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Contents Sign convention on the direction of acceleration and braking force Condition of the optimum acceleration and braking force distribution curve Relationship between tire friction force and gravitational acceleration Basic equation for the optimum force distribution curve Practical example for a car Analysis of the optimum force distributio curve Theoretical base for the important values of curve Conclusion sign convention on the direction of acceleration and braking force Sign convention is redefined to explain both of acceleration and braking Plus sign is for acceleration Minus sign is for braking The shape of the brake force distribution graph moves from upper-right quadrant to lower-left quadrant. it is a point symmetry of the previous one as shown as following graph. Longitudinal force distribution(a) - optimum case Explained in the previous article, the vehicle weight can be expressed as two equations here  in which a is plus for acceleration and minus in braking. ...

 Review of Weight Transfer When we apply the braking force, weight transfer happens to the front. Therefore, front vertical force gets heavier, and rear vertical force gets lighter. Brake force is the horizontal force proportional to the vertical reaction force. The proportional constant is tire friction coefficient μ. The role of rear brake is very important for vehicle stability. Rear brake force should always not only keep its quantity not to provoke wheel locking but also keep its maximum quantity just below the force level causing the rear wheel locked up. That is the way to use the brake system with the maximum efficiency.  Optimum Brake force distribution – Normalized Force The picture above shows an optimum brake force distribution curve. Vertical axis represents normalized braking force of rear wheel F nr , and horizontal axis represents the normalized braking force of front wheel F nf .  Here, the normalized force means its value is dimensionless. The two normal...

  measuring the height of vehicle CG(center of gravity) 1. measuring CG in the longitudinal axis. From the moment equilibrium about y axis passing through the center of tire-road contact patch, From the moment equilibrium about  y axis passing through the center of tire-road contact patch, 2. measuring CG in the inclined vehicle. Hypotenuse of yellow rectangular triangle is (h-R). Therefore, opposite of triangle is (h-R)sinθ. Sum of vertical forces should be zero. Sum of the moment about lateral axis passing through the CG should be zero. 2. measuring CG in the inclined vehicle. Equation of h above can be simplified as follow.