When a tire is orientated at an angle not equal to its direction of motion, a side force acts perpendicular to the plane of the wheel. The relation is nearly linear for small slip angles. The relationship that defines side force as a function of slip angle makes use of the tire cornering stiffness.

The SMAC program calculates tire side forces based
on a nondimensional side force function whereby the small-angle properties of
the tires become progressively "saturated" at larger angles (**Figure 6**). The
"friction circle" concept (**Figure 7)** is used
to approximate interaction between side and circumferential (braking and
tractive) tire forces. This concept is based on the assumption that the maximum
value of the resultant tire friction force is independent of its direction
relative to the wheel plane. The general approach to the modeling of tire
properties is patterned after that of **Reference 12**. The cornering
stiffnesses of the individual wheels are input separately in the SMAC
program.

(**Please note the following**: The track width
and wheelbase used for dual and/or tandem axles should be the location of the
center of the dual/tandem combination. Also note that although the use of an
equivalent cornering stiffness to model dual/tandem tires is adequate and
sufficient, modifications are currently being implemented to permit specifying
dual/tandem distances and individual tire properties to allow comparison and
testing of the use of the equivalent tire model. These modifications should be
implemented by 3^{rd} quarter 1998).

Typical values for the cornering stiffness in lbs.
per degree of slip angle for automobile tires are generally in the range of
16-17% of the load on the tire (Please see page**
****120**** **** “Extended Tire Testing”,
Tapia, Calspan, Nov 1983, Contract DTNH22-81-C-07100, NTIS PB 85
103604** for additional information on automobile tire properties).
Measurement of the cornering stiffness for Truck tires are contained in

Figure 16 Cornering Stiffness Properties of Light truck
tires (Left) and Heavy truck tires (Right) from **Reference 23**

These measurements
for light and heavy truck tires are from **Reference 23**, and lead to the
following approximations of the small angle cornering stiffness for light and
heavy truck tires:

**Light Truck Tires**
@3495 lbs. CSTF approx. 11% of load

@2330 lbs. CSTF approx. 14 % of load

@1665 lbs. CSTF approx. 17 % of load

**Heavy Truck Tires** @7000
lbs. CSTF approx. 8-10% of load

@5430 lbs. CSTF approx. 10 % of load

@2715 lbs. CSTF approx. 13 % of load

The input values for
the small angle cornering stiffness used and published in References 19 – 24
indicate a range of values used for **CSTF from 600 – 722 lbs./degree. **

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