Raccolta casi Working Model, visualNastran & SimWise - 1-year old baby bouncing off bed


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Low-level Fall Simulation: 1-year old baby bouncing off bed

R. J. Reimann, Professor Emeritus of Physics, Boise State University, 22 October 2012 (rev. 7/9/2013)

This simulation was generated using Working Model® software licensed at Boise State University for educational use only.


A mother reported that her large 11-month old son was bouncing on his knees on a 0.76 m high bed while clutching a cell phone near his neck.

He fell off striking the back of his head on a hardwood floor resulting in a concussion, a subdural hematoma (SDH), and retinal hemorrhages (RH).
Medical intervention was successful and the boy is now doing well.
However, Child Protective Services took over custody pending a full investigation.

Working Model® Simulation

The simulation performed with Working model 2D allows flexible joints and other variable parameters to demonstrate one of countless possible scenarios between that described by a witness and other situations where the head does not even hit the floor.
It is intended as a demonstration aid that is more realistic than an artist's conception.

Although the arms slow the descent, the head is still predicted to hit at vy = 4m/s

  • Derived results such as accelerations and forces depend on contact time as explained in Appendix A.
  • Prediction reliability is limited by the choice of model parameters given in Appendix B (mass distribution, joint approximations, elasticity and friction). Any changes to these parameters, initial posture, or rigidity of linked segments may change the outcome significantly.
  • The simulation is based on average dimensions for a 12-month old child crash-test dummy [2] with a stature of 0.74 m and mass of 10.0 kg, including a 2.6 kg head. More details are given in Appendix B.
  • Scale dimensions are in meters. Velocities are displayed for the initial cranial impact point.
  • The integrity of the software was checked by generating accurate predictions for cases with known analytical solutions. These were free-fall for a ball and toppling a long thin vertical rod about an ideal axis fixed at the bottom.
  • Other computer simulations, physical models and video analysis are invited for comparison to help evaluate this simulation.

  • Conclusion

    This simulation clearly shows the potential for severe head injuries from low-level falls.
    The resulting accelerations and forces for the first impact are more than 10 times greater than those that can usually be produced by manually shaking a realistic dummy [3],[4].
    Even the second bounce exceeds that due to shaking.

    Appendix A. Physics Relationships

  • By definition, the average acceleration in the vertical dimension ay = delta vy / Delta t where delta vy is the change in velocity and Delta t is the interaction time with the floor.
  • A toddler head colliding with a rigid surface has Delta t aprox. 0.005 s [3],[4]. Moderate padding extends this to Delta t aprox 0.020 s. Delta t = 0.006 s was chosen as a reasonable value for a hardwood floor.

  • As illustrated, a linear approximation of the acceleration or force between the floor and the head shows that the maximum or peak value is about twice the average [4],[5].
  • Divide accelerations in m/s² by g = 9.8 m/s² to convert into g’s. Multiply accelerations by mass to convert into forces.
  • Appendix B. Model specifications for a typical 12 month old baby [2]

  • By definition, elasticity or coefficient of restitution is modulus of rebound velocity / impact velocity. The bed and floor are assigned values of 0.5 and the body segments are given here below.

  • The torso was also given an initial downwards velocity of 0.5 m/s.

  • Rotational joint values were chosen for realistic response since standards are impossible for a variable organism.
  • Kutta-Merson with 0.0001 second integration step provides accuracy and model stability. Only one step out of every thousand is illustrated.
  • References

  • [1] Baker, Susan P., O'Neill, Brian, Ginsburg, Marvin J., and Li, Guohua. The Injury Fact Book (Oxford University Press 1992), 2nd ed., p.140

  • [2] www.humaneticsatd.com/crash-test-dummies/children

  • [3] Ommaya A K, Goldsmith W and Thibault L. Biomechanics and neuropathology of adult and paediatric head injury. British Journal of Neurosurgery 2002; 16(3): 220-242

  • [4] Goldsmith W and Plunkett J. A biomechanical analysis of the causes of traumatic brain injury in infants and children. The American Journal of Forensic Medicine and Pathology June 2004; 25(2): 89-100

  • [5] Cross, Rod. The Bounce of a Ball. American Journal of Physics March 1999; 67 (3): 222-227

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