

(6)(4)(2)(0)

HV

Vickers

hardness

940900865832800

772746720697674

653633613595577

560544528513498

484471458446434

423412402392382

372363354345336

327318310302294

286279272266260

254248243238230

222213204196188

180173166160

HBBrinell hardness

10mm Ball Load 3000kgf

Standard ball

—————

—————

—————

—500487475464

451442432421409

400390381371362

353344336327319

311301294286279

271264258253247

243237231226219

212203194187179

171165158152

Hult-gren-ball

—————

———613599

587575561546534

519508494481469

455443432421409

400390381371362

353344336327319

311301294286279

271264258253247

243237231226219

212203194187179

171165158152

tungsten-carbide

ball

———739722

705688670654634

615595577560543

525512496481469

455443432421409

400390381371362

353344336327319

311301294286279

271264258253247

243237231226219

212203194187179

171165158152

HRA

A ScaleLoad 60kgf

braleindenter

85.685.084.583.983.4

82.882.381.881.280.7

80.179.679.078.578.0

77.476.876.375.975.2

74.774.173.673.172.5

72.071.570.970.469.9

69.468.968.467.967.4

66.866.365.865.364.7

64.363.863.362.862.4

62.061.561.060.5—

—————

————

Rockwell hardness NOTE 2.

HRB

B ScaleLoad 100kgfDia. 1/16in

Ball

—————

—————

—————

—————

—————

—————

——

(109.0)(108.5)(108.0)

(107.5)(107.0)(106.0)(105.5)(104.5)

(104.0)(103.0)(102.5)(101.5)(101.0)

100.0099.0098.5097.8096.7

095.5093.9092.3090.7089.5

087.1085.5083.5081.7

HRD

D ScaleLoad 100kgf

braleindenter

76.976.175.474.573.8

73.072.271.570.769.9

69.268.567.766.966.1

65.464.663.863.162.1

61.460.860.059.258.5

57.756.956.255.454.6

53.853.152.351.550.8

50.049.248.447.747.0

46.145.244.643.843.1

42.141.640.940.1—

—————

————

HS

Sho

re

hard

ness

9795929188

8785838180

7876757472

7169686766

6463626058

5756555452

5150494847

4644434241

4140383837

3635353433

3231292827

26252424

Tensile Strengthkgf/mm2

(N/mm2)Aprox. value

NOTE 1.

—————

—————

———

212 {2079}205 {2010}

199 {1952}192 {1883}186 {1824}179 {1755}172 {1687}

167 {1638}161 {1579}156 {1530}151 {1481}146 {1432}

141 {1383}136 {1334}132 {1294}127 {1245}124 {1216}

120 {1177}118 {1157}114 {1118}110 {1079}108 {1059}

105 {1030}102 {1000}100 {0981}097 {0951}095 {0932}

093 {0912}090 {0883}088 {0863}086 {0843}084 {0824}

082 {0804}080 {0785}079 {0775}077 {0755}075 {0736}

072 {0706}069 {0677}066 {0647}063 {0618}061 {0598}

059 {0579}056 {0549}054 {0530}053 {0520}

HRC

Rockwell C

Hardness

NOTE 2.

6867666564

6362616059

5857565554

5352515049

4847464544

4342414039

3837363534

3332313029

2827262524

23222120

(18)

(16)(14)(12)(10)(8)

(6)(4)(2)(0)

Approx. hardness

of

principal materials

S45C soft nitriding

SCM415 case hardening

SCM440 induction hardening

S45C induction hardening

SCM415 core hardness

S45C thermal refining

SCM440 core hardness

S45C core hardness

SUS303

REMARK: The boldfaced figures are based on ASTM E 140 Table 3 (SAE-ASM-ASTM)NOTE 1: Approximate values were determined from "Conversion Tables" of JIS Z 8413 and Z 8438. The units and values in parentheses{ } are based on International System of Units (SI). These are shown for reference. Note that 1N/mm2 = 1MPa.NOTE 2: The parenthesized values in the table are not used so frequently.

TABLE OF NUMBERS

11


1.1.00531.01601.04721.05831.06391.09281.14001.14241.1545

1.19681.22761.251.25661.27001.32281.32991.39631.41111.4508

1.47841.51.57081.58751.59591.67551.69331.751.77321.7952

1.81431.93331.95381.99492.2.09442.09992.11672.18552.2166

2.252.28482.30912.34702.39362.49372.52.51332.54002.6456

2.65992.752.79252.82222.8499

02.956803.03.069103.141603.175003.191803.2503.324903.351003.5

03.590403.627103.628603.7503.866603.989804.04.188804.199804.2333

04.433204.504.569604.618204.693904.987305.05.026505.080005.3198

05.505.585105.644405.699806.06.138206.283206.3506.506.6497

07.07.180807.254207.257107.979708.08.377608.399708.466708.8663

09.09.236309.387809.974610.

010.0531010.16010.6395011.011.2889011.3995012.012.2764012.5664012.7000

013.013.2993014.014.5083014.5143015.015.9593016.016.7552016.9333

017.7326018.019.9492020.020.32022.022.7991023.024.025.

025.1327025.4026.026.5989028.029.030.031.4159031.9187032.

033.8663034.036.038.039.8683040.045.050.050.2955050.8

053.1977063.5000079.8019084.6667127.0000

Pitch

11

2 Comparative Table of Gear Pitch

Dimetral pitch

Diametral pitch

Diametral pitch

Pitch PitchModule

mModule

mModule

m

25.400025.265625.24.255024.23.873323.244422.281722.233922.

21.223120.690220.320020.212720.19.201919.098618.191418.17.5071

17.180616.933316.170116.15.915515.159515.14.514314.324014.1489

14.13.138213.12.732412.700012.127612.095812.11.622311.4592

11.288911.117011.10.822510.611710.185910.160010.106310.09.6010

09.549309.236409.095709.08.9127

8.59048.46678.27618.08518.7.95777.81537.63947.57987.2571

7.07447.00237.6.77336.56916.36626.35006.06386.04796.

5.72965.64445.55855.55.41135.09305.08005.05325.4.7747

4.61824.54794.54.45634.23334.13804.04254.3.90773.8197

3.62863.53723.50143.53.18313.17503.03193.02403.2.8648

2.82222.752.70562.54652.5400

2.52662.52.38732.30912.252.22822.11672.06902.02132.

1.95381.90991.81431.75071.751.69331.59151.58751.51601.5

1.43241.41111.27321.27001.251.15451.11411.10431.05831.0160

1.01061.0.97690.95490.90710.87590.84670.80350.79580.7938

0.750.74710.70560.66840.63660.63500.56440.50800.50530.5

0.47750.40.31830.30.2

in in in

3.14163.1⁄83.09223.2.96852.95282.7⁄82.75592.3⁄42.7211

2.5⁄82.55912.51332.1⁄22.47382.3⁄82.36222.1⁄42.22642.1654

2.1⁄82.09442.1.97901.96851.7⁄81.85531.79521.77171.3⁄4

1.73161.5⁄81.60791.57481.57081.1⁄21.49611.48431.7⁄16

1.4173

1.39631.3⁄81.36061.33861.5⁄16

1.25981.25661.1⁄41.23691.3⁄16

1.18111.14241.1⁄81.11321.1024

1.1⁄16

1.04721.02361.0.98950.98430.96660.94490.15⁄16

0.8976

0.7⁄80.86610.86580.83780.13⁄16

0.78740.78540.3⁄40.74800.7421

0.70870.6981011⁄16

0.68030.66950.62990.62830.5⁄80.61840.5906

0.57120.9⁄16

0.55660.55120.52360.51180.1⁄20.49480.48330.4724

0.44880.7⁄16

0.43310.43290.39370.39270.3⁄80.37400.37110.3543

0.34910.34010.33470.31500.3142

.5⁄16

.3092

.2953

.2856

.2783

.2756

.2618

.2559

.1⁄4

.2474

.2417

.2362

.2244

.2165

.2164

.2094

.1969

.1963

.3⁄16

.1855

.1772

.1745

.1575

.1571

.1546

.1428

.1378

.1366

.1309

.1257

.1⁄8

.1237

.1208

.1181

.1122

.1083

.1047

.1⁄10

.0984

.0982

.0928

.0924

.0873

.0827

.0787

.0785

.0698

.0628

.1⁄16

.0618

.0576

.0498

.0394

.0371

.0247

mm mm mm

79.79679.37578.54276.20075.40075.73.02570.69.85069.116

66.67565.63.83763.50062.83560.32560.57.15056.55155.

53.97553.19850.80050.26750.47.62547.12545.59845.44.450

43.98341.27540.84140.39.89838.10038.37.70136.51336.

35.46534.92534.55934.33.33832.31.91931.75031.41730.163

30.29.01728.57528.27528.

26.98826.59926.25.40025.13325.24.55224.23.81322.799

22.22522.21.99121.28020.63820.19.94919.05019.18.849

18.17.73317.46317.28017.16.15.95915.87515.70715.

14.50814.28814.13814.13.29913.12.70012.56812.27612.

11.39911.11311.10.99610.09.97509.52509.509.42609.3

08.86608.63908.508.07.980

7.9387.8547.57.2547.0697.6.6506.56.3506.283

6.1386.5.7005.55.4995.3205.4.9874.7634.712

4.54.4334.3.9903.9273.6273.53.4703.3253.193

3.1753.1423.0693.2.8502.7512.6602.5402.52.494

2.3572.3472.2172.1002.1.9951.7731.5961.5881.570

1.51.2561.0.9420.628


4.4982

4.51224.52624.54024.55434.5683

4.58234.59634.61034.62434.6383

4.65234.66637.63247.64647.6604

7.67447.68857.70257.71657.7305

7.744510.710610.724610.738610.7526

10.766610.780610.794610.808610.8227

13.788813.802813.816813.830813.8448

13.858813.872813.886813.900816.8670

16.881016.895016.909016.923016.9370

16.951016.965016.979019.945219.9592

19.973219.987220.001220.015220.0292

12

z

12345

6789

10

1112131415

1617181920

2122232425

2627282930

3132333435

3637383940

4142434445

4647484950

5152535455

5657585960

z z z

121122123124125

126127128129130

131132133134135

136137138139140

141142143144145

146147148149150

151152153154155

156157158159160

161162163164165

166167168169170

171172173174175

176177178179180

181182183184185

186187188189190

191192193194195

196197198199200

201202203204205

206207208209210

211212213214215

216217218219220

221222223224225

226227228229230

231232233234235

236237238239240

k

22222

22222

22222

22333

33333

34444

44444

55555

55556

66666

66677

77777

k k

77888

88888

89999

99999

1010101010

1010101011

1111111111

1111111212

1212121212

1212131313

1313131313

1314141414

1414141414

1515151515

1515151516

1616161616

1616161717

1717171717

1717181818

1818181818

1819191919

1919191919

2020202020

2020202021

2121212121

2121212222

2222222222

2222232323

2323232323

2324242424

2424242424

2525252525

2525252526

2626262626

2626262727

2727272727

W W W W

20.043220.057223.023323.037323.0513

23.065323.079423.093423.107423.1214

23.135426.101526.115526.129526.1435

26.157526.171526.185626.199626.2136

29.179729.193729.207729.221729.2357

29.249729.263729.277729.291732.2579

32.271932.285932.299932.313932.3279

32.341932.355932.369935.336135.3501

35.364135.378135.392135.406135.4201

35.434135.448138.414238.428238.4423

38.456338.470338.484338.498338.5123

38.526341.492441.506441.520441.5344

41.548441.562441.576541.590541.6045

44.570644.584644.598644.612644.6266

44.640644.654644.668644.682647.6488

47.662847.676847.690847.704847.7188

47.732847.746847.760850.727050.7410

50.755050.769050.783050.797050.8110

50.825050.839053.805153.819253.8332

53.847253.861253.875253.889253.9032

53.917256.883356.897356.911356.9253

56.939456.953456.967456.981456.9954

59.961559.975559.989560.003560.0175

60.031560.045560.059660.073663.0397

63.053763.067763.081763.095763.1097

63.123763.137763.151766.117966.1319

66.145966.159966.173966.187966.2019

66.215966.229969.196169.210169.2241

69.238169.252169.266169.280169.2941

69.308172.274272.288272.302272.3163

72.330372.344372.358372.372372.3863

75.352475.366475.380475.394475.4084

75.422475.436475.450575.464578.4306

78.444678.458678.472678.486678.5006

78.514678.528678.542681.508881.5228

81.536881.550881.564881.578881.5928

3 Span Measurement Over k Teeth of Standard Spur Gear W ( x = 0 ) m = 1 ( α = 20° )

6162636465

6667686970

7172737475

7677787980

8182838485

8687888990

9192939495

96979899

100

101102103104105

106107108109110

111112113114115

116117118119120

k


81.606881.620884.587084.601084.6150

84.629084.643084.657084.671084.6850

84.699087.665187.679187.693287.7072

87.721287.735287.749287.763287.7772

90.743390.757390.771390.785390.7993

90.813390.827490.841490.855493.8215

93.835593.849593.863593.877593.8915

93.905593.919593.933596.899796.9137

96.927796.941796.955796.969796.9837

96.997797.011799.977999.9919

100.0060

100.0200100.0340100.0480100.0620100.0760

100.0900103.0560103.0700103.0840103.0980

3434343434

3535353535

3535353536

3636363636

3636363737

3737373737

3737383838

3838383838

3839393939

3939393939

4040404040

4040404041

13

241242243244245

246247248249250

251252253254255

256257258259260

261262263264265

266267268269270

271272273274275

276277278279280

281282283284285

286287288289290

291292293294295

296297298299300

361362363364365

366367368369370

371372373374375

376377378379380

381382383384385

386387388389390

391392393394395

396397398399400

401402403404405

406407408409410

411412413414415

416417418419420

421422423424425

426427428429430

431432433434435

436437438439440

441442443444445

446447448449450

451452453454455

456457458459460

461462463464465

466467468469470

471472473474475

476477478479480

2727282828

2828282828

2829292929

2929292929

3030303030

3030303031

3131313131

3131313232

3232323232

3232333333

3333333333

3334343434

4141414141

4141414242

4242424242

4242434343

4343434343

4344444444

4444444444

4545454545

4545454546

4646464646

4646464747

4747474747

4747484848

4848484848

4849494949

4949494949

5050505050

5050505051

5151515151

5151515252

5252525252

5252535353

5353535353

5354545454

103.1120103.1260103.1400103.1540103.1680

106.1340106.1480106.1620106.1760106.1900

106.2040106.2180106.2320106.2460109.2120

109.2260109.2400109.2540109.2680109.2820

109.2960109.3100109.3240112.2910112.3050

112.3190112.3330112.3470112.3610112.3750

112.3890112.4030115.3690115.3830115.3970

115.4110115.4250115.4390115.4530115.4670

115.4810118.4470118.4610118.4750118.4890

118.5030118.5170118.5310118.5450118.5590

121.5250121.5390121.5530121.5670121.5810

121.5950121.6090121.6230121.6370124.6030

124.6170124.6310124.6450124.6590124.6730

124.6870124.7010124.7150127.6810127.6960

127.7100127.7240127.7380127.7520127.7660

127.7800127.7940130.7600130.7740130.7880

130.8020130.8160130.8300130.8440130.8580

130.8720133.8380133.8520133.8660133.8800

133.8940133.9080133.9220133.9360133.9500

136.9160136.9300136.9440136.9580136.9720

136.9860137.0000137.0140137.0280139.9940

140.0080140.0220140.0360140.0500140.0640

140.0780140.0920140.1060143.0720143.0860

143.1000143.1140143.1280143.1420143.1560

143.1700143.1840146.1510146.1650146.1790

146.1930146.2070146.2210146.2350146.2490

146.2630149.2290149.2430149.2570149.2710

149.2850149.2990149.3130149.3270149.3410

152.3070152.3210152.3350152.3490152.3630

152.3770152.3910152.4050152.4190155.3850

155.3990155.4130155.4270155.4410155.4550

155.4690155.4830155.4970158.4630158.4770

158.4910158.5050158.5190158.5330158.5470

158.5610158.5750161.5420161.5560161.5700

161.5840161.5980161.6120161.6260161.6400

161.6540164.6200164.6340164.6480164.6620

m = 1 ( α = 20° )

301302303304305

306307308309310

311312313314315

316317318319320

321322323324325

326327328329330

331332333334335

336337338339340

341342343344345

346347348349350

351352353354355

356357358359360

z z z zk k kW W W Wk


4.59994.60524.61064.6160

4.62134.62674.63214.63744.6428

4.64824.65364.65894.66434.6697

4.67504.68044.68584.69117.7380

7.74347.74887.75417.75957.7649

7.77027.77567.78107.78637.7917

7.79717.8024

10.849310.854710.8601

10.865410.870810.876210.881510.8869

10.892310.897610.903010.908413.9553

13.960613.966013.971413.976713.9821

13.987513.992913.998214.003614.0090

14.014314.019717.066617.072017.0773

17.082717.088117.093417.098817.1042

17.109517.114917.120317.125620.1725

20.177920.183320.188620.194020.1994

20.204720.210120.215520.220820.2262

20.231623.278523.283823.289223.2946

23.300023.305323.310723.316123.3214

23.326823.332223.337523.342926.3898

26.395226.400526.405926.411326.4166

26.422026.427426.432726.438126.4435

26.448829.495729.501129.506529.5118

29.517229.522629.527929.533329.5387

14

12345

6789

10

1112131415

1617181920

2122232425

2627282930

3132333435

3637383940

4142434445

4647484950

5152535455

5657585960

121122123124125

126127128129130

131132133134135

136137138139140

141142143144145

146147148149150

151152153154155

156157158159160

161162163164165

166167168169170

171172173174175

176177178179180

181182183184185

186187188189190

191192193194195

196197198199200

201202203204205

206207208209210

211212213214215

216217218219220

221222223224225

226227228229230

231232233234235

236237238239240

22222

22222

22222

22222

22223

33333

33333

33444

44444

44445

55555

55555

55666

66666

66667

77777

77777

78888

88888

88889

99999

99999

910101010

1010101010

1010101011

1111111111

1111111111

1112121212

1212121212

1212121313

1313131313

1313131313

1314141414

1414141414

1414141515

1515151515

1515151515

1516161616

1616161616

1616161717

1717171717

1717171717

1718181818

1818181818

1818181919

1919191919

1919191919

2020202020

29.544029.549429.554829.560232.6070

32.612432.617832.623232.628532.6339

32.639332.644632.650032.655432.6607

32.666135.713035.718435.723735.7291

35.734535.739835.745235.750635.7559

35.761335.766735.772038.818938.8243

38.829738.835038.840438.845838.8511

38.856538.861938.867238.872638.8780

38.883441.930214.935641.941041.9464

41.951741.957141.962541.967841.9732

41.978641.983941.989345.036245.0416

45.046945.052345.057745.063045.0684

45.073845.079145.084545.089945.0952

45.100648.147548.152948.158248.1636

48.169048.174348.179748.185148.1905

48.195848.201248.206651.253451.2588

51.264251.269651.274951.280351.2857

51.291051.296451.301851.307151.3125

51.317954.364854.370154.375554.3809

54.386254.391654.397054.402354.4077

54.413154.418454.423857.470757.4761

57.481457.486857.492257.497557.5029

57.508357.513757.519057.524457.5298

60.576660.582060.587460.592860.5981

4 Span Measurement Over k Teeth of Standard Spur Gear W ( x = 0 ) m = 1 ( α = 14.5° )

6162636465

6667686970

7172737475

7677787980

8182838485

8687888990

9192939495

96979899

100

101102103104105

106107108109110

111112113114115

116117118119120



91.662991.668391.673791.679091.6844

91.689891.695191.700591.705991.7113

91.716691.722094.768994.774294.7796

94.785094.790494.795794.801194.8065

94.811894.817294.822694.827997.8748

97.880297.885697.890997.896397.9017

97.907097.912497.917897.923197.9285

97.933997.9392

100.9860100.9920100.9970

101.0020101.0080101.0130101.0180101.0240

101.0290101.0340101.0400101.0450104.0920

104.0970104.1030104.1080104.1140104.1190

104.1240104.1300104.1350104.1400104.1460

60.603560.608960.614260.619660.6250

60.630360.635760.641163.688063.6933

63.698763.704163.709463.714863.7202

63.725563.730963.736363.741663.7470

66.793966.799366.804666.810066.8154

66.820766.826166.831566.836966.8422

66.847666.853066.858369.905269.9106

69.916069.921369.926769.932169.9374

69.942869.948269.953569.958969.9643

73.011273.016573.021973.027373.0326

73.038073.043473.048773.054173.0595

73.064973.070276.117176.122576.1278

15

2525252525

2525252525

2626262626

2626262626

2626272727

2727272727

2727272727

2828282828

2828282828

2828292929

2929292929

2929292930

241242243244245

246247248249250

251252253254255

256257258259260

261262263264265

266267268269270

271272273274275

276277278279280

281282283284285

286287288289290

291292293294295

296297298299300

361362363364365

366367368369370

371372373374375

376377378379380

381382383384385

386387388389390

391392393394395

396397398399400

401402403404405

406407408409410

411412413414415

416417418419420

421422423424425

426427428429430

431432433434435

436437438439440

441442443444445

446447448449450

451452453454455

456457458459460

461462463464465

466467468469470

471472473474475

476477478479480

2020202020

2020202121

2121212121

2121212121

2222222222

2222222222

2222222323

2323232323

2323232323

2424242424

2424242424

2424252525

3030303030

3030303030

3030313131

3131313131

3131313132

3232323232

3232323232

3232333333

3333333333

3333333334

3434343434

3434343434

3434353535

3535353535

3535353536

3636363636

3636363636

3637373737

3737373737

3737373738

3838383838

3838383838

3839393939

3939393939

76.133276.138676.144076.149376.1547

76.160176.165476.170876.176276.1815

79.228479.233879.239279.244579.2499

79.255379.260679.266079.271479.2767

79.282179.287582.334482.339782.3451

82.350582.355882.361282.366682.3719

82.377382.382782.388082.393482.3988

85.445785.451085.456485.461885.4671

85.472585.477985.483385.488685.4940

85.499485.504788.551688.557088.5624

88.567788.573188.578588.583888.5892

88.594688.599988.605388.610791.6576

104.1510104.1560107.2030107.2090107.2140

107.2190107.2250107.2300107.2360107.2410

107.2460107.2520107.2570107.2620110.3090

110.3150110.3200110.3250110.3310110.3360

110.3420110.3470110.3520110.3580110.3630

110.3680113.4150113.4210113.4260113.4310

113.4370113.4420113.4470113.4530113.4580

113.4640113.4690113.4740113.4800116.5270

116.5320116.5370116.5430116.5480116.5530

116.5590116.5640116.5700116.5750116.5800

116.5860119.6330119.6380119.6430119.6490

119.6540119.6590119.6650119.6700119.6750

m = 1 ( α = 14.5° )

301302303304305

306307308309310

311312313314315

316317338319320

321322323324325

326327328329330

331332333334335

336337338339340

341342343344345

346347348349350

351352353354355

356357358359360



16

5 Charts Indicating Spanned Number of Teeth of Spur and Helical Gears (Maag's data)


0.000014180.000014540.000014910.000015280.00001565

0.000016030.000016420.000016820.000017220.00001762

0.000018040.000018460.000018880.000019310.00001975

0.000020200.000020650.000021110.000021580.00002205

0.000022530.000023010.000023510.000024010.00002452

0.000025030.000025550.000026080.000026620.00002716

0.000027710.000028270.000028840.000029410.00002999

0.000030580.000031170.000031780.000032390.00003301

0.000033640.000034270.000034910.000035560.00003622

0.000036890.000037570.000038250.000038940.00003964

0.000040350.000041070.000041790.000042520.00004327

0.000044020.000044780.000045540.000046320.00004711

0.00004790

0001020304

0506070809

1011121314

1516171819

2021222324

2526272829

3031323334

3536373839

4041424344

4546474849

5051525354

5556575859

60

17

6 Involute Function Table inv α = tan α − α

2°

0.000047900.000048710.000049520.000050340.00005117

0.000052010.000052860.000053720.000054580.00005546

0.000056340.000057240.000058140.000059060.00005998

0.000060910.000061860.000062810.000063770.00006474

0.000065730.000066720.000067720.000068730.00006975

0.000070780.000071830.000072880.000073940.00007501

0.000076100.000077190.000078290.000079410.00008053

0.000081670.000082810.000083970.000085140.00008632

0.000087510.000088710.000089920.000091140.00009237

0.000093620.000094870.000096140.000097420.00009870

0.000100000.000101320.000102640.000103970.00010532

0.000106680.000108050.000109430.000110820.00011223

0.00011364

0.00011360.00011510.00011650.00011800.0001194

0.00012090.00012240.00012390.00012540.0001269

0.00012850.00013000.00013160.00013320.0001347

0.00013630.00013800.00013960.00014120.0001429

0.00014450.00014620.00014790.00014960.0001513

0.00015300.00015480.00015650.00015830.0001601

0.00016190.00016370.00016550.00016740.0001692

0.00017110.00017290.00017480.00017670.0001787

0.00018060.00018250.00018450.00018650.0001885

0.00019050.00019250.00019450.00019650.0001986

0.00020070.00020280.00020490.00020700.0002091

0.00021130.00021340.00021560.00021780.0002200

0.0002222

0.00022220.00022440.00022670.00022890.0002312

0.00023350.00023580.00023820.00024050.0002429

0.00024520.00024760.00025000.00025240.0002549

0.00025730.00025980.00026220.00026470.0002673

0.00026980.00027230.00027490.00027750.0002801

0.00028270.00028530.00028790.00029060.0002933

0.00029590.00029860.00030140.00030410.0003069

0.00030960.00031240.00031520.00031800.0003209

0.00032370.00032660.00032950.00033240.0003353

0.00033830.00034120.00034420.00034720.0003502

0.00035320.00035630.00035930.00036240.0003655

0.00036860.00037180.00037490.00037810.0003813

0.0003845

0.00038450.00038770.00039090.00039420.0003975

0.00040080.00040410.00040740.00041080.0004141

0.00041750.00042090.00042440.00042780.0004313

0.00043470.00043820.00044170.00044530.0004488

0.00045240.00045600.00045960.00046320.0004669

0.00047060.00047430.00047800.00048170.0004854

0.00048920.00049300.00049680.00050060.0005045

0.00050830.00051220.00051610.00052000.0005240

0.00052800.00053190.00053590.00054000.0005440

0.00054810.00055220.00055630.00056040.0005645

0.00056870.00057290.00057710.00058130.0005856

0.00058980.00059410.00059850.00060280.0006071

0.0006115

0.00061150.00061590.00062030.00062480.0006292

0.00063370.00063820.00064270.00064730.0006518

0.00065640.00066100.00066570.00067030.0006750

0.00067970.00068440.00068920.00069390.0006987

0.00070350.00070830.00071320.00071810.0007230

0.00072790.00073280.00073780.00074280.0007478

0.00075280.00075790.00076290.00076800.0007732

0.00077830.00078350.00078870.00079390.0007991

0.00080440.00080960.00081500.00082030.0008256

0.00083100.00083640.00084180.00084730.0008527

0.00085820.00086380.00086930.00087490.0008805

0.00088610.00089170.00089740.00090310.0009088

0.0009145

0.00091450.00092030.00092600.00093180.0009377

0.00094350.00094940.00095530.00096120.0009672

0.00097320.00097920.00098520.00099130.0009973

0.00100340.00100960.00101570.00102190.0010281

0.00103430.00104060.00104690.00105320.0010595

0.00106590.00107220.00107860.00108510.0010915

0.00109800.00110450.00111110.00111760.0011242

0.00113080.00113750.00114410.00115080.0011575

0.00116430.00117110.00117790.00118470.0011915

0.00119840.00120530.00121220.00121920.0012262

0.00123320.00124020.00124730.00125440.0012615

0.00126870.00127580.00128300.00129030.0012975

0.0013048

0.0013050.0013120.0013190.0013270.001334

0.0013420.0013490.0013570.0013640.001372

0.0013790.0013870.0013940.0014020.001410

0.0014170.0014250.0014330.0014410.001448

0.0014560.0014640.0014720.0014800.001488

0.0014960.0015040.0015120.0015200.001528

0.0015360.0015440.0015530.0015610.001569

0.0015770.0015860.0015940.0016020.001611

0.0016190.0016280.0016360.0016450.001653

0.0016620.0016700.0016790.0016880.001696

0.0017050.0017140.0017230.0017310.001740

0.0017490.0017580.0017670.0017760.001785

0.001794

0.0017940.0018030.0018120.0018210.001830

0.0018400.0018490.0018580.0018670.001877

0.0018860.0018950.0019050.0019140.001924

0.0019330.0019430.0019520.0019620.001972

0.0019810.0019910.0020010.0020100.002020

0.0020300.0020400.0020500.0020600.002069

0.0020790.0020890.0021000.0021100.002120

0.0021300.0021400.0021500.0021600.002171

0.0021810.0021910.0022020.0022120.002223

0.0022330.0022440.0022540.0022650.002275

0.0022860.0022970.0023070.0023180.002329

0.0023400.0023500.0023610.0023720.002383

0.002394

0.0023940.0024050.0024160.0024270.002438

0.0024490.0024610.0024720.0024830.002494

0.0025060.0025170.0025280.0025400.002551

0.0025630.0025740.0025860.0025980.002609

0.0026210.0026330.0026440.0026560.002668

0.0026800.0026920.0027030.0027150.002727

0.0027390.0027510.0027640.0027760.002788

0.0028000.0028120.0028250.0028370.002849

0.0028620.0028740.0028870.0028990.002912

0.0029240.0029370.0029490.0029620.002975

0.0029870.0030000.0030130.0030260.003039

0.0030520.0030650.0030780.0030910.003104

0.003117

3° 4° 5° 6° 7° 8° 9° 10° 11°


0001020304

0506070809

1011121314

1516171819

2021222324

2526272829

3031323334

3536373839

4041424344

4546474849

5051525354

5556575859

60

0.0031170.0031300.0031430.0031570.003170

0.0031830.0031970.0032100.0032230.003237

0.0032500.0032640.0032770.0032910.003305

0.0033180.0033320.0033460.0033600.003374

0.0033870.0034010.0034150.0034290.003443

0.0034580.0034720.0034860.0035000.003514

0.0035290.0035430.0035570.0035720.003586

0.0036000.0036150.0036300.0036440.003659

0.0036730.0036880.0037030.0037180.003733

0.0037470.0037620.0037770.0037920.003807

0.0038220.0038380.0038530.0038680.003883

0.0038980.0039140.0039290.0039440.003960

0.003975

18

inv α = tan α − αInvolute Function Table

12°

0.0039750.0039910.0040060.0040220.004038

0.0040530.0040690.0040850.0041010.004117

0.0041330.0041480.0041640.0041800.004197

0.0042130.0042290.0042450.0042610.004277

0.0042940.0043100.0043270.0043430.004359

0.0043760.0043930.0044090.0044260.004443

0.0044590.0044760.0044930.0045100.004527

0.0045440.0045610.0045780.0045950.004612

0.0046290.0046460.0046640.0046810.004698

0.0047160.0047330.0047510.0047680.004786

0.0048030.0048210.0048390.0048560.004874

0.0048920.0049100.0049280.0049460.004964

0.004982

0.0049820.0050000.0050180.0050360.005055

0.0050730.0050910.0051100.0051280.005146

0.0051650.0051840.0052020.0052210.005239

0.0052580.0052770.0052960.0053150.005334

0.0053530.0053720.0053910.0054100.005429

0.0054480.0054670.0054870.0055060.005525

0.0055450.0055640.0055840.0056030.005623

0.0056430.0056620.0056820.0057020.005722

0.0057420.0057620.0057820.0058020.005822

0.0058420.0058620.0058820.0059030.005923

0.0059430.0059640.0059840.0060050.006025

0.0060460.0060670.0060870.0061080.006129

0.006150

0.0061500.0061710.0061920.0062130.006234

0.0062550.0062760.0062970.0063180.006340

0.0063610.0063820.0064040.0064250.006447

0.0064690.0064900.0065120.0065340.006555

0.0065770.0065990.0066210.0066430.006665

0.0066870.0067090.0067320.0067540.006776

0.0067990.0068210.0068430.0068660.006888

0.0069110.0069340.0069560.0069790.007002

0.0070250.0070480.0070710.0070940.007117

0.0071400.0071630.0071860.0072090.007233

0.0072560.0072800.0073030.0073270.007350

0.0073740.0073970.0074210.0074450.007469

0.007493

0.0074930.0075170.0075410.0075650.007589

0.0076130.0076370.0076610.0076860.007710

0.0077350.0077590.0077840.0078080.007833

0.0078570.0078820.0079070.0079320.007957

0.0079820.0080070.0080320.0080570.008082

0.0081070.0081330.0081580.0081830.008209

0.0082340.0082600.0082850.0083110.008337

0.0083620.0083880.0084140.0084400.008466

0.0084920.0085180.0085440.0085710.008597

0.0086230.0086500.0086760.0087020.008729

0.0087560.0087820.0088090.0088360.008863

0.0088890.0089160.0089430.0089700.008998

0.009025

0.0090250.0090520.0090790.0091070.009134

0.0091610.0091890.0092160.0092440.009272

0.0092990.0093270.0093550.0093830.009411

0.0094390.0094670.0094950.0095230.009552

0.0095800.0096080.0096370.0096650.009694

0.0097220.0097510.0097800.0098080.009837

0.0098660.0098950.0099240.0099530.009982

0.0100110.0100410.0100700.0100990.010129

0.0101580.0101880.0102170.0102470.010277

0.0103070.0103360.0103660.0103960.010426

0.0104560.0104860.0105170.0105470.010577

0.0106080.0106380.0106690.0106990.010730

0.010760

0.0107600.0107910.0108220.0108530.010884

0.0109150.0109460.0109770.0110080.011039

0.0110710.0111020.0111330.0111650.011196

0.0112280.0112600.0112910.0113230.011355

0.0113870.0114190.0114510.0114830.011515

0.0115470.0115800.0116120.0116440.011677

0.0117090.0117420.0117750.0118070.011840

0.0118730.0119060.0119390.0119720.012005

0.0120380.0120710.0121050.0121380.012172

0.0122050.0122390.0122720.0123060.012340

0.0123730.0124070.0124410.0124750.012509

0.0125430.0125780.0126120.0126460.012681

0.012715

0.0127150.0127500.0127840.0128190.012854

0.0128880.0129230.0129580.0129930.013028

0.0130630.0130980.0131340.0131690.013204

0.0132400.0132750.0133110.0133460.013382

0.0134180.0134540.0134900.0135260.013562

0.0135980.0136340.0136700.0137070.013743

0.0137790.0138160.0138520.0138890.013926

0.0139630.0139990.0140360.0140730.014110

0.0141480.0141850.0142220.0142590.014297

0.0143340.0143720.0144090.0144470.014485

0.0145230.0145600.0145980.0146360.014674

0.0147130.0147510.0147890.0148270.014866

0.014904

0.0149040.0149430.0149820.0150200.015059

0.0150980.0151370.0151760.0152150.015254

0.0152930.0153330.0153720.0154110.015451

0.0154900.0155300.0155700.0156090.015649

0.0156890.0157290.0157690.0158090.015849

0.0158900.0159300.0159710.0160110.016052

0.0160920.0161330.0161740.0162140.016255

0.0162960.0163370.0163790.0164200.016461

0.0165020.0165440.0165850.0166270.016669

0.0167100.0167520.0167940.0168360.016878

0.0169200.0169620.0170040.0170470.017089

0.0171320.0171740.0172170.0172590.017302

0.017345

0.0173450.0173880.0174310.0174740.017517

0.0175600.0176030.0176470.0176900.017734

0.0177770.0178210.0178650.0179080.017952

0.0179960.0180400.0180840.0181290.018173

0.0182170.0182620.0183060.0183510.018395

0.0184400.0184850.0185300.0185750.018620

0.0186650.0187100.0187550.0188000.018846

0.0188910.0189370.0189830.0190280.019074

0.0191200.0191660.0192120.0192580.019304

0.0193500.0193970.0194430.0194900.019536

0.0195830.0196300.0196760.0197230.019770

0.0198170.0198640.0199120.0199590.020006

0.020054

13° 14° 15° 16° 17° 18° 19° 20° 21°


0.0200540.0201010.0201490.0201970.020244

0.0202920.0203400.0203880.0204360.020484

0.0205330.0205810.0206290.0206780.020726

0.0207750.0208240.0208730.0209210.020970

0.0210190.0210690.0211180.0211670.021217

0.0212660.0213150.0213650.0214150.021465

0.0215140.0215640.0216140.0216650.021715

0.0217650.0218150.0218660.0219160.021967

0.0220180.0220680.0221190.0221700.022221

0.0222720.0223240.0223750.0224260.022478

0.0225290.0225810.0226320.0226840.022736

0.0227880.0228400.0228920.0229440.022997

0.023049

19


0001020304

0506070809

1011121314

1516171819

2021222324

2526272829

3031323334

3536373839

4041424344

4546474849

5051525354

5556575859

60

22°

0.0230490.0231020.0231540.0232070.023259

0.0233120.0233650.0234180.0234710.023524

0.0235770.0236310.0236840.0237380.023791

0.0238450.0238990.0239520.0240060.024060

0.0241140.0241690.0242230.0242770.024332

0.0243860.0244410.0244950.0245500.024605

0.0246600.0247150.0247700.0248250.024881

0.0249360.0249920.0250470.0251030.025159

0.0252140.0252700.0253260.0253820.025439

0.0254950.0255510.0256080.0256640.025721

0.0257780.0258340.0258910.0259480.026005

0.0260620.0261200.0261770.0262350.026292

0.026350

0.0263500.0264070.0264650.0265230.026581

0.0266390.0266970.0267560.0268140.026872

0.0269310.0269890.0270480.0271070.027166

0.0272250.0272840.0273430.0274020.027462

0.0275210.0275810.0276400.0277000.027760

0.0278200.0278800.0279400.0280000.028060

0.0281210.0281810.0282420.0283020.028363

0.0284240.0284850.0285460.0286070.028668

0.0287290.0287910.0288520.0289140.028976

0.0290370.0290990.0291610.0292230.029285

0.0293480.0294100.0294720.0295350.029598

0.0296600.0297230.0297860.0298490.029912

0.029975

0.0299750.0300390.0301020.0301660.030229

0.0302930.0303570.0304200.0304840.030549

0.0306130.0306770.0307410.0308060.030870

0.0309350.0310000.0310650.0311300.031195

0.0312600.0313250.0313900.0314560.031521

0.0315870.0316530.0317180.0317840.031850

0.0319170.0319830.0320490.0321160.032182

0.0322490.0323150.0323820.0324490.032516

0.0325830.0326510.0327180.0327850.032853

0.0329200.0329880.0330560.0331240.033192

0.0332600.0333280.0333970.0334650.033534

0.0336020.0336710.0337400.0338090.033878

0.033947

0.0339470.0340160.0340860.0341550.034225

0.0342940.0343640.0344340.0345040.034574

0.0346440.0347140.0347850.0348550.034926

0.0349960.0350670.0351380.0352090.035280

0.0353520.0354230.0354940.0355660.035637

0.0357090.0357810.0358530.0359250.035997

0.0360690.0361420.0362140.0362870.036359

0.0364320.0365050.0365780.0366510.036724

0.0367980.0368710.0369450.0370180.037092

0.0371660.0372400.0373140.0373880.037462

0.0375370.0376110.0376860.0377610.037835

0.0379100.0379850.0380600.0381360.038211

0.038287

0.0382870.0383620.0384380.0385140.038590

0.0386660.0387420.0388180.0388940.038971

0.0390470.0391240.0392010.0392780.039355

0.0394320.0395090.0395860.0396640.039741

0.0398190.0398970.0399740.0400520.040131

0.0402090.0402870.0403660.0404440.040523

0.0406020.0406800.0407590.0408380.040918

0.0409970.0410760.0411560.0412360.041316

0.0413950.0414750.0415560.0416360.041716

0.0417970.0418770.0419580.0420390.042120

0.0422010.0422820.0423630.0424440.042526

0.0426070.0426890.0427710.0428530.042935

0.043017

0.0430170.0431000.0431820.0432640.043347

0.0434300.0435130.0435960.0436790.043762

0.0438450.0439290.0440120.0440960.044180

0.0442640.0443480.0444320.0445160.044601

0.0446850.0447700.0448550.0449390.045024

0.0451100.0451950.0452800.0453660.045451

0.0455370.0456230.0457090.0457950.045881

0.0459670.0460540.0461400.0462270.046313

0.0464000.0464870.0465750.0466620.046749

0.0468370.0469240.0470120.0471000.047188

0.0472760.0473640.0474520.0475410.047630

0.0477180.0478070.0478960.0479850.048074

0.048164

0.0481640.0482530.0483430.0484320.048522

0.0486120.0487020.0487920.0488830.048973

0.0490630.0491540.0492450.0493360.049427

0.0495180.0496090.0497010.0497920.049884

0.0499760.0500680.0501600.0502520.050344

0.0504370.0505290.0506220.0507150.050808

0.0509010.0509940.0510870.0511810.051274

0.0513680.0514620.0515560.0516500.051744

0.0518380.0519330.0520270.0521220.052217

0.0523120.0524070.0525020.0525970.052693

0.0527880.0528840.0529800.0530760.053172

0.0532680.0533650.0534610.0535580.053655

0.053751

0.0537510.0538490.0539460.0540430.054140

0.0542380.0543360.0544330.0545310.054629

0.0547280.0548260.0549240.0550230.055122

0.0552210.0553200.0554190.0555180.055617

0.0557170.0558170.0559160.0560160.056116

0.0562170.0563170.0564170.0565180.056619

0.0567200.0568210.0569220.0570230.057124

0.0572260.0573280.0574290.0575310.057633

0.0577360.0578380.0579400.0580430.058146

0.0582490.0583520.0584550.0585580.058662

0.0587650.0588690.0589730.0590770.059181

0.0592850.0593900.0594940.0595990.059704

0.059809

0.0598090.0599140.0600190.0601240.060230

0.0603350.0604410.0605470.0606530.060759

0.0608660.0609720.0610790.0611860.061292

0.0614000.0615070.0616140.0617210.061829

0.0619370.0620450.0621530.0622610.062369

0.0624780.0625860.0626950.0628040.062913

0.0630220.0631310.0632410.0633500.063460

0.0635700.0636800.0637900.0639010.064011

0.0641220.0642320.0643430.0644540.064565

0.0646770.0647880.0649000.0650120.065123

0.0652360.0653480.0654600.0655730.065685

0.0657980.0659110.0660240.0661370.066250

0.066364

23° 24° 25° 26° 27° 28° 29° 30° 31°


0.0734490.0735720.0736950.0738180.073941

0.0740640.0741880.0743110.0744350.074559

0.0746840.0748080.0749320.0750570.075182

0.0753070.0754320.0755570.0756830.075808

0.0759340.0760600.0761860.0763120.076439

0.0765650.0766920.0768190.0769460.077073

0.0772000.0773280.0774550.0775830.077711

0.0778390.0779680.0780960.0782250.078354

0.0784830.0786120.0787410.0788710.079000

0.0791300.0792600.0793900.0795200.079651

0.0797810.0799120.0800430.0801740.080306

0.0804370.0805690.0807000.0808320.080964

0.081097

0.0663640.0664780.0665910.0667050.066819

0.0669340.0670480.0671630.0672770.067392

0.0675070.0676220.0677380.0678530.067969

0.0680840.0682000.0683160.0684320.068549

0.0686650.0687820.0688990.0690160.069133

0.0692500.0693670.0694850.0696020.069720

0.0698380.0699560.0700750.0701930.070312

0.0704300.0705490.0706680.0707880.070907

0.0710260.0711460.0712660.0713860.071506

0.0716260.0717470.0718670.0719880.072109

0.0722300.0723510.0724730.0725940.072716

0.0728380.0729590.0730820.0732040.073326

0.073449

20


0001020304

0506070809

1011121314

1516171819

2021222324

2526272829

3031323334

3536373839

4041424344

4546474849

5051525354

5556575859

60

32°

0.0810970.0812290.0813620.0814940.081627

0.0817600.0818940.0820270.0821610.082294

0.0824280.0825620.0826970.0828310.082966

0.0831000.0832350.0833710.0835060.083641

0.0837770.0839130.0840490.0841850.084321

0.0844580.0845940.0847310.0848680.085005

0.0851420.0852800.0854180.0855550.085693

0.0858320.0859700.0861080.0832470.086386

0.0865250.0866640.0868040.0869430.087083

0.0872230.0873630.0875030.0876440.087784

0.0879250.0880660.0882070.0883480.088490

0.0886310.0887730.0889150.0890570.089200

0.089342

0.0893420.0894850.0896280.0897710.089914

0.0900580.0902010.0903450.0904890.090633

0.0907770.0909220.0910670.0912110.091356

0.0915020.0916470.0917920.0919380.092084

0.0922300.0923770.0925230.0926700.092816

0.0929630.0931110.0932580.0934060.093533

0.0937010.0938490.0939980.0941460.094295

0.0944430.0945920.0947420.0948910.095041

0.0951900.0953400.0954900.0956410.095791

0.0959420.0960930.0962440.0963950.096546

0.0966980.0968500.0970020.0971540.097306

0.0974590.0976110.0977640.0979170.098071

0.098224

0.0982240.0983780.0985310.0986850.098840

0.0989940.0991490.0993030.0994580.099614

0.0997690.0999240.1000800.1002360.100392

0.1005480.1007050.1008620.1010190.101176

0.1013330.1014900.1016480.1018060.101964

0.1021220.1022800.1024390.1025980.102757

0.1029160.1030750.1032350.1033950.103555

0.1037150.1038750.1040360.1041960.104357

0.1045180.1046800.1048410.1050030.105165

0.1053270.1054890.1056520.1058140.105977

0.1061400.1063040.1064670.1066310.106795

0.1069590.1071230.1072880.1074520.107617

0.107782

0.1077820.1079480.1081130.1082790.108445

0.1086110.1087770.1089430.1091100.109277

0.1094440.1096110.1097790.1099470.110114

0.1102830.1104510.1106190.1107880.110957

0.1111260.1112950.1114650.1116350.111805

0.1119750.1121450.1123160.1124860.112657

0.1128290.1130000.1131710.1133430.113515

0.1136870.1138600.1140320.1142050.114378

0.1145520.1147250.1148990.1150730.115247

0.1154210.1155950.1157700.1159450.116120

0.1162960.1164710.1166470.1168230.116999

0.1171750.1173520.1175290.1177060.117883

0.118061

0.1180610.1182380.1184160.1185940.118772

0.1189510.1191300.1193090.1194880.119667

0.1198470.1200270.1202070.1203870.120567

0.1207480.1209290.1211100.1212910.121473

0.1216550.1218370.1220190.1222010.122384

0.1225670.1227500.1229330.1231160.123300

0.1234840.1236680.1238530.1240370.124222

0.1244070.1245920.1247780.1249640.125150

0.1253360.1255220.1257090.1258950.126083

0.1262700.1264570.1266450.1268330.127021

0.1272090.1273980.1275870.1277760.127965

0.1281550.1283440.1285340.1287250.128915

0.129106

0.1291060.1292960.1294880.1296790.129870

0.1300620.1302540.1304460.1306390.130832

0.1310250.1312180.1314110.1316050.131798

0.1319930.1321870.1323810.1325760.132771

0.1329660.1331620.1333570.1335530.133750

0.1339460.1341430.1343390.1345360.134734

0.1349310.1351290.1353270.1355250.135724

0.1359230.1361220.1363210.1365200.136720

0.1369200.1371200.1373200.1375210.137722

0.1379230.1381240.1383260.1385280.138730

0.1389320.1391340.1393370.1395400.139743

0.1399470.1401510.1403550.1405590.140763

0.140968

0.1409680.1411730.1413780.1415830.141789

0.1419950.1422010.1424080.1426140.142821

0.1430280.1432360.1434430.1436510.143859

0.1440670.1442760.1444850.1446940.144903

0.1451130.1453230.1455330.1457430.145954

0.1461650.1463760.1465870.1467980.147010

0.1472220.1474350.1476470.1478600.148073

0.1482860.1485000.1487140.1489280.149142

0.1493570.1495720.1497870.1500020.150218

0.1504330.1506500.1508660.1510830.151299

0.1515160.1517340.1519510.1521690.152388

0.1526060.1528250.1530430.1532630.153482

0.153702

0.153700.153920.154140.154360.15458

0.154800.155030.155250.15547015569

0.155910.156140.156360.156580.15680

0.157030.157250.157480.157700.15793

0.158150.158380.158600.158830.15905

0.159280.159510.159730.159960.16019

0.160410.160640.160870.161100.16133

0.161560.161780.162010.162240.16247

0.162700.162930.163170.163400.16363

0.163860.164090.164320.164560.16479

0.165020.166250.165490.165720.16596

0.166190.166420.166660.166890.16713

0.16737

33° 34° 35° 36° 37° 38° 39° 40° 41°


0.167370.167600.167840.168070.16831

0.168550.168790.169020.169260.16950

0.169740.169980.170220.170450.17069

0.170930.171170.171420.171660.17190

0.172140.172380.172620.172860.17311

0.173350.173590.173830.174080.17432

0.174570.174810.175060.175300.17555

0.175790.176040.176280.176530.17678

0.177020.177270.177520.177770.17801

0.178260.178510.178760.179010.17926

0.179510.179760.180010.180260.18051

0.180760.181010.181270.181520.18177

0.18202

21


0001020304

0506070809

1011121314

1516171819

2021222324

2526272829

3031323334

3536373839

4041424344

4546474849

5051525354

5556575859

60

42°

0.182020.182280.182530.182780.18304

0.183290.183550.183800.184060.18431

0.184570.184820.185080.185340.18559

0.185850.186110.186370.186620.18688

0.187140.187400.187660.187920.18818

0.188440.188700.188960.189220.18948

0.189750.190010.190270.190530.19080

0.191060.191320.191590.191850.19212

0.192380.192650.192910.193180.19344

0.193710.193980.194240.194510.19478

0.195050.195320.195580.195850.19612

0.196390.196660.196930.197200.19747

0.19774

0.197740.198020.198290.198560.19883

0.199100.199380.199650.199920.20020

0.200470.200750.201020.201300.20157

0.201850.202120.202400.202680.20296

0.203230.203510.203790.204070.20435

0.204630.204900.205180.205460.20575

0.206030.206310.206590.206870.20715

0.207430.207720.208000.208280.20857

0.208850.209140.209420.209710.20999

0.210280.210560.210850.211140.21142

0.211710.212000.212290.212570.21286

0.213150.213440.213730.214020.21431

0.21460

0.214600.214890.215180.215480.21577

0.216060.216350.216650.216940.21723

0.217530.217820.218120.218410.21871

0.219000.219300.219600.219890.22019

0.220490.220790.221080.221380.22168

0.221980.222280.222580.222880.22318

0.223480.223780.224090.224390.22469

0.224990.225300.225600.225900.22621

0.226510.226820.227120.227430.22773

0.228040.228350.228650.228960.22927

0.229580.229890.230200.230500.23081

0.231120.231430.231740.232060.23237

0.23268

0.232680.232990.233300.233620.23393

0.234240.234560.234870.235190.23550

0.235820.236130.236450.236760.23708

0.237400.237720.238030.238350.23867

0.238990.239310.239630.239950.24027

0.240590.240910.241230.241560.24188

0.242200.242530.242850.243170.24350

0.243820.244150.244470.244800.24512

0.245450.245780.246110.246430.24676

0.247090.247420.247750.248080.24841

0.248740.249070.249400.249730.25006

0.250400.250730.251060.251400.25173

0.25206

0.252060.252400.252730.253070.25341

0.253740.254080.254420.254750.25509

0.255430.255770.256110.256450.25679

0.257130.257470.257810.258150.25849

0.258830.259180.259520.259860.26021

0.260550.260890.261240.261590.26193

0.262280.262620.262970.263320.26367

0.264010.264360.264710.265060.26541

0.265760.266110.266460.266820.26717

0.267520.267870.268230.268580.26893

0.269290.269640.270000.270350.27071

0.271070.271420.271780.272140.27250

0.27285

0.272850.273210.273570.273930.27429

0.274650.275010.275380.275740.27610

0.276460.276830.277190.277550.27792

0.278280.278650.279020.279380.27975

0.280120.280480.280850.281220.28159

0.281960.282330.282700.283070.28344

0.283810.284180.284550.284930.28530

0.285670.286050.286420.286800.28717

0.287550.287920.288300.288680.28906

0.289430.289810.290190.290570.29095

0.291330.291710.292090.292470.29286

0.293240.293620.294000.294390.29477

0.29516

0.295160.295540.295930.296310.29670

0.297090.297470.297860.298250.29864

0.299030.299420.299810.300200.30059

0.300980.301370.301770.302160.30255

0.302950.303340.303740.304130.30453

0.304920.305320.305720.306110.30651

0.306910.307310.307710.308110.30851

0.308910.309310.309710.310120.31052

0.310920.311330.311730.312140.31254

0.312950.313350.313760.314170.31457

0.314980.315390.315800.316210.31662

0.317030.317440.317850.318260.31868

0.31909

0.319090.319500.319920.320330.32075

0.321160.321580.321990.322410.32283

0.323240.323660.324080.324500.32492

0.325340.325760.326180.326610.32703

0.327450.327870.328300.328720.32915

0.329570.330000.330420.330850.33128

0.331710.332130.332560.332990.33342

0.333850.334280.334710.335150.33558

0.336010.336450.336880.337310.33775

0.338180.338620.339060.339490.33993

0.340370.340810.341250.341690.34213

0.342570.343010.343450.343890.34434

0.34478

0.344780.345220.345670.346110.34656

0.347000.347450.347900.348340.34879

0.349240.349690.350140.350590.35104

0.351490.351940.352400.352850.35330

0.353760.354210.354670.355120.35558

0.356040.356490.356950.357410.35787

0.358330.358790.359250.359710.36017

0.360630.361100.361560.362020.36249

0.362950.363420.363880.364350.36482

0.365290.365750.366220.366690.36716

0.367630.368100.368580.369050.36952

0.369990.370470.370940.371420.37189

0.37237

43° 44° 45° 46° 47° 48° 49° 50° 51°


0.433900.434460.435010.435560.43611

0.436670.437220.437780.438330.43889

0.439450.440010.440570.441130.44169

0.442250.442810.443370.443930.44450

0.445060.445630.446190.446760.44733

0.447890.448460.449030.449600.45017

0.450740.451320.451890.452460.45304

0.453610.454190.454760.455340.45592

0.456500.457080.457660.458240.45882

0.459400.459980.460570.461150.46173

0.462320.462910.463490.464080.46467

0.465260.465850.466440.467030.46762

0.46822

0.372370.372850.373320.373800.37428

0.374760.375240.375720.376200.37668

0.377160.377650.378130.378610.37910

0.379580.380070.380550.381040.38153

0.382020.382510.382990.383480.38397

0.384460.384960.385450.385940.38643

0.386930.387420.387920.388410.38891

0.389410.389900.390400.390900.39140

0.391900.392400.392900.393400.39390

0.394410.394910.395410.395920.39642

0.396930.397430.397940.398450.39896

0.399470.399980.400490.401000.40151

0.40202

22


0001020304

0506070809

1011121314

1516171819

2021222324

2526272829

3031323334

3536373839

4041424344

4546474849

5051525354

5556575859

60

52°

0.402020.402530.403050.403560.40407

0.404590.405110.405620.406140.40666

0.407170.407690.408210.408730.40925

0.409770.410300.410820.411340.41187

0.412390.412920.413440.413970.41450

0.415020.415550.416080.416610.41714

0.417670.418200.418740.419270.41980

0.420340.420870.421410.421940.42248

0.423020.423550.424090.424630.42517

0.425710.426250.426800.427340.42788

0.428430.428970.429520.430060.43061

0.431160.431710.432250.432800.43335

0.43390

0.468220.468810.469400.470000.47060

0.471190.471790.472390.472990.47359

0.474190.474790.475390.475990.47660

0.477200.477800.478410.479020.47962

0.480230.480840.481450.482060.48267

0.483280.483890.484510.485120.48574

0.486350.486970.487580.488200.48882

0.489440.490060.490680.491300.49193

0.492550.493170.493800.494420.49505

0.495680.496300.496930.497560.49819

0.498820.499450.500090.500720.50135

0.501990.502630.503260.503900.50454

0.50518

0.505180.505820.506460.507100.50774

0.508380.509030.509670.510320.51096

0.511610.512260.512910.513560.51421

0.514860.515510.516160.516820.51747

0.518130.518780.519440.520100.52076

0.521410.522070.522740.523400.52406

0.524720.525390.526050.526720.52739

0.528050.528720.529390.530060.53073

0.531410.532080.532750.533430.53410

0.534780.535460.536130.536810.53749

0.538170.538850.539540.540220.54090

0.541590.542280.542960.543650.54434

0.54503

0.545030.545720.546410.547100.54779

0.548490.549180.549880.550570.55127

0.551970.552670.553370.554070.55477

0.555470.556180.556880.557590.55829

0.559000.559710.560420.561130.56184

0.562550.563260.563980.564690.56541

0.566120.566840.567560.568280.56900

0.569720.570440.571160.571880.57261

0.573330.574060.574790.575520.57625

0.576980.577710.578440.579170.57991

0.580640.581380.582110.582850.58359

0.584330.585070.585810.586560.58730

0.58804

0.588040.588790.589540.590280.59103

0.591780.592530.593280.594030.59479

0.595540.596300.597050.597810.59857

0.599330.600090.600850.601610.60237

0.603140.603900.604670.605440.60620

0.606970.607740.608510.609290.61006

0.610830.611610.612390.613160.61394

0.614720.615500.616280.617060.61785

0.618630.619420.620200.620990.62178

0.622570.623360.624150.624940.62574

0.626530.627330.628120.628920.62972

0.630520.631320.632120.632930.63373

0.63454

0.634540.635340.636150.636960.63777

0.638580.639390.640200.641020.64183

0.642650.643460.644280.645100.64592

0.646740.647560.648390.649210.65004

0.650860.651690.652520.653350.65418

0.655010.655850.656680.657520.65835

0.659190.660030.660870.661710.66255

0.663400.664240.665090.665940.66678

0.667630.668480.669330.670190.67104

0.671890.672750.673610.674470.67532

0.676180.677050.677910.678770.67964

0.680500.681370.682240.683110.68398

0.68485

0.684850.685730.686600.687480.68835

0.689230.690110.690990.691870.69276

0.693640.694520.695410.696300.69719

0.698080.698970.699860.700750.70165

0.702540.703440.704340.705240.70614

0.707040.707940.708850.709750.71066

0.711570.712480.713390.714300.71521

0.716130.717040.717960.718880.71980

0.720720.721640.722560.723490.72441

0.725340.726270.727200.728130.72906

0.729990.730930.731860.732800.73374

0.734680.735620.736560.737510.73845

0.73940

0.739400.740340.741290.742240.74319

0.744150.745100.746060.747010.74797

0.748930.749890.750850.751810.75278

0.753750.754710.755680.756650.75762

0.758590.759570.760540.761520.76250

0.763480.764460.765440.766420.76741

0.768390.769380.770370.771360.77235

0.773340.774340.775330.776330.77733

0.778330.779330.780330.781340.78234

0.783350.784360.785370.786380.78739

0.788400.789420.790440.791460.79247

0.793500.794520.795540.796570.79759

0.79862

53° 54° 55° 56° 57° 58° 59° 60° 61°


0.798620.799650.800680.801720.80275

0.803780.804820.805860.806900.80794

0.808980.810030.811070.812120.81317

0.814220.815270.816320.817380.81844

0.819490.820550.821610.822670.82374

0.824800.825870.826940.828010.82908

0.830150.831230.832300.833380.83446

0.835540.836620.837700.838790.83987

0.840960.842050.843140.844240.84533

0.846430.847520.848620.849720.85082

0.851930.853030.854140.855250.85636

0.857470.858580.859700.860820.86193

0.86305

23


0001020304

0506070809

1011121314

1516171819

2021222324

2526272829

3031323334

3536373839

4041424344

4546474849

5051525354

5556575859

60

62°

0.863050.864170.865300.866420.86755

0.868680.869800.870940.872070.87320

0.874340.875480.876620.877760.87890

0.880040.881190.882340.883490.88464

0.885790.886940.888100.889260.89042

0.891580.892740.893900.895070.89624

0.897410.898580.899750.900920.90210

0.903280.904460.905640.906820.90801

0.909190.910380.911570.912760.91396

0.915150.916350.917550.918750.91995

0.921150.922360.923570.924780.92599

0.927200.928420.929630.930850.93207

0.93329

0.933290.934520.935740.936970.93820

0.939430.940660.941900.943130.94437

0.945610.946850.948100.949340.95059

0.951840.953090.954340.955600.95686

0.958120.959380.960640.961900.96317

0.964440.965710.966980.968250.96953

0.970810.972090.973370.974650.97594

0.977220.978510.979800.981100.98239

0.983690.984990.986290.987590.98890

0.990200.991510.992820.994140.99545

0.996770.998080.999411.000731.00205

1.003381.004711.006041.007371.00871

1.01004

1.010041.011381.012721.014071.01541

1.016761.018111.019461.020811.02217

1.023521.024881.026241.027611.02897

1.030341.031711.033081.034461.03583

1.037211.038591.039971.041361.04274

1.044131.045521.046921.048311.04971

1.051111.052511.053911.055321.05673

1.058141.059551.060971.062381.06380

1.065221.066651.068071.069501.07093

1.072361.073801.075241.076671.07812

1.079561.081001.082451.083901.08536

1.086811.088271.089731.091191.09265

1.09412

1.094121.095591.097061.098531.10001

1.101491.102971.104451.105931.10742

1.108911.110401.111901.113391.11489

1.116391.117901.119401.120911.12242

1.123931.125451.126971.128491.13001

1.131541.133061.134591.136131.13766

1.139201.140741.142281.143831.14537

1.146921.148471.150031.151591.15315

1.154711.156271.157841.159411.16098

1.162561.164131.165711.167291.16888

1.170471.172061.173651.175241.17684

1.178441.180041.181651.183261.18487

1.18648

1.186481.188101.189721.191341.19296

1.194591.196221.197851.199481.20112

1.202761.204401.206041.207691.20934

1.211001.212651.214311.215971.21763

1.219301.220971.222641.224321.22599

1.227671.229361.231041.232731.23442

1.236121.237811.239511.241221.24292

1.244631.246341.248051.249771.25149

1.253211.254941.256661.258391.26013

1.261871.263601.264351.267091.26884

1.270591.272351.274101.275861.27762

1.279361.281161.282931.284701.28648

1.28826

1.288261.290051.291831.293621.29541

1.297211.299011.300811.302621.30442

1.306231.308051.309861.311681.31351

1.315331.317161.318991.320831.32267

1.324511.326351.328201.330051.33191

1.333761.335621.337491.339351.34122

1.343101.344971.346851.348741.35062

1.352511.354401.356301.358201.36010

1.362011.363911.365831.367741.36966

1.371581.373511.375441.377371.37930

1.381241.383181.385131.387081.38903

1.390981.392941.394901.396871.39884

1.40081

1.400811.402791.404771.406751.40874

1.410731.412721.414721.416721.41872

1.420731.422741.424751.426771.42879

1.430811.432841.434871.436911.43895

1.440991.443041.445091.447141.44920

1.451261.453321.455391.457461.45954

1.461621.463701.465791.467881.46997

1.472071.474171.476271.478381.48050

1.482611.484731.486861.488981.49112

1.493251.495391.497531.499681.50183

1.503991.506141.508311.510471.51264

1.514821.517001.519181.521361.52355

1.52575

1.525751.527941.530151.532351.53456

1.536781.538991.541221.543441.54567

1.547911.550141.552391.554631.55688

1.559141.561401.563661.565931.56820

1.570471.572751.575031.577321.57961

1.581911.584211.586521.588821.59114

1.593461.595781.598101.600431.60277

1.605111.607451.609801.612151.61451

1.616871.619231.621601.623981.62636

1.628741.631131.633521.635921.63832

1.640721.643131.645551.647971.65039

1.652821.655251.657691.660131.66258

1.66503

1.665031.667481.669941.672411.67488

1.677351.679831.682321.684801.68730

1.689801.692301.694811.697321.69984

1.702361.704881.707421.709951.71249

1.715041.717591.720151.722711.72527

1.727851.730421.733001.735591.73818

1.740771.743381.745981.748591.75121

1.753831.756461.759091.761721.76436

1.767011.769661.772321.774981.77765

1.780321.783001.785681.788371.79106

1.793761.796471.799181.801891.80461

1.807341.810071.812801.815551.81829

1.82105

63° 64° 65° 66° 67° 68° 69° 70° 71°


2.684332.689022.693712.698422.70314

2.707872.712622.717372.722142.72692

2.731712.736512.741332.746162.75100

2.755852.760712.765592.770482.77538

2.780292.785222.790162.795112.80007

2.805052.810042.815042.820062.82508

2.830122.835182.840242.845322.85041

2.855522.860642.865772.870922.87607

2.881252.886432.891632.896842.90207

2.907312.912562.917832.923112.92840

2.933712.939032.944372.949722.95509

2.960462.965862.971262.976692.98212

2.98757

1.821051.823801.826571.829341.83211

1.834891.837681.840471.843261.84607

1.848881.851691.854511.857331.86016

1.863001.865841.868691.871541.87440

1.877261.880141.883011.885891.88878

1.891671.894571.897481.900391.90331

1.906231.909161.912101.915041.91798

1.920941.923891.926861.929831.93281

1.935791.938781.941781.944781.94779

1.950801.953821.956851.959881.96292

1.965961.969011.972071.975141.97821

1.981281.984371.987461.990551.99365

1.99676

24


0001020304

0506070809

1011121314

1516171819

2021222324

2526272829

3031323334

3536373839

4041424344

4546474849

5051525354

5556575859

60

72°

1.996761.999882.003002.006132.00926

2.012402.015552.018712.021872.02504

2.028212.031392.034582.037772.04097

2.044182.047402.050622.053851.05708

2.060322.063572.066832.070092.07336

2.076642.079922.083212.086512.08981

2.093132.096452.099772.103102.10644

2.109792.113152.116512.119882.12325

2.126642.130032.133432.136832.14024

2.143662.147092.150532.153972.15742

2.160882.164342.167812.171302.17478

2.178282.181782.185292.188812.19234

2.19587

2.195872.199412.202962.206522.21008

2.213662.217242.220832.334422.22803

2.231642.235262.238892.242532.24617

2.249832.253492.257162.260832.26452

2.268212.271922.275632.279352.28307

2.286812.290552.294302.298072.30184

2.305612.309402.313192.317002.32081

2.324632.328462.332302.336152.34000

2.343872.347742.351622.355512.35941

2.363322.367242.371172.375112.37905

2.383002.386972.390942.394922.39891

2.402912.406922.411942.414972.41901

2.42305

2.423052.427112.431182.435252.43934

2.443432.447532.451652.455772.45990

2.464052.468202.472362.476532.48071

2.484912.489112.493322.497542.50177

2.506012.510272.514532.518802.52308

2.527372.531682.535992.540312.54465

2.548992.553342.557712.562082.56647

2.570872.575272.579692.584122.58856

2.593012.597472.601942.606422.61092

2.615422.619942.624462.629002.63355

2.638112.642682.647262.651862.65646

2.661082.665712.670342.675002.67966

2.68433

2.987572.993042.998523.004013.00952

3.015043.020583.026133.031703.03728

3.042883.048493.054123.059773.06542

3.071103.076793.082493.088213.09395

3.099703.105463.111253.117043.12286

3.128693.134533.140403.146273.15217

3.158083.164013.169953.175913.18188

3.187883.193893.199913.205953.21201

3.218093.224183.230293.236423.24257

3.248733.254913.261103.267323.27355

3.279803.286063.292353.298653.30497

3.311313.317673.324043.330433.33684

3.34327

3.343273.349723.356193.362673.36918

3.375703.382243.388803.395383.40197

3.408593.415233.421883.428563.43525

3.441973.448703.455453.462223.46902

3.475833.482663.489523.496393.50328

3.510203.517133.524083.531063.53806

3.545073.552113.559173.566253.57335

3.580473.587623.594783.601973.60918

3.616413.623663.630943.638233.64555

3.652893.660263.667643.675053.68248

3.689933.697413.704913.712433.71998

3.727553.735143.742753.750393.75806

3.76574

3.765743.773453.781193.788953.79673

3.804543.812373.830233.828113.83601

3.843953.851903.859883.867893.87592

3.883983.892063.900173.908303.91646

3.924653.932863.941103.949373.95766

3.965983.974333.982703.991103.99953

4.007984.016464.024974.033514.04207

4.050674.059294.067944.076624.08532

4.094064.102824.111624.120444.12929

4.138174.147084.156021.164994.17399

4.183024.192084.201184.210304.21945

4.228634.237854.247094.256374.26568

4.27502

4.275024.284394.293794.303234.31270

4.322204.331734.341304.350904.36053

4.370204.379904.389634.399404.40920

4.419034.428904.438804.448744.45871

4.468724.478774.488854.498964.50911

4.519304.529524.539784.550074.56041

4.570774.581184.591624.602104.61262

4.623184.633774.644414.655084.66579

4.676544.687334.698164.709024.71993

4.730884.741864.752894.763964.77507

4.786224.797414.808654.819924.83124

4.842604.854004.865444.876934.88846

4.90003

4.900034.911654.923314.935024.94677

4.958564.970404.982294.994225.00620

5.018225.030295.042405.054565.06677

5.079025.091335.103685.116085.12852

5.141025.153565.166165.178805.19149

5.204245.217035.229875.242775.25572

5.268715.281765.294865.308025.32122

5.334485.347805.361175.374595.38806

5.401595.415185.428825.442515.45626

5.470075.483945.497865.511845.52588

5.539975.554135.568345.582615.59694

5.611335.625785.640305.654875.66950

5.68420

73° 74° 75° 76° 77° 78° 79° 80° 81°

Numerical Formulas and Tables - khkgears.co.jp · 4 Numerical Formulas and Tables square metre...

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