Finding The Sweet Spot

Written by Danny Nowlan

How to specify the damper curves of a racecar is one of the most misunderstood areas
of racecar engineering. Old wives’ tales abound in what the damper curve should look
like and often, when pressed for an explanation, the damper specialist or engineer will
give empirical reasoning as opposed to scientific fact.
Overview

The purpose of this article is to outline a series of tools that can be used to specify a base
damper curve from first principles. More
importantly though, it is also to explain why you might want to put a damper curve together, as
well as how. The basics of a second order system analysis will be shown and then, using
numerical simulation, we will show how to refi ne the results. A number of case studies will
then be presented to show the application of these techniques.

Dampers are such a critical area to get right because they control the tyre load variation of the
car to the road. Also they play a critical roll in controlling the way the chassis pitches androlls.
Not only is this significant for club and saloon racecars, but is even more important when the car
runs large amounts of downforce and the chassis needs to be tightly controlled. When dampers
are set appropriately
they can 'mimic' active suspension and can be used as a tool to load the tyres how we want
them. This is vital for temperature
control of the tyres.

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Finding The Sweet Spot

Written by Danny Nowlan

Figure 1 - ChassisSim simulated output. The damper’s response to bumps can be

The other important aspect of specifying a damper is the ability to simulate what the damper will
do before it runs at the circuit. To model the dampers appropriately, dynamic simulation must be
used as opposed to pseudo static simulation, and here’s where the dynamic simulation program
ChassisSim will be used. It’s dynamic core means that every simulation is the equivalent of
running the car on a seven-post rig with the appropriate circuit data. An example of the output is
shown in figure 1 above.

Understanding the physical interactions of the car and being able to model them are the two
tools that will be used to specify the damper curve.

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Finding The Sweet Spot

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Parameters
-- mB
mT===Ture
Kb
Cb
Kt Mass
Sprungofmass
therate
Spring spring
springmass
unsprung
damping mass
rate (kg)
rate (kg)
(N/m/s)
(N/m/s)
Figure 2 -The standard quarter-car model of a suspension system

To understand the methodology that will be used, consider the classic quarter-car model of a
suspension system, as shown in figure 2 above.

The beauty of the quarter-car model is that while it doesn’t represent the full physics of the car it
provides a powerful tool for understanding what is going on with the suspension. The equations
of motion for the model are quite simple and it is a valuable tool for introducing second order
system analysis to describe what is going on. As a further simplification let’s assume that,

KB « KT
mt « mB
In this case the governing equations of the sprung mass reduce to,   mB · xB ” = –KB · xB –CB
· xB’

What this means in layman’s terms is that the acceleration of the sprung mass is the sum of the
spring rate of the damper times the damper movementand the damping rate times the damper
velocity.

A Laplace transform can then be applied to equation 1 to describe the spring damper system by
a natural frequency and a damping ratio. The Laplace transform is one of the fundamental
transforms of control theory and is heavily utilised in the aerospace industry. Applying the
Laplace transformation to the spring damper system shows,

            CB            KB
0 = s2 + —— · s + ——
            mB             mB

If we compare this to the ideal second order system with natural frequency ω0 and damping

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Finding The Sweet Spot

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ratio ζ it is seen that,

0 = s2 + 2ζ · ω0 · s + ω0 When the two previous equations are compared we now have the
tools to specify our desired damping rate in terms of damping ratios and natural frequency,

             KB
ω0 = √——
             mB
CB = 2 · ω0 · mB · ζ

This is the first point of the analysis. Equation 4 (above top) specifies the natural frequency in
rad/s of the system, and equation 5 (above) means a damper rate based on the damping ratio
that is desired can be specified. Note that the spring rate is specified in N/m and the mass is
specified in kg – what this means is that we can now specify a damping rate based on what we
want the system to do, as opposed toguessing. Also, because of the form of equation 5 this can
be readily applied for both the front and rear.

Now that damping rates can be specified, the next step is to choose the desired damping ratio.
To understand this, consider a typical second order system response to a step input (this would
be equivalent to a driver giving the steering wheel a sudden jolt, for example) and is illustrated
in figure 3 (below).

Figure 3 - Idealised second order system response to a step input

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Finding The Sweet Spot

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What this shows is that the higher the damping ratio the better controlled our system will be to a
sudden jolt. However, as the damping ratio drops, the sprung mass will oscillate. This isn’t ideal
for body control but it is the behaviour that is needed to absorb shock loadings like traversing
bumps or kerbs. From this, two very important relations can be shown:

ζ ≥ 0.5 is ideal for body

control

0.3 ≤ ζ ≤ 0.4 is ideal for bump

control

Armed with this information, the damper ratio selection guide can be shown (see figure 4,
below).

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Finding The Sweet Spot

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Figure 4 - Damping ratio selection guide

What is presented is what the ideal damping force vs peak velocity curve would look like. The
damping curve is broken up into the traditional low speed and high-speed regions. In low-speed
bump body control is critical. Consequently, the ideal damping ratios are 0.5 – 0.7. If the tyres
really need to be worked hard then 1.2 is chosen. As always, tune the damper to the conditions
that are appropriate: if the circuit is bumpy then the low end of the damper guide in fig 4 is
applied, but if the circuit is smooth then larger damping ratios can be used. Remember this is a
tool and, consequently, must be used appropriately.

ROLL AND PITCH RATES

The bypass velocities are fundamentally dictated by the roll and pitch rates of the car. These
can be determined in a number of ways, either from dynamic simulation or logged data. To
determine the velocities, the peak logged longitudinal and lateral accelerations arenoted, and
the steady state pitch and roll angles from this can be calculated. From this, you simply note the
time it takes, and the desired pitch and roll rates can then be deduced by dividing the roll and
pitch angles by the time taken to get there. These are then multiplied by the track for roll or
centre of gravity moment arms from the centre of gravity for pitch motion, and from this the
damper velocities can be determined. As a rough rule of thumb 10 to 25mm/s will suffice for
most racecars.

DAMPER HISTOGRAMS

The next step is to run a vehicle simulation and then produce a damper histogram, a typical
version of which is shown in fig 5 (below). The damper histogram shows the spread of damper
velocities, and what is desired is a bell curve that is symmetric in both bump and rebound. The
range of velocities applied is the mean velocity range of the damper and typically the distribution

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Finding The Sweet Spot

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is 20 per cent of the velocities in the low-speed region in both bump and rebound. The rest is
spread in the typical bell fashion from medium to high speed.

Figure 5 - Damper histogram - ideally what you’re looking for is a curve that is
symmetrical in both bump and rebound
 

To tune this is straightforward. If we have a low percentage in the low speed region ie the bell
curve looks flat, then simply increase the low-speed damping of that area and vice versa.
Alternatively, if we have too much of a peak then we either need to reduce the high-speed
damping or decrease the low-speed damping. This method is extensively used in V8 Supercars.
Remember, the power of numeric simulation is that you can do all this on the PC before ever
hitting the track. Using dynamic simulation you can play with damping ratios and produce as
many histograms as necessary until the desired response is achieved. Before presenting the
case studies though, the damper selection procedure is as follows:

• Choose the bypass velocities that are required

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Finding The Sweet Spot

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To better understand the application of this, let’s look at a case study of the front dampers of a
V8 Supercar. The reason the front dampers only will be evaluated is because of the large
unsprung mass at the rear. The parameters for the V8 Supercar are presented in table 1

Table 1 V8 Supercar

Parameter                         Value

¼ car sprung mass value = 345 kg

¼ car unsprung mass value = 50 kg

Wheel spring rate = 55 000 N/m

Front damper/wheel ratio = 0.63

As most racing circuits in Australia are very bumpy, according to the damper guide in figure 4,
the lower values for the damping ratios were selected. This is summarised in table 2.

Table 2 Lower damping ratios selected

Damping ratio Value

ζLS_BUMP = 0.5

ζOTHERS   = 0.3

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Finding The Sweet Spot

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Taking into account the motion ratio, the comparison between the damper produced by this
specification and the actual damper is shown in figure 7, while the simulated histogram results
using ChassisSim are shown in figure 8, where red is the ideal damper and blue is the actual
damper.

Figure 7 - Comparison between the ideal damper and the actual damper

Figure 8 - A comparison of the simulated histogram results

Figures 7 and 8 indicate that the dampers produced by this method compare very closely to the
dampers that were used on the car. The only significant differences being that the dampers

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specified using our method carried too much low-speed bump, which is evident in the peaks in
the red area seen in the histogram. However, the key point to note is that the differences
between the two dampers could be readily addressed by adjustments in the damper during a
session. Consequently, using this technique a damper has been specified that is very close to
what was used in practice.

The second case study was the specification of the front and rear dampers for a 1976 Porsche
911 that was used in a historic racing category. In fact, it was this case study that inspired the
creation of this technique and provides a telling example of how powerful these techniques
could be. The parameters of the car are shown above in table 3.

Table 4- Historic Porsche 911

Parameter                                            Value

Total car mass                                       1255 kg Total unsprung mass at the front                

Rear wheel rate                                 73 553 N/m

Front weight distribution                        36.6 %

As per the V8 Supercar, because this car would be run on Australian circuits, the damping
ratios used for the V8 Supercar where also translated to this car.

The next step in the process was to construct the dampers and enter them into ChassisSim and
perform the simulation to generate the histogram. The circuit that was used to simulate this was
Wakefield Park since this was where the car would spend the majority of its time. The damper
curves were adjusted until the histogram exhibited the desired characteristics. In that regard
ChassisSim was being used as the equivalent of a seven-post rig. The initial and final front and
rear damper specifications are shown below in figures 10 and 11, while the comparison of the
histograms is shown in figure 12.

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Finding The Sweet Spot

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Figure 10 - Comparison of initial and final front dampers

Figure 11 - Comparison of initial and final rear dampers

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Figure 12 - Comparisons of the histograms (red, initial. blue, final)

As can be seen from figs 10-12 only minor adjustments where needed in the damping, the goal
being to equalise the damper histograms so they exhibited the same behaviour front to rear.

When the final damper specification was put on the car at Eastern Creek the car was four
seconds a lap quicker than with the dampers it was originally fitted with. Though this is only an
example, it shows the potential gains available when the dampers are calculated and simulated
appropriately. Again, remember this gain was made on paper and on the PC before the car ever
turned a wheel on track.

The final case study is the application of these techniques to high downforce open wheelers.
This is where this technique will fall into difficulty because the assumption that the spring rate of
the damper is much less than that of the tyre is not valid, because in these cars they are often
equivalent. Consequently, this technique should be considered a guide rather than a rule in this
application. That being said, when the damping ratios for a typical F3, F3000 or GP2 car are
calculated they match up with what is seen with the damping guide, as illustrated in table 4. The
high-speed values correlate quite closely with the damping ratio guide. The major thing of note
is that the front rebound values are high and that is due to the need to control the front ride
height. So as a rough rule of thumb this technique still does have some validity.

Conclusion

In summary, this technique of specifying a damper curve by natural frequencies and damping

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Finding The Sweet Spot

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ratios is a highly useful tool. Not only does it describe what is going on with the suspension
system, but also with a few simple calculations an engineer can ascertain the characteristics of
what a damper can do.

Obviously, this isn’t the last word on how to specify a damper. The emergence of frequency
sensitive damping and the non-linear requirements that aerodynamics imposes on a car will
dictate that the perfect damper curve will be non linear in nature. However, this technique
should give you the tools to gain more of an insight into what the damper is doing and to tune
the damper before the car turns a wheel in anger. This doesn’t replace track testing or running
the car on a shaker rig, of course, but it will take out some of the guesswork so the car is in top
form before it hits the circuit.

Join The Discussion Here

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