Child safety in vehicles: validation of a mathematical model and development of restraint system design guidelines for 3-year-olds through mathematical simulations

Traffic Inj Prev. 2009 Oct;10(5):467-78. doi: 10.1080/15389580903149243.


Objective: The objectives of this study are to validate a mathematical simulation model of the Q3 ATD in an integrated forward-facing booster-type restraint in the rear seat and to evaluate restraint parameters to further develop design guidelines for this type of restraint system for forward-facing children corresponding to the size of the Q3. Only frontal impact was considered.

Methods: The software MADYMO was used to create and run the model of the restraint system and model of the child. The restraint system consisted of a seat and a safety belt. The child dummy model was the Q3. The complete model was validated to sled tests on 12 response signals: displacements of the dummy model, safety belt forces, and dummy model accelerations. The method used in the evaluation of the restraint parameters was a factorial design of experiments (DOE). The study included a total of 9 parameters: 6 related to the safety belt, such as pretensioner, load limiter, and belt anchor positions; two parameters related to the seat (stiffness and pitch angle); and one related to the foot support. The parameters were evaluated based on their effect on a number of dummy model responses.

Results: The validation study showed that the mathematical model predicted the ATD's kinematics and measurements. Furthermore, the parameters that had the greatest effect on the dummy model responses were the lap belt angle, the D-ring x and y positions (upper belt anchor), the retractor pretensioner, and the retractor load limiter. The lap belt angle had the greatest effects of all parameters. The resulting head x displacement was 7.8 cm shorter with a lap belt angle of 24 degrees to the horizontal, compared to a 73 degrees to the horizontal belt angle; it also resulted in a reduction of the head resultant acceleration by 9.8 g.

Conclusions: In order to decrease the Q3 ATD head, chest, and pelvis accelerations and to limit the Q3 ATD head displacement, the following practices are recommended: first, position the D-ring rearward of the ATD so that the belt encloses the ATD's shoulder; second, position the lap belt anchors to make the lap belt angle 24 degrees to the horizontal, but make sure submarining is not induced; and finally, use a safety belt with pretensioner and load limiter functions. However, these recommendations need to be balanced with the recommendations for other occupant sizes, and any specific settings have to be evaluated further before introduction into vehicles.

Publication types

  • Research Support, Non-U.S. Gov't
  • Validation Study

MeSH terms

  • Acceleration
  • Accidents, Traffic
  • Biomechanical Phenomena
  • Child, Preschool
  • Computer Simulation*
  • Equipment Design
  • Equipment Safety / standards
  • Guidelines as Topic
  • Humans
  • Models, Theoretical*
  • Seat Belts* / statistics & numerical data
  • Software