Using Force Balance to Determine Closing Speeds with StifCalcs

Recently, Daniel Vomhof III, owner of 4N6XPRT, wrote an article in Collision Magazine on how calculating Force-Balance can determine what the closing speeds of an accident is.


StifCalcs programThe article goes through trying to determine the closing speed of a hypothetical accident between an Eastbound traveling 2003 Kia and a 2007 Toyota Yaris trying to make a left hand turn from an intersection. Now, Force-Balance is a tool available to accident investigators that’s based on Newton’s Third Law of Motion: “For every action there is an equal and opposite reaction,” and Newton’s Second Law of Motion “The relationship between an objects mass (m), its acceleration (a) and the applied force (F) is F=ma.”


By using crush test data and both vehicles stiffness values through 4N6XPRT’s StiffCalcs program, they were able to determine the closing speeds of the oncoming 2003 Kia RIO onto the stopped Toyota Yaris. The posted speed limit was 35 mph.


Obviously the more data available, including weights of the vehicles, photos of the accident and the StifCalcs program, will be able to accurately determine the closing speeds. The less data, the less accurate the results will be.


Now, which vehicles could give the most information has to be determined.  Information from the Kia Rio, which had the most intact vehicle compared to Yaris because the Toyota’s bumper was ripped from the car on impact, thus disallowing a completely accurate reading on the Yaris, was going to be used first.


Unfortunately, no frontal impacts tests for the Kia Rio were taken from 03-05. Instead, a summary of four other front impact tests from 2002, 2006, 2007 and 2012 Kia Rio models were taken. Their stiffness values based on reported Average Crush and Reported Vehicle Width, the Force-Balance module contained in the, and inputting the crush and eight data contained in the Traffic Collision report calculated the range of closing speeds for the Rio, which, unfortunately, weren’t very accurate.


The average test determined the closing speeds ranged from 40-77 mph, but the photos found those numbers were probably a bit too high.


So the Yaris would be the “known” vehicle, despite its bumper getting ripped from the car on impact, but that too found inaccurate readings of a potential average speed between 56 and 96 mph.


It was determined that there was a failure point, the Yaris’ bumper, so a measurement was taken 3-inches was subtracted from the crush depth measured, accounting for the front of the covered bumper to bumper bar in undamaged condition.


Also, measurements of the radiator support bar was measured for crush.


After doing this, the results became clearer. The average speed ranged between 35-37 mph on both force-balance tests using the bumper crush depths and support crush depths.


In summary, the more information available the more accurate results. With the information at hand, this calculation process in the 4N6XPRT StifCalcs module takes a matter of minutes to find a valuable and reliable answer.