## Classic Example of Sensitivity of Momentum Solutions

Questions/Topics related to Simplified Momentum Analysis and related computer programs
MSI
Posts: 1741
Joined: Thu Jun 18, 2009 12:37 pm

### Classic Example of Sensitivity of Momentum Solutions

Decided to create a separate topic since I wanted to link to this classic example in our Momentum "Cone of Departure" Question and had to search.
So we made it a separate post. A classic example of problems with the sensitivity of a linear momentum solution which includes the simplifying assumption of an instantaneous exchange of momentum is when it is applied to a t-bone type collision.
• When a lighter car crosses the path of a heavier car/truck and the lighter vehicle is struck in the side by the heavier vehicle. If the heavier striking car/truck happens to swerve before the impact, either to the left or the right, the degree or two of change of impact angle can result in dramatic changes in the results of a linear momentum solution.
Why?
The swerve by the heavier vehicle will produce a change in the separation angles. The change in separation angles, if all attributed to the smaller vehicle speed (which it will be if the impact angle of the striking heavier vehicle is assumed to be 0 (zero) degrees) will dramatically change the linear momentum solution approximated speed of the smaller lighter vehicle.
The result is that depending on the direction of the swerve, the small vehicle will be 'reconstructed' as either going very fast in the forward or reverse direction. Depending on the difference in the weights of the vehicles the assumption for impact angle of the heavier vehicle can result in very large errors in the analysis.
What that ‘classic’ example is meant to illustrate is that when applying a Linear Momentum solution procedure to ANY accident you need to test sensitivities of inputs (angles at impact and angles at separation). If a small change in an angle makes a dramatic change in the results then obviously you need to focus on defining and refining the inputs as well as consider using a more sophisticated solution procedure (like a SMAC simulation).
NEW!! LEASE pricing of msmac3D Software!!
FOR MORE TOPICS see:Forum Index & McHenrySoftware.com
Question? Comment? Please email us (all communications considered confidential)