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### How does SMAC determine the DeltaV and PDOF?

Posted: Sat Jun 20, 2009 2:47 pm
As part of our research for SAE paper 97-0961 we included documentation of the techniques for determination of the DeltaV and PDOF in SMAC and how that compares to the DeltaV and PDOF measured in full-scale testing.

SMAC EQUIVALENT DELTA-V:
In the original form of the SMAC computer program, the speed-change for a given acceleration exposure was determined by the integration of the resultant acceleration. For each time increment, a resultant acceleration was determined by the vector sum of the x and y components of the vehicle accelerations:
Eq9.jpg (4.76 KiB) Viewed 3096 times
• Where:
• ac = resultant acceleration, g-units
ax = acceleration in the vehicle x direction, g-units
ay = acceleration in the vehicle y direction, g-units
• The resultant speed-change was determined by integration of the resultant acceleration from initial contact to separation.
• The initial contact is defined as the first instance where the resultant acceleration goes above 1 g-unit.
• The point of separation is defined as the first time that the acceleration again drops back below 1 g-unit.
• It was assumed that in general handling maneuvers and vehicle spinouts that the resultant acceleration would normally be below 1 g-unit (given that the nominal friction coefficient of roadways is normally less than 1 g-unit).
• The Direction of Principle Force (DOPF) was determined for a given acceleration exposure in the SMAC program as the direction of the acceleration at the instance of peak resultant acceleration by:
• Eq10.jpg (6.04 KiB) Viewed 3096 times
TEST EQUIVALENT DELTA-V:
• For the reported RICSAC full-scale tests the analysis of the accelerometer data to determine the vehicle speed-change consisted primarily of the integration of the vehicle ax & ay accelerometer traces to determine the time histories of velocities.
The velocity time-history plots were then analyzed to determine the magnitude of the changes in the individual velocity components, ?Vx and ?Vy . The resultant speed change and speed-change angle were determined by the following:
• EQ7.jpg (4.86 KiB) Viewed 3096 times
Where:
• leg1.jpg (16.09 KiB) Viewed 3096 times
Eq8.jpg (6.5 KiB) Viewed 3096 times
Where:
• leg2.jpg (17.45 KiB) Viewed 3096 times

### Re: How does SMAC determine the DeltaV and PDOF?

Posted: Mon May 11, 2020 11:35 am
After responding to a recent question on determining DeltaV from acceleration I realized this thread should also include some fundamentals on integration to determine velocity and displacement.
I did a quick search of the internet and here is an example of some related notes: There are also many others are available on the web.