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Acceleration ft/sec/sec |
t vi ve |
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Acceleration Factor |
Free Fall |
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Drag Factor |
Drag factor ¹ coefficient of friction (m ) unless on level; Add or subtract grade (G) |
Roll Resistance .01 - .02 (Free) .1 - .2 (Drive) |
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Velocity – Initial Vi |
t a ve |
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ft/sec |
t a d |
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a ve d |
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S d f |
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Velocity – End Ve |
t a vi |
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ft/sec |
a vi d |
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Velocity Average |
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Constant Velocity - Average |
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Distance d |
t a vi |
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ft |
a vi ve |
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t vi ve |
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S d f |
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Constant Velocity - Average |
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Time |
a vi ve |
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t a d When vi = 0 |
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Constant Velocity - Average |
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Mass |
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Free Fall w = F |
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Force |
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Velocity
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Fall Velocity
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Sideslip Velocity > 10% Grade
Small Grade
Without Superelevation
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Vault / Flip Velocity
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Radius |
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Lateral acceleration
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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
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Collinear |
Collinear |
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If same post collision velocity If same post collision velocity
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Determine velocity for vehicle #2 first, then use in equation for #1
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PDOF = ΔV PDOF Angle = |
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or 
90°
- 180° -X +Y
0 - 90°
+X +Y
180°
- 270° -X -Y
270°
- 360° +X -Y|
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Soh Cah Tah |
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Component Method For 90º Only
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John Daily |
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PDOF #1 α 1 = |
PDOF #2 α 2 = |
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Approach angle V2
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ACTAR Study Guide |
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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)
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
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Δv must be inverse and proportional |
Component System
or
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IPTM α = Alpha PDOF or approach angle V1θ = Theta departure angle V 1′ψ = Psi approach angle V 2Φ =Phi departure angle V 2′ |
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 |
east/west component
north/south component
Energy
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Sliding Energy
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Kinetic Energy
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Velocity
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Potential Energy Pe = mgh |
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or 
Velocities For Same Direction Collision
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Closing
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Rear Vehicle
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Front Vehicle
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Energy From Crush
Two Measurements
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Four Measurements
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Six Measurements
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E=Energy dissipated in-lbs |
A=maximum force w/o permanent damage |
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W= Width of crush region inches |
B=Spring stiffness per inch damage lbs/inch |
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Center of Mass
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Longitudinal
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Vertical
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Resultant Drag Factor
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Drag Factor With Side Slip
Velocity From Gear Position
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v = 0.00436RD |
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D = drive wheel/tire diameter (inches) |
IMPT
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Conversion Factors
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1.467(mph) = ft/sec |
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Impulse = Ft = Δmv = ΔP = lbs-sec |
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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
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Law of Pythagoras
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