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Pitch Optimisation - Including Suspension Frequency

If you have ever had the pleasure of driving a Hydragas equipped MGF you may have noticed how remarkably comfortable it is over a wide range of speeds and conditions. It achieves this by using a suspension system that interconnects both front and rear axles.

 

In most cars when you go over a bump the front and rear axle will rise and fall at different times causing uncomfortable pitching movements.

See Fig 1. Below of MGF suspension

Fig 1.

You can see how although front and rear axles are dealing with some serious undulations the body is staying level.  

Now it IS possible to make a car on Conventional springs and dampers work in a similar fashion. In fact most major car manufacturers put a lot of effort into ensuring that their car is comfortable given the environment it will typically be used in. This is why some cars feel very at home at lower speeds but ungainly at higher speeds and vice versa. The catch is you can only optimise the chassis for a given speed. Above or below that speed it will not be optimised.

Suspension Frequency

It is frustrating to hear conversations about spring rates being interchanged without due regard for motion ratio which affects the wheel rate. For example a 300lb spring in a MacStrut car will typically give a wheel rate of 270lb but in a double wishbone set up the same 300lb spring might only yield 120lb at the wheel.

In addition to this there is also sprung and unsprung weight of the vehicle to consider.

What suspension frequency offers us an easy way to compare the relative stiffness from one vehicle to another. Also enables us to calculate what rear frequency will be needed, to achieve pitch optimisation at a given speed. I know a good link for calculating frequency just send me a request. Here is a useful calculator for Frequency so let us assume we had a sprung weight of 500lb and a wheel rate of 200lb the frequency would be 1.98 Hz. This would be the kind of frequency we'd expect in a car with Sports Suspension.

 

SPRING FREQUENCY
1Hz – 1.5Hz	Majority of Cars
1.5Hz- 2Hz	Cars with “Sports Suspension”
2Hz- 2.5Hz	Typical Track Specification – still road useable
2.5Hz – 3Hz	Race Cars on Slick Tyres
3Hz Plus	Race Cars on Slicks with Aero

 

The fact is the human body can cope with higher frequencies reasonably well - what it hates is pitch occuring front to rear and that is why speedbumps are so uncomfortable to traverse. This is why it is worth pitch optimising. Not for going over speedbumps but for the cars typical average speed.

So how do you pitch optimise a chassis?

With the simple equation below:

Where “L” is the length of the wheelbase in metres and “f” is the frequency of the suspension.

In order to correctly calculate the motion ratio to obtain wheel rate rather than use equations I prefer to just measure the actual movement from spring platform to wheel. With a range of values you can easily work out the average and then square this figure to give the ratio.

 

e.g 

 

Wheel movement mm	Spring movement mm	Ratio
20	17	0.85
40	32	0.8
60	53	0.88
120	102	0.85
	AVERAGE	0.85
	SQUARED	0.71

 

So in this example the wheel rate would be the spring rate multiplied by 0.71. So once you know the motion ratio, the unsprung weight and the corner weights you can calculate the frequency of rear suspension required for your desired pitch optimised speed.

For example: 

 

WHEELBASE (m)	2.54
FRONT FREQUENCY (Hz)	2
REAR FREQUENCY (Hz)	2.5
OPTIMISED SPEED KMH	91.44
OPTIMISED SPEED MPH	56.8

 

In this example the vehicle needed to have a 2.5 Hz rear suspension frequency to optimise it for 56.8 mph. In reality optimising for too low a speed requires a rear frequency to be so high that comfort is then an issue.

Optimisation for 30mph in this example requires a rear frequency of 3.2 Hz which is way too high given that the front frequency is only 2 Hz.

Now there are arguments against pitch optimisation saying that on a race car it's not relevant  due to the effect of dampers in slowing the oscillation but to set out with no regard for pitch optimisation could be unwise. Consider for a moment what happens when people follow established wisdom and run a lower rear frequency on a RWD car for Traction. This can work fine - a Porsche 911 tends to run this kind of set up, but in extremis can result in the front wheel lifting off the ground. 

 

 

WHEELBASE (m)	2.54
FRONT FREQUENCY (hz)	2
REAR FREQUENCY (hz)	1.9
OPTIMISED SPEED KMH	-347.47
OPTIMISED SPEED MPH	-215.82

 

Now by selecting a rear frequency of 1.9 Hz the car is now optimised for travelling at 215 mph IN REVERSE! So it's never going to be pitch optimised in its favoured direction of travel.

Quite often this mistake shows in pictures of a RWD car with the front wheel pawing the air and the rear fully compressed under power exiting a tight corner. Some will tell you there is nothing wrong with this but really the rear spring / roll stiffness needs to be higher. If this creates too much oversteer then the damping rates need refining. Once the spring frequencies front and rear work together then weight transfer should, ideally, be controlled by the anti-roll bars. This will give a better balanced car that is capable of higher outright cornering speed.

 

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