- Choosing the correct spring rates for your car is something that can be confusing for
a lot of people.
Previously in the course we went through the theory of using the undamped natural
frequency of the sprung mass to help us calculate the appropriate spring rates.
In this section, we'll run through the calculations involved in a real example.
It's important to keep in mind that these calculations are intended to get your spring
rates to a sensible starting point for both your car and its specific application.
As we mentioned previously there are many factors like driving style, track layout,
tyre types, surface conditions and much more that'll affect the ideal spring rate.
In saying that, these calculations will give you a good foundation from which you can use
as a base to start tuning your suspension from.
Let's take the case of a rear wheel drive coupe that's occasionally driven on the road
but is really a dedicated circuit racing car.
It has very little downforce so it's what we'd classify as a car that suits a mechanically
biased setup.
Using our suggested table from earlier in the course, and the car we've just described,
let's pick a target frequency of 2 Hz.
Part of the reason I've gone for the upper end of the frequency spectrum is that
comfort is not as much of a concern for this car.
If it was a daily driver that we occasionally used on track days and comfort is more
important to you, I'd recommend staying at the lower end of the spectrum instead.
We have to carry this calculation out twice, once for the front axle and once for the rear.
Before we can start our calculation, we first need to collect a few pieces of
information about the car.
The first is the total weight sitting on the front and the rear axles.
The easiest way to determine this is by using a set of corner weighting scales and measure the
weight on each corner directly.
Remember when you do this to have the car as close as possible to how it'll run on track.
That means having the driver in the car as well as fluids like a suitable amount of fuel
for example.
If you don't have access to a set of corner weight scales, you should at least be able to find the
total approximate weight and how it's shared between the front and rear axles online for
your make and model.
One important thing to remember with these calculations is that being consistent with the
units is critical.
For these calculations, I'm going to use standard SI units, however if you find it easier to work in
imperial units, you'll find the conversions in the handy reference sheet that you can download
from below this video.
Here you'll also find all the formulas you'll need to calculate the spring rates that you'll
need in this module.
Let's say that our car weighs a total of 1375 kg with a driver onboard and a quarter of a tank
of fuel which is representative of what we'd often have in the tank on average when we're
on track.
By summing both front corner weights together, we get 761.5 kg.
Now we have the total weight on the front axle that's being supported by the front tyres.
As we have 1 spring for each corner of the car, we only care about the weight on each
corner.
Dividing the total weight on the front by two, we get 380 kg for each front corner.
But remember we're calculating the natural frequency of the sprung mass only.
That means that we need to subtract the unsprung mass from this front corner weight.
There are a few different approaches for deciding what to use for the unsprung weight.
One is to support the weight of the car, remove the spring and allow the suspension
to fully droop.
With the suspension hanging, you can then put a corner weight scale underneath the
tyre to measure the approximate unsprung weight for that corner of the car.
While not perfect, this is a reasonable approximation of the unsprung weight
at each corner.
If you aren't able to complete this unsprung weight test for yourself. you might be able to
find information online for your make and model.
If not, then a reasonable ballpark figure you can use for most independent
suspensions is 45 kg on an undriven axle and 50 kg on a driven axle.
Let's say for our case we've measured the unsprung weight for one front and one rear
corner.
The unsprung front weight was 43 kg and the rear, 53 kg.
Now we can calculate the amount of sprung weight at each corner of the front axle.
We take the total 380 kg for one front corner, subtract the 43 of unsprung weight,
giving us approximately 338 kg of sprung weight for each of the front corners of
the car.
Next we need the motion ratio for the front axle which is what we went through in a
previous module where we calculate the amount the wheel moves for a given amount
of spring movement.
On the front we have a motion ratio of 1.1, meaning the wheel moves 1.1 what the
spring does.
And 1.3 on the rear.
Now we have all the information we need to calculate the target spring rates.
This is the formula we use to calculate the target spring rates at the wheel.
Reading left to right, we have the sprung mass for that corner of the car, the value of pi
and the target frequency.
From here, it's as simple as substituting our numbers into the equation.
Doing so, we get a value of 5335.
At first glance, this number doesn't look very useful, this is because the resulting sprung
stiffness is being shown as newtons per metre which is the SI unit.
The more commonly used unit for spring rate is newtons per millimetre.
To convert, all we need to do is divide our answer by 1000, giving us 53.3 newtons
per millimetre.
Now we have the target spring rate at the wheel.
If we had a 1:1 motion ratio, this would also be our spring rate, however as we have a motion
ratio of 1.1 on the front axle, we need to convert it to a spring rate.
To do this, we need to multiply the target wheel rate by the motion ratio squared.
This gives us a target spring rate of approximately 65 newtons per millimetre.
Using the conversions listed in the supplied formula sheet below this video, gives us a
target front spring rate of 6.6 kgs per millimetre and 368 pounds per inch.
Obviously, springs are only going to be made in certain increments, so it's unlikely you'll
be able to buy the spring that exactly matches your calculation.
Just go with the closest value you can, no need to get too hung up on finding one
down to the last newton per millimetre or pound per inch.
Now we can repeat the same process for the rear axle.
Using the exact same procedure as before but substituting the numbers for the rear
axle we get a target spring rate of approximately 68 newtons per millimetre
which is 6.9 kg per millimetre or 387 pounds per inch.
Notice that for this example, the rear axle is significantly lighter by around 150 kg.
With all other things being equal, this would mean a softer rear spring to achieve the same
target suspension frequency.
However following the calculations through, and when we take into account the different
motion ratio on the rear axle which is 1.3, we end up needing a stiffer rear spring
as a result.
Some sources will tell you that you need to target a slightly higher rear suspension
frequency relative to the front.
This is based on the idea that for a given disturbance like a bump in the road,
because the front axle will hit this first, you can end up with poor handing qualities
with the front and rear axles moving out of phase from each other, causing excessive
pitching of the chassis.
The wheel base of the car and the road speed will also affect this.
This concept is rooted in the world of road cars and in my experience, when we're
dealing with cars for competition use, it's not necessary to aim for a difference in the target
natural frequencies.
At least, not in the first instance.
What you'll usually find is that after starting with your initially calculated spring rates,
you'll most often end up with a split in the resultant natural frequencies in the normal
process of tuning the balance of the car by trying different combinations of springs.
At this point, paying attention to the natural frequencies isn't as important and you
should be focusing on tuning for balance and grip rather than being focused on a theoretical
target frequency.
As we discussed earlier in this module, the concept of the natural frequency is useful
for a starting point only.
We established earlier in the course that we'd be ignoring the effects of the tyres on many
parts of the suspension and using the concept of the sprung natural frequency in this way,
we're significantly simplifying the system by ignoring the effect of the tyres.
In reality, the tyres themselves can be thought of as having a spring rate and damping
properties of their own.
So in reality, if we're being more accurate, the spring calculation for each corner of the
car should include the effect of having another spring in series with the main
suspension spring.
In saying that, while it's a significant simplification, I don't believe it's
absolutely necessary when considering a suspension in a simplified way as we have
throughout this course.
It's still a valid and useful calculation to do.
Once you've calculated the starting point for your front and rear spring rates,
selected the springs as close as possible to the target and then run them on track, you'll
begin the tuning process.
As we've already alluded to, this may well mean you end up moving away from the
theoretical spring rate you'd calculated, at least at one end of the car in order to
maximise your balance and grip.
Once you've found a suitable balance, you can also try moving your entire spring package
stiffer and softer together to see whether a stiffer or softer overall setup will be more
beneficial for a given car at a given circuit.
This is something we'll be discussing in more detail in the later module on calculating the
lateral load transfer distribution.
A concept we introduced earlier in the course.
For now though, I encourage you to go ahead, make the required measurements on your
own car and carry out these calculations for yourself.
That was just one of the 37 modules taken from our Motorsport Suspension course.
If you want faster, more consistent lap times, along with an understanding of the concepts
and tuning tools used by the pros, then you'l be interested in this course.
You'll start with the basics of motorsport suspension and build on the knowledge in
this course, covering choosing springs, tuning your dampers and adjusting roll
centre heights.
To be able to understand and tune your suspension for yourself.
If you're interested in advancing your skills, this is the course for you.
For more information and to purchase this course, click the link to enrol now.