This article was first published in 2007.

Sometimes it’s easy to lose the wood for the
trees: to forget the fundamentals and think only of the outcomes. Suspension is
one area where that happens a lot. So let’s take a step back and think
about springs.
Nearly all current cars use steel coil springs.
The springs are there to support the weight of the car’s body while still
allowing it to move up and down – or, more accurately, for the wheels to move up
and down while the body stays still.
Spring Rate and Static Deflection
Springs vary in their rate, that is, how much they
compress for a given weight placed on top. Put 1 kilogram on top of a vertical
compression coil spring and its height might be reduced by 1mm. In that case,
the rate of the spring is termed 1 kg/mm. If you put 2kg on top of such a
spring, it will sink by 2mm. Put 20 kg on top of the spring and it will sink by
20mm. And so on. Rates of springs are also often expressed in pounds per inch,
but the same idea applies.
Let’s say we have a small car that has a nice
round mass figure of 1000kg, distributed on all four wheels equally.
Furthermore, we’ll say that the spring compresses by the same amount that each
wheel moves upwards. (That is, the wheel and spring rates are the same.)
The amount the spring compresses with the car’s
250kg weight on top (this is called the static compression) is determined
by the spring rate that we chose. So, with 250kg on top of each spring, a chosen
spring rate of 1 kg/mm will result in the spring compressing by 250mm – or about
10 inches. Remember, that’s where the car sits in its static position – to cater
for bumps in the road, we’re going to need the spring to still have plenty of
travel left. And with 250mm of static spring deflection, arranging even more
travel is going to be difficult unless the car has a way high ride height and an
incredibly long travel suspension.
So let’s stiffen the spring rate to 3kg/mm. Now,
with the same 250kg acting to compress the spring, it will shorten by only
(250/3 =) 83mm, or 3.3 inches. If we have a total suspension travel of 200mm (8
inches), that will put the car 40 per cent down the full suspension travel when
it’s sitting there, unloaded. (So what’s ‘full suspension travel’ then? Full
travel is the vertical distance from maximum bump
[that’s the suspension as
compressed as possible]
to full droop
[which is when the suspension is as
extended as possible, the entire car’s weight off the springs]
.
With the suspension compressed by 83mm of the
available 200mm, there seems to be plenty of room for further travel to absorb
bumps. And in fact, even if the static weight of the car doubled (ie there’s 1g of upwards acceleration over a bump), only 166mm of the available
200mm travel would be used up  so there would still be some left over.
Trouble is, this analysis ignores the weight of
passengers and luggage. If the unloaded compression of the springs (with 250kg
acting through each) is 83mm, add four people at 100kg each and the suspension
travel that's used up increases to 117mm  that’s 117mm of the available 200mm. If you
now hit a 1g vertical bump, there won’t be sufficient travel left to absorb it.
That’s why 1000kg cars with four 100kg people in
them don’t like big bumps...and why bump stops are a prerequisite!
So why use a suspension rate that deflects by so
much with just the static weight? Why not use a stiffer springs that allow more
room for bump absorption, even with our four 100kg people on board?
There are two parts to that answer. The first is
that in addition to bump absorption capability, you also want rebound
travel – that is, you want the wheels to stay in contact with the road when
the car meets a hollow in the road. The suspension must be able to droop
sufficiently for the wheels to do this – and also enough to keep the inside
wheels in contact with the road when body roll occurs in cornering. If you have
a static ride height only 10mm down into the travel, you’ll have (in a worse
case scenario) only about 10mm of droop capability.
But the most important reason why you want to use
springing that allows plenty of static deflection is because of what is called
natural frequency.
Natural Frequency
Imagine a coil spring out of the car sitting
vertically on the ground. You place a weight on it (yep, the spring deflects
proportionally with its rate) and then you carefully push the weight downwards
and release it. The weight will bounce up and down at the spring’s natural
frequency. Over time the bounces will die away (they’ll get smaller) but they’ll
continue to occur at a certain number of cycles per second, or Hertz (Hz), until
the spring is still.
The same applies to springs in a car suspension
system – the suspension has a natural frequency of up/down bounces.
Importantly, the fact that you might have dampers in the system makes very
little difference to the natural frequency!
When thinking about suspension systems, natural
frequency is almost never considered. However, it is vital for two reasons.
Firstly, in terms of ride comfort, the human body likes to sit on a system that
has a natural frequency of about 1Hz, or 1 up/down cycle per second. Secondly,
as the natural frequency of the suspension numerically increases, it gets excited far more
easily by road bumps, making control of the spring more difficult. In short, a
lot more of the vertical accelerations of bumps get through to the cabin.
So what determines natural frequency? For a given
car it depends on how much the springs compress when the static weight of the
car is lowered onto them. And is the natural frequency number easy to work out?
Yep! The natural frequency in cycles per minute (divide by 60 to get Hertz) can
be found by: 188 divided by the square root of the static deflection, measured
in inches.
So in our example above, we ended up with a static
deflection of 3.3 inches. This suspension therefore has a natural frequency of
1.7Hz. That’s quite a long way above our optimalforride natural frequency of
1Hz, but the only way of getting a lower number is to increase the static
deflection, which in turn means we need to have a greater total suspension
travel if we’re still to be able to absorb bumps.
But what if we don’t care much about ride – we
want the stiffer suspension that will help control pitch and roll? Then we’ll be
in the range of 2 – 2.5Hz for sporting cars. (Typical sedans are in the range of
1 – 1.5Hz.)
Some of this we know intuitively – we’ve just
never thought about it in detail.
Think of offroad racing buggies. If you go in one
you’ll find the ride very good, even on stuff which wouldn’t unduly tax a normal
car. But why would a race car ride well on a surface on which it seldom if ever
sees? The answer is that the suspension has a very low natural frequency. After
all, some of these vehicles have a suspension travel of 20 inches... which if the
static deflection is 10 inches, gives a natural frequency of 1Hz! So It might be
a race car but it’s likely to have a ride better than most limousines...
The other example is how we’ve all experienced how
cars ride better with extra people in them. If the car has a static suspension
deflection of 4 inches, the natural frequency of the suspension is 1.6Hz. If the
static deflection increases by another 1.5 inches when 4 people get in the car
(giving a total static deflection of 5.5 inches), the natural frequency of the
suspension has decreased to 1.3Hz. That’s why the ride has improved! (Of course,
if there is insufficient suspension travel and the extra static deflection
causes the bumpstops to be hit, then that’s another story...)
Static Deflection and Natural Frequency
So what do you need for a good result?
Well, you need plenty of static deflection in
order that the natural frequency of the suspension is low – certainly below
2.5Hz, which means not less than about 38mm (1.5 inches) static deflection.
However, clearly that minimum figure limits droop capability quite a lot.
(Sometimes, eg in the back suspension of frontwheel drive cars, having short
droop capability may not be a handling disadvantage. Flying the inner rear wheel
will promote rather quicker changes in direction!) Secondly, to get plenty of
static deflection, the spring rate will need to be relatively low, in turn
requiring that you have a lot of travel to allow you to absorb bumps without
bottomingout.
If you’re designing a car from scratch (or making
really wholesale changes to suspension units), it’s important that you keep a
longtravel suspension capability. That’s not just so that big bumps can be
absorbed but also so you can keep the natural frequency relatively low. This
also has implications for ride height – you don’t want the body dragging on the
ground on big bumps.
If you’re modifying an existing car with the usual
springs and shocks swaps, springs that lower the ride height will be stiffer (so
the car doesn’t bottomout on the same size bumps) and so will have a higher
natural frequency. In addition to ride implications, this also means the tyres
are more likely to get excited by typical road surfaces – requiring strong
damping.
Conclusion
If you reckon you’ve got you head around all that,
think of trucks and buses for a moment.
If a truck has a mass acting on the back wheels of
8 tonnes, but can easily have 16 tonnes added in load, the springs are clearly
going to have to be pretty stiff to cope with the maximum load. In turn that
means a short static deflection in an unloaded state, which means a high natural
frequency. And if you’ve ever ridden in an unladen truck, you’ll know how
horrible the ride is.
But what about buses? Sometimes they might have
two people in them (say a 150kg load) but at other times 40 people in them
(3000kg load). How do you spec the suspension to give a comfortable ride in both
configurations? The answer is with air springs. If you can inflate the springs
to always have (say) 8 inches of static deflection, you’ll be able to maintain a
natural frequency of 1.1Hz, irrespective of load.
We don’t reckon knowing about natural frequencies
of suspension is going to immediately allow you to make profound and effective
changes to your car’s suspension. But we do think it’s an important element in
understanding what’s going on when the car wheels are moving up and down beneath
you....
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