THIRD EDITION - RELEASE DATE 15 JUNE 2002

INDEX

A

"A" in velocity formula 1

ABS brakes - the function of 1

ABS - peculiarities 2

Acceleration rate - formulae 2

Acceleration and deceleration factor - m - formulae 2

Alphabet - Greek see Greek alphabet 38

Angle of takeoff 3

Angle of sliding friction see sliding friction 82

Angular acceleration 3

Angular momentum 3

Angular velocity 3

Aquaplaning see hydroplaning 39 - 40

Arc - height at any point in an arc along the horizontal distance 4

Arc - highest point reached in an arc 5

Arc - horizontal distance to a point opposite the highest point in an arc 5

Arc - maximum height obtained by a know velocity 6

Arc - time to reach any horizontal distance along the path of the arc 6

Arc - time to reach maximum height 6

Arc - value of the length (measuring) 6

Arc - velocity necessary to raise an object to a specific height 6

B

Bicycles - acceleration 7

Bicycles - drive train 7

Bicycles - formulae 7

Bicycles - RPM 7

Bicycles - turns 8

Brakes - collision - sign of front brake use 8

Brake lag 8

Braking and turning - non ABS vehicle 8

C

Cartesian co-ordinates 9

Centre of mass see Gravity - centre of on passenger cars 37

Centre of mass of two bodies 9

Centroid of a damaged area 10

Centrifugal force 11

Centrifugal skid mark 11

Centripetal force 11

Chord 11

Circle 11

Circumference 11

Closing velocity - use of effective mass 12

Co-ordinates - right and left hand 13

Coefficient see friction 34 and 35 , drag factor 22, and stiffness 89

Coefficient of sliding friction see sliding friction 82 and drag factor 22

Collins J.C. - pedestrian speed formula 13 - 14

Combined speeds 14

Combined speeds - formula variation when using slide to stop 14

Consevation of linear momentum - see momentum 50 - 60

Critical speed on curves 14 - 15

Crush - crush for speed estimates (2, 4, and 6 equidistant L measurements) 15 - 16

Crush - equidistant or non-equidistant L measurements 16

Crush - non central - for determining effective mass 16

Crush speed - rules of thumb 17

D

Damage 17

D - the distance in slide to a stop 17

D - the average distance 17

Degree 17

Delta 17

Delta P and Delta V 18

Diagrams - linear momentum 18

Diameter 19

Distance accelerated in time 19

Distance accelerated in time from a stop 19

Distance covered while accelerating from a stop or skidding to a stop (drag and time known) 19

Distance skid in a known time 19

Distance in the slide to stop formula 20

Distance required to bring a vehicle to a stop 20

Distance skid - determining time using a quadratic 21

Dissipation of energy see crush 15 - 16 and energy - kinetic 27 - 28

Division 21

Drag factor - friction force 22

Drag factors for individual wheels (NHTSA values) 22

Drag factor two vehicle system 23

Drag factor for a vehicle towing an unbraked trailer 23

Drag sled - construction 23 - 24

Drift angle see slip angle 84

Dynamics 24

Dynamic Crush 24

E

EBS - equivalent barrier speed 25

EBS and Delta V - when to use the combined speed formula 25 - 27

Energy 27

Energy - kinetic 27 - 28

Energy - principle of conservation of 28

Eubanks - pedestrian and cyclist collision speeds - moving and stopped 28 - 29

Evasion distance and lane change formulae 30 - 31

F

f - the symbol for drag factor 31

F - the symbol for force 31

Fall - formula and derivation 32

Fall and Slide Quadratic - pedestrian impact speed 32 - 33

Fall - speed determination 33

Friction (drag factor) from speed and time 34

Friction (drag factor) from speed and distance 34

Friction (drag factor) from distance and time 34

Friction (drag factor) on a curve 34

Friction - slide to stop 34

Friction - vehicle braking and steering capabilities (friction circle) 35

Force - horizontal 35

Gap skid 36

Glass - fractures from direct impact 36

Gouge marks 36

Grade percent 36

Gravity 37

Gravity - centre of (on passenger cars) 37

Greek alphabet 38

Guardrail deflections 38

H

Heat - thermodynamics 38 - 39

Higgins - vehicle speed - pedestrian collision formula 39

Horsepower 39

Hydroplaning 39 - 40

I

Impact forces 40 - 41

Impact forces - consequences 41

Impulse - momentum equation 41

Inertial parameter estimation 41

Inertial tendancies 42

J&K

Joule 43

Kinematics 43

Kinetic Energy 43

Kinetics 43

K/mh 43

Knot (nautical mile) 43

L

Lane change formula - see evasion 30 - 31

Law of cosines 44

Law of sines 44

Law of tangents 44

Lift off speed - cresting a hill 45

Light - law of inverse squares 46

Light - second law of reflection 46

Light - second law of refraction 46

Light - rotating mirror 46

Limpert R. - pedestrian impact speed formulae 46 - 47

Linear momentum 47 see momentum 50 - 60

Lines, slopes and angles 47 - 48

Low speed rear impact collisions 48

M

m - as a variable in formula 49

Mass 49

Math operation rules and symbols 49

Middle ordinate 49

Minimum speed - slide/skid to stop 49

Moment 50

Moment of inertia 50

Momentum - original 360 degree method 50-51

Momentum - standard 360 degree method 51

Momentum - break apart collisions 52

Momentum - broadside or rear end collision 52

Momentum - conservation of 52

Momentum - head-on collision with no post-collision movement 52

Momentum - head-on collision with post-collision movement 53

Momentum - in-line collision - solve by using simultaneous equations 53 - 58

Momentum - rear end collision while both vehicles moving 58

Momentum - rear end offset collision - lead vehicle stopped 58

Momentum - rear end collision - same speed assumed 58 - 59

Momentum - right angle collision 59

Momentum - vector diagramming 60

Motorcycles - counter-steer 61

Motorcycles - driver injuries 61

Motorcycles - flutter 61

Motorcycles - front tire skid 61

Motorcycles - high siding 61

Motorcycles - lateral friction 61

Motorcycles - lean angle 61

Motorcycles - manipulating a speed range from RPM 62

Motorcycles - problems for riders 63

Motorcycles - rake 63

Motorcycles - rear tire skid 63

Motorcycles - slide outs 63

Motorcycles - trail 63

Motorcycles - trajectory of driver and passenger (the Searle formula) 63

Motorcycles - weave 64

Motorcycles - wobble 64

MPH 64

Multiplication 64

N

Newton 64

Newton's first law 64

Newton's second law 65

Newton's third law 65

Northwestern - pedestrian collision formula 65 - 66

O

Overturning speed - on curves 66

P

Parabola 67

Passing see evasion 30- 31

PDOF 67

Pedestrian impact speeds 67

Perception and reaction time 68

Pi 68

Pole impact speed - frontal collision - Nystrom & Kost formula 68

Pole impact speed - frontal collision - Mak formula 69

Poundal 70

Pultar - pedestrian collision speed 70

Pythagorean theorem 70

Q

Quadratic equations 70 - 71

R

Radian 72

Radius 72

Radius - average used 72

Radius formula standard 72

Radius formula no chord or middle ordinate 72

Radius formula circumscribed circle 73

Radius formula determining with a compass 73

Radius formula using the Pythagorean theorem 74

Radius - degree of curve 74

Radius - maximum and minimum for a turning car 74 - 75

Reaction - distance formula 75

Reaction - time see perception and reaction 68

Reflection and refraction see light 46

Roll over speed - minimum - after striking a curb 78

RR (Rail Road) crossing - AASHTO triangle 79 - 80

S

Salt - road and common - properties of 81

Searle - pedestrian and cyclist speed 81

Seatbelt examination 81

Side scuff 81

Sideslip - yaw 82

Skid - skip skid 82

Sliding friction - the angle of 82

Slide to stop - derivation 83

Slide stop 84

Slide stop - sides of vehicle on two surfaces 84

Slip angle 84

Snowmobile - drag factors 85

Speed 85

Speeds - tachometer and gearing 85

Speed - maximum from which to stop in a given distance 86

Speed - of a rotating vehicle - kinetic energy method 86 - 88

Statics 88

Static Crush 88

Stiffness categories - from crash tests 89

Stiffness categories - from crash tests with impactors (side & rear) 90

Stop - slide to - with weight shift 91

Superelevation 92

Stcherbatcheff - solving for speed from pedestrian throw distance 92

T

Tachometers - for speed 92 - 93

Tangent offset equation 93

Test skids 94

Throw distance 94

Time to skid to a stop or accelerate from a stop 94

Time to slow 94

Time to skid or accelerate from a stop 94

Time in a circular path 95

Tip-over speed see over-turning speed on curves 66 and roll-over speed when tripped by a curb 78

Trailer - drag factor adjustment 95

Trailer - effect of improper loading on friction coefficient 95 - 96

Trailer - tracking 97

Trigonometric equations 98

Truck speed - engine and transmission 98

U&V

Uniform acceleration 98

Vault - derivation of the formula 98 - 101

Vault 101

Vector 101

Velocity 102

Velocity, height and time of a free falling body 102

Velocity/Time/Distance 102

Velocity - initial 102

Velocity at any time in an acceleration or a skid 103

Velocity at any distance in an acceleration or a skid 103

Velocity - initial when distance, time and acceleration rate known 103

View in right angled and oblique angled approaches - for time to collision 103

W

Weight transfer - cornering/braking/accelerating 104

Wind speed - overturning vehicles 105

Wood - pedestrian speed formula 106

Work 106

XYZ

Yaw see critical curve speed 14 - 15

Yaw - critical curve speed derivation 106 - 107

Yaw - COLM - check of pre-collision Yaw speed 108

Yaw - radius of gyration 108 - 109

Yaw - Sine Correlation 109

Yaw - Striations 109

Yaw - Striation Angle Measurement 109

About the author .............

**APPENDIX **

Conversion of Quantities and Units

Weather Facts

Notes for the Expert Witness

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