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For Gearheads Any moving object contains kinetic energy. This energy must be dissipated before the object comes to rest. In the case of a car crash, most of the energy is dissipated by bending metal and other solid objects. The rest is converted to heat and sound. Inside the car a similar thing is happening to the driver's body. At the instant of impact the head and body are moving at the same speed, so there is no kinetic energy in the head relative to the body. But as the body slows the head keeps moving. As the head picks up speed it accumulates kinetic energy which must be dissipated before it can come to rest. With an unprotected driver, the only thing that can absorb this energy is the body itself. From highschool physics we know that kinetic energy is a function of the square of the velocity (KE=0.5mv^2). In a typical crash the acceleration (i.e. increase in velocity) looks like an inverted "V" when plotted against time. So here's the scary part: The energy accumulating in the head is a function of the square of the velocity, which is increasing at an increasing rate. If you plot KE versus time it will look like a rocket launch — almost straight up. Classic "head restraints" work based on position. When the head reaches a certain position the tethers restrain its motion, but until that position is reached the head is collecting kinetic energy at a very rapid rate. This is exactly why positionbased head restraints work best when they are very tight. What is the best way to protect the driver? Do not let the energy accumulate in the first place. How do you do that? Minimize the velocity. How do you do that? Use a device that automatically reacts to velocity — not position, velocity. What device automatically reacts to velocity? A shock absorber. Since the objective was to minimize head and neck loads, the original design equations for Isaac®were written to evaluate the net force on the body as a function of time. The impact force is defined by Newton’s second law of motion, which states that the acceleration of a body varies directly with the force and inversely with the mass. When one constructs a dynamic, freebody diagram of the kinetics associated with Isaac® one finds that the crash force imposed on the head generates an opposing reaction force in the shocks. Since the shock reaction is a function of velocity, not acceleration, the solution to this kinetic system is a second order, first degree ordinary differential equation. Once biomechanicallyderived constraints are applied, the shock damping coefficients can be determined. (Note: This solution assumes twodimensional geometry and linear motion.) 
