Static Margin

The simplified plane-motion vehicle simulation of the SMAC/EDSMAC computer programs includes only limited details in relation to vehicle cornering characteristics. However, the inputs for cornering stiffnesses at the front and rear tires can serve to achieve approximate simulation of understeer/oversteer behavior.

The Static Margin is defined as the longitudinal distance from the center of gravity (CG) to the neutral steer point divided by the wheelbase (Figure 4).  It is positive if the CG is forward of the neutral steer point.   The neutral steer point is the point at which an external lateral force will produce no steady-state yaw velocity (e.g., Reference 1).

When the neutral steer point is behind the CG, the static margin is positive and the vehicle has understeer cornering characteristics.  When the neutral steer point is forward of the CG, the static margin is negative and the vehicle has oversteer characteristics.  A neutral steer point at the CG produces a zero static margin and neutral cornering characteristics.

Static Margin =  Inches

Figure 93 Static Margin

The static margin is defined by the following equation:

                                 (1)

where

C_F, C_R   =       cornering stiffnesses at the front and rear tires respectively, LBS/RADIAN.

a, b       =     longitudinal distances from the CG to the front and rear axles respectively,

INCHES.

(e.g.  Reference 2)

The neutral steer point is determined by the front/rear distribution of cornering stiffnesses.

Equation (1) can be restated in the following form:

 

                                                    (2)

On typical vehicles, the static margin ranges between +0.03 and +0.07 (e.g., Reference 3)

medit includes an automatic procedure for Calculating the Static Margin.

 

REFERENCES:

  1) Vehicle Dynamics Terminology, SAE J670e.

  2) Whitcomb, D.W., Milliken, W.F., “Design Implications of a General Theory of Automobile Stability and Control”,   The Institution of Mechanical Engineers, Proceedings of the Automobile Division, London, Number 7, 1956-7.

  3) Gillespie, Thomas D., Fundamentals of Vehicle Dynamics, Society of Automotive Engineers, 1992.

Sample Application

From Reference [i], the cornering stiffness at each front tire can be approximated from:

C_F ≅ -9.455 * (W_F/2.0) LB/RADIAN                                               (3)

          Where W_F = Wgt. Supported by the front wheels, LBS.

 

          Let     M = 7.764 LB-SEC²/IN (3000 LBS)

                  

 

          Find C_R to produce the following Static Margins:  

SM = 0.00, 0.03, 0.07

 

          From Equation (3),

                   C_F  ≅ -8510. LB/RAD/TIRE

 

          From equation (2),

 

 

The Static Margin can be automatically calculated in msmac. Please see calculating the static margin

 

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