People modifying their car suspension often talk
about spring rates. They might say: “I’ve got 600 pound springs in the front and
400 pound springs in the back.”
At this point someone else might well say: “Hell,
that’s hard. I run only 300 pound springs back and front and my car’s heavier
than yours.”
Trouble is, comparing spring rates between
different cars is useless. That’s because it’s the wheel rates that matter, not
the spring rates. Confused? Let’s take a look at the relationship between spring
and wheel rates.
Spring Rates
A car spring is specified according to how much it
deflects for a given mass placed on top of it. For example, a 400 pounds/inch
spring compresses by 1 inch when 400 pounds is placed on top. (Or a 20 kg/mm
spring compresses by 1mm when 20kg is placed on top.)
Most springs are linear devices, so if you double
this mass, the spring compresses by twice as much.
Wheel Rates
Wheel rates are expressed in the same units as
spring rates. For example, say the car weighs 3000 pounds and this mass is
divided equally between all four wheels, giving a static load of 750 pounds per
wheel. When you lower the car onto its suspension, you find the wheel rises by 3
inches as it supports the weight. 750/3 gives a wheel rate of 250 pounds/inch.
(However, see the ‘Preload?’ box below.)
Motion
Ratios
So what’s the relationship between spring and
wheel rates? That depends entirely on the leverage ratio built into the
suspension. Most suspension systems do not have a 1:1 relationship between wheel
movement and spring movement. In semitrailing arms, wishbones, multilinks and
many others, the spring:wheel movement ratio is not 1:1. (In strut systems it is
close to 1:1.) In most cases, the wheel moves further than the spring.
The relationship between the wheel movement and
the spring compression is called the motion ratio. It can be measured in two
ways. The first way is to measure the suspension arm, working out its leverage
ratio by looking at where the pivot point is relative to the wheel and the
spring. However, it’s easy to make measuring errors in locating the centre of
pivot points and complex suspension designs get very hard to analyse like
this.
A better way is to carefully measure the wheel
travel and the spring travel, preferably over small increments. (Remove the
spring and/or the damper to do this and use a jack to move the wheel through its
travel.) If the wheel moves twice as far as the spring, the motion ratio is 2:1.
Note that motion ratios are seldom neat numerical figures like this – it might
be 2.2:1 or 1.87:1. The motion ratio might even change through the range of
wheel travel and an average may need to be taken.
This table, taken from http://e30m3performance.com/tech_articles/susptech/eff_rate/eff_rate2.htm,
shows one person’s measured values for the rear suspension of an E30 BMW M3.
Note how the motion ratio (called here the displacement ratio) varies from 0.5
to 0.8, with an average of 0.67. (This person has measured the wheel:spring
ratio rather than what we’ve been doing, which is measuring the spring:wheel
ratio. To turn it into a more familiar ratio, just invert it to get 1.49.)
So how do you use this motion ratio to get the
relationship in pounds/inch between the spring and the wheel?
Spring:Wheel Rate Relationship
Here’s the key point: the relationship between the
wheel and spring rates is worked out by squaring the motion ratio.
So if the motion ratio is 2:1, the relationship
between the spring rate (eg in pounds/inch) and the wheel rate (also in
pounds/inch) is 4:1 (2 x 2 = 4). If the motion ratio is 1.87:1, the spring:wheel
rate relationship is 3.5:1 (1.87 x 1.87 = 3.4969).
Taking as an example the motion ratio of 1.87:1
(giving a 3.5:1 spring:wheel rate relationship), a wheel rate of 250 pounds/inch
will require a spring rate of 875 pounds/inch. But if the motion ratio is 2:1
(and so the spring:wheel rate relationship is 4:1), the required spring will be
1000 pounds/inch!
You can see that small changes in motion ratio
make for large changes in the spring:wheel rate relationship. That’s why it’s
pointless comparing the spring rates used across different cars – unless of
course those different cars have exactly the same motion ratios in their
suspensions.
Modifying Springs
To a great extent you don’t need to worry about
motion ratios if you have a car that already has springs. Irrespective of the
motion ratio, upgrading the rate of a spring by (say) 30 per cent will increase
the wheel rate by 30 per cent also. (However, a 1 inch shorter spring will have
a much greater affect on ride height if the suspension uses a high leverage
ratio – again it’s best to use a percentage change.) But even a cursory
understanding of the affect of motion ratios will give you two advantages:

 You won’t try to compare spring rates from
different suspension designs

 You’ll know why some springs are so much stronger
than other springs, even though the car weights and handling outcomes are
similar
If you’re designing a suspension from scratch,
keep in mind that while a high motion ratio has some advantages, it will require
a very strong spring that will be heavy and, for a given diameter, have less
available travel before coilbinding occurs (because of its use of thicker
wire).
Preload?
Note
that how much the car settles on its suspension will depend not only on wheel
rate but also on the spring preload, if any. In some suspension systems (eg
struts), the springs are compressed and then held captive in that compressed
state. Preload holds the spring in place when the strut reaches full extension
(which occurs when the car is jacked up or the wheels leave the road) but it
also means that the car does not settle to the extent that you might first
expect when the weight is on the springs.
For example, a spring might have a rate of 100 pounds/inch and a
free length of 15 inches. When it is mounted on the strut it is compressed to
(say) 11.6 inches, and so the preload is 3.4 inches. To compress the spring by
each inch takes 100 pounds, and so the compressive force acting on the spring
when it is on the strut must be 340 pounds (3.4 inches x 100 pounds per inch
rate). If there are 665 pounds acting through that corner of the car when the
car is stationary, the spring will settle only 3.25 inches, because the first
340 pounds of the car’s weight is needed just to overcome the preload. If there was no preload, the car would settle by 6.65
inches (665 pounds divided by the 100 pounds/inch spring rate).
