Suspension Formulas

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Where *b* is the width
of spring blade (m), *L* is the distance between the eyes of the spring
when laden (m), *t* is the thickness of the blade (m), *n* is the
number of blades, and *E* is the modulus of elasticity, which (modified to
allow for internal friction) is 159 x 10^{6} kN/m^{2}.

For a torsion bar, the spring rate is given as the twisting moment per angular deflection. When a lever is added, this can be converted into a rate for the vertical deflection of the end of the lever.

Spring rate (torsion bar, for deflection at end of lever)

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Where *G* is the modulus
of rigidity, which is 78.5 x 10^{6} kN/m^{2} in this case, *d*
is the diameter of the torsion bar (m); *l* is the effective length of the
torsion bar (m), i.e. half the length of the bar for an anti-roll bar, and *e*
is the length of the lever (m).

Spring rate (coil spring)

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where *G* is the modulus
of rigidity, which is 81.5 x 10^{6} kN/m^{2} in this case, *d*
is the wire diameter (m), *n* is the number of free coils, and *D* is
the mean coil diameter (m). To find the number of free coils it is necessary to
subtract the number of dead coils form the total number of coils. The dead
coils are those that provide the abutment and so cannot be deflected, usually
1.5 to 2 coils.

__Wheel rate:__

The wheel rate is not the
same as the spring rate, and depends on the effective leverage, or the
separation of the springs relative to the track. Thus if the distance from the
centre-line of the car to the spring on a beam axle is *a*, and the
distance from the centre-line of the car to the centre-line of the wheel (i.e.
half the track) is *b*, as shown in Figure 1 (a) then :

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With independent suspension
the formula is similar except that *b* is the length of the suspension arm
and *a* is the distance form its pivot to the axis of the spring (Figure 1
(b)). With double-wishbone suspension the formula is modified to take into
account the effects of the other whish bone on the geometry. The formula
becomes:

Wheel rate
*C _{W}^{ }= (C_{S} *

Where *a, b, c, and d *are
as shown in Figure* *2.

* *

_{} k_{w}
= k_{s}

__Anti-roll bars__

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Where

k_{e} =
equivalent rate

k_{w} =
wheel rate

k_{a} =
anti-roll bar rate measured at the wheel

Example:

The Porsche 928 is provided with a strong anti-roll at the front and a relatively weak one at the rear. The appropriate data are as follows:

Front Rear

Wheel rate (kN/m) 18.63 22.55

Anti-roll rate (at wheel) (kN/m) 83.4 10.2

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