Unit Conversion

Appendix F Units This book is, of course, in S.I. units, but Imperial (‘English’) units are still in everyday engineering use in the USA. The following conversion factors may therefore be useful. Note that lbm denotes pound mass, lbf denotes pound force (the weight force that acts on one pound mass due to standard gravity), kg denotes kilogram mass of course, whilst kgf denotes a ‘kilogram force’, the weight of one kg mass in standard gravity. The kgf is sometimes denoted the kp, the kilopond, which is in common use in Continental Europe. This must not be confused with the kip, a US unit of 1000 lb. The force units kgf and kp are not true S.I., in which forces are always in newtons. The English and international spelling of the length unit is metre, except for the US and Germany who spell it meter. Conversion factors: Length (SI m, metre): 1 inch ¼ 0.025400 m (exact by definition) 1 foot ¼ 0.304800 m 1 m ¼ 39.3701 inch Mass (SI kg): 1 kg ¼ 2.20462 lb m 1 lbm ¼ 0.453592 kg 1 slug ¼ 32.17400 lb m 1 slug ¼ 14.5939 kg (1 lbf s2/ft by definition) 1 snail ¼ 175.127 kg (1 lbf s2/in by definition) 1 lbf s2/ft ¼ 14.5939 kg 1 lbf s2/in ¼ 175.127 kg Density (SI kg/m3): 1 lbm/ft3 ¼ 16.01846 kg/m3 1 oz/ft3 ¼ 1.001154 kg/m3 1 lbm/in3 ¼ 27.67990 kg/dm3 1 lbf s2/in4 ¼ 10.68688 kg/cm3 Force (SI N, newton): 1 N ¼ 0.224809 lbf 1 N ¼ 7.23300 poundal 1 kgf ¼ 1 kp The Shock Absorber Handbook, Second Edition John C. Dixon © 2007 John Wiley & Sons, Ltd. ISBN: 978-0-470-51020-9 1 kgf ¼ 9.80665 N 1 lbf ¼ 4.44822 N 1 lbf ¼ 0.453592 kgf (kp) Pressure (SI Pa¼N/m2, pascal): 1 Pa ¼ 1 N/m2 (by definition) 1 Pa ¼ 1:45038� 10�4 psi 1 Pa ¼ 0.0208855 lbf/ft2 1 MPa ¼ 145.038 psi 1 psi ¼ 6.89476 kPa 1 bar ¼ 100 kPa (definition) 1 Ata ¼ 101325 Pa (standard) Energy (SI J, joule): 1 J ¼ 1 N m (joule, by defintion) 1 J ¼ 0.737562 ft lbf 1 ft lbf ¼ 1.355817 J 1 Btu ¼ 1055.06 J Power (SI W, watt): 1 W ¼ 1 J/s (1 watt, by definition) 1 ft lbf/s ¼ 1.35582 W 1 horsepower ¼ 745.70 W Stiffness (SI N/m): 1 lbf/in ¼ 175.127 N/m� 175 N/m 1 kN/m ¼ 5.71015 lbf/in Damping (SI Ns/m): 1 lbf s/in ¼ 175.127 N s/m� 175 Ns/m 1 kN s/m ¼ 5.71015 lbf s/in 1 kN s/m ¼ 68.5218 lbf s/ft Valve area coefficient (SI m2/Pa): 1 mm2/MPa ¼ 10�12 m4=N ¼ 10�12 m3 s2=kg 1 mm2/MPa ¼ 10:6869� 10�6 in2=psi 1 mm2/MPa ¼ 10.6869 in2/Mpsi Magnetics: 1 T (tesla) ¼ 1 Wb/m2 (flux density) 1 H (henry) ¼ 1 Wb/A (inductance) In S.I., the units of damping coefficient are N m=s ¼ N s=m This reduces to the fundamental units kg/s. The practical-valued unit of kNs/m reduces to t/s (tonne/s) where the tonne is the metric ‘ton’, i.e. 1000 kg. These reduced forms are not commonly used, and kNs/m is preferred. 394 The Shock Absorber Handbook In Imperial units, damper velocities are usually in inches/s and forces in lbf, so the natural unit of damping coefficient is the lbf s/inch, which is a practical size of unit. The lbf s/ft is also usable, but rarer, and reduces to slug/s, although rarely expressed in the latter form. A practical passenger car damper of 2 kN s/m is 11.4 lbf s/in or 137 lbf s/ft. The S.I. unit of kNs/m is reasonable, and is especially in its reduced (but unusual) form of t/s is compact. Perhaps for this reason there has been no move to introduce an explicit S.I. unit for damping coefficient. Such a unit, which tentatively might be named the horock, after the inventor of the telescopic damper, C.L. Horock, of the 1901 patent, would then have the S.I. symbol Ho (to be distinguished from the henry H, unit of magnetic inductance). The practical unit is then the kHo, the kilohorock. Alternatively, an S.I. unit for mass flow rate (kg/s) would be adaptable to damping coefficient, and if introduced would probably become used for the latter. The full naming of kilonewton-seconds per metre is rather laborious, but the simpler ‘k.n.s.m.’ is satisfactory for oral communications, and probably more convenient than a special name such as kilohorock. Even terser would be ‘t.p.s.’ for tonnes per second. From the practical point of view, for the foreseeable future the practical S.I. unit of damping coefficient is likely to remain the kNs/m, with t/s as a compact alternative for the more adventurous. The introduction of magnetorheological dampers brings the magnetic units into relevance. The magnetic field (A/m) must be distinguished from the consequent flux density. The flux at all cross- sections of a simple magnetic circuit is constant, and measured in Wb (webers), or usually mWb for the practical unit. At any particular section there is a cross-sectional area giving a flux density in Wb/m2 (weber/metre2). An alternative name for the Wb/m2 is the tesla, abbreviated T. The reluctance of a magnetic circuit indicates the current-turns product in A-turns required to produce a weber of flux, so is measured in A/Wb, or MA/Wb as a practical unit. The henry (H) is the unit of magnetic inductance, and is just a special name for the Wb/A (weber/ampe`re). All calculations could be expressed in Wb, W/m2 and so on. The units tesla and henry are just conveniences. The permittivity of a material is usually expressed as H/m (henry/metre), but could equally be expressed as Wb/A m. The correct use of capital letters in units is essential. Consider, for example, the possible errors in incorrect use of kg, Kg, KG and kG, which would correctly mean kilogram, kelvin gram, kelvin gauss and kilogauss, although the gauss is not SI). Units 395