Momentum Report
Collision Date
Dec 12,2010
Case Number
1234
Location
Pasadena Drive
Case Name
Fatal
Reconstructionist
Jones
Vehicle 1 Inputs
Results
Weight(lbs)
6400.00
Initial Velocity(mph)
28.64
Departure Angle
39.9
Impact Velocity(mph)
28.64
Pre-Impact Length(ft)
44.86
Separation Velocity(mph)
30.68
Pre-Impact Friction(g)
0.00
Delta V(mph)
20.35
Post-Impact Length(ft)
70.77
PDOF
-75.4
Post-Impact Friction (Average)(g)
0.44
Delta V.x(mph)
-5.12
Delta V.y(mph)
19.69
Velocity at D.C.(mph)
25.82
Friction Zones
Path Length(ft)
Potential Friction(g)
Rollout Friction(g)
70.77
0.70
0.20
Vehicle 2 Inputs
Results
Weight(lbs)
2699.00
Initial Velocity(mph)
63.17
Approach Angle
89.0
Impact Velocity(mph)
63.17
Departure Angle
51.2
Separation Velocity(mph)
21.13
Pre-Impact Length(ft)
40.49
Delta V(mph)
48.25
Pre-Impact Friction(g)
0.00
PDOF
15.6
Post-Impact Length(ft)
35.82
Delta V.x(mph)
-46.47
Post-Impact Friction (Average)(g)
0.42
Delta V.y(mph)
-12.95
Velocity at D.C.(mph)
8.56
Friction Zones
Path Length(ft)
Potential Friction(g)
Rollout Friction(g)
35.82
0.70
0.20
Momentum Vector Diagram
Legend
V1 == Vehicle 1 approach path
V2 == Vehicle 2 approach path
V3 == Vehicle 1 departure path
V4 == Vehicle 2 depareture path
MOMENTUM VECTOR SUM DIAGRAM
Legend
M1 == Pre-Impact Momentum Vehicle 1
M2 == Pre-Impact Momentum Vehicle 2
M3 == Post-Impact Momentum Vehicle 1
M4 == Post-Impact Momentum Vehicle 2
M1 == Delta Momentum Vehicle 1
M2 == Delta Momentum Vehicle 2
MR == Total Momentum (Vehicle 1 + Vehicle 2)
MOMENTUM REFERENCE
The ARAS 360 Momentum solution, Momentum Genius determines impact speeds in two vehicle collisions based on the Law of Conservation of Momentum. Some people refer to
this as the “360 degree method” of momentum analysis.
The solution uses the separation speeds and simultaneously solves for impact speeds, speed changes, separation speeds at the damage centroids, angles of the principal direction
of force, and restitution.
All the equations are found in the instructional literature at Northwestern University’s Traffic Institute, Institute of Police Technology and Management, and other collision
reconstruction training facilities around the World. The solution is founded on the fact that linear momentum is conserved, which means the total momentum of the system (i.e. of the
two vehicles together) is the same immediately before and immediately after impact. Therefore if the post-impact momentum can be quantified, then pre-impact momentum is also
known and can be used to determine the speeds of the vehicles.
Users of the system must always have well documented evidence confirming the basic set of information that provides the input variables to the solution which include:
1. Vehicle positions at impact
2. Vehicle orientations at impact
3. Vehicle positions at rest
4. Vehicle orientations at rest
5. Vehicle masses
6. Vehicle trajectories from impact to rest (i.e. approach and departure angles)
7. Road surface information (i.e. friction, grades, etc.)
The Law of Conservation of Momentum always applies, however in some situations the results become very sensitive to any inaccuracies in the input values. In these cases
Momentum Genius should only be used with caution and with an understanding of these limitations. These situations include:
1.Situations where the above information set is incomplete (i.e. if the separation speeds or angles are estimated, the accuracy of the results will be affected by the accuracy of
those estimations.)
2.Collisions of a more head-on nature where the angle is less than about twenty degrees (in these cases the results will be very sensitive to inaccuracies in the approach and
departure angle for both vehicles).
3.Collisions where the mass disparity of the vehicles exceeds four to one (in these cases the results will be very sensitive to inaccuracies in the angles for both vehicles and to
inaccuracies in the weight and separation speed for the heavier vehicle).
4.Sideswipe collisions where vehicles involved do not completely engage (the Momentum Genius will still work but you will get an error message that the common velocity
assumption was violated. That is expected since in a sideswipe the vehicles are moving past one another even during impact, and therefore no common velocity is achieved. You
can safely ignore this error message in this case).
The accuracy of the linear momentum solution is well known and documented by other specific linear momentum solutions via the ricsac crash tests. *
The Momentum Genius solution has been validated by applying it to a specific case where the evidence is well documented from a staged crash. A crash test performed by
Exponent was used to verify the application of this tool and provided results within 2% of the actual speeds.