Appendix 2

HARDNESS TEST

What is Hardness? Hardness is the property of a material that enables it to resist plastic deformation, usually by penetration. However, the term hardness may also refer to resistance to bending, scratching, abrasion or cutting.

Measurement of Hardness: Hardness is not an intrinsic material property dictated by precise definitions in terms of fundamental units of mass, length and time. A hardness property value is the result of a defined measurement procedure. Hardness of materials has probably long been assessed by resistance to scratching or cutting. An example would be material B scratches material C, but not material A. Alternatively, material A scratches material B slightly and scratches material C heavily. Relative hardness of minerals can be assessed by reference to the Moh's Scale that ranks the ability of materials to resist scratching by another material. Similar methods of relative hardness assessment are still commonly used today. An example is the file test where a file tempered to a desired hardness is rubbed on the test material surface. If the file slides without biting or marking the surface, the test material would be considered harder than the file. If the file bites or marks the surface, the test material would be considered softer than the file. The above relative hardness tests are limited in practical use and do not provide accurate numeric data or scales particularly for modern day metals and materials. The usual method to achieve a hardness value is to measure the depth or area of an indentation left by an indenter of a specific shape, with a specific force applied for a specific time. There are three principal standard test methods for expressing the relationship between hardness and the size of the impression, these being Brinell, Vickers, and Rockwell. For practical and calibration reasons, each of these methods is divided into a range of scales, defined by a combination of applied load and indenter geometry.

Hardness Test Methods:

Rockwell Hardness Test Rockwell Superficial Hardness Test Brinell Hardness Test Vickers Hardness Test Microhardness Test

Moh's Hardness Test Scleroscope and other hardness test methods

Hardness Conversion or Equivalents: Hardness conversion between different methods and scales cannot be made mathematically exact for a wide range of materials. Different loads, different shape of indeters, homogeneity of specimen, cold working properties and elastic properties all complicate the problem. All tables and charts should be considered as giving approximate equivalents, particularly when converting to a method or scale which is not physically possible for the particular test material and thus cannot be verified. An example would be converting HV/10 or HR-15N value on a thin coating to the HRC equivalent.

Appendix 3

Rockwell Hardness Test The Rockwell hardness test method consists of indenting the test material with a diamond cone or hardened steel ball indenter. The indenter is forced into the test material under a preliminary minor load F0 (Fig. 1A) usually 10 kgf. When equilibrium has been reached, an indicating device, which follows the movements of the indenter and so responds to changes in depth of penetration of the indenter is set to a datum position. While the preliminary minor load is still applied an additional major load is applied with resulting increase in penetration (Fig. 1B). When equilibrium has again been reach, the additional major load is removed but the preliminary minor load is still maintained. Removal of the additional major load allows a partial recovery, so reducing the depth of penetration (Fig. 1C). The permanent increase in depth of penetration, resulting from the application and removal of the additional major load is used to calculate the Rockwell hardness number.

HR = E - e F0 = preliminary minor load in kgf F1 = additional major load in kgf F = total load in kgf e = permanent increase in depth of penetration due to major load F1 measured in units of 0.002 mm E = a constant depending on form of indenter: 100 units for diamond indenter, 130 units for steel ball indenter HR = Rockwell hardness number D = diameter of steel ball

Fig. 1.Rockwell Principle

Rockwell Hardness Scales

Scale Indenter Minor Load

F0 kgf

Major LoadF1 kgf

Total LoadF

kgf

Value of E

A Diamond cone 10 50 60 100

B 1/16" steel ball 10 90 100 130

C Diamond cone 10 140 150 100

D Diamond cone 10 90 100 100

E 1/8" steel ball 10 90 100 130

F 1/16" steel ball 10 50 60 130

G 1/16" steel ball 10 140 150 130

H 1/8" steel ball 10 50 60 130

K 1/8" steel ball 10 140 150 130

L 1/4" steel ball 10 50 60 130

M 1/4" steel ball 10 90 100 130

P 1/4" steel ball 10 140 150 130

R 1/2" steel ball 10 50 60 130

S 1/2" steel ball 10 90 100 130

V 1/2" steel ball 10 140 150 130

Typical Application of Rockwell Hardness Scales

HRA . . . . Cemented carbides, thin steel and shallow case hardened steel HRB . . . . Copper alloys, soft steels, aluminium alloys, malleable irons, etc HRC . . . . Steel, hard cast irons, case hardened steel and other materials harder than 100 HRB HRD . . . . Thin steel and medium case hardened steel and pearlitic malleable iron HRE . . . . Cast iron, aluminium and magnesium alloys, bearing metals HRF . . . . Annealed copper alloys, thin soft sheet metals HRG . . . . Phosphor bronze, beryllium copper, malleable irons HRH . . . . Aluminium, zinc, lead HRK . . . . } HRL . . . . } HRM . . . .} . . . . Soft bearing metals, plastics and other very soft materials HRP . . . . } HRR . . . . } HRS . . . . } HRV . . . . } Advantages of the Rockwell hardness method include the direct Rockwell hardness number readout and rapid testing time. Disadvantages include many arbitrary non-related scales and possible effects from the specimen support anvil (try putting a

cigarette paper under a test block and take note of the effect on the hardness reading! Vickers and Brinell methods don't suffer from this effect).

Appendix 4

Rockwell Superficial Hardness Test The Rockwell Superficial hardness test method consists of indenting the test material with a diamond cone (N scale) or hardened steel ball indenter. The indenter is forced into the test material under a preliminary minor load F0 (Fig. 1A) usually 3 kgf. When equilibrium has been reached, an indicating device that follows the movements of the indenter and so responds to changes in depth of penetration of the indenter is set to a datum position. While the preliminary minor load is still applied an additional major load, is applied with resulting increase in penetration (Fig. 1B). When equilibrium has again been reach, the additional major load is removed but the preliminary minor load is still maintained. Removal of the additional major load allows a partial recovery, so reducing the depth of penetration (Fig. 1C). The permanent increase in depth of penetration, e, resulting from the application and removal of the additional major load is used to calculate the Rockwell Superficial hardness number.

HR = E - e F0 = preliminary minor load in kgf F1 = additional major load in kgf F = total load in kgf e = permanent increase in depth of penetration due to major load F1, measured in units of 0.001 mm E = a constant of 100 units for diamond and ball indenters HR = Rockwell hardness number D = diameter of steel ball

Fig. 1.Rockwell Superficial Principle

Rockwell Superficial Hardness Scales

Scale Indenter Type Minor Load

F0 kgf

Major LoadF1 kgf

Total Load F

kgf

Value of E

HR 15 N N Diamond cone 3 12 15 100

HR 30 N N Diamond cone 3 27 30 100

HR 45 N N Diamond cone 3 42 45 100

HR 15 T 1/16" steel ball 3 12 15 100

HR 30 T 1/16" steel ball 3 27 30 100

HR 45 T 1/16" steel ball 3 42 45 100

HR 15 W 1/8" steel ball 3 12 15 100

HR 30 W 1/8" steel ball 3 27 30 100

HR 45 W 1/8" steel ball 3 42 45 100

HR 15 X 1/4" steel ball 3 12 15 100

HR 30 X 1/4" steel ball 3 27 30 100

HR 45 X 1/4" steel ball 3 42 45 100

HR 15 Y 1/2" steel ball 3 12 15 100

HR 30 Y 1/2" steel ball 3 27 30 100

HR 45 Y 1/2" steel ball 3 42 45 100

Appendix 5

The Brinell Hardness Test The Brinell hardness test method consists of indenting the test material with a 10 mm diameter hardened steel or carbide ball subjected to a load of 3000 kg. For softer materials the load can be reduced to 1500 kg or 500 kg to avoid excessive indentation. The full load is normally applied for 10 to 15 seconds in the case of iron and steel and for at least 30 seconds in the case of other metals. The diameter of the indentation left in the test material is measured with a low powered microscope. The Brinell harness number is calculated by dividing the load applied by the surface area of the indentation.

The diameter of the impression is the average of two readings at right angles and the use

of a Brinell hardness number table can simplify the determination of the Brinell hardness. A well structured Brinell hardness number reveals the test conditions, and looks like this, "75 HB 10/500/30" which means that a Brinell Hardness of 75 was obtained using a 10mm diameter hardened steel with a 500 kilogram load applied for a period of 30 seconds. On tests of extremely hard metals a tungsten carbide ball is substituted for the steel ball. Compared to the other hardness test methods, the Brinell ball makes the deepest and widest indentation, so the test averages the hardness over a wider amount of material, which will more accurately account for multiple grain structures and any irregularities in the uniformity of the material. This method is the best for achieving the bulk or macro-hardness of a material, particularly those materials with heterogeneous structures.

Appendix 6

Vickers Hardness Test The Vickers hardness test method consists of indenting the test material with a diamond indenter, in the form of a right pyramid with a square base and an angle of 136 degrees between opposite faces subjected to a load of 1 to 100 kgf. The full load is normally applied for 10 to 15 seconds. The two diagonals of the indentation left in the surface of the material after removal of the load are measured using a microscope and their average calculated. The area of the sloping surface of the indentation is calculated. The Vickers hardness is the quotient obtained by dividing the kgf load by the square mm area of indentation.

F= Load in kgf d = Arithmetic mean of the two diagonals, d1 and d2 in mm

HV = Vickers hardness

When the mean diagonal of the indentation has been determined the Vickers hardness may be calculated from the formula, but is more convenient to use conversion tables. The Vickers hardness should be reported like 800 HV/10, which means a Vickers hardness of 800, was obtained using a 10 kgf force. Several different loading settings give practically identical hardness numbers on uniform material, which is much better than the arbitrary changing of scale with the other hardness testing methods. The advantages of the Vickers hardness test are that extremely accurate readings can be taken, and just one type of indenter is used for all types of metals and surface treatments. Although thoroughly adaptable and very precise for testing the softest and hardest of materials, under varying loads, the Vickers machine is a floor standing unit that is more expensive than the Brinell or Rockwell machines. There is now a trend towards reporting Vickers hardness in SI units (MPa or GPa) particularly in academic papers. Unfortunately, this can cause confusion. Vickers hardness (e.g. HV/30) value should normally be expressed as a number only (without the units kgf/mm2). Rigorous application of SI is a problem. Most Vickers hardness testing machines use forces of 1, 2, 5, 10, 30, 50 and 100 kgf and tables for calculating HV. SI would involve reporting force in newtons (compare 700 HV/30 to HV/294 N = 6.87 GPa) which is practically meaningless and messy to engineers and technicians. To convert a Vickers hardness number the force applied needs converting from kgf to newtons and the area needs converting form mm2 to m2 to give results in pascals using the formula above. To convert HV to MPa multiply by 9.807 To convert HV to GPa multiply by 0.009807

Appendix 7

Microhardness Test The term microhardness test usually refers to static indentations made with loads not exceeding 1 kgf. The indenter is either the Vickers diamond pyramid or the Knoop elongated diamond pyramid. The procedure for testing is very similar to that of the standard Vickers hardness test, except that it is done on a microscopic scale with higher precision instruments. The surface being tested generally requires a metallographic finish; the smaller the load used, the higher the surface finish required. Precision microscopes are used to measure the indentations; these usually have a magnification of around X500 and measure to an accuracy of +0.5 micrometres. Also with the same observer differences of +0.2 micrometres can usually be resolved. It should, however, be added that considerable care and experience are necessary to obtain this accuracy.

Knoop Hardness Indenter Indentation

The Knoop hardness number KHN is the ratio of the load applied to the indenter, P (kgf) to the unrecovered projected area A (mm2)

KHN = F/A = P/CL2 Where: F = applied load in kgf A = the unrecovered projected area of the indentation in mm2 L = measured length of long diagonal of indentation in mm C = 0.07028 = Constant of indenter relating projected area of the indentation to the square of the length of the long diagonal. The Knoop indenter is a diamond ground to pyramidal form that produces a diamond shaped indentation having approximate ratio between long and short diagonals of 7:1. The depth of indentation is about 1/30 of its length. When measuring the Knoop hardness, only the longest diagonal of the indentation is measured and this is used in the above formula with the load used to calculate KHN. Tables of these values are

usually a more convenient way to look-up KHN values from the measurements.

Vickers Pyramid Diamond Indenter Indentation

The Vickers Diamond Pyramid harness number is the applied load (kgf) divided by the surface area of the indentation (mm2)

Where: F= Load in kgf d = Arithmetic mean of the two diagonals, d1 and d2 in mm HV = Vickers hardness The Vickers Diamond Pyramid indenter is ground in the form of a squared pyramid with an angle of 136obetween faces. The depth of indentation is about 1/7 of the diagonal length. When calculating the Vickers Diamond Pyramid hardness number, both diagonals of the indentation are measured and the mean of these values is used in the above formula with the load used to determine the value of HV. Tables of these values are usually a more convenient way to look-up HV values from the measurements.

Knoop vs. Vickers Comparing the indentations made with Knoop and Vickers Diamond Pyramid indenters for a given load and test material: Vickers indenter penetrates about twice as deep as Knoop indenter Vickers indentation diagonal about 1/3 of the length of Knoop major diagonal Vickers test is less sensitive to surface conditions than Knoop test Vickers test is more sensitive to measurement errors than knoop test Vickers test best for small rounded areas

Knoop test best for small elongated areas Knoop test good for very hard brittle materials and very thin sections

There is now a trend towards reporting Vickers and Knoop hardness in SI units (MPa or GPa) particularly in academic papers. Unfortunately, this can cause confusion. Vickers hardness (e.g. HV/30) value should normally be expressed as a number only (without the units kgf/mm2). Rigorous application of SI is a problem. Most Vickers hardness testing machines use forces of 1, 2, 5, 10, 30, 50 and 100 kgf and tables for calculating HV. SI would involve reporting force in newtons (compare 700 HV/30 to HV/294 N = 6.87 GPa) which is practically meaningless and messy to engineers and technicians. To convert a Vickers hardness number the force applied needs converting from kgf to newtons and the area needs converting form mm2 to m2 to give results in pascals using the formula above. To convert HV to MPa multiply by 9.807 To convert HV to GPa multiply by 0.009807

Appendix 7

Moh's Hardness Scale The Moh's hardness scale for minerals has been used since 1822. It simply consists of 10 minerals arranged in order from 1 to 10. Diamond is rated as the hardest and is indexed as 10; talc as the softest with index number 1. Each mineral in the scale will scratch all those below it as follows:

Diamond 10

Corundum 9

Topaz 8

Quartz 7

Orthoclase (Feldspar) 6

Aptite 5

Fluorite 4

Calcite 3

Gypsum 2

Talc 1 The steps are not of equal value and the difference in hardness between 9 and 10 is much greater than between 1 and 2. The hardness is determined by finding which of the standard minerals the test material will scratch or not scratch; the hardness will lie between two points on the scale - the first point being the mineral which is scratched and the next point being the mineral which is not scratched. Some examples of the hardness of common metals in the Moh's scale are copper between 2 and 3 and tool steel between 7 and 8. This is a simple test, but is not exactly quantitative and the standards are purely arbitrary numbers. The materials engineer and metallurgist find little use for the Moh's scale, but it is possible to sub-divide the scale and some derived methods are still commonly used today. The file test is useful as a rapid and portable qualitative test for hardened steels, where convention hardness testers are not available or practical. Files can be tempered back to give a range of known hardness and then used in a similar fashion to the Moh's method to evaluate hardness.

Appendix 8

The Scleroscope Hardness Test The Scleroscope test consists of dropping a diamond tipped hammer, which falls inside a glass tube under the force of its own weight from a fixed height, onto the test specimen. The height of the rebound travel of the hammer is measured on a graduated scale. The scale of the rebound is arbitrarily chosen and consists on Shore units, divided into 100 parts, which represent the average rebound from pure hardened high-carbon steel. The scale is continued higher than 100 to include metals having greater hardness. In normal use the shore scleroscope test does not mark the material under test. The Shore Scleroscope measures hardness in terms of the elasticity of the material and the hardness number depends on the height to which the hammer rebounds, the harder the material, the higher the rebound. Advantages of this method are portability and non-marking of the test surface.

The Durometer The Durometer is a popular instrument for measuring the indentation hardness of rubber and rubber-like materials. The most popular testers are the Model A used for measuring softer materials and the Model D for harder materials. The operation of the tester is quite simple. The material is subjected to a definite pressure applied by a calibrated spring to an indenter that is either a cone or sphere and an indicating device measures the depth of indentation.

Appendix 9

Hardness Conversion Table

Approximate Hardness Equivalents Covering Range of Rockwell C and Rockwell B Scales

VPN ROCKWELL SCALES BRINELL SCLERO-SCOPE U.T.S.

DPH HV/10 A B C D E F G H K 15N 30N 45N 15T 30T 45T BHN

500kgBHN

3000kg Kpsi Mpa

1865 92 80 87 97 92 87 1787 92 79 86 96 92 87 1710 91 78 85 96 91 86 1633 91 77 84 96 91 85 1556 90 76 83 96 90 84 1478 90 75 83 95 89 83 1400 89 74 82 95 89 82 1323 89 73 81 95 88 81 1245 88 72 80 95 87 80 1160 87 71 80 94 87 79 1076 87 70 79 94 86 78 1011004 86 69 78 94 85 77 99

940 86 68 77 93 84 75 97900 85 67 76 93 84 74 95865 85 66 75 93 83 73 92832 84 65 75 92 82 72 739 91800 84 64 74 92 81 71 722 88772 83 63 73 91 80 70 705 87746 83 62 72 91 79 69 688 85720 82 61 72 91 79 68 670 83697 81 60 71 90 78 67 654 81 320 2206674 81 59 70 90 77 66 634 80 310 2137653 80 58 69 89 76 64 615 78 300 2069633 80 57 69 89 75 63 595 76 290 2000613 79 56 68 88 74 62 577 75 282 1944595 79 120 55 67 88 73 61 560 74 274 1889577 78 120 54 66 87 72 60 543 72 266 1834560 78 119 53 65 87 71 59 523 71 257 1772544 77 119 52 65 86 70 57 512 69 245 1689528 77 118 51 64 86 69 56 496 68 239 1648513 76 117 50 63 86 69 55 481 67 233 1607

498 75 117 49 62 85 68 54 469 66 227 1565484 75 116 48 61 85 67 53 455 64 221 1524471 74 116 47 61 84 66 51 443 63 217 1496458 74 115 46 60 84 65 50 432 62 212 1462446 73 115 45 59 83 64 49 421 60 206 1420434 73 114 44 59 83 63 48 409 58 200 1379423 72 113 43 58 82 62 47 400 57 196 1351412 72 113 42 57 82 61 46 390 56 191 1317402 71 112 41 56 81 60 44 381 55 187 1289392 71 112 40 55 80 60 43 371 54 182 1255382 70 111 39 55 80 59 42 362 52 177 1220372 70 110 38 54 79 58 41 353 51 173 1193363 69 110 37 53 79 57 40 344 50 169 1165354 69 109 36 52 78 56 38 336 49 165 1138345 68 109 35 52 78 55 37 327 48 160 1103336 68 108 34 51 77 54 36 319 47 156 1076327 67 108 33 50 77 53 35 311 46 152 1048318 67 107 32 49 76 52 34 301 44 147 1014310 66 106 31 48 91 76 51 33 294 43 144 993302 66 105 30 48 91 75 50 31 286 42 140 965294 65 104 29 47 89 75 50 30 279 41 137 945286 65 104 28 46 88 74 49 29 271 41 133 917279 64 103 27 45 87 73 48 28 264 40 129 889272 64 103 26 45 86 73 47 27 258 39 126 869266 63 102 25 44 85 72 46 26 253 38 124 855260 63 101 24 43 84 72 45 24 247 37 121 834254 62 100 23 42 83 71 44 23 93 82 72 201 240 36 118 814248 62 99 22 42 81 71 43 22 93 82 71 195 234 35 115 793243 61 98 21 41 79 70 42 21 93 81 70 189 228 35 112 772238 61 97 20 40 78 69 42 20 92 81 69 184 222 34 109 752234 60 97 19 77 92 80 69 181 218 34 107 738230 59 96 18 76 92 80 68 179 214 33 106 731226 59 96 17 75 92 80 68 177 210 33 104 717222 58 95 16 74 92 79 67 175 208 32 102 703217 58 95 15 73 92 79 67 171 205 31 100 690213 58 94 14 73 91 79 66 169 203 31 99 683208 57 93 13 71 91 78 66 167 200 30 98 676204 57 92 12 70 100 91 78 65 163 195 30 96 662200 56 92 11 69 100 91 77 64 162 193 29 95 655196 56 91 10 68 100 90 77 64 160 190 28 93 641192 56 90 9 66 99 90 76 63 157 185 27 91 627

188 55 89 8 64 98 90 76 62 154 180 26 88 607184 54 88 7 63 97 90 75 61 151 176 26 86 593180 54 87 6 61 97 89 75 60 148 172 26 84 579176 53 86 5 59 96 89 74 59 145 169 25 83 572172 53 85 4 58 95 89 74 58 142 165 25 81 558168 52 84 3 56 94 88 73 57 140 162 25 79 545164 51 83 2 54 93 88 72 56 137 159 24 78 538160 51 82 1 53 92 88 72 55 135 156 24 76 524156 50 81 0 51 91 87 71 54 133 153 24 75 517152 50 80 49 91 87 70 53 130 150 73 503148 49 79 48 90 87 70 52 128 147 144 49 78 46 89 86 69 51 126 144 141 48 77 44 88 86 68 50 124 141 139 47 76 43 87 86 68 49 122 139 137 47 75 100 41 86 85 67 49 120 137 135 46 74 99 39 85 85 66 48 118 135 132 46 73 99 38 85 85 66 47 116 132 130 45 72 98 36 84 84 65 46 114 130 127 45 71 100 98 35 83 84 64 45 112 127 125 44 70 100 97 33 82 84 64 44 110 125 123 44 69 99 96 31 81 83 63 43 109 123 120 43 68 98 96 30 80 83 62 42 107 121 118 43 67 98 95 28 79 83 62 41 106 119 116 42 66 97 95 27 78 82 61 40 104 117 115 42 65 96 94 25 78 82 60 39 102 116 114 42 64 96 94 24 77 82 60 38 101 114 113 41 63 95 93 22 76 81 59 37 99 112 112 41 62 95 92 21 75 81 58 36 98 110 111 40 61 94 92 19 74 81 57 35 96 108 110 40 60 93 91 18 73 81 57 34 95 107 108 39 59 93 91 16 72 80 56 32 94 106 107 39 58 92 90 15 71 80 55 31 92 104 106 38 57 91 90 13 71 80 55 30 91 102 105 38 56 91 89 12 70 79 54 29 90 101 104 38 55 90 88 10 69 79 53 28 89 99 103 37 54 90 88 9 68 79 53 27 87 102 37 53 89 87 7 67 78 52 26 86 101 36 52 88 87 6 66 78 51 25 85 100 36 51 88 86 4 65 78 51 24 84 100 35 50 87 86 3 65 77 50 23 83

99 35 49 87 85 64 77 49 22 82

98 35 48 86 85 63 77 49 21 81 97 34 47 85 84 62 76 48 20 80 96 34 46 85 83 61 76 47 19 79 95 33 45 84 83 60 76 46 18 79 95 33 44 84 82 59 75 46 17 78 94 32 43 83 82 58 75 45 16 77 93 32 42 82 81 58 75 44 15 76 92 31 41 82 81 57 74 44 14 75 91 31 40 81 80 56 74 43 13 74 90 31 39 80 79 55 74 42 11 74 90 30 38 80 79 54 73 42 10 73 89 30 37 79 78 53 73 41 9 72 88 29 36 79 78 100 52 73 40 8 71 88 29 35 78 77 100 52 72 40 7 71 87 28 34 77 77 99 51 72 39 6 70 87 28 33 77 76 99 50 72 38 5 69 86 28 32 76 75 99 49 71 38 4 68 86 27 31 76 75 98 48 71 37 3 68 85 27 30 75 74 98 47 71 36 2 67 85 26 29 74 74 98 46 70 36 1 66 84 26 28 74 73 97 45 70 35 66 84 25 27 73 73 97 45 70 34 65 83 25 26 73 72 97 44 69 33 65 83 24 25 72 71 96 42 69 33 64 82 24 24 71 71 96 42 69 32 64 82 24 23 71 70 96 41 68 31 63 81 23 22 70 70 95 40 68 31 63 81 23 21 70 69 95 39 68 30 62 80 22 20 69 69 95 38 68 29 62 80 22 19 68 68 94 38 67 29 61 79 21 18 68 67 94 37 67 28 61 79 21 17 67 67 93 36 67 27 60 78 21 16 67 66 93 35 66 26 60 78 20 15 66 66 93 34 66 26 59 77 14 65 65 92 33 66 25 59 77 13 65 65 92 32 65 24 58 76 12 64 64 92 32 65 24 58 76 11 64 64 91 31 65 23 57 75 10 63 63 91 30 64 22 57 75 9 62 62 91 29 64 22 56 74 8 62 62 90 28 64 21 56

74 7 61 61 90 27 63 20 56 73 6 61 61 90 26 63 20 55 73 5 60 60 89 26 63 19 55 72 4 59 60 89 25 62 18 55 72 3 59 59 88 24 62 17 54 71 2 58 58 88 23 62 17 54 71 1 58 58 88 22 61 16 53 70 0 57 57 87 21 61 15 53

DPH HV/10 A B C D E F G H K 15N 30N 45N 15T 30T 45T BHN

500kgBHN

3000kg Kpsi Mpa

VPN ROCKWELL SCALES BRINELL SCLERO-SCOPE U.T.S.

Appendix 9

Hardness Scale Relationship Chart

Appendix 10

Rockwell Hardness Comparison Chart

Appendix 11

Brinell and Vickers Hardness Scale and Tensile Strength Comparison Chart

Appendix 12

HARDNESS CONVERSION TABLE

Approximate Equivalents of Rockwell C Hardness Numbers for Hard Materials

VICKERS DPH ROCKWELL BRINELL

BHN SCLERO- SCOPE U.T.S.

HV/10 A C D 15-N 30-N 45-N 3000kg Kpsi MPa1865 92 80 87 97 92 87 1787 92 79 86 96 92 87 1710 91 78 85 96 91 86 1633 91 77 84 96 91 85 1556 90 76 83 96 90 84 1478 90 75 83 95 89 83 1400 89 74 82 95 89 82 1323 89 73 81 95 88 81 1245 88 72 80 95 87 80 1160 87 71 80 94 87 79 1076 87 70 79 94 86 78 101 1004 86 69 78 94 85 77 99

940 86 68 77 93 84 75 97 900 85 67 76 93 84 74 95 865 85 66 75 93 83 73 92 832 84 65 75 92 82 72 739 91 800 84 64 74 92 81 71 722 88 772 83 63 73 91 80 70 705 87 746 83 62 72 91 79 69 688 85 720 82 61 72 91 79 68 670 83 697 81 60 71 90 78 67 654 81 320 2206674 81 59 70 90 77 66 634 80 310 2137653 80 58 69 89 76 64 615 78 300 2068633 80 57 69 89 75 63 595 76 290 1999613 79 56 68 88 74 62 577 75 282 1944595 79 55 67 88 73 61 560 74 274 1889577 78 54 66 87 72 60 543 72 266 1834560 78 53 65 87 71 59 523 71 257 1772

544 77 52 65 86 70 57 512 69 245 1689528 77 51 64 86 69 56 496 68 239 1648513 76 50 63 86 69 55 481 67 233 1606498 75 49 62 85 68 54 469 66 227 1565484 75 48 61 85 67 53 455 64 221 1524471 74 47 61 84 66 51 443 63 217 1496458 74 46 60 84 65 50 432 62 212 1462446 73 45 59 83 64 49 421 60 206 1420434 73 44 59 83 63 48 409 58 200 1379423 72 43 58 82 62 47 400 57 196 1351412 72 42 57 82 61 46 390 56 191 1317402 71 41 56 81 60 44 381 55 187 1289392 71 40 55 80 60 43 371 54 182 1255382 70 39 55 80 59 42 362 52 177 1220372 70 38 54 79 58 41 353 51 173 1193363 69 37 53 79 57 40 344 50 169 1165354 69 36 52 78 56 38 336 49 165 1138345 68 35 52 78 55 37 327 48 160 1103336 68 34 51 77 54 36 319 47 156 1076327 67 33 50 77 53 35 311 46 152 1048318 67 32 49 76 52 34 301 44 147 1014310 66 31 48 76 51 33 294 43 144 993302 66 30 48 75 50 31 286 42 140 965294 65 29 47 75 50 30 279 41 137 945286 65 28 46 74 49 29 271 41 133 917279 64 27 45 73 48 28 264 40 129 889272 64 26 45 73 47 27 258 39 126 869266 63 25 44 72 46 26 253 38 124 855260 63 24 43 72 45 24 247 37 121 834254 62 23 42 71 44 23 240 36 118 814248 62 22 42 71 43 22 234 35 115 793243 61 21 41 70 42 21 228 35 112 772238 61 20 40 69 42 20 222 34 109 752

HV/10 A C D 15-N</B< TD> 30-N 45-N 3000kg Kpsi MPaVICKERS

DPH ROCKWELL BRINELLBHN

SCLERO- SCOPE U.T.S.

Appendix 13

HARDNESS CONVERSION TABLE

Approximate Equivalents of Rockwell B Hardness Numbers for Soft Metals

VICKERS DPH ROCKWELL BRINELL

BHN HV/10 B E F G H K 15-T 30-T 45-T 500kg 3000kg

254 100 83 93 82 72 201 240 248 99 81 93 82 71 195 234 243 98 79 93 81 70 189 228 238 97 78 92 81 69 184 222 234 97 77 92 80 69 181 218 230 96 76 92 80 68 179 214 226 96 75 92 80 68 177 210 222 95 74 92 79 67 175 208 217 95 73 92 79 67 171 205 213 94 73 91 79 66 169 203 208 93 71 91 78 66 167 200 204 92 70 100 91 78 65 163 195 200 92 69 100 91 77 64 162 193 196 91 68 100 90 77 64 160 190 192 90 66 99 90 76 63 157 185 188 89 64 98 90 76 62 154 180 184 88 63 97 90 75 61 151 176 180 87 61 97 89 75 60 148 172 176 86 59 96 89 74 59 145 169 172 85 58 95 89 74 58 142 165 168 84 56 94 88 73 57 140 162 164 83 54 93 88 72 56 137 159 160 82 53 92 88 72 55 135 156 156 81 51 91 87 71 54 133 153 152 80 49 91 87 70 53 130 150 148 79 48 90 87 70 52 128 147 144 78 46 89 86 69 51 126 144 141 77 44 88 86 68 50 124 141 139 76 43 87 86 68 49 122 139 137 75 100 41 86 85 67 49 120 137 135 74 99 39 85 85 66 48 118 135 132 73 99 38 85 85 66 47 116 132 130 72 98 36 84 84 65 46 114 130

127 71 100 98 35 83 84 64 45 112 127 125 70 100 97 33 82 84 64 44 110 125 123 69 99 96 31 81 83 63 43 109 123 120 68 98 96 30 80 83 62 42 107 121 118 67 98 95 28 79 83 62 41 106 119 116 66 97 95 27 78 82 61 40 104 117 115 65 96 94 25 78 82 60 39 102 116 114 64 96 94 24 77 82 60 38 101 114 113 63 95 93 22 76 81 59 37 99 112 112 62 95 92 21 75 81 58 36 98 110 111 61 94 92 19 74 81 57 35 96 108 110 60 93 91 18 73 81 57 34 95 107 108 59 93 91 16 72 80 56 32 94 106 107 58 92 90 15 71 80 55 31 92 104 106 57 91 90 13 71 80 55 30 91 102 105 56 91 89 12 70 79 54 29 90 101 104 55 90 88 10 69 79 53 28 89 99 103 54 90 88 9 68 79 53 27 87 102 53 89 87 7 67 78 52 26 86 101 52 88 87 6 66 78 51 25 85 100 51 88 86 4 65 78 51 24 84 100 50 87 86 3 65 77 50 23 83

99 49 87 85 64 77 49 22 82 98 48 86 85 63 77 49 21 81 97 47 85 84 62 76 48 20 80 96 46 85 83 61 76 47 19 79 95 45 84 83 60 76 46 18 79 95 44 84 82 59 75 46 17 78 94 43 83 82 58 75 45 16 77 93 42 82 81 58 75 44 15 76 92 41 82 81 57 74 44 14 75 91 40 81 80 56 74 43 13 74 90 39 80 79 55 74 42 11 74 90 38 80 79 54 73 42 10 73 89 37 79 78 53 73 41 9 72 88 36 79 78 100 52 73 40 8 71 88 35 78 77 100 52 72 40 7 71 87 34 77 77 99 51 72 39 6 70 87 33 77 76 99 50 72 38 5 69 86 32 76 75 99 49 71 38 4 68

86 31 76 75 98 48 71 37 3 68 85 30 75 74 98 47 71 36 2 67 85 29 74 74 98 46 70 36 1 66 84 28 74 73 97 45 70 35 66 84 27 73 73 97 45 70 34 65 83 26 73 72 97 44 69 33 65 83 25 72 71 96 42 69 33 64 82 24 71 71 96 42 69 32 64 82 23 71 70 96 41 68 31 63 81 22 70 70 95 40 68 31 63 81 21 70 69 95 39 68 30 62 80 20 69 69 95 38 68 29 62 80 19 68 68 94 38 67 29 61 79 18 68 67 94 37 67 28 61 79 17 67 67 93 36 67 27 60 78 16 67 66 93 35 66 26 60 78 15 66 66 93 34 66 26 59 77 14 65 65 92 33 66 25 59 77 13 65 65 92 32 65 24 58 76 12 64 64 92 32 65 24 58 76 11 64 64 91 31 65 23 57 75 10 63 63 91 30 64 22 57 75 9 62 62 91 29 64 22 56 74 8 62 62 90 28 64 21 56 74 7 61 61 90 27 63 20 56 73 6 61 61 90 26 63 20 55 73 5 60 60 89 26 63 19 55 72 4 59 60 89 25 62 18 55 72 3 59 59 88 24 62 17 54 71 2 58 58 88 23 62 17 54 71 1 58 58 88 22 61 16 53 70 0 57 57 87 21 61 15 53

HV/10 B E F G H K 15-T 30-T 45- 500kg 3000kg VICKERS

DPH ROCKWELL BRINELL BHN

Appendix 14

Hardness Conversion Chart for Soft Metals ( Rockwell B Scale )

Appendix 15

Minimum Thickness of Test Piece for Rockwell Hardness Testing ( Ball Indenters )

TEST ROCKWELL SUPERFICIAL ROCKWELL SPECIMEN 1/16" Ball Indentor 1/16" Ball Indentor THICKNESS HR 15 T HR 30 T HR 45 T HRF HRB HRG inches mm 15 kg 30 kg 45 kg 60 kg 100 kg 150 kg 0.005 0.13 93 N N N N N 0.010 0.25 90 87 N N N N 0.015 0.38 78 77 77 N N N 0.020 0.51 Y 58 62 100 N N 0.025 0.63 Y Y 26 92 92 90 0.030 0.76 Y Y Y 67 68 69 0.035 0.89 Y Y Y Y 44 46 0.040 1.02 Y Y Y Y 20 22

Appendix 17

Test Piece Minimum Thickness for Rockwell Hardness Test ( diamond indenter )

TEST ROCKWELL SUPERFICIAL ROCKWELL SPECIMEN Diamond "N" Brale Indentor Diamond Brale Indenter

THICKNESS HR 15 N HR 30 N HR 45 N HRA HRD HRC inches mm 15 kg 30 kg 45 kg 60 kg 100 kg 150 kg

0.006 0.15 92 N N N N N 0.008 0.2 90 N N N N N 0.010 0.25 88 N N N N N 0.012 0.3 83 82 77 N N N 0.014 0.36 76 80 74 N N N 0.016 0.41 68 74 72 86 N N 0.018 0.46 Y 66 68 84 N N 0.020 0.51 Y 57 63 82 77 N 0.022 0.56 Y 47 58 78 75 69 0.024 0.61 Y Y 51 76 72 67 0.026 0.66 Y Y 37 71 68 65 0.028 0.71 Y Y 20 67 63 62 0.030 0.76 Y Y Y 60 58 57 0.032 0.81 Y Y Y Y 51 52 0.034 0.86 Y Y Y Y 43 45 0.036 0.91 Y Y Y Y X 37 0.038 0.97 Y Y Y Y Y 28 0.040 1.02 Y Y Y Y Y 20

Appendix 18

Hierarchy of Decimal Numbers

Number Name How many

0 zero

1 one 2 two 3 three 4 four 5 five 6 six 7 seven 8 eight 9 nine 10 ten 20 twenty two tens

30 thirty three tens

40 forty four tens

50 fifty five tens

60 sixty six tens

70 seventy seven tens

80 eighty eight tens

90 ninety nine tens

Number Name How Many

100 one hundred ten tens

1,000 one thousand ten hundreds

10,000 ten thousand ten thousands

100,000 one hundred thousand one hundred thousands

1,000,000 one million one thousand thousands

Some people use a comma to mark every 3 digits. It just keeps track of the digits and makes the numbers easier to read.

Beyond a million, the names of the numbers differ depending where you live. The places are grouped by thousands in America and France, by the millions in Great Britain and Germany.

Name American-French English-German

million 1,000,000 1,000,000

billion 1,000,000,000 (a thousand millions) 1,000,000,000,000 (a million millions) trillion 1 with 12 zeros 1 with 18 zeros

quadrillion 1 with 15 zeros 1 with 24 zeros

quintillion 1 with 18 zeros 1 with 30 zeros

sextillion 1 with 21 zeros 1 with 36 zeros

septillion 1 with 24 zeros 1 with 42 zeros

octillion 1 with 27 zeros 1 with 48 zeros

googol 1 with 100 zeros

googolplex 1 with a google of zeros

Fractions Digits to the right of the decimal point represent the fractional part of the decimal number. Each place value has a value that is one tenth the value to the immediate left of it.

Number Name Fraction

.1 tenth 1/10

.01 hundredth 1/100

.001 thousandth 1/1000

.0001 ten thousandth 1/10000

.00001 hundred thousandth 1/100000

Examples:

0.234 = 234/1000 (said - point 2 3 4, or 234 thousandths, or two hundred thirty four thousandths)

4.83 = 4 83/100 (said - 4 point 8 3, or 4 and 83 hundredths)

SI Prefixes

Number Prefix Symbol 10 1 deka- da 10 2 hecto- h 10 3 kilo- k 10 6 mega- M 10 9 giga- G 10 12 tera- T 10 15 peta- P 10 18 exa- E 10 21 zeta- Z 10 24 yotta- Y

Number Prefix Symbol 10 -1 deci- d 10 -2 centi- c 10 -3 milli- m 10 -6 micro- u (greek mu)10 -9 nano- n 10 -12 pico- p 10 -15 femto- f 10 -18 atto- a 10 -21 zepto- z 10 -24 yocto- y

Roman Numerals

I=1 (I with a bar is not used)

V=5 _ V=5,000

X=10 _ X=10,000

L=50 _ L=50,000

C=100 _ C = 100 000

D=500 _ D=500,000

M=1,000 _ M=1,000,000

Examples:

1 = I 2 = II 3 = III 4 = IV 5 = V 6 = VI 7 = VII 8 = VIII 9 = IX 10 = X

11 = XI 12 = XII 13 = XIII 14 = XIV 15 = XV 16 = XVI 17 = XVII 18 = XVIII 19 = XIX 20 = XX 21 = XXI

25 = XXV 30 = XXX 40 = XL 49 = XLIX 50 = L 51 = LI 60 = LX 70 = LXX 80 = LXXX 90 = XC 99 = XCIX

There is no zero in the roman numeral system.

The numbers are built starting from the largest number on the left, and adding smaller numbers to the right. All the numerals are then added together.

The exception is the subtracted numerals, if a numeral is before a larger numeral, you subtract the first numeral from the second. That is, IX is 10 - 1= 9.

This only works for one small numeral before one larger numeral - for example, IIX is not 8, it is not a recognized roman numeral.

There is no place value in this system - the number III is 3, not 111.

Number Base Systems

Decimal(10) Binary(2) Ternary(3) Octal(8) Hexadecimal(16) 0 0 0 0 0

1 1 1 1 12 10 2 2 23 11 10 3 34 100 11 4 45 101 12 5 56 110 20 6 67 111 21 7 78 1000 22 10 89 1001 100 11 9

10 1010 101 12 A11 1011 102 13 B12 1100 110 14 C13 1101 111 15 D14 1110 112 16 E15 1111 120 17 F16 10000 121 20 1017 10001 122 21 1118 10010 200 22 1219 10011 201 23 1320 10100 202 24 14

Each digit can only count up to the value of one less than the base. In hexadecimal, the letters A - F are used to represent the digits 10 - 15, so they would only use one character.

Appendix 19

Surface Area Formulas In general, the surface area is the sum of all the areas of all the shapes that cover the surface of the object.

Note: "ab" means "a" multiplied by "b". "a2" means "a squared", which is the same as "a" times "a". Surface Area of a Cube = 6 a 2

(a is the length of the side of each edge of the cube)

In words, the surface area of a cube is the area of the six squares that cover it. The area of one of them is a*a, or a 2 . Since these are all the same, you can multiply one of them by six, so the surface area of a cube is 6 times one of the sides squared.

Surface Area of a Rectangular Prism = 2ab + 2bc + 2ac

(a, b, and c are the lengths of the 3 sides)

In words, the surface area of a rectangular prism is the are of the six rectangles that cover it. But we don't have to figure out all six because we know that the top and bottom are the same, the front and back are the same, and the left and right sides are the same.

The area of the top and bottom (side lengths a and c) = a*c. Since there are two of them, you get 2ac. The front and back have side lengths of b and c. The area of one of them is b*c, and there are two of them, so the surface area of those two is 2bc. The left and right side have side lengths of a and b, so the surface area of one of them is a*b. Again, there are two of them, so their combined surface area is 2ab.

Surface Area of Any Prism

(b is the shape of the ends)

Surface Area = Lateral area + Area of two ends

(Lateral area) = (perimeter of shape b) * L

Surface Area = (perimeter of shape b) * L+ 2*(Area of shape b)

Surface Area of a Sphere = 4 pi r 2

(r is radius of circle)

Surface Area of a Cylinder = 2 pi r 2 + 2 pi r h

(h is the height of the cylinder, r is the radius of the top)

Surface Area = Areas of top and bottom +Area of the side

Surface Area = 2(Area of top) + (perimeter of top)* height

Surface Area = 2(pi r 2) + (2 pi r)* h

In words, the easiest way is to think of a can. The surface area is the areas of all the parts needed to cover the can. That's the top, the bottom, and the paper label that wraps around the middle.

You can find the area of the top (or the bottom). That's the formula for area of a circle (pi r2). Since there is both a top and a bottom, that gets multiplied by two.

The side is like the label of the can. If you peel it off and lay it flat it will be a rectangle. The area of a rectangle is the product of the two sides. One side is the height of the can, the other side is the perimeter of the circle, since the label wraps once around the can. So the area of the rectangle is (2 pi r)* h.

Add those two parts together and you have the formula for the surface area of a cylinder.

Surface Area = 2(pi r 2) + (2 pi r)* h

Appendix 20

Perimeter Formulas The perimeter of any polygon is the sum of the lengths of all the sides.

Note: "ab" means "a" multiplied by "b". "a2" means "a squared", which is the same as "a" times "a".

Use the same units for all measurements

square = 4a

rectangle = 2a + 2b

triangle = a + b + c

circle = 2pi r

circle = pi d (where d is the diameter)

The perimeter of a circle is more commonly known as the circumference.

Appendix 21

Definition: A circle is the locus of all points equidistant from a central point.

Definitions Related to Circles

arc: a curved line that is part of the circumference of a circle

chord: a line segment within a circle that touches 2 points on the circle.

circumference: the distance around the circle.

diameter: the longest distance from one end of a circle to the other.

origin: the center of the circle

pi ( ): A number, 3.141592..., equal to (the circumference) / (the diameter) of any circle.

radius: distance from center of circle to any point on it.

sector: is like a slice of pie (a circle wedge).

tangent of circle: a line perpendicular to the radius that touches ONLY one point on the circle.

Diameter = 2 x radius of circle

Circumference of Circle = PI x diameter = 2 PI x radius where PI = = 3.141592...

Area of Circle:

area = PI r2

Length of a Circular Arc: (with central angle ) if the angle is in degrees, then length = x (PI/180) x r if the angle is in radians, then length = r x

Area of Circle Sector: (with central angle ) if the angle is in degrees, then area = ( /360)x PI r2 if the angle is in radians, then area = (( /(2PI))x PI r2

Equation of Circle: (Cartesian coordinates)

for a circle with center (j, k) and radius (r): (x-j)^2 + (y-k)^2 = r^2

Equation of Circle: (polar coordinates) for a circle with center (0, 0): r( ) = radius

for a circle with center with polar coordinates: (c, ) and radius a: r2 - 2cr cos( - ) + c2 = a2

Equation of a Circle: (parametric coordinates) for a circle with origin (j, k) and radius r: x(t) = r cos(t) + j y(t) = r sin(t) + k

Appendix 22

Conic Sections

Circle Ellipse (h) Parabola (h) Hyperbola (h)

Definition: A conic section is the intersection of a plane and a cone.

Ellipse (v) Parabola (v) Hyperbola (v)

By changing the angle and location of intersection, we can produce a circle, ellipse, parabola or hyperbola; or in the special case when the plane touches the vertex: a point, line or 2 intersecting lines.

Point Line Double Line

The General Equation for a Conic Section: Ax2 + Bxy + Cy2 + Dx + Ey + F = 0

The type of section can be found from the sign of: B2 - 4AC

If B2 - 4AC is... then the curve is a... < 0 ellipse, circle, point or no curve. = 0 parabola, 2 parallel lines, 1 line or no curve. > 0 hyperbola or 2 intersecting lines.

The Conic Sections. For any of the below with a center (j, k) instead of (0, 0), replace each x term with (x-j) and each y term with (y-k).

Circle Ellipse Parabola Hyperbola Equation (horiz. vertex): x2 + y2 = r2 x2 / a2 + y2 / b2

= 1 4px = y2 x2 / a2 - y2 / b2 = 1

Equations of Asymptotes: y = ± (b/a)x

Equation (vert. vertex): x2 + y2 = r2 y2 / a2 + x2 / b2

= 1 4py = x2 y2 / a2 - x2 / b2 = 1

Equations of Asymptotes: x = ± (b/a)y

Variables: r = circle radius

a = major radius (= 1/2 length major axis) b = minor radius (= 1/2 length minor axis) c = distance center to focus

p = distance from vertex to focus (or directrix)

a = 1/2 length major axis b = 1/2 length minor axis c = distance center to focus

Eccentricity: 0 c/a 1 c/a Relation to Focus: p = 0 a2 - b2 = c2 p = p a2 + b2 = c2 Definition: is the locus of all points which meet the condition...

distance to the origin is constant

sum of distances to each focus is constant

distance to focus = distance to directrix

difference between distances to each foci is constant

Appendix 23

Length Conversion Factors

Length To convert from to multiply by mile (US Statute) kilometer (km) 1.609347 inch (in) millimeter (mm) 25.4 * inch (in) centimeter (cm) 2.54 * inch (in) meter (m) 0.0254 * foot (ft) meter (m) 0.3048 * yard (yd) meter (m) 0.9144 *

Area Conversion Factors

Area To convert from to multiply by square foot (sq ft) square meter (sq m) 0.09290304 E square inch (sq in) square meter (sq m) 0.00064516 E square yard (sq yd) square meter (sq m) 0.83612736 E acre (ac) hectare (ha) 0.4047

Volume Conversion Factors

Volume To convert from to multiply by cubic inch (cu in) cubic meter (cu m) 0.00001639 cubic foot (cu ft) cubic meter (cu m) 0.02831685 cubic yard (cu yd) cubic meter (cu m) 0.7645549 gallon (gal) liter 4.546 Canada liquid gallon (gal) cubic meter (cu m) 0.004546 Canada liquid gallon (gal) liter 3.7854118 U.S. liquid** gallon (gal) cubic meter (cu m) 0.00378541 U.S. liquid fluid ounce (fl oz) milliliters (ml) 29.57353 fluid ounce (fl oz) cubic meter (cu m) 0.00002957

Force Conversion Factors

Force To convert from to multiply by kip (1000 lb) kilogram (kg) 453.6 kip (1000 lb) newton (N) 4,448.222 pound (lb) kilogram (kg) 0.4535924 avoirdupois pound (lb) newton (N) 4.448222

Pressure or Stress Conversion Factors

Pressure or stress kip per square megapascal (MPa) 6.894757 inch (ksi) pound per kilogram per 4.8824 square foot (psf) square meter (kg/sq m) pound per square pascal (Pa) 47.88 foot (psf) pound per square pascal (Pa) 6,894.757 inch (psi) pound per square megapascal (MPa) 0.00689476 inch (psi)

Mass Conversion Factors

Mass (weight) pound (lb) kilogram (kg) 0.4535924 avoirdupois ton, 2000 lb kilogram (kg) 907.1848 grain kilogram (kg) 0.0000648 Mass (weight) per length kip per linear kilogram per meter (kg/m) 0.001488 foot (klf) pound per linear kilogram per meter (kg/m) 1.488 foot (plf) Mass per volume (density) pound per cubic kilogram per cubic 16.01846 foot (pcf) meter (kg/cu m) pound per cubic kilogram per cubic 0.5933 yard (lb/cu yd) meter (kg/cu m)

Temperature Conversion Factors

Temperature degree Fahrenheit (F) degree Celsius (C) tc=(tF-32)/1.8 degree Fahrenheit (F) kelvin (K) tk = (tF+459.7)/1.8 kelvin (K) degree Celsius (C) tc=tk-273.15 Energy and heat British thermal joule (J) 1055.056 unit(Btu) calorie (cal) joule (J) 4.1868E Btu/degree F x hr x ft2 W/m2 - degree K 5.678263 kilowatt-hour (kwh) joule (J) 3,600,000E British thermal calories per gram 0.55556 unit per pound (Btu/lb) (cal/g) British thermal unit watt (W) 0.2930711 per hour (Btu/hr)

Power Conversion Factors

Power horsepower (hp) watt (W) 745.6999 E (550 ft-lb/sec) Velocity mile per hour (mph) kilometer per hour(km/hr) 1.60934 mile per hour (mph) meter per second (m/s) 0.44704 Permeability darcy centimeter per 0.000968 second (cm/sec) feet per day (ft/day) centimeter per 0.000352 second (cm/sec) ---------- *indicates that the factor given is exact. **One U.S. gallon equals 0.8327 Canadian gallon. t--A pascal equals 1.000 newton per square meter. Note: One U.S. gallon of water weighs 8.34 pounds (U.S.) at 60 degrees F. One cubic foot of water weighs 62.4 pounds (U.S.). One milliliter of water has a mass of 1 gram and has a volume of one cubic centimeter. One U.S. bag of cement weighs 94 lbs.

More Useful Conversion Factors

Quantity From English To Metric Multiply Units Units by* Length mile km 1.609347 yard m 0.9144** foot m 0.3048** inch mm 25.40** Area square mile km 2 2.590 acre m 2 4047 acre hectare 0.4047 square yard m 2 0.8361 square foot m 2 0.092 90 square inch mm 2 645.2 Volume acre foot m 3 1 233 cubic yard m 3 0.7646 cubic foot m 3 0.028 32 cubic foot L (1000 cm 3) 28.32 100 board feet m 3 0.2360 gallon L (1000 cm 3) 3.785 Mass lb kg 0.4536 kip (1000 lb) metric ton (1000kg) 0.4536 Mass/unit length plf kg/m 1.488 Mass/unit area psf kg/m 2 4.882 Mass density pcf kg/m 3 16.02 Force lb N 4.448 kip kN 4.448 Force/unit length plf N/m 14.59 klf kN/m 14.59

Pressure, stress, modules of elasticity psf Pa 47.88 ksf kPa 47.88 psi kPa 6.895 ksi MPa 6.895 Bending moment, t-lb N . m 1.356 torque, moment of forceft-kip kN . m 1.356 --------------------- * 4 significant digits **denotes exact conversion Quantity From English Units To Metric Units Multiply by* Moment of mass lb . ft kg . m 0.1383 Moment of inertia lb . ft2 kg . m 2 0.042 14 Second moment of area in4 mm4 416 200 Section modulus in3 mm3 16 390 Power ton (refrig) kW 3.517 Btu/s kW 1.054 hp (electric) W 745.7 Btu/h W 0.2931 Volume rate of flow ft 3/s m 3/s 0.028 32 cfm m 3/s 0.000 471 9 cfm L/s 0.4719 mgd m 3/s 0.0438 Velocity, speed ft/s m/s **0.3048 Acceleration f/s 2 m/s 2 0.3048 Momentum lb . ft/sec kg . m/s 0.1383 Angular momentum lb . ft 2/s kg . m 2/s 0.042 14 Plane Angle degree rad 0.017 45 mrad 17.45 --------------------------------- * 4 significant digits **denotes exact conversion

Sheet Metal Conversion Factors

SHEET METAL Most specification references use gage number followed by the decimal inch thickness. Example: 22 gage (0.034 inch) Metric specifications use the absolute mm thickness. It is not the intent of this guidance to change the thickness of currently used sheeting. The following chart may be used to specify sheet metal. The thickness under "Specify" is thinner than the actual gage thickness, since specifications give minimum thickness.

Gage Inch Exact Specify Percent Thinner (mm) (mm) Than "Exact" Value 32 0.0134 0.3404 0.34 0.1 30 0.0157 0.3988 0.39 2.2 28 0.0187 0.4750 0.47 1.1 26 0.0217 0.5512 0.55 0.2 24 0.0276 0.7010 0.70 0.1 22 0.0336 0.8534 0.85 0.4 20 0.0396 1.0058 1.0 0.6 18 0.0516 1.3106 1.3 0.8 16 0.0635 1.6129 1.6 0.8 14 0.0785 1.9939 1.9 4.7 12 0.1084 2.7534 2.7 1.9 10 0.1382 3.5103 3.5 0.3 8 0.1681 4.2697 4.2 1.6

Sieve Conversion Factors

SIEVES Sieve Designation (W) Nominal Permissible Variation Intermediate Maximum Nominal Sieve of Average Opening Tolerance Individual Wire Opening from the Standard (x) Opening Diameter (in.) Sieve Designation (x) (mm) (y) + or 125 mm 5 in. 5 3.70 mm 130.0 mm 130.9 mm 8.00 106 mm 4.24 in. 4.24 3.20 mm 110.2 mm 111.1 mm 6.40 100 mm 4 in. 4 3.00 mm 104.0 mm 104.8 mm 6.30 90 mm 3 1/2 in. 3.5 2.70 mm 93.6 mm 94.4 mm 6.08 75 mm 3 in. 3 2.20 mm 78.1 mm 78.7 mm 5.80 63 mm 2 1/2 in. 2.5 1.90 mm 65.6 mm 66.2 mm 5.50 53 mm 2.12 in. 2.12 1.60 mm 55.2 mm 55.7 mm 5.15 50 mm 2 in. 2 1.50 mm 52.1 mm 52.6 mm 5.05

45 mm 1 3/4 in. 1.75 1.40 mm 46.9 mm 47.4 mm 4.85 37.5 mm 1 1/2 in. 1.5 1.10 mm 39.1 mm 39.5 mm 4.59 31.5 mm 1 1/4 in. 1.25 1.00 mm 32.9 mm 33.2 mm 4.23 26.5 mm 1.06 in. 1.06 0.80 mm 27.7 mm 28.0 mm 3.90 25.0 mm 1 in. 1 0.80 mm 26.1 mm 26.4 mm 3.80 22.4 mm 0.875 0.70 mm 23.4 mm 23.7 mm 3.50 19.0 mm 3/4 in. 0.750 0.60 mm 19.9 mm 20.1 mm 3.30 16.0 mm 0.625 0.50 mm 16.7 mm 17.0 mm 3.00 13.2 mm 0.530 in. 0.530 0.41 mm 3.83 mm 14.05 mm 2.75 12.5 mm 1/2 in. 0.500 0.39 mm 3.10 mm 13.31 mm 2.67 11.2 mm 7/16 in. 0.438 0.35 mm 11.75 mm 11.94 mm 2.45 9.50 mm 0.375 0.30 mm 9.97 mm 1 0.16 mm 2.27 8.00 mm 5/16 in. 0.312 0.25 mm 8.41 mm 8.58 mm 2.07 6.70 mm 0.265 in. 0.265 0.21 mm 7.05 mm 7.20 mm 1.87 6.30 mm 1/4 in. 0.250 0.20 mm 6.64 mm 6.78 mm 1.82 5.60 mm No. 3 1/2 0.223 0.18 mm 5.90 mm 6.04 mm 1.68 4.75 mm No. 4 0.187 0.15 mm 5.02 mm 5.14 mm 1.54 4.00 mm No. 5 0.157 0.13 mm 4.23 mm 4 35 mm 1.37 3.35 mm No. 6 0.132 0.11 mm 3.55 mm 3.66 mm 1.23 2.80 mm No. 7 0.11 0.095 mm 2.975 mm 3.070 mm 1.10 2.36 mm No. 8 0.0937 0.080 mm 2.515 mm 2.600 mm 1.00 2.00 mm No. 10 0.0787 0.070 mm 2.135 mm 2.215 mm 0.900 1.70 mm No. 12 0.0661 0.060 mm 1.820 mm 1.890 mm 0.810 1.40 mm No. 14 0.0555 0.050 mm 1.505 mm 1.565 mm 0.725 1.18 mm No. 16 0.0469 0.045 mm 1.270 mm 1.330 mm 0.650 1.00 mm No. 18 0.0394 0.040 mm 1.080 mm 1.135 mm 0.580 0.850 mm No. 20 0.0331 0.035 mm 0.925 mm 0.970 mm 0.510 0.710 mm No. 25 0.0278 0.030 mm 0.775 mm 0.815 mm 0.450 0.600 mm No. 30 0.0234 0.025 mm 0.660 mm 0.695 mm 0.390 0.500 mm No. 35 0.0197 0.020 mm 0.550 mm 0.585 mm 0.340 0.425 mm No. 40 0.0165 0.019 mm 0.471 mm 0.502 mm 0.290 0.355 mm No. 45 0.0139 0.016 mm 0.396 mm 0.425 mm 0.247 0.300 mm No. 50 0.0117 0.014 mm 0.337 mm 0.363 mm 0.215 0.250 mm No. 60 0.0098 0.012 mm 0.283 mm 0.306 mm 0.180 0.212 mm No. 70 0.0083 0.010 mm 0.242 mm 0.263 mm 0.152 0.180 mm No. 80 0.0070 0.009 mm 0.207 mm 0.227 mm 0.131 0.150 mm No. 100 0.0059 0.008 mm 0.174 mm 0.192 mm 0.110 0.125 mm No. 120 0.0049 0.007 mm 0.147 mm 0.163 mm 0.091 0.106 mm No. 140 0.0041 0.006 mm 0.126 mm 0.141 mm 0.076 0.090 mm No. 170 0.0035 0.005 mm 0.108 mm 0.122 mm 0.064 0.075 mm No. 200 0.0029 0.005 mm 0.091 mm 0.103 mm 0.053 0.063 mm No. 230 0.0025 0.004 mm 0.077 mm 0.089 mm 0.044 0.053 mm No. 270 0.0021 0.004 mm 0.066 mm 0.076 mm 0.037 0.045 mm No. 325 0.0017 0.003 mm 0.057 mm 0.066 mm 0.030 0.038 mm No. 400 0.0015 0.003 mm 0.048 mm 0.057 mm 0.025 0.032 mm No. 450 0.0012 0.003 mm 0.042 mm 0.050 mm 0.028 0.025 mm No. 500 0.0010 0.003 mm 0.034 mm 0.041 mm 0.025 0.020 mm No. 635 0.0008 0.003 mm 0.029 mm 0.035 mm 0.020

Pipe Conversion Factors

Pipe is one of the most ubiquitous products in construction. It is made of a wide variety of materials, including galvanized steel, black steel, copper, cast iron, concrete, and various plastics such as ABS, PVC, CPVC, polyethylene, and polybutylene, among others. But like wood 2-by-4's which are not really 2 inches by 4 inches, pipe is identified by "nominal" or "trade" names that are related only loosely to actual dimensions. For instance, a 2-inch galvanized steel pipe has n inside diameter of about 2-1/8 inches and an outside diameter of about 2-5/8 inches. It is called "2-inch pipe" only for the sake of convenience. Since few, if any, pipe products have actual dimensions that are in even, round inch-pound numbers, there is no need to convert them to even, round metric numbers. Instead, only their names will change--from inch-pound to metric. Pipe cross sections will not change. Fittings, flanges, couplings, valves, and other piping components will be renamed in like manner as will pipe threads. Here are the inch-pound names for pipe products (called NPS or "nominal pipe size") and their metric equivalents (called DN or "diameter nominal"). The metric names conform to International Standards Organization (ISO) usage and apply to all plumbing, natural gas, heating oil, drainage, and miscellaneous piping used in buildings and civil works projects.

NPS DN NPS DN ---------------------------------------- 1/8" 6 mm 8" 200 mm 3/16" 7 mm 10" 250 mm 1/4" 8 mm 12" 300 mm 3/8" 10 mm 14" 350 mm 1/2" 15 mm 16" 400 mm 5/8" 18 mm 18" 450 mm 3/4" 20 mm 20" 500 mm 1" 25 mm 24" 600 mm 1-1/4" 32 mm 28" 700 mm 1-1/2" 40 mm 30" 750 mm 2" 50 mm 32" 800 mm 2-1/2" 65 mm 36" 900 mm 3" 80 mm 40" 1000 mm 3-1/2" 90 mm 44" 1100 mm 4" 100 mm 48" 1200 mm 4-1/2" 115 mm 52" 1300 mm 5" 125 mm 56" 1400 mm 6" 150 mm 60" 1500 mm **(For pipe over 60 inches, use 1 inch equals 25 mm)

TABLE 1 PROPOSED METRIC CSP DIAMETER SIZES Proposed Metric (mm) Current Standard (inches) 150 6 200 8 250 10 300 12 375 15 450 18 525 21 600 24 675 27 750 30 825 33 900 36 1050 42 1200 48 1350 54 1500 60 1650 66 1800 72 1950 78 2100 84 2250 90 2400 96 2550 102 2700 108 2850 114 3000 120 3150 126 3300 132 3450 138 3600 144 CORRUGATION SIZES CURRENT PROPOSED (Inches) (Millimeters) 2 2/3 x 1/2 68 x 13 3 x 1 76 x 25 5 x 1 125 x 25 3/4 x 3/4 x 7 1/2 19 x 19 x 191 3/4 x 1 x 11 1/2 19 x 25 x 292

PIPE WALL THICKNESS CURRENT NOMINAL PROPOSED Thickness NOMINAL Thickness GATE (Inches) (millimeters) 16 0.064 1.6 14 0.079 2.0 12 0.109 2.8 10 0.138 3.5 8 0.168 4.3

PIPE ARCH SIZES Corrugations Corrugations Inches Millimeters Inches Millimeters 2 2/3 x 1/2 68 x 13 3 x 1 & 5 x 1 76 x 25 & 125 x 25 Span x Rise Span x Rise Span x Rise Span x Rise 17 x 13 425 x 325 53 x 41 1325 x 1025 21 x 15 525 x 375 60 x 46 1500 x 1150 24 x 18 600 x 450 66 x 51 1650 x 1275 28 x 20 700 x 500 73 x 55 1825 x 1375 35 x 24 875 x 600 81 x 59 2025 x 1475 42 x 29 1050 x 725 87 x 63 2175 x 1575 49 x 33 1225 x 825 95 x 67 2375 x 1675 57 x 38 1425 x 950 103 x 71 2575 x 1775 64 x 43 1600 x 1075 112 x 75 2800 x 1875 71 x 47 1775 x 1175 117 x 79 2925 x 1975 77 x 52 1925 x 1300 128 x 83 3200 x 2075 83 x 57 2075 x 1425 137 x 87 3425 x 2175 142 x 91 3550 x 2275 Note: millimeters equal to inches x 25. Assumed pipe diameters will be x 25.

PIPE ARCH SIZES CORRUGATIONS Inches Millimeters 3/4 x 3/4 x 7 1/2 19 x 19 x 191 Span x Rise Span x Rise 20 x 16 500 x 400 23 x 19 575 x 475 27 x 21 675 x 525 33 x 26 825 x 650 40 x 31 1000 x 775 46 x 36 1150 x 900 53 x 41 1325 x 1025 60 x 46 1500 x 1150 66 x 51 1650 x 1275 73 x 55 1825 x 1375 81 x 59 2025 x 1475 87 x 63 2175 x 1575 95 x 67 2375 x 1675 Note: millimeters equal to inches x 25. Assumed pipe diameters will be x 25.