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1 GENERAL ENGINEERING INFORMATION Index Section L WARNING & SAFETY REMINDER OPPOSITE PAGE ITEM PAGE HORSEPOWER/TORQUE L-2 L-6 ELECTRICAL L- ELECTRICAL MOTORS L-8 SHAFT SELECTION L-9 L- FLYWHEEL L-2 WEIGHTS OF STEEL L- PROPERTIES OF STEEL L-4 PROPERTIES OF VARIOUS METALS L- HARDNESS CONVERSION CHART L-6 DECIMAL EQUIVALENT CHART L- ENGLISH/METRIC CONVERSIONS L-8 L-9 ENGINEERING FORMULAS & CONSTANTS L-20 CIRCUMFERENCES/AREAS OF CIRCLES L-2 TRIGONOMETRIC FORMULAS/FUNCTIONS L-22 L-24 CONVERSION TABLES L-2 L-28 L-

2 Horsepower/Torque Horsepower One HP is the rate of work required to raise,000 pounds one foot in one minute. ONE FOOT PER MINUTE,000 LBS. ONE HORSEPOWER HP = Force x FPM,000 HP = Torque (in Pound-Inches) x RPM 6,02 HP = Torque (in Pound-Feet) x RPM,22 Torque: The twisting or turning effort around a shaft tending to cause rotation. Torque is determined by multiplying the applied force times the distance from the point where force is applied to the shaft center. TQ = F (force) x R (radius) 6,02 x HP Torque (in Pound-Inches) = RPM = Force x Lever Arm (in Inches) Torque (in Pound-Feet) = Torque Calculation Example,22 x HP 20 HP at 00 RPM = 2,60 Pound-Inches Torque RPM = Force x Lever Arm (in Feet) 2.0 HP at 0 RPM = 2,60 Pound-Inches Torque Force = Working Loads in Pounds FPM = Feet per Minute RPM = Revolutions per Minute Lever Arm = Distance from the Force to the center of rotation on Inches or Feet An overhung load is a bending force imposed on a shaft due to the torque transmitted by V-drives, chain drives, and other power transmission devices, other than flexible couplings. Most motor and reducer manufacturers list the maximum values allowable for overhung loads. It is desirable that these figures be compared with the load actually imposed by the connected drive. Overhung loads may be calculated as follows: 6,000 x HP x F O.H.L. = N x R Where: HP = Transmitted HP x Service Factor N = RPM of shaft R = Radius of sprocket, pulley, etc. F = Factor Overhung Loads Weights of the drive components are usually negligible. The formula is based on the assumption that the load is applied at a point equal to one shaft diameter from the bearing face. Factor F depends on the type of drive used: F =.00 for single chain drives.0 for TIMING belt drives.2 for spur or helical gear or double chain drives.0 for V-belt drives 2.0 for flat belt drives Example: Find the overhung load imposed on a reducer by a double chain drive transmitting 0 RPM. The pitch diameter of the sprocket is 0 ; service factor is.. Solution: O.H.L = (6,000)( x.) (.2) = 4,80 lbs. (0) () L-2 Horsepower/Speed/Torque Relationships HP Speed (RPM) Torque Constant Increases Decreases Constant Decreases Increases Increases Constant Increases Decreases Constant Decreases Increases Increases Constant Decreases Decreases Constant

3 Torque (in Pound-Inches) For Horsepower/RPM Torque for RPM Revolutions per Minute HP L-

4 Torque (in Pound-Inches) For Horsepower/RPM Torque for RPM Revolutions per Minute HP L-4

5 Torque (in Pound-Inches) For Horsepower/RPM Torque for RPM Revolutions per Minute HP L-

6 Torque (in Pound-Inches) For Horsepower/RPM Torque for RPM Revolutions per Minute HP L-6

7 Electrical Formulas Electrical Formulas Alternating Current Alternating or To Find Single-Phase Three-Phase To Find Direct Current Amperes when HP x 46 HP x 46 Amperes when voltage and E horsepower is known E x Eff. x pf. x E x Eff. x pf resistance is known R Amperes when Kw x 000 Kw x 000 Voltage when resistance kilowatts are known E x pf. x E x pf and current are known IR Amperes when Kva x 000 Kva x 000 Resistance when voltage E Kva are known E. x E and current are known I Kilowatts I x E x pf. x I x E x pf General Information (Approximation) { At 800 RPM, a motor develops 6 lb.-in. per hp Kva I x E. x I x E At 200 RPM, a motor develops 4 lb.-in. per hp At volts, a -phase motor draws amp per hp Horsepower = (Output) I x E x Eff. x pf. x I x E x Eff. x pf At 460 volts, a -phase motor draws.2 amp per hp At 20 volts, a -phase motor draws 2. amp per hp I = Amperes; E = Volts; Eff. = Efficiency; pf = power factor; At 20 volts, a single-phase motor draws amp per hp Kva = Kilovolt amperes; Kw = Kilowatts; R = Ohms At volts, a single-phase motor draws 0 amp per hp All Values At 00% Load Temperature Conversion: Deg C = (Deg F - 2) x 9 Deg F = (Deg C x 9 ) + 2 Motor Full Load Alternating Current Alternating Current Alternating Current Alternating Current Single Single Single Single HP Phase -Phase DC HP Phase -Phase DC HP Phase -Phase DC HP Phase -Phase DC Values are for all speeds and 20 volts. Amperage other than 20 volts can be figured: 20 x Amp from Table V = New Voltage Example: For 60 HP, 0 volts: (20 x 0) 0 = 62 amps. Power Factor 80% for most motors. Efficiency is usually 80-90%. NEMA Electrical Enclosure Types Type Description Type Description NEMA Type For indoor use wherever oil, dust, NEMA Type Used for excluding dust (All NEMA 2 and JIC (General Purpose) or water is not a problem Dust Tight enclosures are usually suitable for NEMA use) (Non-Hazardous) NEMA Type 2 Used indoors to exclude falling NEMA Type 9 For locations where combustible dusts (Driptight) moisture and dirt Dust Tight are present (Hazardous)* NEMA Type Provides protection against rain, NEMA Type 2 Used for excluding oil, coolant, flying dust, (Weatherproof) sleet, and snow (Industrial Use) lint, etc NEMA Type 4 Needed when subject to great (Watertight) amounts of water from any angle such as areas which are repeatedly hosed down NOTE: Joint Industry Conference (JIC) enclosures are similar in design to NEMA 2 s. For more complete details see NEMA or JIC Standards for enclosures. Not designed to be submerged. * Class II Groups E, F, and G. L-

8 NEMA Frame Designation Frame Assignments NEMA Frame Designation Motor Speed, RPM Motor Speed, RPM HP HP T, 26U 24T, 284U 284T, 24U 286T, 26U T, 284U 26T, 286U 286T, 26U 24T, 64U T, 286U 284T, 24U 24T, 64U 26T, 6U TS, 24S 286T, 26U 26T, 6U 64T, 404U TS, 26S 24T, 64U 64T, 404U 6T, 40U 2 4T 0 24TS, 64US 26T, 6U, 6US 6T, 40U 404T, 444U 4 4T 4T 60 26TS, 6US 64TS, 404U, 404US 404T, 444U 40T, 44U 4T 4T 82T 64TS, 404US 6TS, 40U, 40US 40T, 44U 444T 2 4T 4T 82T 84T 00 6TS, 40US 404TS, 444US 444T 44T 2 4T 4T 84T 2T 2 404TS, 444US 40TS, 44US 44T 4T 82T 2T 2T, 24U 0 40TS, 44US 444TS 82T 84T 2T, 24U 24T, 26U TS 44TS 2 84T 2T, 24U 24T, 26U 26T, 284U 20 44TS 0 2T, 24U 2T, 26U 26T, 284U 284T, 286U Motor Frame Dimensions Frame H Dia. U V Size D E 2F (4) Holes Dia. BA Min. Key FLAT x 6x 8 4T x 6x 8 4T x 6x 8 82T x 4x 4 84T x 4x 4 MIN. KEY 2T T U T U T x 6x2 8 6x 6x2 8 6x 6x2 4 8x 8x2 8 6x 6x2 4 8x 8x2 8 DIA. 284U x 8x 4 284T x 2x 4 284TS x 8x 8 286U x 8x 4 286T x 2x 4 286TS x 8x 8 24U x 2x4 4 24T x 2x 8 24TS x 2x2 26U x 2x4 4 26T x 2x 8 26TS x 2x2 64U x 2x 64US x 2x2 64T x 8x4 4 64TS x 2x2 6U x 2x 6US x 2x2 6T x 8x4 4 6TS x 2x2 H DIA. 4 HOLES 404U US T TS U US T TS U US T TS U US T TS x 8x x 2x x 4x x 2x x 8x x 2x x 4x x 2x x 4x x 2x x 8x x 8x x 4x x 2x x 8x x 8x Shaded area indicates typical single phase standard squirrel-cage, open type, a-c motors. Balance of table same except three phase, design A and B. When these motors are used with V-belt or chain drives, the correct frame size is the one with the suffix S omitted consult manufacturer. L-8

9 Shaft Selection Shaft Selection Important factors to consider when calculating shaft size (a) shafting is subject to a bending moment and a torsional moment. (b) bending moment is that force which tends to bend a shaft. (c) torsional moment is that force which tends to twist a shaft. (d) shaft size is determined by the combined action of the bending and torsional moments. Refer to Shaft Selection Charts 2 and developed by the American Society of Mechanical Engineers to simplify selection. The charts should be used in conjunction with Service Factors (Table ) to modify the selection for conditions under which the shaft will operate. A = Shaft length from center of bearing to center of load L = Unbalanced load in pounds W = Suspended weight of elevator (chain, buckets, etc.) in pounds R = Radius of wheel in inches B = Bending moment T = Torsional moment B = A L + W inch pounds 2 T = R x L inch pounds Selection Procedure. compute the Bending Moment from the above formula. 2. determine the Service Factor for bending that will suit conditions from Table.. compute the Torsional Moment from the above formula. 4. determine the Service Factor for torsion that will suit conditions from Table.. draw a horizontal line across Selection Chart 2 or on pages L-0 and L-, from the point where the torsional moment intersects its selected Service Factor line. 6. draw a vertical lineup Selection Chart 2 or from the point where the bending moment intersects its selected factor line.. intersection of above lines will give required shaft size. 8. for shafts not weakened by keyways, multiply the shaft size obtained by.9 for the corrected shaft size. See note at the bottom of Selection Chart. Horsepower required may be computed directly from the righthand side of Selection Charts by correcting the figure in line with the horizontal torsional moment line by the speed in RPM. Table Service Factors Service Factor Type of Loading For Bending For Torsion Stationary Shafts Gradually applied loads.0.0 Suddenly applied loads. to 2.0. to 2.0 Rotating Shafts Gradually applied or steady loads..0 Suddenly applied loads Minor shock only. to to. Suddenly applied loads Heavy shock 2.0 to 2.. to 2. Selection Example: Select shaft size for head shaft of chain conveyor subject to following requirements: (a) Torsion (inch/lbs) 20,00 (b) Bending moment (inch/lbs),00 (c) Service Factors: torsion.0 bending. At the extreme left on Selection Chart 2, the torsion moment may be found for the Service Factor of.0. Draw a horizontal line to the right from the 20,00 point. The bending moment is given at the bottom of the chart. Find the,00 point; draw a line from this point to the right on the diagonal until it intersects the. Service Factor line, then project the line upward vertically until it intersects the horizontal line drawn from the 20,00 torsion point. At this intersection point, it is found that a shaft of approximately 2 /6 diameter is required. Select the nearest standard size shaft which is 2 /6. For a shaft subjected to the same conditions, but not weakened by keyways, the size of the shaft required would be (.9 x 2.82) or 2.6 (2 9 /6 ). See note at the bottom of the charts. On this same chart at the right, the horsepower ratings at 00 RPM are given based on the formula: HP = TS 6,000 T = Torque in inch-pounds S = Speed in RPM The horsepower is directly proportional to the speed of the shaft in RPM. L-9

10 Shaft Tables L-0

11 Shaft Tables L-

12 Flywheel Formulas Flywheels are occasionally used on a few machines, such as air compressors, to even out load pulsations. These formulas are useful in designing entire flywheel rims. It is also possible to use V-Belt sheaves as a flywheel thus eliminating the need for a separate flywheel in the system. Consult Martin with specific requirements. Formulas for Entire Flywheel W = weight (pounds) R = radius of gyration (feet) N = speed (RPM) t = time to change from N to N 2 (seconds) F = face of rim (inches) D = outside diameter of rim (inches) d = inside diameter of rim (inches) P = weight per cubic inch of material (pounds) Kinetic energy of rotation of a flywheel (foot pounds) =.0000 N 2 (WR 2 )*. Torque to accelerate or decelerate a flywheel uniformly =.0908(N 2 N )(WR 2 )*, (pound inches) t where N 2 = final RPM and N = initial RPM Velocity at outside diameter (feet per minute) = ND *WR 2 = flywheel effect (pounds x feet 2 ). See table below for WR 2 of rims. Ordinarily the WR 2 of the rim only is considered. In unusual instances the relatively small WR 2 values of the hub and arms or web can be added directly to the WR 2 of the rim if desired. To find the WR 2 of a hub or web use the WR 2 formula for rims, substituting the hub or web outside diameter, inside diameter, and width for D, d, and F respectively. When arms are used instead of a web an approximate WR 2 value of the arms is the total weight of the arms in pounds times the square of the radius in feet from the shaft center line to the mid-point of the arms between hub and rim. Formulas for Flywheel Rims Cast Iron Rim Steel Rim Rim Rim of any Material Property (Based on.26 lbs per cubic inch) (Based on.28 lbs per cubic inch) Weighing P Pounds per cubic inch Volume (Cubic Inches).84F(D 2 d 2 ).84F(D 2 d 2 ).84F(D 2 d 2 ) W Weight (Pounds).2042F(D 2 d 2 ).222F(D 2 d 2 ).84FP(D 2 d 2 ) R.868(D 2 + d 2 ).868(D 2 + d 2 ).868(D 2 + d 2 ) Radius of Gyration (Feet) WR 2.F(D 4 d 4 ).929F(D 4 d 4 ).688FP(D 4 d 4 ) Wt. x Sq. of Radius of Gyration (Lbs. x Ft. 2 ) Ts.08FN 2 (D d ).0FN 2 (D d ).84PFN 2 (D d ) Tensile Load in Rim (Lbs.),000,000,000,000,000,000 Centrifugal force causes this tensile load at each and every section of the rim. Thus on rims split into two or more sections, the fastening at each joint should be designed to take the full load as calculated from the formula below. Centrifugal Force R N v g = Distance from the axis of rotation to the center of gravity of the body (feet) = Revolutions per minute (RPM) = Velocity of the center of gravity of the body (feet per second) = Acceleration due to gravity (2.6 commonly) F = Wv2 = WRN2 =.0004 WRN 2 gr 29 F = Centrifugal force tending to move the body outward from the axis of rotation (pounds) W = Weight of body (pounds) L-2

13 Weights of Steel NOTE: The steel weights in this section are nominal and are based on an approximate weight of pounds per square foot, one inch thick. There may be differences between nominal weights and actual scale weights because of variation in manufacturing practices. Hot Rolled and Cold Finished Steel Products Nominal Weight Product Thickness Width Length Formulas Thickness Diameter Inches Inches Inches.28 x T x W x L Plate Circles Inches Inches.222 x T x D 2 Plates, Strip Inches Inches Feet.4 x T x W x L Inches Feet 2.0 x T x D 2 and Flats Inches Feet Feet 40.8 x T x W x L Sheet Circles Inches Inches.228 x T x D 2 USS. Ga No. Feet Feet Wt./Sq. Ft. x W x L Inches Feet 2.8 x T x D 2 Wt. per Sq. Ft. Feet Feet Wt./Sq. Ft. x W x L Diameter Length Inches Inches Inches.2904 x T x W x L { Square Inches Feet.4 x D 2 x L Hot and C.R. Inches Inches Feet.48 x T x W x L Round Inches Feet 2.6 x D Bars x L Sheets Inches Feet Feet 4.82 x T x W x L Hexagon Inches Feet 2.94 x D 2 x L USS. Ga No. Feet Feet Wt./Sq. Ft. x W x L Octagon Inches Feet 2.8 x D 2 x L Wt. per Sq. Ft. Feet Feet Wt./Sq. Ft. x W x L T = thickness L = length W = width D = diameter Steel Rounds Size in Pounds Per Size in Pounds Per Inches Foot Inches Foot Standard Sheet Weights Ga. Thickness Weight Per Square Number in Inches Foot in Pounds Over 6 are plates Carbon Steel Plates Size Weight Per Square in Inches Foot in Pounds NOTE: Stainless Steel Weights approximately 0% more than Carbon Steel. L-

14 Steel Properties Properties of Steel The information shown below is offered as a general guide to physical properties of steel in common use. Lower tensile properties are to be expected in large sections; the values of strength decrease as the size of the section increases. These values are not guaranteed and must NOT be used in specifying the raw materials or as a basis for acceptance or rejection of material. It must not be assumed that these properties will be obtained in all cases as they vary widely with permissible variations in analysis, size of section, rolling conditions, grain size and methods of heat treatment. Dependable physical properties can only be obtained through carefully controlled analysis and heat treatment. Average Properties of Standard Steels AISI SAE Strength in000 PSI % Elong. % Red. Hardness Machinability Number Number Condition of Steel Tensile Yield in 2 of Area Brinell Rockwell % of B2 CD B2 2 COLD DRAWN BESSEMER B 00 C08 08 NATURAL HOT ROLLED COLD DRAWN B 6 RD.CARBURIZED AT 00 F., COOLED IN BOX, REHEATED, QUENCHED CORE PROPERTIES B... C NATURAL HOT ROLLED B 0 COLD DRAWN B 60 C NATURAL HOT ROLLED COLD DRAWN B 90 RD.CARBURIZED AT 00 F., COOLED IN BOX, REHEATED, QUENCHED CORE PROPERTIES C... C0 0 NATURAL HOT ROLLED COLD DRAWN B 6 RD. QUENCHED, TEMPERED 000 F B C NATURAL HOT ROLLED COLD DRAWN B 62 RD. QUENCHED, TEMPERED 000 F C 2 C NATURAL HOT ROLLED COLD DRAWN RD. QUENCHED, TEMPERED 000 F C04 04 NATURAL HOT ROLLED COLD DRAWN B 8 RD. QUENCHED, TEMPERED 000 F C 4 C4 4 NATURAL HOT ROLLED COLD DRAWN RD. QUENCHED, TEMPERED 000 F C44 44 NATURAL HOT ROLLED COLD DRAWN C 8 RD. QUENCHED, TEMPERED 000 F C... C00 00 NATURAL HOT ROLLED RD. QUENCHED, TEMPERED 000 F C HOT ROLLED, ANNEALED B COLD DRAWN, ANNEALED C 6 HEAT TREATED, COLD DRAWN C 4 RD. QUENCHED, TEMPERED 000 F C... 2 RD. QUENCHED, TEMPERED 000 F C... RD. QUENCHED, TEMPERED 000 F C... E HOT ROLLED, ANNEALED RD. QUENCHED, TEMPERED 000 F C NATURAL HOT ROLLED B COLD DRAWN B 60-0 RD. CARBURIZED 00 F., COOLED IN BOX, REHEATED, QUENCHED CORE PROPERTIES C NATURAL HOT ROLLED C 48- HOT ROLLED, ANNEALED C 4 2 RD. QUENCHED, TEMPERED 000 F C... RD. QUENCHED, TEMPERED 000 F C NATURAL HOT ROLLED C 4-0 COLD DRAWN, ANNEALED B 60 RD. QUENCHED, TEMPERED 000 F C... 2 RD. QUENCHED, TEMPERED 000 F C... L-4

15 Metal Properties Physical Properties of Various Metals Stress in Thousands of Pounds per Square Inch Modulus of Metals and Alloys Tension Tension Compression Shear Elasticity Elongation % Ultimate Yield Point Ultimate Ultimate,000,000 Lbs. ALUMINUM, TYPE 00-0, ANNEALED ALUMINUM, TYPE 00-H8, HARD ALUMINUM, TYPE 02-0, ANNEALED ALUMINUM, TYPE 02-H8, HARD ALUMINUM, TYPE 06-0, ANNEALED ALUMINUM, TYPE 204-0, ANNEALED ALUMINUM, TYPE 204-T4, HEAT TREATED ALUMINUM, TYPE C4A, CASTING, SOLUTION HEAT TREAT ALUMINUM, TYPE SC, AS DIE CAST BRASS, ALUMINUM, ANNEALED BRASS, RED, % ZN, ANNEALED BRASS, RED, % ZN, HARD BRASS, RED, LEADED, CAST, GRADE 4A BRASS, RED, LEADED, CAST, GRADE 4B BRASS, YELLOW, % ZN, ANNEALED BRASS, YELLOW, % ZN, HARD BRONZE, ALUMINUM, AS CAST BRONZE, COMMERCIAL, 0% ZN, ANNEALED BRONZE, MANGANESE, ANNEALED BRONZE, PHOSPHOR, ANNEALED BRONZE, TIN, HIGH LEADED, CAST BRONZE, TIN, LEADED, CAST COPPER, BERYLLIUM, ANNEALED INCONEL, CAST INCONEL, S, CAST IRON, CAST, CLASS IRON, CAST, CLASS IRON, MALLEABLE, CLASS IRON, MALLEABLE, CLASS IRON, NODULAR (DUCTILE) CLASS IRON, NODULAR (DUCTILE) CLASS IRON, PEARLITIC, MALLEABLE IRON, WROUGHT, HOT ROLLED LEAD, HARD, ROLLED MONEL, CAST MONEL, S, CAST MONEL, SHAPES, PLATE, ETC., ANNEALED NICKEL, CAST NICKEL, SILVER, ANNEALED STEEL, CAST CARBON, CLASS 0,000 NORMALIZED STEEL, CAST LOW ALLOY, CLASS 00,000, NORMALIZE & TEMPERED STEEL, CAST LOW ALLOY, CLASS 20,000, QUENCHED AND TEMPERED STEEL, CAST LOW ALLOY, CLASS 200,000, QUENCHED AND TEMPERED STEEL, SHEETS STEEL, STAINLESS, AUSTENITIC, TYPES 04, STEEL, STAINLESS, MARTENSITIC, TYPE STEEL, STRUCTURAL, BRIDGE AND BUILDING, ASTM A STEEL, STRUCTURAL, HIGH STRENGTH, LOW ALLOY, ASTM A ZINC, DIE CAST ALLOY, XXIII When hardened, strength values are higher, elongation less. Compression yield point. L-

16 Hardness Conversion Chart Brinell, Rockwell, and Scleroscope Hardness Numbers with Corresponding Tensile Strength Brinell Rockwell C Tensile Strength 0 MM Ball 20 Cone Scleroscope 000 Pound 000 Kg. 0 Kg. Shore Model C Per Square Inch Rockwell B /6 Ball 00 Kg L-6

17 Decimal and Millimeter Equivalents of Fractions Decimal Equivalent Table Inches Inches Inches Fractions Decimals Millimeters Fractions Decimals Millimeters Fractions Decimals Millimeters Decimal Equivalents of Millimeters MM Inches MM Inches MM Inches MM Inches MM Inches MM Inches MM Inches MM Inches L-

18 English Metric System Equivalents Length Equivalents Unit Millimeters Centimeters Inches Feet Yards Meters MILLIMETER = CENTIMETER = INCH = FOOT = YARD = METER = Unit Feet Yards Meters Rods Furlongs Miles (Statute) ROD = ( 40).002 (/20) FURLONG = ( 8) KILOMETER = MILE (STATUTE) = NAUTICAL MILE = FEET =. STATUTE MILES = LEAGUE. LIGHT YEAR =.89 TRILLION MILES = 9.46 TRILLION KILOMETERS. Weight Equivalents Unit Grains Grams Ounces (Troy) Ounces (Avoir.) Pounds (Troy) Pounds (Avoir.) Kilograms GRAIN = GRAM = OUNCE (TROY) = OUNCE (AVOIR.) = POUND (TROY) = POUND (AVOIR.) = KILOGRAM = Unit Kilograms Pounds (Troy) Pounds (Avoir.) Metric Tons Net (Short) Tons Gross (Long) Tons METRIC TON = NET (SHORT) TON = GROSS (LONG) TON = Volume and Capacity Equivalents Unit Cubic Centimeters Cubic Inches Liters Quarts (Liquid) Quarts (Dry) Gallons (Liquid) Gallons (Dry) Cubic Feet CU. CENTIMETER = CU. INCH = GILL = PINT (LIQUID) = PINT (DRY) = LITER = QUART (LIQUID) = QUART (DRY) = GALLON (LIQUID) = GALLON (DRY) = PECK = CU. FOOT = BUSHEL = BARREL = CU. YARD = CU. METER = L-8

19 English Metric System Equivalents Area Equivalents Unit Square Inches Square Feet Square Yards Square Meters SQUARE FOOT = SQUARE YARD = SQUARE METER = SQUARE ROD = ARE = ACRE = SQUARE MILE (640 ACRES) = SQUARE KILOMETER = Power Equivalents Unit BTU/Hour Foot-Pound/Hour Foot-Pound/Minute HP HP (Metric) Watt Kilowatt BTU/HR. = FT.LB./HR. = x0 -.2x x0 - FT.LB./MIN. = x0 -.02x x0 - HP = HP MET. = WATT = NOTE: Foot-Pounds indicates energy. Pound-Feet indicates torque (Page L-2). Length meter (m) = { 0 decimeters(dm) 00 centimeters(cm),000 millimeters(mm) dekameter (dkm) = 0 meters (m) hectometer (hm) = 00 meters (m) kilometer (km) =,000 meters (m) Weight gram (g) = { 0 decigrams (dg) 00 centigrams (cg),000 milligrams (mg) dekagram (dkg) = 0 grams (g) hectogram (hg) = 00 grams (g) kilogram (kg) = 000 grams (g) metric ton = 000 kilograms (kg),000,000 grams (g) Volume & Capacity { Metric System Area { square meter (m 2 ) 00 square decimeters (dm 2 ) centare (ca) = 0,000 square centameters (cm 2 ),000,000 square millimeters (mm 2 ) square dekameter (dkm are (a) = 2 ) hectare (ha) = 00 square meters (m 2 ) 00 ares (a) 0,000 square meters (m 2 ) square kilometer =,000,000 square meters (m 2 ) (km 2 ) Other prefixes commonly used: micro one millionth deca 0 times (same as deka) myria 0,000 times mega,000,000 times { { { cubic decimeter(dm ) 0 deciliters (dl) liter (l) = 00 centiliters(cl),000 milliliters (ml),000 cubic centimeters (cm or cc) dekaliter (dkl) = 0 liters (l) hectoliter (hl) = 00 liters (l) { cubic meter (m ) kiloliter (kl) = stere (s),000 liters (l) L-9

20 Engineering Formulas and Constants Circle Area = Square of Diameter x.84 or square of Radius x.46 Circumference = Diameter x.46 Diameter = Circumference x.8 Doubling diameter increases area four times; tripling diameter increases area nine times, etc. Square Area = Square of Side Diagonal = Side x.442 Side = Diagonal x.0 Square Inscribed in Circle Side of Square = Diameter of Circle x.0 or Circumference of Circle x.22 Diameter of Circle = Side of Square x.442 Circumference of Circle = Side of Square x Square and Circle with Equal Area Side of Square = Diameter of Circle x.8862 Diameter of Circle = Side of Square x.28 Circumference of Circle = Side of Square x.4 Rectangle Area = Length x Width Diagonal = Square root of sum of squares of Width and Length Triangle Area = Base x 2 of Perpendicular Height Sphere Area of Surface = Square of Diameter x.46 Volume = Cube of Diameter x.26 Cube Area of Surface = Square of Side x 6 Volume = Cube of Side Diagonal = Side x.2 Cylinder Area of Curved Surface = Diameter x Length x.46 Volume = Square of Diameter x Length x.84 Cone Area of Curved Surface = Diameter of Base x Slant Height x.08 Volume = Diameter of Base Squared x Perpindicular Height x.268 or Area of Base x Perpendicular Height HP =,000 Foot-pounds of work per minute. BTU = Heat required to raise pound of water F. Kilowatt Hour = 4 BTU Radian =.296 degrees. Register Ton = 00 cubic feet U.S. Shipping Ton = 40 cubic feet British Shipping Ton = 42 cubic feet Cubic Foot/Minute = cubic cm/second Cubic Foot/Minute =.246 gallons (U.S.)/second Cubic Foot/Second = cubic yards/minute Gallon (U.S.)/Minute = cubic feet/hour Gallon (U.S.)/Minute =.842 liter/minute Liter/Minute = cubic feet/hour Cubic Mitre/Minute = Gallons (U.S.)/Minute Pound/Gallon (U.S.) =.4809 pound/cubic feet Mile/Hour = 88 feet/minute Foot/Minute =.0664 miles/hour Pound per Square Inch Pressure (PSI) = 44 pounds/square foot = 2.09 feet fresh water at 62 F = 2.0 inches mercury at 2 F = inches mercury at 62 F =.068 atmospheres. Water Pressure (pounds per square inch) =.4 x height of water in feet (Fresh water at 62 F). Weight of cubic foot of fresh water = 62. pounds at 62 F = 9.6 pounds at 22 F. Weight of gallon (U.S.) water = 8.4 pounds Weight of cubic foot of Air at 4. lbs per square inch Pressure =.0608 pounds at 62 F =.080 pounds at 2 F. Watts = Amperes x Volts Watt-Hour =.424 BTU = Calorie = 600 Joule. g = Acceleration due to gravity at Sea Level, Latitude 4 = 2.26 Feet/Second squared. pound-foot (torque) =.88 Newton-Metre. L-20

21 Area/Circumference Table Circumferences and Areas of Circles ( 8 Diameters) Diameter Circumference Area Diameter Circumference Area Diameter Circumference Area Diameter Circumference Area L-2

22 Trigonometric Functions COTANGENT COSINE Trigonometric Formulas (See pages that follow for functions) SINE TANGENT Right Angle Triangle RADIUS SECANT COSECANT Formulas for Finding Functions of Angles Side Opposite = Sine Hypotenuse Side Adjacent = Cosine Hypotenuse Side Opposite = Tangent Side Adjacent Side Adjacent = Cotangent Side Opposite Hypotenuse = Secant Side Adjacent Hypotenuse = Cosecant Side Opposite Formulas for Finding Sides of Right Angle Triangles with an Angle and Side Known To Find: Length of side opposite To Find: Length of side adjacent To Find: Length of hypotenuse { { { Hypotenuse x Sine Hypotenuse Cosecant Side Adjacent x Tangent Side Adjacent Cotangent Hypotenuse x Cosine Hypotenuse Secant Side Opposite x Cotangent Side Opposite Tangent Side Opposite x Cosecant Side Opposite Sine Side Adjacent x Secant Side Adjacent Cosine To Find Angles and Sides of Right Angle Triangles To Find: C C C C C C B B B B B B To Find Angles Formulas c = Sine C a b = Cosine C a c = Tan. C b b = Cotan. C c a = Secant C b a = Cosec. C c b = Sine B a c = Cosine B a b = Tan. B c c = Cotan. B b a = Secant B c a = Cosec. B b To Find: To Find Sides Formulas a b 2 + c 2 a a a a c x Cosec. C c x Secante B b x Cosec. B b x Secante C c Sine C c Cosine B b Sine B b Cosine C b a 2 c 2 b b b b a x Sine B a x Cos. C c x Tan. B c x Cot. C a Cosecant B a Secant C c Cotan. B c Tangent C c a 2 b 2 c c c c a x Cos. B a x Sine C b x Cot. B b x Tan. C a Secant B a Cosecant C b Tangent B b Cotan. C Oblique Angle Triangle To Find Angles and Sides of Oblique Angle Triangles To Find Known Formulas To Find Known Formulas C A, B 80 (A +B) A B, C 80 (B + C) b a, B, A a x Sin. B Cos. A a, b, c b 2 + c 2 a 2 Sin. A 2bc c a, A, C a x Sin. C Sin. C c, A, a c x Sin. A Sin. A a Tan. A a, C, b a x Sin. C Cot. B a, C, b a x Cosec. C Cot. C b (a x Cos. C) b B A, C 80 (A + C) c b, C, B b x Sin. C x Cosec. B Sin. B b, A, a b x Sin. A a L-22

23 Trigonometric Tables Trigonometric Functions Sine Tan. Cotan. Cosine Sine Tan. Cotan. Cosine INFINITE Cosine Cotan. Tan. Sine Cosine Cotan. Tan. Sine NOTE: For functions from 4-0 to 68 read from bottom of table upward. L-2

24 Trigonometric Tables Trigonometric Functions Sine Tan. Cotan. Cosine Sine Tan. Cotan. Cosine Cosine Cotan. Tan. Sine Cosine Cotan. Tan. Sine NOTE: For functions from 4-0 to 68 read from bottom of table upward. L-24

25 Conversion Tables Given Multiply By To Find ABAMPERE 0 AMPERE ACRES HECTARE ACRES 460 SQUARE FEET ACRES SQUARE METERS ACRES.62x0 - SQUARE MILES ARE 06.9 SQUARE FEET ATMOSPHERES 6 CMS. OF MERCURY ATMOSPHERES.8984 FEET OF WATER ATMOSPHERES INCHES OF MERCURY ATMOSPHERES POUNDS/SQUARE INCH BAGS CEMENT 94 POUNDS CEMENT BARRELS OIL.648 CUBIC FOOT BARRELS OIL 8.98 LITER BARRELS OIL 42 GALLONS OIL BARRELS (US DRY).2829 BUSHELS (US) BARRELS (US DRY) 4.08 CUBIC FEET BARRELS (US DRY).62 LITER BARRELS (US LIQ.) CUBIC FEET BARRELS (US LIQ.) CUBIC METERS BARRELS (US LIQ.) GALLONS (BRIT.) BARRELS (US LIQ.). GALLONS (US) BARRELS CEMENT 6 POUNDS CEMENT BTU CALORIE BTU 8.69 FOOT POUNDS FORCE BTU.902x0-4 HORSEPOWER HOURS BTU 0.22 KILOGRAM CALORIES BTU 0.86 KILOGRAM METERS BTU 2.90x0-4 KILOWATT HOURS BTU 0.06 JOULE BTU/MIN FOOT POUNDS/SEC. BTU/MIN HORSEPOWER BTU/MIN KILOWATTS BTU/MIN..96 WATTS BUSHELS (BRIT.).020 BUSHELS (US) BUSHELS (BRIT.) 8 GALLONS (BRIT.) BUSHELS (US) BARRELS (US DRY) BUSHELS (US) CUBIC FEET BUSHELS (US) 9.09 GALLONS (US LIQ.) CALORIE JOULE CALORIE.9682x0 - BTU CALORIE.0880 FOOT POUND FORCE CENTARES (CENTIARES) SQUARE METERS CENTIMETERS INCHES CENTIMETERS.9008 INCH CENTIMETERS 0.0 METERS CENTIMETERS 0 MILLIMETERS CENTIMTRS. OF MERCURY 0.06 ATMOSPHERES CENTIMTRS. OF MERCURY FEET OF WATER CENTIMTRS. OF MERCURY 6 KGS./SQUARE METER CENTIMTRS. OF MERCURY 2.8 POUNDS/SQUARE FT. CENTIMTRS. OF MERCURY 0.94 POUNDS/SQUARE INCH CENTIPOISE 0.00 PASCAL SECOND CHAIN (RAMSDEN S) 00 FEET CHAIN (GUNTER S) 66 FEET CORD 28 CUBIC FEET CORD.624 STERE COULOMB AMPERE SECOND CUBIC CENTIMETER CUBIC INCHES CUBIC CENTIMETER 0.00 LITER CUBIC CENTIMETER MILLILETER CUBIC DECIMETER 0.0 CUBIC FEET CUBIC FEET 2 BOARD FEET CUBIC FEET BUSHELS (US) CUBIC FEET 28 CUBIC INCHES CUBIC FEET CUBIC METERS CUBIC FEET 28. CUBIC DECIMETERS CUBIC FEET 0.00 CUBIC YARD CUBIC FEET GALLONS (BRIT.) CUBIC FEET.4809 GALLONS (US) CUBIC FEET LITERS CUBIC FEET 2.40 QUARTS (US DRY) CUBIC FEET/HOUR.869 CUBIC CM./SEC. CUBIC FEET/HOUR LITER/MIN. CUBIC FEET/MIN GALLONS (US)/SEC. CUBIC FEET/POUND CUBIC METER/KILOGRAM CUBIC METER BARREL (US DRY) Given Multiply By To Find CUBIC METER BARREL (US LIQ.) CUBIC METER.46 CUBIC FEET CUBIC METER.09 CUBIC YARDS CUBIC METER GALLONS (US) CUBIC METER 000 LITER CUBIC YARDS 2 CUBIC FEET CUBIC YARDS CUBIC METER CUBIC YARDS GALLONS (US) CUBIC YARDS/MIN. 0.4 CUBIC FEET/SEC. CUBIC YARDS/MIN GALLONS (US)/SEC. CUBIT 8 INCH CUP MILLILITER CUP (METRIC) 200 MILLILITER DEGREE 0.04 RADIAN DEGREE/SEC REVOLUTION/MIN. DENIER 0.( 9) TEX DRACHM (BRIT. FLUID) DRAM (U.S. FLUID) DRAM (APOTH) 60 GRAINS DRAM (AVOIR) 2.4 GRAINS DRAM (U.S. FLUID) CUBIC INCHES ELL 4 INCH ERG x0 - JOULE FATHOM 6 FEET FEET OF WATER ATMOSPHERES FEET OF WATER INCHES OF MERCURY FEET OF WATER 04.8 KGS./SQUARE METER FEET OF WATER 62.4 POUNDS/SQUARE FT. FEET OF WATER 0.4 POUNDS/SQUARE INCH FEET/MIN CENTIMETERS/SEC. FEET/MIN FEET/SEC. FEET/MIN KILOMETERS/HOUR FEET/MIN METERS/MIN FEET/MIN MILES/HOUR FEET/SEC CENTIMETERS/SEC. FEET/SEC..09 KILOMETERS/HOUR FEET/SEC KNOTS FEET/SEC METERS/MIN. FEET/SEC MILES/HOUR FEET/SEC MILES/MIN. FERKIN (US) 9 GALLONS (US) DRY FOOT 0.48 CENTIMETER FOOT 2 INCH FOOT/MINUTE METER FOOT/MINUTE KILOMETER/HOUR FOOT/SECOND MILE/HOUR FOOT/SECOND METER/SECOND FOOT POUNDS FORCE MILE/HOUR FOOT POUNDS FORCE.00x0 - HORSEPOWER HOURS FOOT POUNDS FORCE.82 JOULES FOOT POUNDS FORCE.24x0-4 KILOGRAM CALORIES FOOT POUNDS FORCE 0.8 KILOGRAM METERS FOOT POUNDS FORCE.66x0 - KILOWATT HOURS FOOT POUNDS FORCE.286x0 - BTU FOOT POUNDS/MIN..286x0 - BTU/MIN. FOOT POUNDS/MIN FOOT POUNDS/SEC. FOOT POUNDS/MIN..00x0-4 HORSEPOWER FOOT POUNDS/MIN..24x0-4 KG. CALORIES/MIN. FOOT POUNDS/MIN x0 - KILOWATTS FOOT POUNDS/SEC..x0-2 BTU/MIN. FOOT POUNDS/SEC..88x0 - HORSEPOWER FOOT POUNDS/SEC..94x0-2 KG. CALORIES/MIN. FOOT POUNDS/SEC..88 WATTS FURLONG 660 FEET FURLONG 0 CHAIN GALLON (BRIT.) CUBIC FT./HOUR GALLON (BRIT.) CUBIC METER/HOUR GALLONS (US)/MIN CUBIC FEET/HOUR GALLONS (US)/MIN CUBIC METER/HOUR GALLON (DRY) CUBIC INCH GALLONS (LIQ.) 8.42 CUBIC CENTIMETERS GALLONS (LIQ.) CUBIC FEET GALLONS (LIQ.) 2 CUBIC INCHES GALLONS (LIQ.).8x0 - CUBIC METERS GALLONS (LIQ.) 4.9x0 - CUBIC YARDS GALLONS (LIQ.) GALLONS (BRIT.) GALLONS (LIQ.).842 LITERS L-2

26 Conversion Tables Given Multiply By To Find GALLONS (LIQ.) 8 PINTS (LIQ.) GALLONS (LIQ.) 4 QUARTS (LIQ.) GALLONS WATER 8.4 POUNDS OF WATER GALLONS WATER/MIN TONS WATER/24 HOURS GALLONS IMPERIAL.2009 U.S. GALLONS GALLONS U.S IMPERIAL GALLONS GALLONS (US)/MIN x0 - CUBIC FEET/SEC. GALLONS (US)/MIN CUBIC FEET/HOUR GALLONS (US)/MIN Litros/SEC. GILL.28 CUBIC INCH GILL 4 OUNCE (U.S.) GILL (BRIT.).2009 GILL (U.S.) GRAINS (TROY) GRAMS GRAINS/U.S. GAL..8 PARTS/MILLION GRAINS/U.S. GAL POUNDS/MILLION GAL. GRAINS/U.S. GAL PARTS/MILLION GRAMS 980. DYNES GRAMS.428 GRAINS GRAMS 0 - KILOGRAMS GRAMS 0 MILLIGRAMS GRAMS OUNCES GRAMS 0.02 OUNCES (TROY) GRAMS 2.20x0 - POUNDS GRAMS 0.69 SCRUPLE GRAMS (TROY) 2.08x0 - OUNCES (TROY) GRAMS/CM..600x0 - POUNDS/INCH GRAMS/CU. CM POUNDS/CUBIC FOOT GRAMS/CU. CM POUNDS/CUBIC INCH GRAMS/LITER 8.4 GRAINS/GAL. GRAMS/LITER 8.4 POUNDS/000 GALS. GRAMS/LITER POUNDS/CUBIC FOOT GRAMS/LITER 000 PARTS/MILLION GROSS 2 DOZEN HAND 4 INCH HECTARE ACRE HECTARE 069. SQUARE FT. HOGSHEAD 6 GALLONS HORSEPOWER BTU/MIN. HORSEPOWER 000 FOOT POUNDS/MIN. HORSEPOWER 0 FOOT POUNDS/SEC. HORSEPOWER.04 HORSEPOWER (METRIC) HORSEPOWER 0. KG. CALORIES/MIN. HORSEPOWER 0.4 KILOWATTS HORSEPOWER 4. WATTS HORSEPOWER (BOILER) 49 BTU/HOUR HORSEPOWER (BOILER) KILOWATT HORSEPOWER HOURS 24 BTU HORSEPOWER HOURS.98x0 6 FOOT POUNDS HORSEPOWER HOURS 64. KILOGRAM CALORIES HORSEPOWER HOURS 2.x0 KILOGRAM METERS HORSEPOWER HOURS 0.4 KILOWATT HOURS INCH 000 MILS INCH 2.4 MILLIMETERS INCHES OF MERCURY ATMOSPHERES INCHES OF MERCURY. FEET OF WATER INCHES OF MERCURY 4. KGS./SQUARE METER INCHES OF MERCURY 0. LBS./SQUARE FT. INCHES OF MERCURY LBS./SQUARE INCH INCHES OF WATER ATMOSPHERES INCHES OF WATER 0.0 INCHES OF MERCURY INCHES OF WATER 2.4 KGS./SQUARE METER INCHES OF WATER 0.8 OUNCES/SQUARE INCH INCHES OF WATER.202 POUNDS/SQUARE FOOT INCHES OF WATER 0.06 POUNDS/SQUARE INCH JOULE BTU JOULE CALORIE KILOGRAMS DYNES KILOGRAMS POUNDS KILOGRAMS.02x0 - TONS (SHORT) KILOGRAMS 0 GRAMS KILOGRAMS CALORIES.968 BTU KILOGRAMS CALORIES 086 FOOT POUNDS KILOGRAMS CALORIES.8x0 - HORSEPOWER HOURS KILOGRAMS CALORIES.62x0 - KILOWATT HOURS KILOMETERS 0 CENTIMETERS KILOMETERS FEET Given Multiply By To Find KILOMETERS 0 METERS KILOMETERS MILES KILOMETROS 094 YARDS KILOMETERS/HOUR 2.8 CENTIMETERS/SEC. KILOMETERS/HOUR 4.68 FEET/MIN. KILOMETERS/HOUR 0.9 FEET/SEC. KILOMETERS/HOUR 0.96 KNOTS KILOMETERS/HOUR 6.6 METERS/MIN. KILOMETROS/HOUR MILES/HOUR KILOWATT HOURS 4 BTU KILOWATT HOURS 2.6x06 FOOT POUNDS KILOWATT HOURS.4 HORSEPOWER HOURS KILOWATT HOURS.6x0 6 JOULE KILOWATT HOURS 860. KILOGRAM CALORIES KILOWATT HOURS.6x0 KILOGRAM METERS KILOWATTS BTU/MIN. KILOWATTS 442. FOOT POUNDS/MIN. KILOWATTS.6 FOOT POUNDS/SEC. KILOWATTS.402 HORSEPOWER KILOWATTS 4.08 KG. CALORIES/MIN. KILOWATTS 0 - WATTS KNOTS.09 MILES (STATUTE)/HOUR LEAGUE (STATUTE) MILES (STATUTE) LIGHT YEAR.88x0 2 MILES LINK 0.0 CHAIN LINK.92 INCHES LITERS 0 CUBIC CENTIMETERS LITERS 0.0 CUBIC FEET LITERS 6.02 CUBIC INCHES LITERS 0 - CUBIC METERS LITERS.08x0 - CUBIC YARDS LITERS GALLONS LITERS 2. PINTS (LIQ.) LITERS QUARTS (DRY) LITERS.06 QUARTS (LIQ.) LITERS/MIN..886x0-4 CUBIC FT./SEC. LITERS/MIN..98 GALLON (BRIT.)/HOUR LITERS/MIN. 4.40x0 - GALLONS/SEC. LITERS/SEC CUBIC FT./MIN. METERS 00 CENTIMETERS METERS FEET METERS 9. INCHES METERS 0 - KILOMETROS METERS 0 MILLIMETERS METERS.096 YARDS METERS/MIN..66 CENTIMETERS/SEC. METERS/MIN..28 FEET/MIN. METERS/MIN FEET/SEC. METERS/MIN KILOMETROS/HOUR METERS/MIN MILES/HOUR METERS/SEC FEET/MIN. METERS/SEC..28 FEET/SEC. METERS/SEC..6 KILOMETER/HOUR METERS/SEC KILOMETROS/MIN. METERS/SEC MILES/HOUR METERS/SEC MILES/MIN. MIL 0.00 INCH MIL MILLIMETER MILES 20 ROD MILES.609x0 CENTIMETERS MILES 280 FEET MILES.609 KILOMETROS MILES 60 YARDS MILES/HOUR 44. CENTIMETERS/SEC. MILES/HOUR 88 FEET/MIN. MILES/HOUR.46 FEET/SEC. MILES/HOUR.609 KILOMETROS/HOUR MILES/HOUR KNOTS MILES/HOUR Metros/MIN. MILES/HOUR KILOMETROS/HOUR MILES/HOUR KNOTS MILES/MIN CENTIMETERS/SEC. MILES/MIN. 88 FEET/SEC. MILES/MIN..609 KILOMETROS/MIN. MILES/MIN. 60 MILES/HOUR MILLIGRAMS 0 - GRAMS L-26

27 Conversion Tables Given Multiply By To Find MILLIGRAMS/LITER PARTS/MILLION MILLILITERS CUBIC INCH MILLILITERS FLUID OUNCES MILLILITERS 0 - LITERS MILLIMETERS 0. CENTIMETERS MILLIMETERS 0.09 INCHES MILLION GALS./DAY.42 CUBIC FT./SEC. MINER S INCHES. CUBIC FT./MIN. MINUTES (ANGLE) 2.909x0-4 RADIANS NEWTON METER 0.62 FOOT POUNDS FORCE OUNCES 6 DRAMS OUNCES 4. GRAINS OUNCES POUNDS OUNCES GRAMS OUNCES 0.9 OUNCES (TROY) OUNCES 2.90x0 - TONS (LONG) OUNCES 2.8x0 - TONS (METRIC) OUNCES (FLUID).80 CUBIC INCHES OUNCES (FLUID) LITERS OUNCES (FLUID) 0 MILLILITERS OUNCES (FLUID) OUNCES (BRIT. FLUID) OUNCES (TROY) 480 GRAINS OUNCES (TROY) 20 PENNYWEIGHTS (TROY) OUNCES (TROY) 0.08 POUNDS (TROY) OUNCES (TROY).048 GRAMS OUNCES (TROY).094 OUNCES (AVOIR.) OUNCES/SQUARE INCH POUNDS/SQUARE INCH PACE 2. FEET PALM INCH PARTS/MILLION GRAINS/U.S. GAL. PARTS/MILLION GRAINS/IMP. GAL. PARTS/MILLION 8.4 POUNDS/MILLION GAL. PASCAL POUNDS FORCE/SQ. FT. PECK (BRIT.) 2 GALLON (BRIT) PECKS (US) 8 QUARTS (US DRY) PENNYWEIGHTS (TROY) 24 GRAINS PENNYWEIGHTS (TROY). GRAMS PENNYWEIGHTS (TROY) 0.0 OUNCES (TROY) PENNYWEIGHTS (TROY) 4.66x0 - POUNDS (TROY) PERCH (MASONRY) 24. CUBIC FEET POINT (U.S.-PRINT) 0.08 INCH POLE (BRIT.) 6. FEET POTTLE (BRIT.). GALLONS POUNDS 6 OUNCES POUNDS 26 DRAMS POUNDS 000 GRAINS POUNDS TONS (SHORT) POUNDS GRAMS POUNDS.228 POUNDS (TROY) POUNDS 4.8 OUNCES (TROY) POUNDS OF WATER CUBIC FEET POUNDS OF WATER 2.68 CUBIC INCHES POUNDS OF WATER 0.98 GALLONS POUNDS OF WATER/MIN. 2.60x0-4 CUBIC FT./SEC. POUNDS (TROY) 60 GRAINS POUNDS (TROY) 40 PENNYWEIGHTS (TROY) POUNDS (TROY) 2 OUNCES (TROY) POUNDS (TROY).24 GRAMS POUNDS (TROY) POUNDS (AVOIR.) POUNDS (TROY).6 OUNCES (AVOIR.) POUNDS (TROY).6x0-4 TONS (LONG) POUNDS (TROY) 4.4x0-4 TONS (SHORT) POUNDS (TROY) 4.66x0 - TONS (METRIC) POUNDS/CUBIC FOOT GRAMS/CUBIC CM. POUNDS/CUBIC FOOT 6.02 KGS./CUBIC METERS POUNDS/CUBIC FOOT.8x0-4 POUNDS/CUBIC INCH POUNDS/CUBIC INCH 2.68 GRAMS/CUBIC CM. POUNDS/CUBIC INCH 2.68x0 4 KGS./CUBIC METER POUNDS/CUBIC INCH 28 POUNDS/CUBIC FOOT POUNDS/FOOT.488 KGS./METER POUNDS/INCH 8.6 GRAMS/CM. POUNDS/SQUARE FOOT FEET OF WATER POUNDS/SQUARE FOOT 4.88 KGS./SQUARE METER POUNDS/SQUARE FOOT 6.94x0 - POUNDS/SQUARE INCH POUNDS/SQUARE INCH ATMOSPHERES POUNDS/SQUARE INCH 2.0 FEET OF WATER Given Multiply By To Find POUNDS/SQUARE INCH INCHES OF MERCURY POUNDS/SQUARE INCH 0. KGS./SQUARE METER PSI POUND FORCE/SQ. IN. PUNCHEON 84 GALLONS PUNCHEON (BRIT.) 0 GALLON (BRIT.) QUARTS (DRY) 0.02 BUSHEL QUARTS (DRY) CUBIC INCHES QUARTS (DRY).0 LITERS QUARTS (LIQ). CUBIC INCHES QUARTS (LIQ) LITER QUARTS (LIQ) QUART (BRIT.) QUARTS (LIQ) QUART (DRY) QUINTAL, ARGENTINE 0.28 POUNDS QUINTAL, BRAZIL 29.4 POUNDS QUINTAL, CASTILE, PERU 0.4 POUNDS QUINTAL, CHILE 0.4 POUNDS QUINTAL, METRIC POUNDS QUINTAL, MEXICO 0.4 POUNDS RADIANS.298 DEGREES RADIANS 4.4 MINUTES RADIANS QUADRANTS RADIANS/SEC.. DEGREES/SEC. RADIANS/SEC REVOLUTIONS/SEC. RADIANS/SEC REVOLUTIONS/MIN. REAMS 00 SHEETS REVOLUTIONS 60 DEGREES REVOLUTIONS 4 QUADRANTS REVOLUTIONS 6.28 RADIANS REVOLUTIONS/MIN. 6 DEGREES/SEC. REVOLUTIONS/MIN RADIANS/SEC. REVOLUTIONS/MIN REVOLUTIONS/SEC. REVOLUTIONS/SEC. 60 DEGREES/SEC. REVOLUTIONS/SEC RADIANS/SEC. REVOLUTIONS/SEC. 60 REVOLUTIONS/MIN. RODS 6. FEET ROPE 20 FEET SCRUPLE 20 GRAINS SEAM (BRIT.) 64 GALLON (BRIT.) SLUG 4.99 KILOGRAMS SPAN 9 INCHES SQUARE CM. 0-4 SQUARE METERS SQUARE CM. 00 SQUARE MILLIMETERS SQUARE FEET 2.296x0 - ACRES SQUARE FEET 929 SQUARE CENTIMETERS SQUARE FEET 44 SQUARE INCHES SQUARE FEET SQUARE METERS SQUARE FEET.8x0 - SQUARE MILES SQUARE FEET 9 SQUARE YARDS SQUARE INCHES 6.42 SQUARE CENTIMETERS SQUARE INCHES 6.944x0 - SQUARE FEET SQUARE INCHES 64.2 SQUARE MILLIMETERS SQUARE KILOMETERS 24. ACRES SQUARE KILOMETERS 0.6x0 6 SQUARE FEET SQUARE KILOME 0 6 SQUARE METERS SQUARE KILOMETERS 0.86 SQUARE MILES SQUARE KILOMETERS.96x0 6 SQUARE YARDS SQUARE METERS 2.4x0-4 ACRES SQUARE METERS 0.6 SQUARE FEET SQUARE METERS.86x0 - SQUARE MILES SQUARE METERS.96 SQUARE YARDS SQUARE MILES 640 ACRES SQUARE MILES 2.88x0 6 SQUARE FEET SQUARE MILES 2.9 SQUARE KILOMETERS SQUARE MILES.098x0 6 SQUARE YARDS SQUARE MILLIMETERS 0.0 SQUARE CENTIMETERS SQUARE MILLIMETERS.0x0 - SQUARE INCHES SQUARE YARDS 2.066x0-4 ACRES SQUARE YARDS 9 SQUARE FEET SQUARE YARDS 0.86 SQUARE METERS SQUARE YARDS.228x0 - SQUARE MILES STERE CUBIC METER STERE 0.29 CORD STONE 4 POUNDS TABLESPOON 4.9 MILLILITERS TEASPOON MILLILITERS TEMP.(oC.)+.8.8 TEMP.(oF.) L-2

28 Conversion Tables Given Multiply By To Find TEMP.(oF)-2 /9 TEMP.(oC.) THERM 00,000 BTU TONS OF WATER/24 HRS. 8. POUNDS WATER/HOUR TONS OF WATER/24 HRS GALLONS/MIN. TONS OF WATER/24 HRS..49 CUBIC FT./HOUR TONS (LONG) KILOGRAMS TONS (LONG).0604 TONS (METRIC) TONS (LONG) 2240 POUNDS TONS (LONG).2 TONS (SHORT) TONS (METRIC) 0 KILOGRAMS TONS (METRIC) 220 POUNDS TONS (SHORT) 2000 POUNDS TONS (SHORT) 2000 OUNCES TONS (SHORT) KILOGRAMS TONS (SHORT) POUNDS (TROY) TONS (SHORT) TONS (LONG) TONS (SHORT) 2966 OUNCES (TROY) TONS (SHORT) TONS (METRIC) Given Multiply By To Find WATT HOUR 600 JOULE WATTS BTU/MIN. WATTS FOOT POUNDS/MIN. WATTS 0.6 FOOT POUNDS/SEC. WATTS.4x0 - HORSEPOWER WATTS KG. CALORIES/MIN. WATTS 0 - KILOWATTS WATTS HOURS.424 BTU WATTS HOURS 26 FOOT POUNDS FORCE WATTS HOURS.4x0 - HORSEPOWER HOURS WATTS HOURS 600 JOULES WATTS HOURS KILOGRAM CALORIES WATTS HOURS 6. KILOGRAM Metros WATTS HOURS 0 - KILOWATT HOURS YARDS 9.44 CENTIMETERS YARDS 6 INCHES YARDS Metros L-28

29 L - L2 //0 :0 PM Page 29 FOR MORE INFORMATION CALL CLARK Worldwide Locations Through steady, planned expansion, Martin has developed a network of modern manufacturing and service centers. The ever increasing demand for high quality Martin products from many industries and markets has been met by continuous modernization and expansion of manufacturing and marketing facilities. Now, with plants located in key industrial areas throughout the United States, Martin is able to produce and deliver quality products to best serve the needs of every market in virtually any quantity. Distributors are located in all fifty states and throughout the world to HEADQUARTERS - ARLINGTON, TX provide total product availability. It s through this manufacturing and marketing organization that Martin makes good its claim of serving industry wherever machinery is in motion and materials are on the move. ARLINGTON, TX ATLANTA, GA BOSTON, MA CHARLOTTE, NC CHICAGO, IL CLARKSVILLE, TX DALLAS, TX ABILENE, TX L-29

30 L - L2 //0 :0 PM Page 0 FOR MORE INFORMATION CALL CLARK DENVER, CO DETROIT, MI FT. WORTH, TX HOUSTON, TX KANSAS CITY, MO LOS ANGELES, CA MANSFIELD, TX MINNEAPOLIS, MN MONTPELIER, OH PARAGOULD, AR PORTLAND, OR SACRAMENTO, CA TAMPA, FL WAYNE, NJ AYR, CANADA TORONTO, CANADA MEXICO DANIELSVILLE, PA L-0

31 INVENTORY: Martin delivers with incredible fill rates from one of its many facilities strategically located across North America. SERVICE: Martin ships rebores and other alterations within hours - not days... MTO s in days - not weeks. PEOPLE: When you call Martin you get a person, not voice mail. We are ready, able and willing to help...now! USA General Offices Sales and Manufacturing Arlington, TX 00 Sprocket Drive P.O. Box 988 Arlington, Texas (FAX 8-28-) Sales and Manufacturing Danielsville, PA 6 Delps Road 808 P.O. Box 26 Danielsville, PA (FAX 60-8-) Ft. Worth, TX (Conveyor, Sheave & Tool Divisions) 600 McCart Ave. Ft. Worth, TX (FAX 8-28-) Montpelier, OH 0 S. Airport Road Montpelier, OH (FAX ) Sacramento, CA 99 Vine Street Sacramento, CA (FAX ) Scottdale, GA 0 Church Street P.O. Box 886 Scottdale, GA (FAX ) Mini Manufacturing Centers Boston, MA Fortune Boulevard Milford, MA (FAX ) Charlotte, NC 90 Scott Futrell Drive Charlotte, NC (FAX ) Chicago, IL 0 Birchwood Avenue Des Plaines, IL (FAX ) Denver, CO 0800 East 4th Avenue Denver CO (FAX 0--6) Detroit, MI 2 Belden Ct. Livonia, MI (FAX ) Houston, TX 990 Bent Oak Drive Houston, TX (FAX ) Kansas City, MO 20 N. Commerce Avenue Kansas City, MO (FAX ) Los Angeles, CA 920 S. Triangle Drive Commerce, CA (FAX ) Minneapolis, MN 060 Hampshire Avenue South Bloomington, MN (FAX ) Portland, OR 00 N.W. Industrial Portland, OR (FAX ) Tampa, FL 20 Queen Palm Drive Tampa FL (FAX ) Wayne, NJ High Point Drive Wayne, NJ (FAX ) Manufacturing Only Abilene, TX Clarksville, TX Dallas, TX Mansfield, TX Paragould, AR (Includes the Plastics Div.) CANADA Sales and Manufacturing Martin Sprocket & Gear Canada Inc. 896 Meyerside Drive Mississauga, Ontario, Canada LT R (FAX ) Martin Sprocket & Gear Canada Inc. (Conveyor Division) 00 Industrial Road Ayr, Ontario, Canada NOB EO (FAX ) Chengdu Fuzhou Hong Kong Shanghai Tianjin Zhongshan CHINA MEXICO Sales and Manufacturing Martin Sprocket & Gear de Mexico, S.A. de C.V. Km 2 Carretera, Naucalpan-Toluca Calle, Manzana VII, Lote Parque Industrial Toluca 2000 Toluca, Edo. de México (Fax: ) L-