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Acceleration

ft/sec/sec

t vi ve

     

     

Acceleration Factor

Free Fall

   

     

Drag Factor

Drag factor coefficient of friction (m ) unless on level; Add or subtract grade (G)

Roll Resistance .01 - .02 (Free)

.1 - .2 (Drive)

     

     

Velocity Initial Vi

t a ve

ft/sec

t a d

 

a ve d

 

S d f

     

Velocity End Ve

t a vi

ft/sec

a vi d

     

Velocity Average

 

Constant Velocity - Average

 

 

 

 

Distance d

t a vi

ft

a vi ve

 

t vi ve

 

S d f

Constant Velocity - Average

 

     

Time

a vi ve

 

t a d

When vi = 0

     

Constant Velocity - Average

 

     

Mass

Free Fall w = F

 

     

Force

Velocity

Fall Velocity

 

 

 

 

Sideslip Velocity

> 10% Grade

 

 

Small Grade

 

Without Superelevation

Vault / Flip Velocity

 

 

 

Radius

   

Lateral acceleration

Momentum

If q < 10 = Collinear

If one vehicle stopped must be collinear

If partial Both must be in same direction

Vehicle 1 must be on x axis & vector tails must be at origin (direction) for angle determination

Collinear

Collinear

If same post collision velocity If same post collision velocity

Determine velocity for vehicle #2 first, then use in equation for #1

PDOF = ΔV

PDOF Angle =

   

or

 

90 - 180 -X +Y

0 - 90 +X +Y

180 - 270 -X -Y

270 - 360 +X -Y

Soh Cah Tah

   

Component Method For 90 Only

 

John Daily

 

   

PDOF #1

α1 =

PDOF #2

α2 =

 

Approach angle V2

ACTAR Study Guide

 

Establish weight ratio between vehicles w1=1, w2=w2 /w1

Determine post impact speeds

If vehicle 1 on east/west axis 0 180 then

Solve for S1

If vehicle 2 on north/south axis 90 270 then

Solve for S2

Δv=

Speed & direction at impact

Speed & direction post impact

Break post impact movement into components for example west (x axis) & south (y axis)

east/west component

north/south component

Δv west= Pre impact speed east/west axis +/- post impact speed on east/west axis

Δv south = Pre impact speed north/south axis +/- post impact speed on north/south axis

or

Δv must be inverse and proportional

Component System

or

   

IPTM

α = Alpha PDOF or approach angle V1

θ = Theta departure angle V1

ψ = Psi approach angle V2

Φ =Phi departure angle V2

V1 = v1 =Vehicle #1 approach speed (S) or v

V2 = v2 =Vehicle #2 approach speed (S) or v

V3 = v1′ =Vehicle #1 departure speed (S) or v

V4 = v2′ =Vehicle #2 departure speed (S) or v

   

Energy

Sliding Energy

 

Kinetic Energy

or

Velocity

     

Potential Energy

Pe = mgh

   
     

Velocities For Same Direction Collision

Closing

 

Rear Vehicle

 

Front Vehicle

 

 

 

Energy From Crush

Two Measurements

Four Measurements

Six Measurements

     

E=Energy dissipated in-lbs

A=maximum force w/o permanent damage

 

W= Width of crush region inches

B=Spring stiffness per inch damage lbs/inch

Center of Mass

Longitudinal

 

Vertical

 

Resultant Drag Factor

Drag Factor With Side Slip

Velocity From Gear Position

v = 0.00436RD

D = drive wheel/tire diameter (inches)

IMPT

 

 

Conversion Factors

1.467(mph) = ft/sec

Impulse = Ft = Δmv = ΔP = lbs-sec

Newton #1 A body will remain at rest or in constant motion unless acted upon by an unbalanced force

Newton #2 a) Describes what happens when force is applied b) quantifies force in magnitude and direction

Newton #3 Forces are equal and opposite

Quadratic Equation Where

Law of Pythagoras

 

 

 

 

 

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