Traffic noise prediction

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Traffic noise prediction

Ser

TRAFFIC N O I S E PREDICTION by

R . E . Halliwell and J . D . Quirt

SNTRQDUCT I O N

In 1977 the Canada Mortgage and Housing Corporation [CMHC), with the technical assistance of the Division o f B u i l d i n g Research, produced the publication "Road and Rail Noise: Effects on Housing". That paper presented procedures f o r p r e d i c t i n g t h e n o i s e from road and railway traffic, and s p e c i f i e d acoustical requirements f o r residential buildings in t h e i r v i c i n i x y . 'l'he procedures were simplified to t h e p o i n t where

they can b e handled by persons with Limited mathematical t r a i n i n g and no knowledge of acoustics. The o b j e c t i v e of this present p a p e r i s to des-

c r i b e t h e u n d e r l y i n g acoustical principles and explain how t h e y relate

to t h e procedures g i v e n in t h e CMHC document. The paper is d i v i d e d i n t o n i n e sections, roughly paralleling t h e s t e p s in t h e CMHC document.

1. N O I S E EMITTED BY ROAD TRAFFIC

The main factors t h a t govern noise generated by freely-flowing

road traffic i n c l u d e the number of vehicles p a s s i n g per u n i t time, t r a f f i c speed, t h e f r a c t i o n of heavy vehicles, and the type and con- d i t i o n of t h e road surface.

In formulating a n o i s e p r e d i c t i o n model, a reasonable s t a r t i n g p o i n t is t h e noise e m i t t e d by typical individual v e h i c l e s . For sim-

plicity t h i s model uses only two v e h i c l e categories: "'light vehicles'" comprising passenger automobiles and similar four-wheel v e h i c l e s , and "heavy v e h i c l e s " d e f i n e d as anything having more than four wheels.

The r e l a t i o n s h i p between the maximum passby noise e m i t t e d by l i g h t

and heavy v e h i c l e s , as illustrated in F i g u r e 1 . 1 , was based on analysis

o f all available d a t a from several sources.

The n o i s e from light vehicle passbys has been the s u b j e c t o f

numerous studies [I to 5 ) . All t h e d a t a e x h i b i t a steady increase i n t h e maximum passby n o i s e w i t h i n c r e a s i n g vehicle speed. In most cases an expression o f t h e form a + b l o g (5) (where S is t h e traffic speed in kilometers per hour and a and b are regression coefficients) has

been f i t t e d to the data. There is some v a r i a t i o n in t h e coefficients

from one study to another, which may i n l a r g e p a r t be explained by differences in the road surfaces. Some t a b u l a t e d r e s u l t s follow:

Study Coefficient - b

Rathe [dry asphalt) Rathe (dry concrete)

(11

Lewis ( a l l s i t e s ] 133

Ullriche (all sites) (4

3

41.2

A median value of b = 35 was found to give

a

reasonably good fit

to all available d a t a s e t s and was adopted f o r this model,

The n o i s e e m i t t e d by heavy vehicles has a more complicated depen-

dence on v e h i c l e speed. Studies of the passby nsise f r o m individual

heavy v e h i c l e s ( 2 , 6 ) show t h a t noise from the power t r a i n (engine, ex-

h a u s t , erc.) tends t o dominate at law s p e e d s , b u t t i r e noise becomes

increasingly significant at h i g h e r speeds and t e n d s t o dominate a t s p e e d s

above 80 km/h, A t speeds where tire noise dominates, the speed dependence o f the n s i s e emissions is very similar t o t h a t f o r light vehicles. A t speeds below about 80 krn/h, t h e noise depends primarily

on

engine speed

and because d r i v e r s t e n d t o s h i f t gears often to m a i n t a i n optimum e n g i n e speed, the noise is less dependent

on

vehicle speed. The f i n a l form of t h e curve for heavy vehicles

in

Figure 1.1 was obtained by a detailed corn- p a r i s o n with actual f i e l d measurements.

For light vehicles, the assumed speed dependence of t h e maximum p a s s -

by n o i s e l e a d s to an expression f o r the equivalent sound l e v e l n e a r t h e

where S is t h e speed

in

kilometres p e r hour, N is t h e number of light vehicles per 24 hours and R is a constant that depends primarily on t h e

l o c a t i o n of t h e point of reception and on the type o f r o a d surface.

The v a r i a t i o n in a c t u a l road surfaces w i l l presumably be one s o u x e of scatter

i n

t h e r e l a t i o n s h i p between measured and predicted n o i s e Levels. Because at any s p e c i f i c site this f e a t u r e may change appreciably due t o

a g i n g and deliberate changes

i n

surface, it seems reasonable t o ignore it in a model used for long-term planning.

Equation 1 . 1 can b e adapted for a t r a f f i c flow i n c l u d i n g heavy

v e h i c l e s by t r e a t i n g each heavy vehicle as equivalent t o t light vehicles.

The value of t f o r any t r a f f i c speed is such that 10 log10

_It)

equals the d i f f e r e n c e between the maximum passby n o i s e emirted by light and heavy vehicles at t h a t speed, as sham in Figure 1 . 1 . The values of t for common traffic speeds are presented

in

T a b l e 1.1.

Table 1.1

Values sf t f o r Cornon Traffic Speeds

Traffic Speed (km/h) Appropriate Value of t

40 2 1

5 0 18

60 16

70 14

80 o r greater 13

Using t h e s e v a l u e s , t h e expression f o r t h e equivalent sound l e v e l 30 m from t h e road c e n t r e l i n e nay be expressed as:

where x i s t h e f r a c t i o n o f N t h a t arc heavy v e h i c l e s t is t h e appropriate value from T a b l e 1.1.

The value of R = 26 dB was obtained by fitting Eq 1 . 2 to a c t u a l traffic n o i s e data, taking

S

to be the posted speed. The curves

i n

Figure 1 . 2 present the levels predicted by Eq 1 . 2 f o r common p o s t e d t r a f f i c speeds. Note that t h e s e curves and t h e equation assume free- flowing t r a f f i c on a l e v e l road, and r e q u i r e f u r t h e r corrections in t h e presence of barriers or ground a t t e n u a t i o n . These corrections a r e d i s -

V E H l C L E S P E E D , k m l h F I G U R E 1 . 1 A S S U M E D R E L A T I V E P E A K N O I S E L E V E L S FOR I N D l V I D U A C V E H I C L E P A S S - B Y S . THE S O L I D L l N E A N D D A S H E D L l N E R E P R E S E N T THE P E A K L E V E L S

F O R

H E A V Y V E H I C L E S A N D L I G H T V E H I C L E S , R E S P E C T I V E L Y 1 2 5 10 20

50

100 200 E F F E C T I V E T R A F F I C F L O W ( N e t f l , 1000 V E H l C L E S i Z 4 h F I G U R E

1.2

P R E Q l C T E D E Q U I V A L E N T S O U N D L E V E L l L e q 124 h l l A T 30 m F R O M C E N T R E L I N E ( B E F O R E C O R R E C T I O N S )

2. CORRECTION FOR ROAD Gk4UIENT

The e f f e c t of a r o a d gradient on the n o i s e emitted by t r a f f i c has been discussed in several studies (7 t o 1 0 ) . There is general agreement t h a t n o i s e

emission from

light

vehicles

i s

not

appreciably affected by typical road gradients. With regard to heavy v e h i c l e s , most s t u d i e s agree t h a t t h e r e is some e f f e c t , b u t t h e y differ a p p r e c i a b l y in

their

conclusions a s to t h e magnitude of the e f f e c t and its dependence on gradient. In p a r t

t h i s may be ascribed t o t h e different noise d e s c r i p t o r s used i n t h e v a r i o u s

s t u d i e s or to d i f f e r e n c e s between the vehicle populations s t u d i e d . The

differences, however, may also be due to o t h e r parameters (such as t h e

length o f t h e incline) which have generally been i g n o r e d .

When analysed with respect to an individual vehicle, t h e problem i s r a t h e r complicated, On an upgrade, the i n s t a n t a n e o u s engine and exhaust n o i s e a r e increased because of the increased power requirement, b u t i n - stantaneous tire noise is decreased i f t h e r e i s a reduction in vehicle s p e e d . On a downgrade t h e converse is true. Because o f the difference in passby d u r a t i o n , the noise from vehicles on t h e upgrade will c o n t r i b u t e more of the t o t a l sound energy t h a n would be i n f e r r e d from the maximum passby sound l e v e l s a l o n e . The balance between these effects f o r an a c t u a l road with traffic travelling in both directions depends on the c h a r a c t e r - i s t i c s of the heavy vehicles and on the speed profile of t h e passbys

(which in turn depends on t h e posted speed l i m i t and t h e l e n g t h of t h e incline). The problem may be f u r t h e r complicated if t h e r e c e i v i n g point is near t h e end of t h e inclined s e c t i o n , o r i f t h e d i s t a n c e s from the

r e c e i v i n g p o i n t to the uphill and downhill lanes are appreciably d i f f e r e n t . The c o r r e c t i o n t o t h e e q u i v a l e n t sound l e v e l presented in F i g u r e 2 . 1

i s based on t h e approximate correction proposed i n Ref.

[ l o ) ,

which appears

to b e based on t h e most complete analysis of t h e relevant v a r i a b l e s a n d -

f a l l s in the mid range of t h e corrections proposed i n t h e l i t e r a t u r e . Some extrapolation was necessary to extend the correction to situations where

t h e percentage of heavy v e h i c l e s is less than 10 per c e n t , b u t t h e possible

0

1

2

3

5

1 0

20

P E R C E N T A G E OF H E A V Y

V E H I C L E S

F I G U R E 2 . 1

C O R R E C T I O N T O

P R E D I C T E D

L e q

( 2 4

h ) T O A L L O W F O R R O A D

G R A D I E N T S

3 .

NOISE

SOURCE LOCATION

The preceding s e c t i o n s d e a l w i t h The sound energy emitted by t r a f f i c . In o r d e r to p r e d i c t how much of t h a t sound energy reaches a receiver l o c a t i o n , it is necessary t o d e f i n e the position of t h e source relative to t h e receiver. Because a multilane road with a mixture of

l i g h t and heavy vehicles is a complicated distributed source, the r u l e s

formulated here f a r l o c a t i n g a nominal s i n g l e source position involve some approximations. '1'0 keep t h e r e s u l t i n g errors,within reasonable bounds, it i s sometimes necessary t o t r e a t a road system as two or more s e p a r a t e sources, and to c a l c u l a t e t h e t o t a l sound level by combining

the sound energy r e a c h i n g t h e r e c e i v e r from each source.

This model u s e s the b a s i c rule t h a t the nominal source position i s

midway between the o u t e r edges o f t h e paved road surface [ i . e . , at t h e

c e n t r e l i n e o f t h e r o a d ) .

If

t h e distance from t h e receiver p o s i t i o n to the nearest edge o f t h e pavement i s l e s s t h a n h a l f t h e d i s t a n c e to t h e nominal source p o s i t i o n , t h e source should be d i v i d e d into t w o or more sources each of which s a t i s f i e s the above requirement. This procedure is illustrated

in

Figure 3.1 f o r t h e common case o f a four-lane highway with a wide median s t r i p . The t r a f f i c f l o w i s assumed t o be e q u a l l y

d i v i d e d among t h e lanes.

The attentuation o f n o i s e when propagated over a d i s t a n c e (particu- larly if the path is interrupted by a b a r r i e r ) depends on t h e h e i g h t of

t h e source relative t o t h e ground and to t h e top of the barrier.

The primary sources of n o i s e from automobiles and l i g h t t r u c k s a r e t h e power t r a i n , t h e exhaust, and the interaction of the tires w i T h t h e

r o a d surface. Exhaust outlets on l i g h t v e h i c l e s a r e u s u a l l y s i t u a t e d

a b o u t 0 . 3 m above the read surface. Noise from the tire-road interaction i s generated very near the road surface, b u t reflections from t h e vehicle

underbody and rattle from t h e undercarriage may a l s o c o n t r i b u t e , Taking

a l l these f a c t o r s i n t o a c c o u n t , a source h e i g h t of 0.3 m is cansidered a p p r o p r i a t e f o r light vehicles,

For heavy vehicles, a larger f r a c t i o n of t h e sound energy is a t t r i -

b u t e d to engine compartment and exhaust n o i s e , particularly a t Pow s p e e d s .

A t speeds below 30 kmJh the noise emitted by such v e h i c l e s appears to be

reasonably well represented by a s i n g l e source located approximately 2.4 m above t h e road surface. Since engine speeds are generally h e l d within close limits, the maximum passby noise from t h i s s o u r c e tends to be i n d e - pendent of speed ( 2 , 6 ) . As in t h e case of light vehicles, t h e t i r e - r o a d

interaction produces a level t h a t increases with increasing speed and is the dominant source at h i g h speeds. Bearing in mind t h e contributions

of

t h e power train, undercarriage rattIe, and reflections from t h e underbody,

t h i s source was a s s i g n e d a h e i g h t o f 0.3 rn.

Thus a line o f t r a f f i c can be viewed as two l i n e sources;

one

a t 0.3 m and one at 2.4 m above the road surface with t h e i r relative s t r e n g t h s de- pending on the traffic speed and the fraction o f heavy v e h i c l e s .

require a separate c a l c u l a t i o n f o r each o f t h e t w o sources, with the two calculated levels combined according t o t h e i r energy to give the resultant l e v e l .

To

simplify t h i s calculation, a single e f f e c t i v e source height can be d e r i v e d t h a t , for any combination o f t r a f f i c speed and mix, will g i v e approximately t h e same resultant sound level as t h e combination

of

the two sources.

The f r a c t i o n of the t o t a l sound energy generated by heavy v e h i c l e s

can be determined from the expression

wherc

x

= f r a c t i o n of heavy v e h i c l e s ,

t = coefficient from Table 1.1 (p.

1

f o r each speed and traffic mix. Assuming t h a t a t 110 km/h t h e n o i s e emitted from heavy vehicles is dominated by tire noise (90 per cent of t h e t o t a l sound power) which decreases by 12 dB p e r halving of t h e speed," and u s i n g Figure 1 . 1 , t h e fraction of heavy v e h i c l e noise emitted at a height of 2.4 m for each t r a f f i c speed can be determined. Using these

two results i t is possible t o c a l c u l a t e t h e f r a c t i o n of the t o t a l sound energy a s s o c i a t e d w i t h each of t h e two source h e i g h t s as a function o f both speed and fraction of heavy vehicles. The f r a c t i o n associated with each source

is

then easily reduced to a noise l e v e l (in decibels) relative

t o t h e t o t a l n o i s e .

If a b a r r i e r i n t e r r u p t s t h e propagation o f t h e t r a f f i c noise, t h e

a t t e n u a t i o n due to t h e barrier will depend on t h e d i f f e r e n c e in h e i g h t

between t h e top of t h e barrier and each source; thus t h e two sources a t

0.3 and 2.4 m will be a t t e n u a t e d d i f f e r e n t l y . The resultant level a f t e r attenuation by t h e barrier is obtained by considering each of the sources separately and then combining the two l e v e l s .

If t h e difference between t h e resultant level behind t h e barrier

and t h e level in the absence of t h e b a r r i e r i s taken as t h e barrier

a t t e n u a t i o n , it is possible t o invert t h e calculation and derive the h e i g h t of a single source which would g i v e t h e same o v e r - a l l barrier attenuation as obtained by considering the two sources s e p a r a t e l y . T h i s h e i g h t is t h e e f f e c t i v e source h e i g h t and is a function of speed and f r a c t i o n of heavy vehicles.

This calculation was performed far 72 different barrier c o n f i g u r a t i a r s

and the arithmetic average o f t h e results taken to o b t a i n t h e curves i s

shown in Figure 3.2. The spread in values, of t h e effective source h e i g h t ,

on the average was about *0.3 rn which translates i n t o a p o s s i b l e error of r o u g h l y t 1 dB f o r most practical barrier configurations.

"This is equivalent to assuming that at 30 km/h t h e noise e m i t t e d from

4. CORRECTIONS FOR DISTANCE AND GROUND ATTENUATION

The preceding t w o s e c t i o n s a r e concerned w i t h t h e prediction of t h e

sound e n e r g y emitted by road t r a f f i c under various traffic conditions.

The p r e d i c t e d value is t h e nominal sound pressure l e v e l t h a t would be observed at a reference point 30 m from thc centreline if t h e ground surface i s f l a a and p e r f e c t l y r e f l e c t i n g and i f t h e source may be t r e a t e d as an i n f i n i t e l y long s t r a i g h t l i n e over t h a t surface. It

is

necessary

to provide a means of calculating the sound level at d i s t a n c e s o t h e r t h a n 30 m from t h e noise source, and to provide corrections to allow for devia- t i o n s from the idealized representation o f t h e source and ground surface.

Because materials such as concrete, a s p h a l t , and hard-packed e a r t h

provide l i t t l e a c o u s t i c a l a b s o r p t i o n , c a l c u l a t i n g the propagation over a p e r f e c t l y reflective surfacc provides a reasonable estimate of t h e actual situation in t h e s e cases. This estimate is used i n t h e present model if

more than h a l f the ground between the s o u r c e and the r e c e i v e r h a s a "hard'"

s u r f a c e s u c h as those noted above. In such cases, f o r a line source t h e correction for the actual source-receiver distance is g i v e n by:

?

~ t t e n u d i o n w i t h distance = 10 log (D/30) _{E4 13}

\

where D i s the horizontal d i s t a n c e i n metres from the receiving point to

t h e s o u r c e .

A l t h o u g h t h i s has t h e same form as the u s u a l expression f o r geome-

t r i c a l spreading from a line source, only the horizontal component o f t h e sourcc-receiver d i s t a n c e is used. T h i s r e s u l t s in a p r e d i c t e d i n c i d e n t

sound level which i s h i g h e r t h a n t h a t e x p e c t e d f o r geometrical spreading

by 5 l o g (1 + h2/Il2) where h is the h e i g h t of t h e receiver relative t o

t h e s o u r c e . This approach was adopted because the design procedure i s

aimed primarily at p r e d i c t i n g the indoor sound level. The e f f e c t of u s i n g

horizontal r a t h e r t h a n s l a n t distance is compensated f o r by the reduction o f the facadets sound transmission loss as t h e r a n g e of angles of incidence

s h i f t s f u r t h e r from normal incidence. I n t h e idealized case o f a limp

partition, t h e n o i s e reduction v a r i e s approximately a s 10 l o g ( c o s 8 )

where B is t h e angle o f incidence relazive to the normal to the facade

(11 t o 1 3 ) . For a real wall t h e dependence on t h e a n g l e of incidence i s

more

complicated, particularly

in

t h o s e cases where t h e facade h a s irre- gularities such as balconies o r recessed windows, but t h e trend towards lower n o i s e r e d u c t i o n with h i g h e r angles o f i n c i d e n c e s t i l l p e r t a i n s .

For most suburban situations t h e d i f f e r e n c e between horizontal and

s l a n t d i s t a n c e is insignificant. T h e r e is o n e obvious situation, however, i n which t h e slant distance t e n d s t o be much larger t h a n t h e horizontal

distance, i . e . , t h e case o f h i g h - r i s e buildings i n an urban core. In such situations t h e rate o f decrease in the outdoor sound level with increasing receiver height is much less t h a n would be predicted f o r geometrical

spreading from a line source because of multiple reflections from building

facades. I n t h e s e cases the present model (which assumes the outdoor

sound level t o be independent of r e c e i v e r height) provides a more accurate

p r e d i c t i o n o f the outdoor l e v e l t h a n would r e s u l t from use of t h e slant distance.

I n most s i t u a t i o n s , much of t h e ground s u r f a c e between the n o i s e source and

a

building facade may be covered with g r a s s , shrubs,

o r

o t h e r v e g e t a t i o n . T h i s causes a further seduction of t h e sound

( i n

addition

t o the

distance

correction af E q . 4 - 1 1 commonly referred to as '?excess

ground attenuationR'. Current understanding of the physics o f this effect i s s t i l l incomplete, although t h e major features can be explained (14,151.

A detailed physical evaluation o f t h e ground effect requires a knowledge of atmospheric turbulence and the acoustical impedance of t h e surface, and involves

extensive

c a l c u l a t i o n s that would be o u t of p l a c e

i n

a simple p r e d i c t i o n model such as this. Fortunately, it i s possible t o i n c l u d e many of t h e relevant physical considerations in a simple empirical model.

Our treatment of t h i s problem is largely based on a model developed in

Sweden (lo), w i t h some modifications and extensions to s u i t p r e s e n t re- quirements. Figure 4 . 1 shows the predicted ground attenuation as a func- tion o f t h e d i s t a n c e from t h e source to t h e r e c e i v i n g p o s i t i o n , and a parameter called the "total effective h e i g h t " . The curves in t h i s Figure are very c l o s e approximations to the corresponding curves in Figure 1 2 of Ref. 10.

The effective t o t a l h e i g h t (denoted 14 in E q . 4.2) was introduced ta deal with the effect

on

t h e ground a t t e n t u a t i o n of v a r i a t i o n s

i n

t h e source or t h e receiver heights above the ground surface, or the intro- d u c t i o n of an obstacle between t h e s o u r c e and receiver.

For a n o i s e source c l o s e to a f l a t grassy s u r f a c e , with no inter- vening b a r r i e r , t h e e f f e c t i v e

t o t a l

h e i g h t i s simply equal to t h e h e i g h t of t h e r e c i e v e r r e l a t i v e to t h e ground surface, as shown i n F i g u r e 4 . 2 [ a ) . This situation has been extensively studied b a t h theoretically and experi- mentally and is the case for which tlze curves o f Figure 4 . 1 were initially f o r m u l a t e d ( 1 4 ) - For receiver heights more than a few metres above the

ground surface, t h e ground attenuation depends primarily on the angle o f

t h e propagation path r e l a t i v e t o the surface. For propagation paths v e r y

near t h e ground surface, t h e attenuation is limited due to t h e e f f e c t o f so-called ground and surface waves.

If the n o i s e source i s raised appreciably above t h e surface, the ground attenuation is reduced. As i n d i c a t e d in F i g u r e 4.2Cb) this i s in- corporated i n t h e model by using the sum o f source and reciever h e i g h t s as

the

effective total height f o r c a l c u l a t i n g t h e ground attenuation.

T h i s approach is based on the premise that the angle between the reflected

r a y and t h e surface is t h e primary physical variablc d e t e r m i n i n g t h e ground

attenuation, as shown in Figure 4 . 3 . This is equivalent to a s s u m i n g t h a t ground a t t e n u a t i o n , f o r a given horizontal separation, is determined by the average h e i g h t above t h e ground s u r f a c e of the d i r e c t r a y from t h e

source to the receiver. In practice, interference between t h e d i r e c t and r e f l e c t e d r a y s , and o t h e r physical c o n s i d e r a t i o n s lead to some d e v i a t i o n s from this model, b u t it does provide an easy-to-use correction w i t h t h e

appropriate trend.

Because

much of t h e noise

from

road t r a f f i c comes

from n e a r t h e road surface, t h e e f f e c t

of

this adjustment t o t h e effective t o t a l h e i g h t is usually r a t h e r small.

expected

if

a roadside barrier or o t h e r obstruction interferes with sound waves r e f l e c t e d

from

the surface. In some cases t h i s r e d u c t i o n

in

ground attenuation may be so large that adding a b a r r i e r actually increases t h e sound r e a c h i n g some receiver positions (16,17). '[he calculation of t h e e f f e c t i v e total height f o r some common configurations i s illustrated

in

F i g u r e s 4.2(c) to [g]. In t h e s e cases it was assumed t h a t t h e ground a t t e n u a t i o n depends on t h e arithmetic mean o f t h e average heights above t h e ground s u r f a c e o f the d i r e c t r a y from t h e source to t h e top of the obstruction and the d i r e c t ray f r o m there t o the receiver. These rules f o r calculating the e f f e c t i v e t o t a l h e i g h t do not deal p e r f e c t l y with all possible configurations, bur do produce the correct trends in most situa-

t i o n s

as v e ~ i f i e d by comparison w i t h experimental r e s u l t s .

The r e s u l t i n g effective t o t a l height and the horizontal source- r e c e i v e r d i s t a n c e can then be used to o b t a i n the ground attentuation from

Figure 4 - 1 or from the mathematical expression:

Excess ground attenuation = 8 . 2 l o g [ _{2 + H + H2JGO} D _{+ 60/D} ] - 3 d B 1 4 . 2 1

where D is t h e horizontal distance from t h e source t o the receiver and-H is t h e "effective total h e i g h t ' ? [discussed below), b o t h expressed in metres. T h i s correction

is

a p p l i e d in this model when more than h a l f t l ~ e ground

surface between t h e source and receiver i s acoustically " s o f t " , and is subject to the following mathematical limits:

(a] If Fl is less than 1.5 m, t h e v a l u e 11 = 1.5 is used. (bl If D is g r e a t e r than 400 m, the value D = 400 i s u s e d .

( c ) If t h e value calculated using E q . 4.2 is n e g a t i v e , t h e excess ground attenuation = 0 dB.

T h i s , t o g e t h e r w i t h the predicted noise l e v e l at 30 rn from t h e c e n t r e -

l i n e , and t h e d i s t a n c e attenuation correction of E q . 4.1 y i e l d s t h e pre- dicted sound l e v e l at the r e c e i v i n g p o i n t , i n the absence of a b a r r i e r .

H O F I Z O N T A L D I S T A N C E . n C O R A L t T l O N T O P R E D I C I E P I T O A L L O W F O R G R O U N D A T T E N U A T I O N e q S O U R C E R E C E I V E R / 4 - I / 0 I 0 0 / / /

,

E F F E C T I V E 1 0 /- T O T A L 0 H E t G H T = r+S X 7 I? I S , *T

'T

R I 5 \ % ,-..>4. . . >

( a l TOTAL EFFECTIVE HEIGHT = R _{lbl TOTAP EFFECTIVE HEIGHT 4 - 5}

I c l rOTAL EFFECTIVE HEICtlT = 5 t P R _{lrll TOTAL EFFECTIVE HE! GHT} s + P

-

H

lgl tOT4i EFFECTIVE HEIGHT = 5

-

t - 3 . R F I G U R E 4 . 2 C A L C U L A T I O N O F T O T A L E F F E C T I V E H E I G H T FDR 50:,iE CORlAlON C O N F I G U R A r l Q N S F I G U R E 4 . 3 DETERMINI M G E F F E C T I V E T O T A L H E I G H T F O R G R O U N D A T T E N U A T l ON C A L C U L A T i O N 5

5 . ATTENUATION BY

AN

INFINITELY

LONG BARRIER

T h e most widely used model f o r predicting b a r r i e r attenuation i s that developed by Maekawa f o ~ a p o i n t noise source above

a

hard ground surface (181. It: i s based

on

experimental data, but an approximate ana-

l y t i c a l expression i n terms of t h e F r e s n e l number (N) has been d e r i v e d

( 1 g ) . Although t h e r e is an i n h e r e n t frequency dependence of t h e b a r r i e r

attenuation, i t i s commonly assumed t h a t t h e b a r r i e r a t t e n u a t i o n f o r A- weighted t r a f f i c noise can be approximated by t h e attenuation at 50U Hz,

far which M = 26/A = 3 . 3 6 where 6 i s t h e p a t h l e n g t h d i f f e r e n c e and X is t h e wavelength i n metres (19). With t h i s s u b s t i t u t i o n , the b a r r i e r atte-

nuation f u ~ a p o i n t source can be expressed as:

Barrier attenuation = 20 l ~ ~ [ ~ / t a n h G ] + 5 dB, f o r 6>0

= 20 16 l / t a n a ] 6 1 ] + 5 dB, f o r -0.6m <6<0

= 0 dB, f o r 6 ~ - 0 . 0 6 m C5.11

A f u r t h e r e x t e n s i o n was p r o v i d e d by Kurze and Anderson who con-

s i d e r e d the case of an incoherent l i n e source ( 1 9 ) . T h e i r a n a l y s i s was

s u b j e c t to f o u r major simplifying assumptions:

1. The source is an i n f i n i t e l y long, straight i n c o h e r e n t line source o f u n i f o r m strength per u n i t l e n g t h .

2 . The barrier i s o f uniform h e i g h t throughout its l e n g t h and

i s p a r a l l e l t o t h e source.

3 . No effects such as turbulence o r a t m o s p h e r i c a b s o r p t i o n are associated with the propagation medium.

4 . The ground surface i s f l a t and p e r f e c t l y r e f l e c t i n g .

Although these assumptions permit a s t r a i g h t f o r w a r d m a t h e m a t i c a l

treatment of t h e problem, they do n o t a p p l y very well t o t h e conditions actually encountered in roadside barrier applications, Hence a somewhat d i f f e r e n t treatment o f barrier attenuation has been adopted f o r t h e p r e s e n t model. Because it i s b e l i e v e d that r e f l e c t i o n s from other surfaces and atmospheric e f f e c t s such as wind and turbulence w i l l l i m i t the e f f e c t i v e - n e s s o f a b a r r i e r , an upper limit of 20 dB was put on t h e p r e d i c t e d b a r r i e r attenuation. F o r the o t h e r extreme, t h e original CMllC model made the sim- p l i f y i n g assumption that a t t e n u a t i o n approached zero at zero path l e n g t h d i f f e r e n c e , but recent extensive observations (20) demonstrated t h a t t h i s was an o v e r - s i m p l i f i c a t i o n . Accordingly, it was necessary to extend t h e

model t o i n c l u d e negative p a t h l e n g t h d i f f e r e n c e s , i . e . , receiving p o i n t s

that l i e outside t h e geometrical shadow zone o f t h e barrier as shown in F i g u r e 5.1. Although t h e b a r r i e r does n o t interrupt t h e d i r e c t sound r a y , d i f f r a c t i o n f r o m t h e b a r r i e r edge may provide up to 5 dB of a t t e n u a t i o n f o r s m a l l n e g a t i v e values of 6 . A smooth transition from 0 dB to 5 dB o f b a r r i e r a t t e n u a t i o n , essentially consisrent with t h e p o i n t source e x p r e s - s i o n i n Eq. 5.1, was developed.

In t h e intermediate situations where b a r r i e r attenuation i s between

5 dB and 20 dB, an appreciable scatter in the performance of barriers may

ground attenuation t e n d t o produce h i g h e r a t t e n u a t i o n s t h a n would be predicted from t h e K U T Z ~ and Anderson r e s u l t , as discussed i n Section 6

On

t h e o t h e r hand, reflections from nearby buildings tend to reduce t h e attenuation at most urban and suburban sites. Depending

on

its d i r e - ction, wind may increase or decrease t h e e f f e c t i v e attenuation, b u t t h e decreases in a t t e n u a t i o n tend to be more significant (16,

17).

Bearing these considerations i n mind, an expression t h a t p r e d i c t s slightly Power barrier attenuations than t h e Kurze and Anderson result was selected. The p r e d i c t e d attenuation may b e obtained e i t h e r from Figure 5.2 or from the equations:

Barrier attenuation = 20 dB

,

f o r b 6 m

= 7 . 7 logs + 14

dB

,

for .3 m<S<6 m = - 1 0 . 4 ( 6 + . 0 6 )

*

2 2 . 8 ( & + .06)', f o r -.06 m<6<.3 rn

6 BARRIERS OF FINITE LENGTH

A b a r r i e r of f i n i t e length provides less sound attenuation t h a n

an

i n f i n i t e l y long b a r r i e r because of the sound energy coming

past the

ends o f the barrier. The f r a c t i o n of the t o t a l received sound energy t h a t comes around t h e ends of a barrier depends not j u s t on t h e p o s i t i o n and s i z e o f t h e barrier but also

on

the type of ground surface. The limiting cases with a p e r f e c t l y r e f l e c t i n g surface and w i t h a n a b s o r p t i v e s u r f a c e are analysed in the following subsections, and the intermediate s o l u t i o n

used i n t h i s model is p r e s e n t e d .

6 . 1 Barrier End Corrections (Hard Ground Surface)

In the simple case where t h e ground s u r f a c e is assumed t o be f l a t and perfectly r e f l e c t i n g , it is a straightforward problem to determine t h e attenuation provided by a b a r r i e r of finite l e n g t h . The line source

may b e treated as a s e t of incoherent l i n e segments and t h e sound energy

r e a c h i n g the receiver from a l l of

these

segments combined to g i v e t h e

r e s u l t a n t sound level.

The geometry of t h e problem is shown in Figure 6 . 1 . For propagation over a f l a t perfectly reflecting surface,

in

t h e absence of b a r r i e r a t t e - nuation

{or

any other attenuation except geometrical spreading), it can be shown t h a t equal sound energy reaches R from any segment o f t h e l i n e

source subtending d 0 , independent of t h e angle B, Each segment dB (ex- pressed in degrees) c o n t r i b u t e s dBJ180 of t h e total sound energy arriving

at R from the l i n e source.

Tf

a barrier is introduced between the r e c e i v e r and a given source segment, the sound energy from that segment is t h e n reduced t o be d8/180 where

and Bfl i s t h e appropriate barrier attenuation f o r t h a t segment.

If

d @ is

sufficiently small, t h e segments may be treated as p o i n t sources and the Waekawa expression f o r barrier a t t e n u a t i o n w i t h a p o i n t source may b e used

f o r Be. F a r an i n f i n i t e l y long barrier parallel to t h e line source, numer-

i c a l , i n t e g r a t i o n u s i n g t h i s procedure y i e l d s the result obtained by Kurze

and Anderson for an incoherent line s o u r c e .

For

a l l

t h e calculations discussed below, the

l i n e

s o u r c e was d i v i d e d i n t o 6Q segments each subtending an angle dB of 3 degrees; for t h e case of an i n f i n i t e l y long barrier, t h i s was found t o g i v c essentially t h e same r e s u l t as t h e use o f 1 degree increments and it provided reasonable resolution for e v a l u a t i n g t h e effect of shortening t h e barrier. 'The b a r -

rier attenuation was calculated u s i n g the expression Barrier a t t e n u a t i o n = -10 log(Eb d0/CdO)

0 0

where 0 ranges from -88.5 degrees to +88.5 degrees and bg = 1 i f that segment o f the source i s visible beyond t h e end o f the b a r r i e r . The r e s u l t s of t h e s e c a l c u l a t i o n s are p r e s e n t e d i n Figure 6 . 2 as a f u n c t i o n of t h e angle subtended b y the barrier at t h e receiving paint-

6.2 Barrier End C o r r e c t i o n s (With Ground Attenuation]

Ground a t t e n u a t i o n lessens the change in barrier attenuation caused by r e d u c i n g t h e l e n g t h of t h e b a r r i e r . The f r a c t i o n of the total energy t h a t comes from t h e more d i s t a n t segments of the

l i n e

source is

reduced

by the ground e f f e c t , and t h e r e f o r e the change i n sound energy

caused

by t h e b a r r i e r screening those segments is a smaller fraction o f t h e t a t a l sound energy t h a n it would be f o r the hard ground case. In addition, t h e

decreased a t t e n u a t i o n a s s o c i a t e d with removing a segment o f the barrier

i s partially o f f s e t by increased ground a t t e n u a t i o n because t h e h e i g h t o f

t h e p r o p a g a t i o n p a t h i s decreased f o r t h a t segment.

I n order t o proceed w i t h a calculation of the e f f e c t o f barrier

length, an expression f o r ground attenuation with a p o i n t source was r e - q u i r e d . F o r t h e simple case with a p o i n t source at t h e ground surface,

t h e ground a t t e n u a t i o n i s given approximately by:

2Z

Grotlnd attenuation = -20 l o g [ ( L } s i n $ ]

21

where Z1 i s t h e characteristic impedance of a i r and Z2

is

t h e acoustic impedance of the surface (143. Although the equation is nominally f o r t h e case where t h e source i s on t h e ground plane, defining t h e angle $ as t h e arctangent a f t h e r a t i o s f e f f e c t i v e t a t a l h e i g h t t o h o r i z o n t a l dis- tance would introduce a dependence on thc s o u r c e h e i g h t o r o b s t r u c t i o n

h e i g h t formally equivalent to t h a t presented in Section 4 . It must be

recognized, however, t h a t Eq. 6 . 3 is a s i m p l i f i e d expression for a very complex phenomenon, and i s not f u l l y s a t i s f a c t o r y , p a r t i c u l a r l y f o r small values of $ where surface wave e f f e c t s introduce a f u r t h e r c o m p l i c a t i o n .

The e x p r e s s i o n was t h e r e f o r e recast i n t h c form

C

Ground Artenuation = 20 l o g j a s i n ( $

*

b +

d ]

where D i s t h e horizontal source-receiucr d i s t a n c e , and a, b and c are

coefficients selected to minimize differences between the line source expression of E q . 4 . 2 and the r e s u l t of i n t e g r a t i n g this p o i n t source ex-

p r e s s i o n a l o n g a l i n e sourcc. Although a p e r f e c t f i t i s not p o s s i b l e with

t h i s functional form, t h e e r r o r does n o t exceed I dB j.n t h e rangc covered

i n Figure 4 . 1 if t h e coefficients a r e given the values a = 15.5, b = .011,

c = - 5 5 and negative attenuations are t r e a t e d a s 0 dB.

F o l l o w i n g the same approach to t h e c a l c u l a t i o n o f b a r r i e r end e f f e c t s

as was used In Part 6 . 1 , t h e sound energy reaching t h e receiver from a

g i v e n segment of t h e line source i s bggedO where t h e expression g, corres- ponding to E q . 6 . 4 takes t h e form:

where b o t h the angle I) and t h e horizontal distance D depend on 0 . 'l'he

s u b j e c t t o the same conditions on dB, b and t h e summation over 8 as B

ware n o t e d f o r E q . 6.2. The second term

i n

Eq. 6 . 6 i s the ground a t t e - nuation that would be p r e d i c t e d in t h e presence o f

an

i n f i n i t e l y long barrier. To maintain consistency with t h e l i n e source model, this must

be subtracted off t o obtain t h a t p o r t i o n of t h e excess attenuation asso- c i a t e d specifically with ?'barrier attenuation". The ground attenuation expression is denoted g& in t h e second term to i n d i c a t e t h a t for each 8

it i s calculated u s i n g an e f f e c t i v e t o t a l height t h a t includes barrier h e i g h t . In t h e first term go = gJ if t h e source segment at 0 is behind

t h e barrier, but was otherwise calculated using the smaller effective total h e i g h t applicable in the absence of a barrier.

Equation 6 . 6 was evaluated far a receiver behind t h e midpoint of a barrier subtending a n g l e s ranging from 0 to 180 degrees in steps o f 6

degrees. Because of t h e i n t e r a c t i o n of ground e f f e c t and barrier attenu- ation, t h e results obtained depend on t h e positions

of

t h e barrier and s e c e i v e r r e l a t i v e to t h e source. The calculations were performed for t h e

7 7 configurations n o t e d i n Table 6 . 2 , and the mean results (averaged over a l l configurations] are presented

in

Figure 6 . 3 . The nominal barrPer a t t e n u a t i o n indicated on the curves in F i g u r e 6 . 3 is t h e attenuation ob-

tained by i n t e g r a t i n g the expression of E q . 4 . 2 for an i n f i n i t e l y long b a r r i e r [which is essentially t h e same as the line s o u r c e result of Kurze and A n d e r s o n ) . Figure 6.4 shows t h e rangc of values f o r t h e s p e c i f i c case w i t h nominal b a r r i e r a t t e n u a t i o n of 20 dB, to p r o v i d e an indication of t h e v a r i a t i o n associated with changes in the configuration. The curves have limiting values for very s h o r t and v e r y long barriers, t h a t (at l e a s t a t f i r s t glance) a r e quite disturbing.

T a b l e 6 . 2

Positions of Barrier and Receiver (Relative

t o t h e Source) Used for Calculating F i g u r e 6 . 3

Source-Receiver Source-Barrier Receiver Heights

Distance (ft) Distances (ft)

l f t l

30, 50 0, 5, 1 0 , 15, 20, 2 5 , 30

30, SO, 1100 0 , 5, 10, 15, 20, 2 5 , 30

30, 50, 100 0 , 5, 1 0 , 15, 20, 25, 30

30, 50, 100 0, 5, 10, 15, 20, 2 5 , 30

F o r a b a r r i e r of zero length, this calculation predicts a s i g n i f i c a n t

b a r r i e r attenuation as illustrated in F i g u r e 6 . 3 .

This

attenuation is simply t h e d i f f e r e n c e between t h e ground attenuation in the absence of a

infinitely long barrier (the second term in E q . 6.61. T h i s might be

d e s c r i b e d as the s i t u a t i o n where a telephone p o l e is t r e a t e d as a b a r -

rier. The ground a t t e n u a t i o n c a l c u l a t i o n (as p r e s e n t e d i n Section 4)

allows f o r only two cases: a b a r r i e r i s , or is n o t , present. Implicitly, if there is a b a r r i e r the ground e f f e c t i s a d j u s t e d as i f t h a t b a r r i e r

were a f f e c t i n g propagation from t h e e n t i r e l i n e source. Thus in t h e case of a short barrier t h e basic ground e f f e c t

calculation

underestimates t h e ground attenuation f a r those portions o f t h e source beyond t h e ends o f t h e b a r r i e r . 'l'he apparent attenuation fox a b a r r i e r of z e r o length is the appropriate adjustment of t h e ground attenhation.

The second apparent problem w i t h t h e curves

in

F i g u r e 6 . 3

is

t h a t

t h e calculated barrier attenuation for a very long barrier is greater

t h a n the nominal value. 'l'his difference a r i s e s because b a r r i e r a t t e n u -

ation and ground attenuation are not simply additive. The nominal atte- nuation for an infinitely long b a r r i e r was obtained u s i n g E q . 6 . 2 (or the Kurze and Anderson r e s u l t ) which applies if t h e ground surface is hard.

I n c l u d i n g t h e ground a t t e n u a t i o n provides more attenuation f o r t h e more d i s t a n t segments, and t h e r e f o r e i n c r e a s e s the f r a c t l a n o f x h e t o t a l sound

e n e r g y coming to the receiver from t h e nearest source segments. These

a r e the segments for which t h e path l e n g t h differences (and hence t h e

b a r r i e r attenuation) are largest. Thus the effective '!averageu b a r r i e r a t t e n u a t i o n s h o u l d be somewhat l a r g e r t h a n i s expected f o r a l i n e source on h a r d ground. In general, t h e result s h o u l d lie somewhere between t h e

Kurse and Anderson result and that predicted by Maekawa for a p o i n t source 6 . 3 Barrier End Corrections (Typical Applications)

To simplify t h e c a l c u l a t i o n s in the CMHC d e s i g n procedure, a single correction, to be used In both t h e hard and s o f t ground cases, was

desired. Because most s l t e s in urban and suburban areas have some ground surface of both types, this compromise is generally preferable t o either

o f t h e extremes considered above. The r e s u l t i n g curves agree w i t h t h e

h a r d ground r e s u l t in the limits of v e r y long or very s h o r t b a r r i e r s , and

lie between the h a r d ground and s o f t ground r e s u l t s f o r intermediate c a s e s .

Because b a r r i e r s are seldom symmetric about the r e c e i v i n g p o i n t o f interest, a set o f curves appropriate for e v a l u a t i n g t h e e f f e c t of sound

coming around only one end of t h e b a r r i e r is given in Figure 6 . 5 . The a t t e n u a t i o n provided by a b a r r i e r of f i n i t e l e n g t h i n both d i r e c t i o n s i s

o b t a i n e d by correcting first for the

short

end of t h e b a r r i e r and t h e n

using that adjusted attenuation as the nominal barrier attenuation when c a l c u l a t i n g the correction for the o t h e r end. The curves in Figurc 6 . 5

show t h e attenuation as a function of the "barrier a s p e c t ratlo"; c a l c u -

l a t i o n of this r a t i o 1s illustrated in F i g u r e 6.6.

The s~tuation may arise where there i s a b a r r i e r s h i e l d i n g p a r t of

t h e road from t h e r e c e i v i n g p o i n t , b u t t h e barrier does n o t i n t e r s e c t che l i n e from t h e r e c e i v e r t o t h e nearest p o i n t an t h e road, a s i l l u s -

trated in Figure 6 . 7 . In t h i s case a first approximation o f the barrier attenuation is calculated in the manner described previousl}?, using b a r r i e r

(1 -61/02) to obtain the p r e d i c t e d b a r r i e r

a t t e n u a t i o n .

It should b e noted t h a t the barrier attenuation in such cases

is

never more than 3 dB, and i s l e s s than 1 d B

if

t h e angle

subtended

by t h e barrier is l e s s than 3O degrees.

If

t h e predicted barrier attenuation is less than 2 dB, it is generally more accurate to ignore t h e barrier and apply only a ground attenuation correction (omitting the barrier

in

evaluating the e f f e c t i v e t o t a l height).

L I N E S O U R C E ( R O A D ) F I G U R E 6 . 1 G E O M E T R I C A L C O N S 1 D E R A T I O N S F O R B A R R I E R E N D C O R R E C T I O N A N G L E ,

8

F I G U R E 6 . 2 B A R R I E R A T T E N U A T I O N F O R S Y M M E T R I C B A R R I E R S S U B T E N D I N G T H E A N G L E

20

F O R P R O P A G A T I O N O V E R H A R D GRflllNn I P 3 I I.

C O R R E C T I O N TO THE B A R R I E R A T T E N U A T I O N TO

A L L O W FOR S O U N D C O M I N G A R O U N D ONE E N D

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I I -* _{R E C E I V E R} F I G U R F 6.6 D E T E R M I I U I N G THE " B A R R I E R A S P E C T R A T I O h ONE END DF A B A R R I E R F I G U R f 6 . 7 D E T E R M t M l N G A N G L E S F O R O F F S E T B A R R I E R

7. CURVES AND SEGMENTED

BARRIERS

The p r e d i c t i o n scheme described s o f a r assumes t h a t t h e roadway under conslderatlon 15 straight and infinitely long. T h i s assumption is adequate

in

mast situations, but t h e r e are many cases where allowance

must be made far other than a straight road,

It

can

b e shown t h a t

f o r

the case of an infinitely long, s t r a i g h t l i n e source on a smooth p e r f e c t l y reflecting plane the sound energy reaching a point due to any Pine segment depends only on t h e angle s u b - tended by that segment. T h a t i s , line segments subtending equal angles c o n t r i b u t e equal sound energy. This i s no longer true if t h e r e is ground attenuation, as in this case the segments closer to the receiving p o i n t contribute proportionately more energy. For t h e purposes of this model, however, it will be assumed that t h e rule of equal angles contributing equal energy gives an adequate approximation. On t h i s basis a procedure can be developed t o deal w i t h curved roads such as t h a t p o r t r a y e d in Figure 7.1.

The roadway s h o r n in F i g u r e 7.1 can readily be t r e a t e d as t w o

straight r o a d segments, numbered 1 and 2 , each of which contributes sound energy to t h e receiving point P . The analysis is now straightforward.

Let L1 be the sound level p r e d i c t e d a t point P i f road k , a t distance DL,

were t h e only road contributing, and L2 be t h e sound level p r e d i c t e d a t p o i n t P if road 2, at distance D Z , were the only road contributing. The

fraction of the sound energy from road 1 which actually does contribute

i s g i v e n by Q1/180 and from soad 2, by B 2 / 1 8 U [if t h e equal a n g l e , equal

energy rule is a p p l i e d ) . l'hus the sound level at poin-t: P i s g i v e n by ( i o L ~ / l Q 1

e

( 1 0 ~ 2 / 1 ~

L = 10 log [ -I-

'

fla]

180

I n more comp.licaterl situations it may be necessary to decompose t h e road- way into more t h a n t w o s t r a i g h t roads, however the e x t e n s i o n of t h e pro- cedure is straightforward.

dlsllghtXy different although closely related problem is t h a t o f a long barrier with gaps in it, such as a row of buildings between t h e re- c e i v i n g p o i n t and t h e roadway under consideration. In t h i s case L1 is

t h e level p r e d i c t e d f o r t h e situation with a continuous b a r r i e r and

L2

i s

t h e l e v e l p r e d i c t e d i n the absence o f the barrier. The angle €I1 subtcnded

by the b a r r i e r is o b t a i n e d by adding the angles subtended by each of t h e

b a r r i e r segments, and the angle O2 associated w i t h t h e gaps

is

o b t a i n e d from f12 = 1813 - b l . 'l'he resultant l e v e l is now easily o b t a i n e d by u s i n g E q . 7 . 1 .

F I G U R E

7 . 1

S E P A R A T I O N

OF

C U R V E D

R O A D

I N T O T W O

R O A D S . R O A D 1

A T D I S T A N C E

Dl, S U B T E N D I N G

A N G L E

O1

A N D

R O A D 2

A T D I S T A N C E

D 2 ,

S U B T E N D I N G A N G L E

e2

8 .

INTERRUPTED FLOW

The traffic noise source levels calculated in S e c t i o n 1 are based on t h e assumption t h a t t h e t r a f f i c is flowing f r e e l y a t constant speed.

While t h i s is usually the situation

an

freeways, it is n o t t h e s i t u a t i o n on most urban roadways where t r a f f i c l i g h t s and stop s i g n s are used t o c o n t r a 1 traffic flow and speed.

'L'he emitted sound power from each vehicle decreases as t h e vehicle decelerates approaching the s t o p , increases to a maximum a s the vehicle accelerates away from the stop, and f i n a l l y s e t t l e s back to t h e l e v e l characteristic fox free-flowing t r a f f i c when t h e v e h i c l e reaches its

c r u i s i n g speed. The equivalent sound l e v e l follows a slightly d i f f e r e n t

pattern, because the slower motion of t h e v e h i c l e s near the s t o p r e s u l t s

in t h e i r spending a longer time interval ( w i t h a corresponding increase i n t h e ~ n t e g r a t e d sound energy) in the segments o f the soad n e a r t h e s t o p

F i e l d measurements w i t h single vehicles (21) and computer studies

for single lanes o f vehicles (22) suggest that very c l o s e t o the roadslde t h e r e i s a maximum decrease i n t h e equivalent sound level o f I to 2 dB on

the approach t o a t r a f f i c l i g h t and a maximum increase o f a b o u t 5 dB on t h e accelerating side, I f t w o l i n e s of v e h i c l e s t r a v e l l i n g

i n

opposite directions a r e considered t h e n t h e r e is a r e s u l t a n t increase in equivalent sound l e v e l of up to 3 dB f o r a s h o r t distance in b o t h directions from t h e

t r a f f i c light, when measured at a distance of under 10 m from t h e r o a d s i d e .

On t h e b a s i s of these studies, t h e increase in t h e time-averaged sound power emitted from the source has b e e n assumed to have a p r o f i l e as shown i n F i g u r e 8 . 1 in the r e g i o n about t h e traffic light. T h i s p r o f i l e

ignores any t r a f f i c on t h e cross s t r e e t . The distance X a depends on The

stopping d i s t a n c e and acceleration rate and is t h e r e f o r e a f u n c t i o n of

b o t h t h e speed limit and v e h i c l e t y p e . The values given in TabIe 8 . 1 are

a first approximation o f t h e appropriate values f o r automobiles, obtained

fram Ref. 123). Information on comparative s t o p p i n g distances and acce- lerations suggests t h a t X2 is approximately f i v e times as large f o r heavy vehicles a s f o r automobiles travelling at t h e same speed.

T a b l e 8.1

Distance Travelled d u r i n g Acceleration (from test f o r some common speeds)

Speed Dlstance to reach Speed

.Ikm/h

1

x7 Cn)

The sound level at any receiving p o i n t w a s o b t a i n e d by dividing t h e