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# Measuring wheel suspension rates

## A very easy way of comparing spring stiffness between different cars

### by Julian Edgar

Click on pics to view larger images

At a glance...

• Directly measure wheel suspension rates
• Need only smartphone and cheap app
• Measure bounce, pitch and roll rates
• Can measure through static bouncing or by road testing
• Immediately see what has previously been a mystery!
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Let's say you’ve built a unique car – say a Clubman. You’re trying to sort your suspension, and you are admiring a Clubby that is set up really well – its handling and ride are excellent.

You say to the owner: "What rate springs are you running, mate?"

The bloke tells you what they are in pounds/inch and then adds: "But my car’s motion ratio is different to yours – and the motion ratio on my car actually varies through the wheel travel."

The motion ratio is how much the spring compresses for a given movement of the wheel. So you think: hmm, that means that the rate at the wheels is going to be (1) different to the rate at the spring, and (2) at any given suspension deflection, is likely to have a different wheel rate to your car.

And then it gets worse.

The owner of the other car then adds: "...and of course my car's weight distribution is different to yours, what with this heavier engine and its slightly different location in the wheelbase. And don't forget I am a fat bastard and that will change weight amounts too."

Gosh, you think. Those variations in mass will affect how the car's suspension reacts for a given bump - even if the motion ratio and spring rate in his car were identical to your car.

You think: Damn! I thought comparing spring rates would be easy!

Well there is an approach that allows you to compare the suspension rates between different cars. It’s a technique that takes into account motion ratio, spring rate, and mass acting through the wheels.

So what do you do? You just measure the natural frequency of the suspension, one end at a time, and then you have a direct means of comparisons between different cars.

It's why pretty well all professional suspension engineering books refer to suspension frequencies, not spring rates.

The difficulty in the past is been: how do you measure natural frequencies with a reasonable degree of accuracy? But now that’s no longer a difficulty – you just use a \$6 app and an iPhone or iPad.

So how does it all work? And what actually are suspension natural frequencies?

### Natural (resonant) frequencies

Let’s say we take a coil spring out of a car and mount it vertically on a surface. We then put a 200kg weight on top of it and push down firmly on the weight. When released, the weight bounces up and down at (say) three times per second – so at a frequency of 3 Hertz (Hz).

Now it doesn’t matter how far we push the weight down before releasing it, this combination of spring and weight “likes” bouncing at 3Hz.

This is called the system’s natural or resonant frequency.

If we were to keep the spring the same but change the weight, the resonant frequency of the system would change. It would also change if we kept the mass the same but altered the spring characteristics.

To put this another way, there is a direction relationship between mass (acting downwards through the spring in this case), spring stiffness and the resulting resonant frequency.

So if we can directly measure the resonant frequency of the suspension, we get a number that takes into account the spring stiffness, the motion ratio of the suspension, and the mass that is working through the spring.

Sound hard? It takes less than a few minutes.

### Using the iPhone

This approach uses an iPhone or iPad as the measuring tool – you just need to install a cheap app. The app is produced by Diffraction Limited Design (see http://www.dld-llc.com/Diffraction_Limited_Design_LLC/Vibration.html) and is called Vibration. At the time of writing, it costs just US\$5.50. (We're told that similar apps also exist for other smartphone operating systems.)

The software takes advantage of the fact that the iPhone has an inbuilt 3-axis accelerometer. It can measure up to plus/minus 2.0g and has a sensitivity of about 0.02g. Those characteristics make it ideal for measuring suspension behaviour.

The software can be set to sample at up to 100Hz (100 times a second) and the data can be displayed as graphs, or emailed as spreadsheets.

### Static bouncing

The first step is to download and then have a play with the Vibration app to see how it works. It’s pretty straightforward, but like a lot of things, much quicker to learn by exploring the software functions on the phone than through our writing about it here.

Note: in this story, click on any of the screen grabs to enlarge them.

Set the logging so it occurs for 10 seconds at the highest sampling rate possible - 100Hz. You can also set the sensitivity to suit the accelerations – when statically bouncing the car, start off with 0.2g per vertical division. Finally, you can put in a delay that will occur prior to sampling starting – this allows you to get the car bouncing well before the logging actually begins.

After you have the functionality sorted, do the following:

Place the phone on one end of the car – say on the bonnet locking platform with the bonnet up. Bounce that end of the car up and down. The suspension will strongly resist being bounced at anything but its natural frequency, so you very soon get a feel for when to push. (This is just like with a child’s swing – it’s obvious when to do the pushing.) With a car having stiff damping and/or spring rates, you might need a helper.

Press the sample button on the software and start logging as the car is being bounced. You should end up with an up/down trace that looks something like this (the bottom yellow trace shows vertical accelerations). This is the front suspension of a 2006 Honda Legend.

Switch the app to ‘Frequency’ and place the cursor on the peak. If there are many peaks, look for the one in the range of 1-2.5Hz – that will be the suspension frequency. Here the cursor has been placed on the peak that reads as 1.42Hz (note the ellipse we’ve placed around that number).

Make a note of the reading. You can then do the same at the other end of the car.

In the case of the Honda, the front suspension frequency was 1.4Hz and the rear was 1.8Hz. The higher the resonant frequency, the stiffer is the suspension. In order to reduce pitch, most – but not all - cars have a higher rear than front frequency.

Below are the results of testing a mid-Eighties W123 Mercedes 230, one equipped with hydraulic self-levelling suspension at the rear.

Front: 1.3Hz

Rear: 1.3Hz

Note that overall, the suspension of the Mercedes is quite a lot softer than that of the Honda.

There’s another thing to note as well. To be most representative of reality, during static testing the car should be loaded as it normally is – e.g. with one or two people. Note that the Honda and Mercedes were statically tested while unloaded.

### Dynamic testing

Now if you’re thinking to yourself, ‘couldn’t the testing just be done by driving up and down the road?’, you’re right.

Here is the recorded vertical accelerations (again, bottom trace) for the Mercedes 230 when driven on the road. You can see that the ‘forcing frequencies’ that road bumps impart are much more complex and varied than was achieved by simple bouncing of the car.

And here is the frequency analysis. In static bouncing we got a frequency of 1.3Hz for both the front and rear suspension. In this test we got 1.15 Hz – rounded, let’s call it 1.2Hz.

So why is it lower on the road?

In the road testing there were two adults and a 30kg child in the car, so causing a greater suspension deflection. This in turn will cause a lower resonant frequency to be recorded (that’s why a fully loaded car rides better than one with just one occupant).

### Other frequency testing

In addition to testing for bounce frequencies, this sort of testing can be easily carried out for roll frequencies (i.e. how stiff the car is in roll) and pitch frequencies (how stiff the car is in pitching – where when the back is up, the front is down, and vice versa).

These are easiest to do statically by pushing on the car (to do pitch testing, you’ll need two people working in a co-ordinated manner).

The roll frequency will be typically higher than the bounce frequencies – that’s because of the additional spring of the anti-roll bars. However, that isn’t the case with the Honda Legend:

Front: 1.4Hz

Rear: 1.8Hz

Roll: 1.8Hz

The roll frequency of the Honda is the same as the rear frequency. This is presumably the case because the front springs are being stiffened enough by the anti-roll bar that in roll they are as stiff as the rear springs. (And the rear anti-roll bar is very soft – which it appears to be.)

The pitch frequency of the Honda is 1.6Hz – as you’d expect, numerically between the front and rear frequencies.

### Conclusion

If you want to make detailed comparisons between the suspension systems of different cars, or you simply want to know for fun what natural frequencies your car has in bounce, pitch and roll, the cheapness of the app and the ease with which you can do the testing presents a whole new world.

It is also makes understanding suspension design textbooks so much easier when you can picture what a ‘1.6Hz roll frequency’ actually means!