HIPAA Rules Equations Paper Facts Paper Chisel Cosmos Age Paper Digital/ Film
Acceleration ft/sec/sec 
t v_{i }v_{e} 




Acceleration Factor 
Free Fall 

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) 









Velocity – Initial V_{i} 
t a v_{e} 

ft/sec 
t a d 

a v_{e }d 

S d f 

Velocity – End V_{e} 
t a v_{i} 

ft/sec 
a v_{i} d 

Velocity Average 

Constant Velocity  Average 
Distance d 
t a v_{i} 

ft 
a v_{i} v_{e} 

t v_{i} v_{e} 

S d f 

Constant Velocity  Average 

Time 
a v_{i} v_{e} 

t a d When v_{i} = 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 90º Only
















John Daily 





PDOF #1 α_{1} = 
PDOF #2 α_{2} = 

Approach angle V_{2} 
ACTAR Study Guide 

Establish weight ratio between vehicles w_{1}=1, w_{2}=w_{2} /w_{1} Determine post impact speeds If vehicle 1 on east/west axis 0 – 180 then Solve for S_{1} If vehicle 2 on north/south axis 90 – 270 then Solve for S_{2} 
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 V_{1} θ = Theta departure angle V_{1}′ ψ = Psi approach angle V_{2} Φ =Phi departure angle V_{2}′ 
V_{1} = v_{1} =Vehicle #1 approach speed (S) or v V_{2} = v_{2} =Vehicle #2 approach speed (S) or v V_{3} = v_{1}′ =Vehicle #1 departure speed (S) or v V_{4} = v_{2}′ =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 inlbs 
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 = lbssec 
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 

