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Villiers Singles Improvements Handbook

Villiers Handbook
Authors
Introduction
History
Crankcases
Crankshafts
Pistons
Primary Drive
Gearbox
Ignition
Induction
Exhaust
Silencing

Silencing

Work at Queen's University Belfast has continued for many years on the basis that the only real way to predict gas behaviour is through the use of unsteady gas dynamics rather than acoustics, which they have done much to discredit. A number of papers by Coates and Blair give us some tools to work with, as opposed to putting a perforated steel tube in an aluminium can and stuffing with glass wool and hoping for the best.

As might be expected, the shape of the exhaust port has a significant effect on the exhaust note as well as on engine performance. The experimental data confirms this, with the "square" exhaust port profile giving a steep fronted wave compared with the gentler profile of the truly oval port shape, see Fig 21 . Research has shown that the soft oval port shape will give a primary sound frequency around five times the engine pulse rate, whereas the squared tuned exhaust port with its steep fronted wave will give a primary sound frequency at around twenty times the engine pulse rate.

Engine	Port shape
RPM	Oval	Squared
4000	267 Hz	1333 Hz	Primary sound frequency
6000	500	2000
8000	533	2667

Since all exhaust ports are somewhere between oval and square, this gives a rather large frequency band to target a silencer at, and the more unfortunate as the human ear is particularly sensitive in the 2000 - 2500 Hz range.

We have three basic techniques which we can use when designing a silencer

Frequency tuned diffuser (Fig 22 )
Frequency tuned resonator (Fig 23 )
Frequency absorption by certain materials, such as glass wool.

A typical silencer will make use of some or all of these techniques. In a worked example, we will use each technique and predict the amount of sound that the silencer will absorb and at which frequencies. This example produces a silencer too long for some applications, but it does illustrate how some science may be applied to what was previously a black art form, our schematic design is shown in Fig 24 .

The dimensions assumed throughout are

Can diameter 76 mm

Pipe diameter 28.6 mm
Pipe thickness 1.5 mm

Sonic speed 32,000 cm/sec

The expansion chamber baffle cone bleeds away its pressure through the stinger pipe, and it is the stinger pipe which passes through the silencer. The gas passes through chamber A (resonance), then chamber B (diffuser), then chamber C (resonance) and then through an amount of perforated tube surrounded by glass wool, which tends to absorb the higher frequencies.

The design criteria for the three chambers are

A B C
Chamber length (mm) 150 250 50

Number of holes 2 2 16

Hole diam (mm) 8.0 28.6 2.6

Tuned frequency (Hz) 480 845 1112
Attenuation (dB) 43 46 42

Predicted sound absorption of silencer design

Appendix A contains a data sheet of resonant frequencies for a range of chamber sizes and holes. Few readers will have access to measuring facilities which will indicate what sound frequencies that their engine is producing, but the data sheet has value in that it is now possible to modify an existing system, to remove the frequencies most irritating to the human ear.

To calculate the resonant frequency (ie: the frequency which will be absorbed) and the attenuation (ie: how much sound will be absorbed) for any individual chamber or compartment within the silencer, proceed as follows:

NV is net volume of the outer chamber, calculated from main chamber volume less the volume of the stinger pipe.

PA is the cross sectional area of the stinger pipe

Cr Coefficient of resonance, calculated as
(hole area x hole count) / (pipe thickness + 0.8 x hole diameter)

RF Resonant frequency sonic/p x (Cr/NV)^(1/2)

Fx Exhaust primary frequency, which you must estimate based on port shape

Cs Coefficient of sound ( Cr x NV )^(1/2) / (2 x PA )

Cx Coefficient of excitation (Fx/Cr) - (Cr/Fx)

AT Attenuation dB 10 x LOG10 (1 +(Cs/Cx )2 )