Engineering Constants and Tables

Engineering Constants and Tables

Engineering Constants and Tables

What the tool holds

Ten reference tables, every row from a public-domain government publication and carrying its source, with three small calculators that work on them. A blank search lists the first rows of each table with the count; a search term keeps only the rows that hold every word of it; one table at a time can be chosen and the row limit raised; the shown rows are offered as CSV. Nothing in the tables is typed from a copyrighted handbook: where a standard owns a table (ASME B1.1, ASME B36.10M, ISO 261, ISO 898-1, FED-STD-H28/2B and /21) the tool takes the same dimensions from the public-domain NBS handbooks that preceded it, or states the closed form, and cites the standard.

Exactness, as NIST prints it

SP 811 writes every factor as a number between 1 and 10 times a power of ten, to seven significant figures, and prints in boldface the factors that are exact by definition (1 ft = 0.3048 m, 1 lb = 0.453 592 37 kg, 1 atm = 101 325 Pa, 1 cal_IT = 4.1868 J). The tool keeps the boldface as the "exact" flag and the seven printed digits as the value; it does not replace a rounded value by a longer exact one (the pound-force is listed as 4.448 222 N, though 0.453 592 37 × 9.806 65 = 4.448 221 615 2605 N exactly), because the table is a transcription of the publication. The converter therefore reproduces a chain of two rounded factors to about one part in ten million, which is the precision NIST intends for Appendix B. The web edition of Appendix B differs from the 2008 PDF in two rows, both updated by NIST to later CODATA values: the electronvolt (1.602 177 × 10⁻¹⁹ J on the web, 1.602 176 in the 2008 print) and the faraday based on carbon 12 (9.648 531 × 10⁴ C against 9.648 534 × 10⁴). The tool carries the web values; the test script holds both parses and records the two differences.

The CODATA listing marks "exact" the seven defining constants of the 2019 SI (Δν_Cs, c, h, e, k, N_A, K_cd) and every value fixed by them (the molar gas constant, the Stefan–Boltzmann constant, the Josephson and von Klitzing constants, the standard acceleration of gravity and standard atmosphere, the electron volt in joules). Every other value carries its standard uncertainty. The brief for this tool asked for the 2018 adjustment; NIST now publishes the 2022 adjustment at the same address, so the table holds 2022 and the 2018 listing is filed beside it for comparison (the exact constants are identical by construction; the measured ones moved by parts in 10⁷ to 10⁹).

The converter's unit algebra

Each of the two fields is read as a whole first (an SP 811 symbol such as lbf·ft, Btu/h, ft3/min, or a name such as pound-force foot, circular mil, mile, nautical) and otherwise as an expression of symbols joined by ·, *, a space or a hyphen for a product, / for a quotient, ^ or a trailing 2, 3 or 4 for a power, with parentheses. Each symbol is resolved in this order: a deliberate alias (lbm, mph, cfm, gpm, kn, ksi, Msi, psf, degF, degR, R for °R, Btu for Btu_IT, cal for cal_IT, kWh, nmi, cmil, kcmil, ton for the short ton, tonf, yr); an SI unit name (meter, newton, kilopascal …) or a common plural (feet, inches, pounds); an exact SI symbol (so rad is the radian, not the absorbed-dose rad, and g the gram); an SP 811 symbol or name; an SI symbol with a prefix (kPa, MPa, µm, kJ). Every symbol becomes a factor to the SI base units and an exponent vector over m, kg, s, A, K, mol, cd and the radian; a product adds the vectors, a quotient subtracts them, a power multiplies them. The two sides must agree in every dimension, and the result is the ratio of the two factors times the value. A mismatch is reported in words with both dimension vectors. Temperatures typed as °C, °F, K or °R are treated as points on a scale by the SP 811 formulas (T/K = t/°C + 273.15, T/K = (t/°F + 459.67)/1.8, T/K = (T/°R)/1.8); for an interval, combine the unit with others (Btu/(lb·°F)) or type the SI kelvin.

The SI side of every SP 811 row ("newton meter (N · m)", "watt per meter kelvin [W/(m · K)]") is parsed by the same algebra from the symbol NIST prints, so a row's factor is applied once and its base-unit vector follows from the SI symbol, never from a second table. The test script compares forty of the resulting factors with the site's unit dictionary and with the Unit Calculator Pad's own SP 811 table.

Threads: the H28 formulas

For a unified thread of basic major diameter D (in) and n threads per inch, p = 1/n and the sharp-V height is H = 0.866 025 p. Handbook H28 tabulates the basic pitch diameter E = D − 0.649 519 p (D − 3H/4), the minor diameter of the internal thread K_n = D − 1.082 532 p (D − 5H/4, a flat of H/4 at the root), the minor diameter of the external thread in the design form K_s = D − 1.226 869 p (D − 17H/12), the lead angle λ at the pitch diameter with tan λ = 1/(nπE), the sectional area at the minor diameter D − 2h_b with h_b = 0.649 519 p, and the tensile stress area A_t = 0.7854 (D − 0.9743/n)² = π(E/2 − 3H/16)², the handbook's area for computing the tensile strength of steel parts up to 180,000 psi (Appendix A5). The tool computes all of these for any D and n and, when the pair is a UNC, UNF or UNEF size, prints the handbook's table row beside them. The test script checks all 82 printed rows against the formulas: the diameters to the printed 0.0001 in, the areas and lead angles to their printed rounding, and finds one misprint, the lead angle of 1.375-18 UNEF printed 0° 48′ where the formula gives 0° 45′ (the preceding 1.3125-18 row is 48′), kept as printed.

The shear areas follow Appendix A5 of the handbook. With materials of equal strength failure is taken at the pitch diameter, AS = πE L_e/2. When the external thread is the stronger the internal thread strips at the major diameter of the screw, AS_n = π n L_e D_s,min [1/(2n) + 0.577 35 (D_s,min − E_n,max)]; when the internal thread is the stronger the screw strips at the minor diameter of the nut, AS_s = π n L_e K_n,max [1/(2n) + 0.577 35 (E_s,min − K_n,max)]; the handbook's simplified forms are 3πE L_e/4 and 5πE L_e/8. At basic dimensions (the maximum-material case of Table A5.2, tolerances and allowance zero) the brackets reduce to 0.875 π D and 0.75 π K_n per inch of engagement. The length of engagement that develops the full strength of the screw is L_e = 4A_t/(πE) for equal materials and L_e = 2A_t/(AS per inch) otherwise, the factor 2 being the handbook's requirement that the shear area be twice the stress area (NBS tests of 1929 gave 1.7 to 2.0). The calculator prints these at basic dimensions; a design with class tolerances and an allowance uses the limits of size from FED-STD-H28/2B or ASME B1.1, which the tool cites and does not reproduce.

The ISO metric thread has the same 60° profile: d₂ = d − 0.649 519 p, D₁ = d − 1.082 532 p, d₃ = d − 1.226 869 p, and the stress area A_s = (π/4)[(d₂ + d₃)/2]² = (π/4)(d − 0.938 194 p)², printed in ISO 898-1 with the rounded 0.9382 (M10 × 1.5 gives 58.0 mm²). The coarse and fine pitches of the series come from the 1957 edition of Handbook H28, Part III, Tables 14.1 and 14.2, which carried the ISO metric threads then under trial; they are the pitches of the present ISO 261 for every size listed (the table prints threads per inch beside each pitch, 25.4/p rounded, and the test checks that too).

Wire: the AWG law and Handbook 100

The American Wire Gage is a geometric series: No. 0000 is 0.4600 in and No. 36 is 0.0050 in, 39 gage steps apart, so the diameter of gage n is d = 0.005 × 92^{(36 − n)/39} in (0000, 000, 00 and 0 are n = −3, −2, −1 and 0), each step a ratio of 1.1229 in diameter and 1.2610 in area, so three gage steps double the area and six double the diameter. The circular-mil area is the square of the diameter in mils. The resistance of standard annealed copper (the International Annealed Copper Standard, 100 % conductivity) is 10.371 Ω·cmil/ft at 20 °C, equivalent to the mass resistivity 0.153 28 Ω·g/m², with the temperature coefficient 0.003 93 per °C at 20 °C and the density 8.89 g/cm³ (Handbook 100, section 1 and the notes to Table 5). The calculator prints the diameter, areas, resistance per 1,000 ft and per km at 20 °C and at the entered temperature, R_T = R₂₀[1 + 0.003 93 (T − 20)], and the mass per length; the table shows the handbook's printed columns for gages 0000 to 40. The handbook computes the small gages from the diameter rounded to 0.1 mil, so No. 20 is 1020 circular mils and 10.1 Ω per 1,000 ft (32.0²; the exact diameter gives 1021.5 and 10.15). One misprint was found: No. 19 is printed as 1200 circular mils where 35.9² = 1289 and the row's own 0.001 01 in² and 8.05 Ω agree with 1289; the tool keeps the printed 1200 and the test flags it.

Atmosphere, water, air, materials

The 1976 standard's Part 1 constants are listed as printed (T₀ = 288.15 K, P₀ = 101 325 Pa, g₀ = 9.806 65 m/s², R* = 8.314 32 J/(mol·K), M₀ = 28.9644 kg/kmol, γ = 1.4, the Sutherland constants, the effective Earth radius) with the seven temperature layers, and the sea-level density, speed of sound, viscosities and conductivity are the tabulated values of Tables I to III, which the computed rows reproduce from the Part 1 equations (ρ₀ = P₀/(RT₀) = 1.2250 kg/m³, a₀ = √(γRT₀) = 340.29 m/s, μ₀ = 1.7894 × 10⁻⁵ Pa·s). The standard's own conductivity equation gives 2.5326 × 10⁻² W/(m·K) against the tabulated 2.5362 × 10⁻², a 0.14 % inconsistency the site's Standard Atmosphere tool recorded earlier; the table value is listed with that note. Water is the NIST WebBook's IAPWS-95 isobar at 0.101 325 MPa, every ten degrees from 0.01 to 99.61 °C with 25 °C added. The metals are rows of the MIL-HDBK-5J database the site already holds (the handbook's density in lb/in³, E and G in Msi, ν, F_tu and F_ty at the stated direction and basis, read at run time so that they follow any correction of the database), and the woods are the clear-specimen values of the Wood Handbook's Tables 5-3a (metric) and 5-3b (inch-pound) as printed, green and at 12 % moisture; the wood density shown is the specific gravity times the density of water, an approximation of the handbook's definition.

Limits

The converter knows the SP 811 symbols, the SI symbols with prefixes and the aliases above; a spelling it does not know is refused by name rather than guessed. Rows that SP 811 defines by a formula (temperature scales) convert only on their own. The thread calculator gives basic dimensions, not limits of size, allowances or tolerance classes, and the stress-area formula is the handbook's for steels up to 180 ksi. The wire calculator is for solid standard annealed copper; stranded conductors, hard-drawn copper (about 2.5 % higher resistivity) and other metals need their own factors. The pipe table holds fourteen nominal sizes in two schedules. The metals are a selection of 25 rows; the MIL-HDBK-5J tool and the Material Finder hold the whole database.