Conversion Factors. Length. Speed. Acceleration

Transcription

1 Conversion Factors Most scientific measurements and calculations make use of the SI (metric) system of units. The English system of units is more commonly used by baseball and softball fans. Some useful conversion factors and baseball/softball measures are listed below. Length 1inch(in.)D 25.4 mm 12 in. D 1 foot D mm 3 feet D m 1 metre (m) D 100 cm D 1,000 mm D in. D feet (ft) 1kmD 1,000 m D mile 1 mile D 5,280 ft D km Diameter of 12 in. softball: in. (96.01 mm) to in. (98.03 mm) Diameter of baseball: in. ( mm) to in. (74.788mm) Length of typical bat: 33 in. D mm 34 in. D mm Distance between bases in softball D 60 ft D m Distance between bases in baseball D 90 ft D m Speed 1ms 1 D 3.6 km h 1 D ft s 1 D mph 100 mph D km h 1 D m s km h 1 D mph D m s 1 50 m s 1 D mph Acceleration Acceleration due to gravity D 9.80 m s 2 D ft s 2 R. Cross, Physics of Baseball & Softball, DOI / , 317 c Springer Science+Business Media, LLC 2011

2 318 Conversion Factors Area 1sqin.D sq cm 10,000 cm 2 D 1m 2 1 sq cm D sq in. Mass 1kgD 1,000 g D lb D oz 1 lb D 16 oz D kg 1ozD g Mass of 12 in. softball: 6.25 oz ( g) to 7 oz ( g) Mass of baseball: 5 oz ( g) to 5.25 oz (148.84g) Typical bat mass: 30 oz D g 31 oz D g 32 oz D g Density Density of dry air (0% humidity) D kg m 3 D lb ft 3 at 20 ı C(68 ı F) and standard atmospheric pressure ( millibars) 1kgm 3 D lb ft 3 Moment of Inertia 1ozin. 2 D 1: kg m 2 1kgm 2 D 54,674 oz in. 2 The swing weight of a bat for rotation about an axis in the handle, 6 in. from the knob, is given in oz in. 2 to a good approximation by I 6 =.0:76B= L 0:2/ML 2 where M is the bat mass in oz, L is bat length in inches, and B is the balance distance from the center of mass to the knob in inches. Spin 1revs 1 D 60 rpm D 6.28 rad s 1 1,000 rpm D rev s 1 D radian s 1 3,000 rpm D 50 rev s 1 D radian s 1 Force 1Newton(N)D lb 1 lb D N (lb here is a unit of force) In the USA 1 lb can be a unit of mass or force in everyday use.

3 Conversion Factors 319 Pressure Standard air pressure at sea level D millibars D kpa D psi 1 millibar D 100 Pa 1 Pa D 1Nm 2 1psiD 6,895 N m 2 Temperature 0 ı C D 32 ı F D ı K To convert a temperature, T C in degrees Celsius to degrees Fahrenheit (T F )use T F D 32 C 1:8T C. For example, 0 ı C D 32 ı F, 30 ı C D 86 ı F and 40 ı C D 104 ı F. Stiffness 1Nm 1 D lb in. 1 1lbin. 1 D N m 1 The dynamic stiffness of a baseball or softball (when compressed rapidly) is typically about 1,000,000N m 1 D 5,710 lb in. 1 or more. The static stiffness, when compressed slowly, is about 1,500 lb in. 1 Energy 1JD ft lb 1 ft lb D J

4 Index A Acceleration, definition, 3 4 Aluminum bats, 19, 22 23, 28 31, 33 35, 118, , 159, 164, 165, , 191, 204, 210, 212, 229, , 271, 302, 306, 310 Amateur Softball Association (ASA), 22, 27, 185, 189, 192, Angular acceleration, definition, Angular speed, 12 14, 176, 179, 194, 271, 275 Area moment of inertia, 208, 217 ASA. See Amateur Softball Association B Backspin, 12, 45 48, 54, 55, 59 64, 67, 68, 71, 72, 76, 261, 265, 266, 272, 273, , 295 Balance point, Project 6, Ball exit speed ratio (BESR), 28, 185, 186 Balls compression, 25, 113, 130, 139, 141, 142, 146, 148, 151, 152, 223, 227, 233 mass-spring model, , 230 stiffness, 25, 33, 116, 118, 119, 124, 130, 132, 133, , 145, 146, 187, 196, 225, , 308 typical properties, Ball speed, calculations, 3, 10, 51, 52, 54, 59, 62, 118, 157, , 170, 176, 185, 190, 197, 227, 247, 268, , 276, 281, 282, 288 Baseball, history, 20 21, 155 Bat-ball collision, project 10, Bat performance factor, 28, Bats aluminum (see Aluminum bats) broken, 21, 30, 230, 259 composite, 19, 23, 129, 135, 146, 161, 174, 186, 195, 212, 226, 261, 302 diameter, 20 22, 24, 26 32, 34, 103, 106, 185, 212, 224, 243, 303 drop, 27, 183 Easton BK7, 28, 31, 164, 246, 310 flexible handle, 31, 216, hand-held, 169, 170, , 238, 240, 241, 245, 254, 277, 283 history, Louisville Slugger, 28, 30, 164, 243, 251 performance tests, 19 21, 27 28, 118, , 251, 252, 254 rules, 20 21, 25 27, , 192, 197 softball, 4, 22, 24, 26, 144, 183, 185, 188, 189, 195, 197, 215, 235 stiffness, 32, 34, 224, 225, , 233 three section, toy, typical properties, wood (see Wood bats) wood vs.aluminum, Batter, decision time, 3 Bat vibrations, , 166, 169, 170, 193, 195, 197, , 221, 227, 230, 231, 237, , 256, 259, 299, 311 Baum hitting machine, 185 Beam equation, 218, 219, 227, 230 Bending wave, 129, 169, 170, 199, 203, 208, 211, 213, 214, 216, 218, 253, , 315 BESR. See Ball exit speed ratio Billiard balls, 161, 162, 224, 306 Bounce oblique, , 274, , 291 off inclined surface, 262, of spinning ball, 120, , 282, 286,

5 322 Index Bounce equations, 147, 152, 160, 166, 234, 256, 274, 288, 292 Bounce factor, 159, 161, 162, 164, 166, 167, , 185, 190, 191, 194, 195, , , 260, 277, 288, defined, 159, 175 project 10, 311 vs.swing weight, 174, 191 Bounce models, Break, of pitched ball, 55, 65 66, 68 Bunting, 105, 172 C Catching a ball, 108 Center of percussion (COP), 28, 178, 200, , 245, 246, 300, 301 Project 5, 300, 301 Centripetal force, 14, 15, 92, 94, Circular motion, 12 17, 92 Coefficient of restitution (COR), , , 162, , 200, 229, vs.ball stiffness, 25, 118, 146, 187, 196, 227, for bat-ball collision, 167, 192, 229 vs.bounce speed, 121, , , 276 defined by Newton, 124, 157 as fraction of energy lost, 125, 126, 141, 144, 157, 170, 200 on hard, heavy surface, 121, 273, 290 for pivoted bat, project 10, 247, in tangential direction, , 275, 277, 290, 291 vs.temperature and humidity, 131 for two colliding balls, Collisions bat and ball, 5, 8, , 133, , , , 200, 213, 226, 235, 237, 276, 286, billiard balls, 161, 162, 224 elastic, 162 equations, 126, history, inelastic, 158 Composite bats, 19, 23, 129, 135, 146, 161, 174, 186, 195, 212, 226, 261, 302 Conservation of momentum, 4, 178, 276 Contact time, 113, 115, 215, 254 Conversion factors, 1, 2, 13 COP. See Center of percussion COR. See Coefficient of restitution Corking a bat, 159 Couple, on bat, 23, Creep, 138 Cricket balls, 70, 86, 145, 146, 252 bats, 86, 218, 252 Curve ball, 60, 65, 289, 290 D Dead spot, 162 Derivative, definition, 2 Dispersion, 214 Double pendulum, 81 84, 88 Drag force direction, 41, 43, 51, 66, 69, 71 drag coefficient, 38, 39, 42, 51, 53, 54, 74, 289, 290 Project 4, E Effective mass, 135, 159, , , 190, 191, 198, 200, 201, 206, 227, 230, 231, 257 vs.swing weight, , 179 Elastic energy, 34, 118, 120, , 129, 130, , 138, 140, 146, 149, 150, 157, 196, 216, 221, , , , 269, 276, 306 Elastic materials, 119, 129 Energy, kinetic, 6, 7, 43, 79, 83, , 125, 126, , 132, 133, 135, 141, 155, 157, 158, 169, 223, 225, 231, 232, 246, 260, 276, 282, 314 F Fast ball, 48, 60, 65, 108, 111, 289, 290 Fast pitch softball, 22, 24, 26, 27, 59 62, 72, 168, 171, 183, 192, 198 Field dimensions, 59, Flight of ball effect of drag force, 42, 46, 47, 53, 69, 70, effect of gravity, 37, 38, 42, 46, 69, 71, effect of lift force, 55, effect of Magnus force, 46, 55, 71, 72, Force on a bat, 89, 91 92, , 130 on bouncing ball, 115, 132, 141, 275

6 Index 323 centripetal, 14, 15, 92, 94, definition, 5 6 on different objects, 5, 6, 9, 12, 16, 40, 42, 78, 79, 89 92, 156, 157, 206, 295, 299 to throw a ball, 6, 7, 9, 43, 80 Fundamental mode, 248 G Gravity, Project 1, 10, Grip force, , 275, 282 Gyroball, 54, H Happy balls, 125 Height problem, History of baseball, 20 21, 155 of softball, 22 Home runs, 20, 131, 146, 261, Hoop mode, , 216, 302 Hysteresis in baseballs, , dynamic, , 146 at high ball speed, 42, 117, 131, 273, 288, 290, 308 static, I Impact duration, Project 9, Impact force on a bat/ball, 25, 40, 115, 116, 147, 150, 187, 247, 307 on a player, 25, , 187 K Kenko ball, 33, 40, 117, 118 Kinetic energy, 6, 7, 43, 79, 83, , 125, 126, 128, 130, 132, 135, 141, 155, 157, 158, 169, 223, 225, 231, 232, 246, 260, 276, 282, 314 definition, 79 Knuckleball, 70, 72, 289 L Lift force lift coefficient, 54, 55, 68, 74 Project 3, Linear motion, 1 8, 12 Louisville Slugger, 28, 30, 243, 251 M Magnus force calculation, 54 description, 44, 63, 295 direction, 44 47, 54, 63, 67, 71, 72, 295, 296 Project 2, 44, Mass vs.weight, , 179, 180, 305 Minimum MOI rule, 185 Minus 3 rule, 184, 192, 197 Moment of inertia (MOI), 15 17, 80, 97, 163, 172, 176, , 184, 185, 188, 190, 200, 208, 217, 262, 274, 304 Momentum in collisions, 44, 133, 135, 156, 166, 176, 178, 276 definition, 4 5, 157 N National Collegiate Athletic Association (NCAA), 22, 26 27, 118, 137, 156, 157, , 191, 192, Newton s Laws, 5, 9 10, 120, 235, 297 Node point, 207, 210, 211, 230, 242, 243, 245, 246, 258, 300, 301 O Oblique bounce, , 274, , 291 Overtones, P Performance, of bats, 19 21, 27 28, 118, , 251, 252, 254 Piezoelectric disk force measurement, 116, 307 Project 9, 307 PITCHf/x system, technical details, 69 Pitching baseball trajectories, 21, 55, 59 65, 67, 68, 70, 72 74, 77 break of ball, 55, 65 66, 68 fast pitch trajectories, 24, 168, 183 physics, 65, slow pitch trajectories, 22, 24, 26, 59 61, 72, 168, 183, 188, 192, 196 strike zone, 59, 62, 64, 65 thrown ball, 76, 78 timing accuracy, types, 67, 70, 106 windmill style, 59

7 324 Index Power, definition, 6 7 Psychology of hitting a ball, 111 of sound, 20 R Radian, definition, 13 Reaction time, 104 Red dot, on approaching ball, 71 Reference frames, 7 8, 124, 134, 135, 156, 160, 282, 288 Rolling ball, 268, 269, 271, 275, 290 Rotation axis, of bat, 100, 174, 201 Rules of baseball, 21, 39, 103, , 184 of softball, S Safety issues, 21, 27, 116 aluminum bats, 118 Scattering, , Size-weight illusion, 111 Sliding friction, 269, 270, 273, 276 Softball history, 22 slow pitch, 22, 24, 26, 59 61, 72, 168, 183, 188, 192, 196 Spatial perception, 108 Speed, definition, 2 3 Static friction, 269 Stereo vision, Stiffness of ball, 25, 33, 116, 118, 119, 124, 130, 132, 133, , 145, 146, 187, 196, 225, , 308 of bat, 32, 34, 224, 225, , 233 of beam, , 218, 257 Stress relaxation, , 144, 146 Strike zone, 59, 62, 64, 65 in tennis, 103, 221, 276 Sweet spot, 27, , , , 175, , 198, 203, 211, 218, 219, 227, 231, , , 299 as center of percussion, , 245, 246, Project 5, size, Swinging a bat end of swing, 87, 92, 93, 97, 99 film of swing, start of swing, 86, 92, 93, 96, 98, 100 Swing speed vs.swing weight, 184, 185, Swing weight, 16, 29 31, 167, 168, , 179, 180, , 196, 198, 201, 299, 302 Project 7, T Tennis strings, 138, Throwing effect of wrist, 71, 77, 80, 83, 84, 86 throw force, 6, 7, 9, 43, 55, 78 80, 83, 84, 89 throw speed, 77 81, 189, 252 Timing problem in batting, 104 in pitching, 104, 105 Topspin, 45, 48, 56, 59, 60, 62 64, 67, 68, 71, 72, 265, 266, , 289 Torque on a bat, 93, 97, 98, 101, 176 definition, exertedbywrist,99 Trajectory of ball through air, 9 12, 48, 55, 70 effects of gravity, 9 12, 37, 38, 59 Trampoline effect, 23, 34, 35, 118, 129, 130, 146, 159, 161, 169, 171, 174, 184, 186, 195, 196, 210, 212, , 251, 311, 313 Project 8, 306 U Units, 1, 2, 5, 26, 32, 149, 171, 217, 223, 246 V Vibrations, , 142, 143, 155, 166, , 175, 193, 195, 197, 199, 200, , 221, 225, , 237, 239, , , 299, 300, 302, 311 W Wood bats, 19 22, 26, 28 31, 33 35, 118, 129, 130, 135, 146, 159, 161, 164, 165, 170, 174, 175, 183, 185, 186, 192, 193, 196, 198, 204, 210, 224, , 243, 246, 251, 255, 261, Work definition, 6, 79 to throw a ball, 6, 7, 71, 77, 79, 83, 84