Differentiate Side crash as per NHTSA and IIHS

NHTSA's side-impact test represents a vehicle struck on the left side by a 3,015-pound car traveling at 38.5 mph. Such a scenario mimics what could happen if you were hit on the side at an intersection.

The IIHS side-impact test is more severe than NHTSA's. The test uses a heavier striking barrier at 3,300 pounds, compared with NHTSA's at 3,015 pounds. Further, the IIHS barrier strikes higher up on the tested vehicle to simulate a car being hit on the side at 90 degrees by a typical-height SUV or truck. The IIHS bases its scores on head, neck, chest, abdomen, pelvis, and leg injury.

Differentiate Frontal Crash as per NHTSA and IIHS

As per NHTSA's Frontal crash regulation, A car accelerates directly onto a rigid barrier at 35mph with the entire width of the vehicle hitting the barrier. Instrument bearing, seat belted crash test dummies placed in the two front seats record the crash forces on the head, neck, chest and legs.

As per IIHS' Frontal crash regulation, they are quite different from the NHTSA's as they are designed to highlight the vehicles structural integrity as well as restraint performance. There are two test methods, one that engages 40% of a vehicle's front and a newer test inaugrated in 2012 that uses a smaller overlap of 25% of the car's front.
 The IIHS test simulates what would happen if two cars of same weight would and type crashed head on, partially overlapping.

What is the NHTSA and IIHS?

The National Highway Traffic Safety Administration(NHTSA), is a branch of the Department of Transportation, and the Insurance Institute for Highway Safety (IIHS), is an independent safety-research group sponsored by auto insurers. Using different methodologies, both organizations conduct front and side-impact crash tests. In addition, NHTSA tests for rollover propensity and the IIHS evaluates rear-crash protection and roof strength.

As part of its New Car Assessment Program, NHTSA scores its tests using a scale of one to five stars; the more the stars, the lesser the likelihood of injury or death. The IIHS uses a four-level scale: Poor, Marginal, Acceptable, and Good.

What is a Side impact? And what parameters need to be recorded?

NHTSA's side-impact test represents a vehicle struck on the left side by a 3,015-pound car traveling at 38.5 mph. 
This represents,what could happen if you were hit on the side at an intersection. Individual side-impact star-rating scores are assigned to the driver and left-rear passenger.
Parameters
For pre-2011 models, only a chest-injury measure dictated the score. 
For 2011 and later models, the score factors in head, chest, abdomen, and pelvis data for the driver and injury to the head and pelvis for the rear-seat passenger.

The IIHS side-impact test is comparatively more severe than NHTSA's. Thestriking barrier at 3,300 pounds is heavier.Also, the IIHS barrier strikes higher up on the tested vehicle to simulate a car being hit on the side at 90 degrees by a typical-height SUV or truck. 
Parameters
The IIHS bases its scores on head, neck, chest, abdomen, pelvis, and leg injury.

What is a singular matrix?

A singular matrix is a matrix that has no inverse because its determinant is zero

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