- Email: [email protected]
Noise from road traffic (interrupted flow)
Journal of Sound and Vibration (1977) 51(2), 171-181
NOISE FROM ROAD TRAFFIC (INTERRUPTED FLOW) D. GILBERT
Department of Civil Enghzeerhtg, hnperial College of Science and Technology, London SIV7 2AZ, England (Receired 16 September 1976) An equation for predicting Llo levels in urban streets has been derived from an analysis of measurements made at 190 sites in Edinburgh and elsewhere. The validity of the equation has been confirmed by an analysis of 134 measurements made in Sheffield and Rotherham. This equation included traffic variables which are at present difficult to predict, and an alternative equation that uses easily predictable variables has been derived from the Sheffield and Rotherham data. The standard errors of the two prediction methods were almost 3 riB(A). It has been shown that this error is not significantly affected by the instrumentation deployed, provided that it reaches industrial grade standards, or by the sampling period of the measured levels, provided this is not less than 15 minutes. Over the range of data studied the standard error was not significantly affected by non-linearities or discontinuities in the 22 numerical variables considered in the regression analysis nor did it vary systematically with any of 11 descriptive variables that were examined. There was some indication, however, that the regression analysis technique was not detecting significant interactions between variables. When certain of the variables dismissed as non-significant were aggregated in a level of service term and the regression analysis repeated, a significant reduction in the prediction standard error was achieved. 1. INTRODUCTION At present, a number of equations are available for predicting Llo noise levels for roads where traffic is freely flowing. These equations were derived from a consideration of the noise generally created by freely flowing traffic and cannot properly be applied to typical urban streets since intersections, traffic signals and other features often influence the traffic and result in interrupted flow characteristics. N o predictive models have been developed specifically for use in such traffic situations and yet most of the urban development, housing, etc. that is vulnerable to traffic noise is located along such interrupted flow streets. A number of studies have therefore been made at the Department of Civil Engineering, Imperial College, with the aim of evolving an effective model for the prediction of Llo levels in typical urban streets1-. This paper summarizes the initial work carried out at Imperial College to develop a provisional prediction equation. It then describes how that equation was tested and modified by using data recently acquired at Sheffield and Rotherham. The provisional equation includes a variable, the index of dispersion, whose value cannot at present be predicted. But an alternative equation is described which uses only currently predictable variables. It is based on the data from Sheffield and Rotherham. 2. THE PROVISIONAL IMPERIAL COLLEGE Llo PREDICTION EQUATION In the initial field studies, data were obtained from a wide range o f u r b a n streets in Edinburgh, London, Canterbury and elsewhere. Some 300 sites were surveyed. Traffic volumes 1"The work described in this paper was completed before the preparation of the Department of the Environment publication "Calculation of Road Traffic Noise" commenced and the information given in this paper was taken into consideration when the calculation method was drafted. 1'71
172
D. GILBERT
ranged from about 100 to about 2000 vehicles per hour (vph) and traffic flows were generally interrupted in character. The basic noise data were obtained by using Dawe sound level meters placed 1-5 metres above ground level at the kerbside. The analyses ofL~o, Lso, etc., were based on meter readings (at 4-second intervals) taken from time lapse films. Several traffic and layout characteristics were recorded, including vehicle speeds and types. Two classes of vehicles were identified--light vehicles, up to 1-5 tons, and heavy vehicles at over i-5 tons. The pattern of distribution of vehicles in the traffic stream was thought to be potentially important. The method adopted for measuring this was as follows. The pattern of arrival was recorded in terms of the distribution, by 10-second intervals, of vehicle arrivals at the site during the survey period. The data so obtained were analysed in terms of the Index of Dispersion, T, which is the ratio of the variance to the mean of the number of vehicles arriving in each 10-second interval. An index in the range 0-85 to 1.15 was taken to indicate a random or near random distribution pattern. An index below 0.85 was taken as approaching a uniform type of flow; and over 1.15 as approaching a platoon type flow. Other characteristics of the site were recorded, including the distance between building lines and the carriageway width. The gradients at almost all of the sites were less than 1 ~o. The noise, traffic and site data were then subjected to a stepwise multiple regression analysis. Though various transformations of the independent variables were tried, it was assumed that a logarithmic transformation of the volume might offer a possible basis for deriving a single model applicable to the whole range of traffic volumes likely to be encountered. To test this assumption a series of separate regression analyses were carried out for selected traffic volume ranges (200 vehicle/h bands). These analyses showed that the significant variables, the magnitude and sign of the regression coefficients were similar over a wide range of flows. The notable exception was vehicle speed which did not prove to be a significant variable when the full sample (300 sites) was analysed, but was significant for traffic flows of 1000 vehicle/h or less. The final analyses were developed for the 190 sites whose traffic volumes were 1000 vehicle/h or less. The kerbside prediction equation, eventually evolved, took the form Lao = 55.7 + 9.18 log~o Q(I + 0.09H) - 4.20 logto Vy + 2-31 T, R = 0.82, S.E.= 2"7,
(1)
where Q is the traffic volume (vph), H is the proportion of vehicles exceeding 1.525 Mg (~o), Tis the index of dispersion, Vis the mean speed of traffic (km/h) and y is the carriageway width (m). This equation explains 67 ~o of the total variation in Llo values which occurred in the 190 low traffic volume cases which were examined. The Standard Error of the estimate of the L~o value is 2-7 dB(A). Thus 95 ~o of the Lao estimates are expected to be within +5.4 dB(A) of the observed values. The substantial range of +5.4 dB(A) may largely be due to the magnitude ofthe sampling and calibration errors inherent in the technique used in recording and measuringLao levels. It may also be explained as follows: for a given traffic volume (on a street with interrupted flow) the level of L~o, as measaured over a number of 15-minute periods, can vary considerably. This question is discussed further at the end of the paper because it may have an important bearing on the validity and on the suitability for practical use ofl~9th the models developed here. 3. A RE-ASSESSMENT OF THE PROVISIONAL EQUATION To check whether a significant part of the prediction standard error arose from measurement or calibration problems, further measurements" were undertaken in Sheffield and Rotherham, but with precision-grade equipment being used. Noise levels were recorded on a Uher report L tape recorder with a Briiel and Kjaer (B & K) precision-grade sound level meter,
NOISE FRO.",!ROAD TRAFFIC
173
90
80
~ 7o
c~5~Da
e ,.4
G~
60
I
I
Lo
9
r
'
115II
:
:
!
' 'TIll
r
!00
iO
:
u n;~'
~
I000
JO000
TrcffJc volume (vehic!e/h)
Figure I. Scatter diagram showing L~o levels (short period) at 134 representative sites in Sheffield and Rotherham. Proportion HGV (~,~): o, 0--4; O, 5-9; zx, 10-19; a, 20+.
Type 2208 set to A weighting. Each survey started and ended with a pistonphone calibration signal recorded on "linear" weighting, to check the stability o f the recording. The tapes were analysed by playing them back through a B & K type 2606 measuring amplifier, a B & K type 2305 level recorder, and a statistical distribution of noise levels was obtained from a B & K type 4420 statistical distribution analyser. Sound recordings were made for 15 minutes at each of 134 sites in Sheffield and Rotherham. The sites were selected so that traffic and layout characteristics were broadly similar to those surveyed at Edinburgh and elsewhere (see Figure 1). The Edinburgh noise measurements were made at the kerbside, but the new measurements were taken with the microphone positioned 1-5 m above ground and 1 m from the building line. At most sites in the central areas of Sheffield and Rotherham, the building line coincided with the building facade, but in some suburban streets the survey points were located at the back of the footpath with the building facade no more than 2 or 3 metres further back.t Traffic, land use and layout characteristics (including gradient) were measured at each site. Speeds were recorded only at 36 sites because of limited manpower, but since most ofthe other
~g
B[
9 N
I
i
I
g
.
2~. ~.
...-
-
r149
.,. a~
-z
9
..
y
.. -not
(z~
1
I
I
i
I
I
I
~
61-.;
I
200
.
9
~
.
..
:',
9
., 9 %
}.
9
9 9
:
400
9
e
9
.."
9
,
0o
9
.
..
"
9
9
~ @
..
I
600
"
800
1
I
I
I
I
I000
1200
1400
1600
1800
TrGff~c
volume
I
!
2 0 0 0 2 2 0 0 2400
(vehicle/h}
Figure 2. Scatter diagram of LLo residuals for 134 survey sites in Sheffield and Rotherham.
1"Oakes and Tomlinson [1] compared noise measurements made at kerbside and at I metre from facades in urban streets where the pavement width varied from 3-5 metres. They concluded that in central urban areas with continuous building facades traffic noise levels at the facades do not differ significantly fi'om levels at the kerbside.
174
D. GILBERT
sites were within the central areas of the two towns, it is unlikely that the variations of mean speeds was large, and most speeds were estimated to be between 30 and 40 km/h. The provisional predictive equation was tested by comparing measured levels with predicted levels for all 134 sites, it being assumed that the traffic speed was 40 km/h at those sites where it had not been measured. The differences between predictions and measurements ranged from +5-7 dB(A) to -7-6 dB(A) (see Figure 2). The mean difference or error was -0-4 riB(A) and the standard deviation 2.7 dB(A). Significance testing of this difference revealed that it was not significant, and it was concluded that the Sheffield data had not shown any need to modify the parameters of the provisional equation. The net effect of a mean difference o f - 0 . 4 dB(A) and a standard deviation of 2.7 dB(A) is a prediction standard error of 2.8 dB(A). The scatter of the errors of the provisional equation shown in Figure 2 suggests that there is constant variance over a wide range of volumes, and certainly from 200 vehicle/h upwards. A regression analysis of the scatter data confirmed that there was no correlation between the magnitude of the error and traffic volume. 4. ALTERNATIVE PREDICTION EQUATIONS The data from the 134 sites were then used in an entirely new regression analysis, the object being to reduce the standard error inherent in the provisional predictive equation, and to develop an equation in which only currently predictable variables are used. To reduce any error caused by the omission of significant explanatory variables (e.g., street layout characteristics such as intersection frequency, distance of site from signals), the range of traffic and layout characteristics was extended. In all, 33 such characteristics were recorded. These variables are listed in Table 1. It was beyond the resources of the study to derive linear transformations of the descriptive variables for use in the multiple regression analysis. Consequently the analysis was restricted first to the 22 variables amenable t.o transformation. Finally, the analysis was restricted to the eleven most significant variables. These are shown in Table 2. The variables listed were intended to provide an adequate coverage of all the traffic and layout characteristics which might influence Llo noise levels. The only major omission in this respect was a characteristic for describing the "roughness of the traffic flow" (i.e., the amount of acceleration and deceleration in the stream of vehicles). Measures such as the level of service, index of dispersion, or the frequency of junctions are not entirely satisfactory in this respect. A number of analyses were run and the following equations were obtained for the 134 sites and the 36 samples with speed measurement: (a) for tile 134 sites, L1o = 48.50 + 10.52 logto Q(l + 0.04H) - 5.741O01o(dk + 0-5y) + 2.38 loglo G, (0"61)t (1.85)t (0"94)t R = 0-83, S.E. = 2"91 dB(A);
(2)
(b) for the 36 sites, L~o = 50"70 + 8"48 Iogto Q(I + 0.09H) - 6-11 log~o dk + 3-79 log~o G, (1 "27)t (I "86)'[" (1 "55)t R = 0.78, S.E. = 2"24 d B(A);
(3)
where Q is the traffic volume (vehicle/h), H is the proportion of vehicles exceeding 1-525 Mg ( ~ ) , y is the carriageway width, dk is the distance to the kerb from the measurement "f Figures in brackets are the standard errors of the regression coefficients.
175
NOISE FROM ROAD TRAFFIC
TABLE 1
Summary of variables recorded during Sheffield noise surveys No.
Description of variable
Variable symbol
Measurement unit
A. Quantitative 1 2 3 4 5 6 7
Q H Y d n G d~
Vehicle/h of HGV Metres Metres Number
d+ dp f fp f~, Ks V h, hI C. Cs Z,
Metres Metres No./kmt No./km No./km Peds/km km/h Metres Metres (proportion of st. length) (proportion of st. length) ~o (proportion of 6 m bays occupied) % (proportion of 6 m bays occupied) Ratio variance/mean of flow distribution No./km
8 9 10 11 12 13 14 15 16 17 18 19
Traffic volume Traffic composition Carriageway width Overall street width Number of lanes Road gradient (in excess of 1 ~o) Distance from measurement point to kerb Distance to major intersection Distance to pedestrian crossing Frequency of intersections Frequency of major intersections Frequency of uncontrolled intersections Mean pedestrian density on pavements Mean traffic speed Mean height of building (nearside) Mean height of building (farside) Continuity of building facade (nearside) Continuity of building facade (farside) Parking density (nearside)
20
Parking density (farside)
21
Index of dispersion
T
22
Frequency of bus stops
f~
%
Metres
B. Qualitative Variables 23
Level of service
24 25 26
Horizontal curvature of road Street layout Predominant land use
27
Second land use
28 29
Source of background noise Type of road
30 31 32 33
Time of survey Condition of road surface Form of control at major intersection Form of control at major pedestrian crossing
Descriptive (as Highway Capacity Manual) Descriptive Descriptive Descriptive (e.g., residential shopping) Descriptive (e.g., residential shopping) Descriptive Descriptive (e.g., single/dual carriageway) Descriptive (peak-off peak) Descriptive Descriptive Descriptive
t One uncontrolled intersection assumed equivalent to 0"5 major intersections.
point (m) and G = I, or the percentage gradient, whichever is the larger ( ~ ) . These equations differ from the provisional equation (1) in that they do not include the mean traffic speed, V, the carriageway width alone, y, or the index of dispersion, T, but, since measurements were made at the back of the footpath, do include the distance from the measurement point to the kerb, dR, and the road gradient, G. The coefficients of the log flow term vary slightly but not
176
D. GILBERT TABLE 2 Mean and standard deviation of selected variables for 134 Sheffield sites Variable Llo Q T y f~ f,, d~ G f0 d~ d
noise level (dB(A)) volume (vehicle/h) Index of Dispersion carriageway width (In) frequency of major intersections (no./km) frequency of minor intersections (no./km) distance to kerb (m) gradient (~o) frequency of bus stops (no./km) distance to nearest major intersection (m) overall street width (In)
Mean
Standard deviation
74-28 711-2 1.15 10"28 1"34 3"33 3"87 2.62 1.84 64-89 25"6
5-21 485"3 0.35 3-42 0.93 2.28 3.36 2.21 1.71 67-88 12.04
significantly between the three equations (see Table 3). In equation (2) the coefficient of H, 0.04, is markedly different in size to that in the other two equations. However, since this low coefficient of H is associated with the highest coefficient of the logarithmic term, the predictions will not differ greatly over the most likely range of traffic compositions. A major peculiarity of the results is the failure of the regression analysis to produce for this data an equation whose standard e~'ror, 2.9 dB(A), is less than the standard error, 2.8 dB(A), obtained when using the provisional equation. This may reflect a weakness in the multiple regression programme, in that it sorts the variables individually as significant or insignificant and does not apparently have the facility to examine groups of the individually insignificant variables. This characteristic of regression analysis has incidentally brought the advantage that all the variables in equations (2) and (3) are separately identifiable and predictable, whereas the index of dispersion, T, and the mean traffic speed, V, which are variables of the provisional equation, are not easy to predict (see reference [2]]'). The absence of a speed term in the equation is a further interesting feature of the regression analysis. For free flow noise predictions speed is an important explanatory variable but for interrupted flow it is likely that noise levels are largely independent of speed in the range 25--45 km/h. Attempts to include speed as an explanatory variable for all 134 sites by estimating speeds from D O E speed-flow relationships did not prove at all satisfactory. When mean speeds are low it is difficult to measure speeds reliably, particularly since in these circumstances traffic'streams are usually in a start-stop situation. The data from the 134 sites were re-examined with the object of identifying any factor which could explain the residuals (the differences between measured and predicted levels) produced by equation (2). In particular, the descriptive variables were used to see whether they explained the larger differences between prediction and measurement. The few sites where measurements were made other than at the building facade, or where the building facade was not essentially continuous, were also examined for evidence of any systematic bias. None of these I This study [21 was an investigation of how far it was possible to predict patterns of arrival for particular streets, where the other relevant traffic and layout characteristics were known. It was concluded from the study that the analysis undertaken did not provide an adequate method for predicting the typical pattern of flow in a street. However, a rule of thumb method was devised for estimating the pattern of flow based on regression analysis. This method requires the calculation of an explanatory factor, l = f 2QH/IOOy(for the meanings of the symbols see Table l). When the value of this factor is less than 60 the flow pattern can be described as uniform (T = 0"50). When the value of the factor is 180 or more the flow is platooned (T= 1"5) and in the range of 60-180 the flow is random (T= 1.0).
NOISE FROM ROAD TRAFFIC
177
TABLE 3
Vahtes of the correlation coefficients of selected explanatory variables (134 SllefiTeldsites) Correlation with Llo level (R) .A.
Variable
36 sites
134 sites
loglo Q(I + 0-09H) loglo Q(I + 0.04H) T logd logd, fp Q log~od~
0.637 0-629 0-253 0-295 0.075 0.294 0.288 0-186
0.808 0.813 0.146 0.163 0-241 0.228 0.643 0.089
examinations produced any evidence of such bias in the observations or any new significant explanatory variables. However, in this re-examination, 35 sites were identified for which a reasonable case could be made for removing them from the data set on the grounds that they had either significant levels of extraneous (generally non-traffic) noise, or exceptional weather or traffic layout conditions. Further analyses were then run using only the remaining 99 cases. An analysis using the same variables as for the derivation of equation (2) resulted in no significant changes in the values of the regression coefficient. But the standard error of estimate fell from 2"91 to 2.66 dB(A), a figure which is about equat to that of the provisional equation. For subsequent regression analyses, some of the insignificant variables were aggregated arbitrarily in a composite variable, the level of service index, S, where, S = frequency of intersection (no./km) • index of dispersion _ f T no. of traffic lanes • distance t o major intersection n • d," The regression analysis of the 99 sample sites gave the equation Llo = 54.96 + 9.66 loglo Q(1 + 0.08H) - 5.77 log~o (d, + 0-53,) + 3.1 loglo G + 0.93 Iog~o S, (0" 62)t (1.06) t (0.54) t R = 0.87, S.E. = 2"51, (4) where S appears as a significant variable. Further, the standard error of this equation is less than that of the provisional equation. The equation does not produce (for typical conditions) a significantly different result, in terms of prediction of Lao levels, from equation (2). However, it should be noted that the equation includes a "weighting" of H G V much closer to that of the IC provisional equation. The level of service term, S, produces a difference in estimate of L~o of up to 3.5 dB(A) between a site with few intersections and a congested city centre site with many intersections. 5. ERRORS IN THE PREDICTION EQUATIONS The standard errors of the equations derived are disappointingly high: that is, they are in the range 2"5 to 2.90 dB(A) and this means that the 95 % confidence limits on a predicted value are about +5 dR(A). The sources of this error may arise simply from vehicle-to-vehicle variations, acoustic propagation variability, etc., or (a) from faulty instrumentation and t Figures in brackets are the standard errors of the regression coefficients.
178
D. GILBERT
analysis, (b) as a result of short-term sampling, (c) from the omission of significant variables, or (d) from the assumed linearity of the included variables. The precision grade measuring equipment, statistical analyses, etc., were purchased to eliminate or reduce errors of the first sort. Since the standard errors obtained in Sheffield and Rotherham when using the new equipment were not significantly different from those obtained in the earlier studies when using the industrial-grade equipment, it seems unlikely that the instrumentation of data analysis techniques can be regarded as significant sources of error. Traffic characteristics vary appreciably from one 15-minute period to another, and even within a 15-minute period. Further, at low flows, sound levels can be greatly affected by the presence or absence of one or two very noisy vehicles. To examine these effects a series of surveys was undertaken at 20 sites similar to the sites encountered in Sheffield and Rotherham. Lao levels were recorded over four 15-minute periods for which traffic conditions remained essentially unchanged. Table 4 summarizes the results of these surveys. It shows that at six of the twenty sites the range of L1o values (the difference be.tween the lowest and highest recorded values) was greater than 2.0 dB(A) and in one case 5.0 dB(A). If standard errors of the predictive equations arose simply from inter-sample variation, aggregating four similar 15-minute samples should halve the standard error. The samples were aggregated in two ways: first by taking the average traffic and noise variables and comparing the average measured L~o with the L~o predicted from the average traffic variables by using equation (2) and secondly, by aggregating the separate 15-minute periods at each site to give an effective measuring period of 60 minutes and then deriving L~o and traffic Variables for this longer term period. Table 5 shows the mean differences, standard deviations and prediction errors obtained when using these different sampling techniques. There is no evidence in the data that the variations ofsampling technique significantly affect either the mean difference between prediction and observation or the variance of the predicted levels. Thus the use of 15-minute TABLE 4 Variation o f Lao at seleeted sites: means and ranges observed hi four, 15-minute surveys Volume (vehicle/h)
HGV (
Site
Mean
Range
Mean
Range
A B C D E F G H I J " K L M N O P Q R S T
110 293 336 358 435 589 646 718 862 880 1005 1146 1459 1475 1523 1685 1692 1727 2178 2259
80-124 280-304 316-318 308--444 376-496 516-704 624-660 628-808 748-936 816--1012 852-1136 1064-1204 1368-1572 1352-1572 1468-1584 1640-1780 1640-1748 1616-1856 2016-2376 2104-2364
4"5 3"8 11-5 7-8 21-8 13"4 9"4 13.1 21-0 10.5 25"6 19.8 16-9 28-7 14-9 18-6 17"9 20.0 16'9 18"9
0-10.3 1"4-5'4 4.8-15-5 5.1-9.0 16.7-33"4 10.6-15"5 7.1-11-5 9.0-15"9 19"7-21"9 7.0-18"6 24-3-27-0 17-9-23"6 15"6-18"I 26.7-31.0 12.3-18.9 14.9-20.9 16.2-20-2 14.1-31-2 14-9-18"9 17-2-21.2
Llo dB(A) ~' Mean Range 65"7 69-5 77-4 74"5 77"4 77-7 74"8 77.5 81.7 75-5 81.5 79'0 82"0 81.2 82.4 81"0 80.5 80.5 83.0 84"1
64.0-67.7 68.5-70.0 76"0-78-0 72"0-76"7 76.4-78.0 77-0-78-5 74-3-75.5 77.5-78'0 78"5-83"5 75"4-76"3 81"4-81-7 78"8-79"5 81.5-82.5 83"0-85.3 81.5-83-4 80.3-81-5 79.7-82.0 79.5-81.2 82.5-83.4 83.3-84.7
Max Llo less min Llo 3.7 1"5 2.0 4.7 1.6 1.5 1-2 0.5 5"0 0'9 0.3 0"7 1-0 2"3 1-9 1"2 2.7 1.7 0"9 1-4
179
NOISE FROM ROAD TRAFFIC
TABLE 5 Prediction error (when ushlg equation (2)) and measurement sample thne at 20 sites Mean difference between observed Standard deviation and predicted L~o of differences Measurement sample 80 x 15 minute samples 20 • 60 minute samples 20 • (mean of 4 • 15 minute samples)
(dB(A)) +1"35 +1.46 +1.37
(dB(A)) 1.91 1.83 1-75
Standard error of prediction (dB(A)) 2.34 2.34 2"22
sampling in Sheffield and Rotherham does not seem to have contributed to the variance of the prediction equation. Errors may also arise from the omission of significant variables, either as a result of experimental design or in the multiple regression analysis. The variables considered in this investigation were as listed in Table 1 and the 16 linear variables from this set were subjected to the multiple regression analysis. The residuals in equation (2) were examined to see if they could be related to any of the descriptive variables, but without success. The stepped multiple regression eliminated T, d~ a n d f a s insignificant. But when these were combined in the level of service term, S was found to be significant, and the standard error of the equation including this term was significantly lower than the standard error of the previously derived equation. It is possible that a further sub-division of vehicle classes or the inclusion of a roughness of traffic flow term would improve the predictive power of the equations. These ideas deserve further study. It is further implicit in multiple regressionanalysis that L~o varies continuously and linearly with the suggested variables loglo Q, Iog~oS, Iog~o v, etc., which are themselves continuous. In an ideal experiment, the linearity and continuity of each variable could be checked by allowing it to vary slowly while the other variables were held constant. But in the real world of traffic such experimental control is not possible, and one is largely confined to the passive role of observer. Certainly there is no evidence in the data of non-linearities or discontinuities and if such effects are present in the range of situations so far studied, they are nevertheless too small to figure significantly in the standard errors of the predictive equations. Of course this must not be taken as implying that non-linearities and discontinuities do not exist outside the range of variables studied (e.g., for flows below, say, 200 vehicle/h or speeds above 50 km/h), and it may well be that separate equations are needed to predict traffic noise for these conditions.
6. CONCLUSIONS An equation for predicting kerbside Lio levels in urban streets has been derived, based on measurements at 190 sites in Edinburgh and elsewhere. These measurements were made by using industrial-grade sound level meters and a simple analysis technique. The validity of the equation so obtained has been confirmed by an analysis of 134 measurements made in Sheffield and Rotherham. The provisional equation included a dependence on the index of dispersion, T. Since this is difficult to predict, given our present understanding of traffic, a further equation including only predictable variables was derived by using the Sheffield and Rotherham data. This equation did not include either the index of dispersion, T, or the mean traffic speed, V, and should therefore be easier to use than the provisional equation, but it gives a somewhat higher standard error.
180.
D. GILBERT
Both equations are valid for traffic volumes in the range 1000-2000 vehicle/h and for proportions of heavy goods vehicles ranging from 0 to 3 0 ~ of the total flow. The provisional equation predicts kcrbside L~o levels and may be used for streets where the carriageway width is in the range 6 to 15 metres and speeds are in the range 20-50 km/h. The Sheffield equation (2) predicts L~o levels from kerbside up to 6 metres from the kerb and over pavement. This equation can be applied to streets where the carriageway width ranges from 6 to 14 metres and where the gradient does not exceed 5 ~ . The Standard Error associated with all the derived equations was high. The investigations reported in this paper indicate that the standard error is not significantly affected either by the instrumentation deployed, provided it reaches industrial grade standards and is used carefully, or by the sampling period, provided the survey period is not less than 15 minutes. An examination of the residuals indicated that the standard error was not significantly affected by non-linearities or discontinuities in the 16 variables included in the regression analysis. This examination also showed that the residuals did not vary systematically with any of the 17 other variables, and it was concluded that these did not significantly affect the standard error. It could be argued that the standard errors associated with the derived equations is due largely to vehicle-to-vehicle variations in noise level and variations in acoustic propagation. However, current studies suggest that when sites are chosen with a restricted range of street layouts, then the standard error falls substantially. When a level ofservice term, aggregating several of the variables which had been eliminated as insignificant in the multiple regression, was submitted to the regression analysis, the standard error of the resulting predict.lye equation was markedly lower than that of the equations previously obtained. It was concluded from this that the multiple regression analysis used in this investigation was unable explicitly to detect significant interactions between variables, and that some significant part of the standard error of the predictive equations arises from these interactions. The multiple regression analysis used in the study rejected as insignificant certain variables whose interaction subsequently was found to be significant. It would seem advisable therefore in any further analysis to test for the significance of variable interactions. During this investigation it has become apparent that further work should be undertaken to explore the effect of further divisions of vehicle category, layout variables, and the effect of roughness of flow. In this latter respect, the concepts of index of dispersion and level of service index are potentially useful additions to the field of traffic noise prediction. There are problems, however, associat.cd with estimating values of these variables. In the last analysis, and if we cannot reliably estimate these roughness of flow variables, there may well be a high standard error. But all the evidence suggests that there is still room for improvement to prediction equations for Llo levels associated with urban traffic.
ACKNOWLEDG M ENTS This paper was prepared in the Transport Section, Department of Civil Engineering, Imperial College. It is based on the work of D. H. Crompton and D. Gilbert, assisted for part of the study by L. George. The work described in this paper was started under contract to the Department of the Environment (Supervising Qfficer A. kassiere), and continued under contract to the Transport and Road Research Laboratory (Supervising Officer D. G. Harland).
NOISE FROM ROAD TRAFFIC
181
REFERENCES 1. B. OAKESand M. A. TOMLINSON 1973 Applied Acoustics 6, 319-322. A note on the measurement of traffic noise in congested urban situations. 2. Anon. 1971 Inlperial College of Science and Technology Department of Civil Engineering Report. Prediction of traffic arrival patterns.
NOISE FROM ROAD TRAFFIC (INTERRUPTED FLOW) D. GILBERT
Department of Civil Enghzeerhtg, hnperial College of Science and Technology, London SIV7 2AZ, England (Receired 16 September 1976) An equation for predicting Llo levels in urban streets has been derived from an analysis of measurements made at 190 sites in Edinburgh and elsewhere. The validity of the equation has been confirmed by an analysis of 134 measurements made in Sheffield and Rotherham. This equation included traffic variables which are at present difficult to predict, and an alternative equation that uses easily predictable variables has been derived from the Sheffield and Rotherham data. The standard errors of the two prediction methods were almost 3 riB(A). It has been shown that this error is not significantly affected by the instrumentation deployed, provided that it reaches industrial grade standards, or by the sampling period of the measured levels, provided this is not less than 15 minutes. Over the range of data studied the standard error was not significantly affected by non-linearities or discontinuities in the 22 numerical variables considered in the regression analysis nor did it vary systematically with any of 11 descriptive variables that were examined. There was some indication, however, that the regression analysis technique was not detecting significant interactions between variables. When certain of the variables dismissed as non-significant were aggregated in a level of service term and the regression analysis repeated, a significant reduction in the prediction standard error was achieved. 1. INTRODUCTION At present, a number of equations are available for predicting Llo noise levels for roads where traffic is freely flowing. These equations were derived from a consideration of the noise generally created by freely flowing traffic and cannot properly be applied to typical urban streets since intersections, traffic signals and other features often influence the traffic and result in interrupted flow characteristics. N o predictive models have been developed specifically for use in such traffic situations and yet most of the urban development, housing, etc. that is vulnerable to traffic noise is located along such interrupted flow streets. A number of studies have therefore been made at the Department of Civil Engineering, Imperial College, with the aim of evolving an effective model for the prediction of Llo levels in typical urban streets1-. This paper summarizes the initial work carried out at Imperial College to develop a provisional prediction equation. It then describes how that equation was tested and modified by using data recently acquired at Sheffield and Rotherham. The provisional equation includes a variable, the index of dispersion, whose value cannot at present be predicted. But an alternative equation is described which uses only currently predictable variables. It is based on the data from Sheffield and Rotherham. 2. THE PROVISIONAL IMPERIAL COLLEGE Llo PREDICTION EQUATION In the initial field studies, data were obtained from a wide range o f u r b a n streets in Edinburgh, London, Canterbury and elsewhere. Some 300 sites were surveyed. Traffic volumes 1"The work described in this paper was completed before the preparation of the Department of the Environment publication "Calculation of Road Traffic Noise" commenced and the information given in this paper was taken into consideration when the calculation method was drafted. 1'71
172
D. GILBERT
ranged from about 100 to about 2000 vehicles per hour (vph) and traffic flows were generally interrupted in character. The basic noise data were obtained by using Dawe sound level meters placed 1-5 metres above ground level at the kerbside. The analyses ofL~o, Lso, etc., were based on meter readings (at 4-second intervals) taken from time lapse films. Several traffic and layout characteristics were recorded, including vehicle speeds and types. Two classes of vehicles were identified--light vehicles, up to 1-5 tons, and heavy vehicles at over i-5 tons. The pattern of distribution of vehicles in the traffic stream was thought to be potentially important. The method adopted for measuring this was as follows. The pattern of arrival was recorded in terms of the distribution, by 10-second intervals, of vehicle arrivals at the site during the survey period. The data so obtained were analysed in terms of the Index of Dispersion, T, which is the ratio of the variance to the mean of the number of vehicles arriving in each 10-second interval. An index in the range 0-85 to 1.15 was taken to indicate a random or near random distribution pattern. An index below 0.85 was taken as approaching a uniform type of flow; and over 1.15 as approaching a platoon type flow. Other characteristics of the site were recorded, including the distance between building lines and the carriageway width. The gradients at almost all of the sites were less than 1 ~o. The noise, traffic and site data were then subjected to a stepwise multiple regression analysis. Though various transformations of the independent variables were tried, it was assumed that a logarithmic transformation of the volume might offer a possible basis for deriving a single model applicable to the whole range of traffic volumes likely to be encountered. To test this assumption a series of separate regression analyses were carried out for selected traffic volume ranges (200 vehicle/h bands). These analyses showed that the significant variables, the magnitude and sign of the regression coefficients were similar over a wide range of flows. The notable exception was vehicle speed which did not prove to be a significant variable when the full sample (300 sites) was analysed, but was significant for traffic flows of 1000 vehicle/h or less. The final analyses were developed for the 190 sites whose traffic volumes were 1000 vehicle/h or less. The kerbside prediction equation, eventually evolved, took the form Lao = 55.7 + 9.18 log~o Q(I + 0.09H) - 4.20 logto Vy + 2-31 T, R = 0.82, S.E.= 2"7,
(1)
where Q is the traffic volume (vph), H is the proportion of vehicles exceeding 1.525 Mg (~o), Tis the index of dispersion, Vis the mean speed of traffic (km/h) and y is the carriageway width (m). This equation explains 67 ~o of the total variation in Llo values which occurred in the 190 low traffic volume cases which were examined. The Standard Error of the estimate of the L~o value is 2-7 dB(A). Thus 95 ~o of the Lao estimates are expected to be within +5.4 dB(A) of the observed values. The substantial range of +5.4 dB(A) may largely be due to the magnitude ofthe sampling and calibration errors inherent in the technique used in recording and measuringLao levels. It may also be explained as follows: for a given traffic volume (on a street with interrupted flow) the level of L~o, as measaured over a number of 15-minute periods, can vary considerably. This question is discussed further at the end of the paper because it may have an important bearing on the validity and on the suitability for practical use ofl~9th the models developed here. 3. A RE-ASSESSMENT OF THE PROVISIONAL EQUATION To check whether a significant part of the prediction standard error arose from measurement or calibration problems, further measurements" were undertaken in Sheffield and Rotherham, but with precision-grade equipment being used. Noise levels were recorded on a Uher report L tape recorder with a Briiel and Kjaer (B & K) precision-grade sound level meter,
NOISE FRO.",!ROAD TRAFFIC
173
90
80
~ 7o
c~5~Da
e ,.4
G~
60
I
I
Lo
9
r
'
115II
:
:
!
' 'TIll
r
!00
iO
:
u n;~'
~
I000
JO000
TrcffJc volume (vehic!e/h)
Figure I. Scatter diagram showing L~o levels (short period) at 134 representative sites in Sheffield and Rotherham. Proportion HGV (~,~): o, 0--4; O, 5-9; zx, 10-19; a, 20+.
Type 2208 set to A weighting. Each survey started and ended with a pistonphone calibration signal recorded on "linear" weighting, to check the stability o f the recording. The tapes were analysed by playing them back through a B & K type 2606 measuring amplifier, a B & K type 2305 level recorder, and a statistical distribution of noise levels was obtained from a B & K type 4420 statistical distribution analyser. Sound recordings were made for 15 minutes at each of 134 sites in Sheffield and Rotherham. The sites were selected so that traffic and layout characteristics were broadly similar to those surveyed at Edinburgh and elsewhere (see Figure 1). The Edinburgh noise measurements were made at the kerbside, but the new measurements were taken with the microphone positioned 1-5 m above ground and 1 m from the building line. At most sites in the central areas of Sheffield and Rotherham, the building line coincided with the building facade, but in some suburban streets the survey points were located at the back of the footpath with the building facade no more than 2 or 3 metres further back.t Traffic, land use and layout characteristics (including gradient) were measured at each site. Speeds were recorded only at 36 sites because of limited manpower, but since most ofthe other
~g
B[
9 N
I
i
I
g
.
2~. ~.
...-
-
r149
.,. a~
-z
9
..
y
.. -not
(z~
1
I
I
i
I
I
I
~
61-.;
I
200
.
9
~
.
..
:',
9
., 9 %
}.
9
9 9
:
400
9
e
9
.."
9
,
0o
9
.
..
"
9
9
~ @
..
I
600
"
800
1
I
I
I
I
I000
1200
1400
1600
1800
TrGff~c
volume
I
!
2 0 0 0 2 2 0 0 2400
(vehicle/h}
Figure 2. Scatter diagram of LLo residuals for 134 survey sites in Sheffield and Rotherham.
1"Oakes and Tomlinson [1] compared noise measurements made at kerbside and at I metre from facades in urban streets where the pavement width varied from 3-5 metres. They concluded that in central urban areas with continuous building facades traffic noise levels at the facades do not differ significantly fi'om levels at the kerbside.
174
D. GILBERT
sites were within the central areas of the two towns, it is unlikely that the variations of mean speeds was large, and most speeds were estimated to be between 30 and 40 km/h. The provisional predictive equation was tested by comparing measured levels with predicted levels for all 134 sites, it being assumed that the traffic speed was 40 km/h at those sites where it had not been measured. The differences between predictions and measurements ranged from +5-7 dB(A) to -7-6 dB(A) (see Figure 2). The mean difference or error was -0-4 riB(A) and the standard deviation 2.7 dB(A). Significance testing of this difference revealed that it was not significant, and it was concluded that the Sheffield data had not shown any need to modify the parameters of the provisional equation. The net effect of a mean difference o f - 0 . 4 dB(A) and a standard deviation of 2.7 dB(A) is a prediction standard error of 2.8 dB(A). The scatter of the errors of the provisional equation shown in Figure 2 suggests that there is constant variance over a wide range of volumes, and certainly from 200 vehicle/h upwards. A regression analysis of the scatter data confirmed that there was no correlation between the magnitude of the error and traffic volume. 4. ALTERNATIVE PREDICTION EQUATIONS The data from the 134 sites were then used in an entirely new regression analysis, the object being to reduce the standard error inherent in the provisional predictive equation, and to develop an equation in which only currently predictable variables are used. To reduce any error caused by the omission of significant explanatory variables (e.g., street layout characteristics such as intersection frequency, distance of site from signals), the range of traffic and layout characteristics was extended. In all, 33 such characteristics were recorded. These variables are listed in Table 1. It was beyond the resources of the study to derive linear transformations of the descriptive variables for use in the multiple regression analysis. Consequently the analysis was restricted first to the 22 variables amenable t.o transformation. Finally, the analysis was restricted to the eleven most significant variables. These are shown in Table 2. The variables listed were intended to provide an adequate coverage of all the traffic and layout characteristics which might influence Llo noise levels. The only major omission in this respect was a characteristic for describing the "roughness of the traffic flow" (i.e., the amount of acceleration and deceleration in the stream of vehicles). Measures such as the level of service, index of dispersion, or the frequency of junctions are not entirely satisfactory in this respect. A number of analyses were run and the following equations were obtained for the 134 sites and the 36 samples with speed measurement: (a) for tile 134 sites, L1o = 48.50 + 10.52 logto Q(l + 0.04H) - 5.741O01o(dk + 0-5y) + 2.38 loglo G, (0"61)t (1.85)t (0"94)t R = 0-83, S.E. = 2"91 dB(A);
(2)
(b) for the 36 sites, L~o = 50"70 + 8"48 Iogto Q(I + 0.09H) - 6-11 log~o dk + 3-79 log~o G, (1 "27)t (I "86)'[" (1 "55)t R = 0.78, S.E. = 2"24 d B(A);
(3)
where Q is the traffic volume (vehicle/h), H is the proportion of vehicles exceeding 1-525 Mg ( ~ ) , y is the carriageway width, dk is the distance to the kerb from the measurement "f Figures in brackets are the standard errors of the regression coefficients.
175
NOISE FROM ROAD TRAFFIC
TABLE 1
Summary of variables recorded during Sheffield noise surveys No.
Description of variable
Variable symbol
Measurement unit
A. Quantitative 1 2 3 4 5 6 7
Q H Y d n G d~
Vehicle/h of HGV Metres Metres Number
d+ dp f fp f~, Ks V h, hI C. Cs Z,
Metres Metres No./kmt No./km No./km Peds/km km/h Metres Metres (proportion of st. length) (proportion of st. length) ~o (proportion of 6 m bays occupied) % (proportion of 6 m bays occupied) Ratio variance/mean of flow distribution No./km
8 9 10 11 12 13 14 15 16 17 18 19
Traffic volume Traffic composition Carriageway width Overall street width Number of lanes Road gradient (in excess of 1 ~o) Distance from measurement point to kerb Distance to major intersection Distance to pedestrian crossing Frequency of intersections Frequency of major intersections Frequency of uncontrolled intersections Mean pedestrian density on pavements Mean traffic speed Mean height of building (nearside) Mean height of building (farside) Continuity of building facade (nearside) Continuity of building facade (farside) Parking density (nearside)
20
Parking density (farside)
21
Index of dispersion
T
22
Frequency of bus stops
f~
%
Metres
B. Qualitative Variables 23
Level of service
24 25 26
Horizontal curvature of road Street layout Predominant land use
27
Second land use
28 29
Source of background noise Type of road
30 31 32 33
Time of survey Condition of road surface Form of control at major intersection Form of control at major pedestrian crossing
Descriptive (as Highway Capacity Manual) Descriptive Descriptive Descriptive (e.g., residential shopping) Descriptive (e.g., residential shopping) Descriptive Descriptive (e.g., single/dual carriageway) Descriptive (peak-off peak) Descriptive Descriptive Descriptive
t One uncontrolled intersection assumed equivalent to 0"5 major intersections.
point (m) and G = I, or the percentage gradient, whichever is the larger ( ~ ) . These equations differ from the provisional equation (1) in that they do not include the mean traffic speed, V, the carriageway width alone, y, or the index of dispersion, T, but, since measurements were made at the back of the footpath, do include the distance from the measurement point to the kerb, dR, and the road gradient, G. The coefficients of the log flow term vary slightly but not
176
D. GILBERT TABLE 2 Mean and standard deviation of selected variables for 134 Sheffield sites Variable Llo Q T y f~ f,, d~ G f0 d~ d
noise level (dB(A)) volume (vehicle/h) Index of Dispersion carriageway width (In) frequency of major intersections (no./km) frequency of minor intersections (no./km) distance to kerb (m) gradient (~o) frequency of bus stops (no./km) distance to nearest major intersection (m) overall street width (In)
Mean
Standard deviation
74-28 711-2 1.15 10"28 1"34 3"33 3"87 2.62 1.84 64-89 25"6
5-21 485"3 0.35 3-42 0.93 2.28 3.36 2.21 1.71 67-88 12.04
significantly between the three equations (see Table 3). In equation (2) the coefficient of H, 0.04, is markedly different in size to that in the other two equations. However, since this low coefficient of H is associated with the highest coefficient of the logarithmic term, the predictions will not differ greatly over the most likely range of traffic compositions. A major peculiarity of the results is the failure of the regression analysis to produce for this data an equation whose standard e~'ror, 2.9 dB(A), is less than the standard error, 2.8 dB(A), obtained when using the provisional equation. This may reflect a weakness in the multiple regression programme, in that it sorts the variables individually as significant or insignificant and does not apparently have the facility to examine groups of the individually insignificant variables. This characteristic of regression analysis has incidentally brought the advantage that all the variables in equations (2) and (3) are separately identifiable and predictable, whereas the index of dispersion, T, and the mean traffic speed, V, which are variables of the provisional equation, are not easy to predict (see reference [2]]'). The absence of a speed term in the equation is a further interesting feature of the regression analysis. For free flow noise predictions speed is an important explanatory variable but for interrupted flow it is likely that noise levels are largely independent of speed in the range 25--45 km/h. Attempts to include speed as an explanatory variable for all 134 sites by estimating speeds from D O E speed-flow relationships did not prove at all satisfactory. When mean speeds are low it is difficult to measure speeds reliably, particularly since in these circumstances traffic'streams are usually in a start-stop situation. The data from the 134 sites were re-examined with the object of identifying any factor which could explain the residuals (the differences between measured and predicted levels) produced by equation (2). In particular, the descriptive variables were used to see whether they explained the larger differences between prediction and measurement. The few sites where measurements were made other than at the building facade, or where the building facade was not essentially continuous, were also examined for evidence of any systematic bias. None of these I This study [21 was an investigation of how far it was possible to predict patterns of arrival for particular streets, where the other relevant traffic and layout characteristics were known. It was concluded from the study that the analysis undertaken did not provide an adequate method for predicting the typical pattern of flow in a street. However, a rule of thumb method was devised for estimating the pattern of flow based on regression analysis. This method requires the calculation of an explanatory factor, l = f 2QH/IOOy(for the meanings of the symbols see Table l). When the value of this factor is less than 60 the flow pattern can be described as uniform (T = 0"50). When the value of the factor is 180 or more the flow is platooned (T= 1"5) and in the range of 60-180 the flow is random (T= 1.0).
NOISE FROM ROAD TRAFFIC
177
TABLE 3
Vahtes of the correlation coefficients of selected explanatory variables (134 SllefiTeldsites) Correlation with Llo level (R) .A.
Variable
36 sites
134 sites
loglo Q(I + 0-09H) loglo Q(I + 0.04H) T logd logd, fp Q log~od~
0.637 0-629 0-253 0-295 0.075 0.294 0.288 0-186
0.808 0.813 0.146 0.163 0-241 0.228 0.643 0.089
examinations produced any evidence of such bias in the observations or any new significant explanatory variables. However, in this re-examination, 35 sites were identified for which a reasonable case could be made for removing them from the data set on the grounds that they had either significant levels of extraneous (generally non-traffic) noise, or exceptional weather or traffic layout conditions. Further analyses were then run using only the remaining 99 cases. An analysis using the same variables as for the derivation of equation (2) resulted in no significant changes in the values of the regression coefficient. But the standard error of estimate fell from 2"91 to 2.66 dB(A), a figure which is about equat to that of the provisional equation. For subsequent regression analyses, some of the insignificant variables were aggregated arbitrarily in a composite variable, the level of service index, S, where, S = frequency of intersection (no./km) • index of dispersion _ f T no. of traffic lanes • distance t o major intersection n • d," The regression analysis of the 99 sample sites gave the equation Llo = 54.96 + 9.66 loglo Q(1 + 0.08H) - 5.77 log~o (d, + 0-53,) + 3.1 loglo G + 0.93 Iog~o S, (0" 62)t (1.06) t (0.54) t R = 0.87, S.E. = 2"51, (4) where S appears as a significant variable. Further, the standard error of this equation is less than that of the provisional equation. The equation does not produce (for typical conditions) a significantly different result, in terms of prediction of Lao levels, from equation (2). However, it should be noted that the equation includes a "weighting" of H G V much closer to that of the IC provisional equation. The level of service term, S, produces a difference in estimate of L~o of up to 3.5 dB(A) between a site with few intersections and a congested city centre site with many intersections. 5. ERRORS IN THE PREDICTION EQUATIONS The standard errors of the equations derived are disappointingly high: that is, they are in the range 2"5 to 2.90 dB(A) and this means that the 95 % confidence limits on a predicted value are about +5 dR(A). The sources of this error may arise simply from vehicle-to-vehicle variations, acoustic propagation variability, etc., or (a) from faulty instrumentation and t Figures in brackets are the standard errors of the regression coefficients.
178
D. GILBERT
analysis, (b) as a result of short-term sampling, (c) from the omission of significant variables, or (d) from the assumed linearity of the included variables. The precision grade measuring equipment, statistical analyses, etc., were purchased to eliminate or reduce errors of the first sort. Since the standard errors obtained in Sheffield and Rotherham when using the new equipment were not significantly different from those obtained in the earlier studies when using the industrial-grade equipment, it seems unlikely that the instrumentation of data analysis techniques can be regarded as significant sources of error. Traffic characteristics vary appreciably from one 15-minute period to another, and even within a 15-minute period. Further, at low flows, sound levels can be greatly affected by the presence or absence of one or two very noisy vehicles. To examine these effects a series of surveys was undertaken at 20 sites similar to the sites encountered in Sheffield and Rotherham. Lao levels were recorded over four 15-minute periods for which traffic conditions remained essentially unchanged. Table 4 summarizes the results of these surveys. It shows that at six of the twenty sites the range of L1o values (the difference be.tween the lowest and highest recorded values) was greater than 2.0 dB(A) and in one case 5.0 dB(A). If standard errors of the predictive equations arose simply from inter-sample variation, aggregating four similar 15-minute samples should halve the standard error. The samples were aggregated in two ways: first by taking the average traffic and noise variables and comparing the average measured L~o with the L~o predicted from the average traffic variables by using equation (2) and secondly, by aggregating the separate 15-minute periods at each site to give an effective measuring period of 60 minutes and then deriving L~o and traffic Variables for this longer term period. Table 5 shows the mean differences, standard deviations and prediction errors obtained when using these different sampling techniques. There is no evidence in the data that the variations ofsampling technique significantly affect either the mean difference between prediction and observation or the variance of the predicted levels. Thus the use of 15-minute TABLE 4 Variation o f Lao at seleeted sites: means and ranges observed hi four, 15-minute surveys Volume (vehicle/h)
HGV (
Site
Mean
Range
Mean
Range
A B C D E F G H I J " K L M N O P Q R S T
110 293 336 358 435 589 646 718 862 880 1005 1146 1459 1475 1523 1685 1692 1727 2178 2259
80-124 280-304 316-318 308--444 376-496 516-704 624-660 628-808 748-936 816--1012 852-1136 1064-1204 1368-1572 1352-1572 1468-1584 1640-1780 1640-1748 1616-1856 2016-2376 2104-2364
4"5 3"8 11-5 7-8 21-8 13"4 9"4 13.1 21-0 10.5 25"6 19.8 16-9 28-7 14-9 18-6 17"9 20.0 16'9 18"9
0-10.3 1"4-5'4 4.8-15-5 5.1-9.0 16.7-33"4 10.6-15"5 7.1-11-5 9.0-15"9 19"7-21"9 7.0-18"6 24-3-27-0 17-9-23"6 15"6-18"I 26.7-31.0 12.3-18.9 14.9-20.9 16.2-20-2 14.1-31-2 14-9-18"9 17-2-21.2
Llo dB(A) ~' Mean Range 65"7 69-5 77-4 74"5 77"4 77-7 74"8 77.5 81.7 75-5 81.5 79'0 82"0 81.2 82.4 81"0 80.5 80.5 83.0 84"1
64.0-67.7 68.5-70.0 76"0-78-0 72"0-76"7 76.4-78.0 77-0-78-5 74-3-75.5 77.5-78'0 78"5-83"5 75"4-76"3 81"4-81-7 78"8-79"5 81.5-82.5 83"0-85.3 81.5-83-4 80.3-81-5 79.7-82.0 79.5-81.2 82.5-83.4 83.3-84.7
Max Llo less min Llo 3.7 1"5 2.0 4.7 1.6 1.5 1-2 0.5 5"0 0'9 0.3 0"7 1-0 2"3 1-9 1"2 2.7 1.7 0"9 1-4
179
NOISE FROM ROAD TRAFFIC
TABLE 5 Prediction error (when ushlg equation (2)) and measurement sample thne at 20 sites Mean difference between observed Standard deviation and predicted L~o of differences Measurement sample 80 x 15 minute samples 20 • 60 minute samples 20 • (mean of 4 • 15 minute samples)
(dB(A)) +1"35 +1.46 +1.37
(dB(A)) 1.91 1.83 1-75
Standard error of prediction (dB(A)) 2.34 2.34 2"22
sampling in Sheffield and Rotherham does not seem to have contributed to the variance of the prediction equation. Errors may also arise from the omission of significant variables, either as a result of experimental design or in the multiple regression analysis. The variables considered in this investigation were as listed in Table 1 and the 16 linear variables from this set were subjected to the multiple regression analysis. The residuals in equation (2) were examined to see if they could be related to any of the descriptive variables, but without success. The stepped multiple regression eliminated T, d~ a n d f a s insignificant. But when these were combined in the level of service term, S was found to be significant, and the standard error of the equation including this term was significantly lower than the standard error of the previously derived equation. It is possible that a further sub-division of vehicle classes or the inclusion of a roughness of traffic flow term would improve the predictive power of the equations. These ideas deserve further study. It is further implicit in multiple regressionanalysis that L~o varies continuously and linearly with the suggested variables loglo Q, Iog~oS, Iog~o v, etc., which are themselves continuous. In an ideal experiment, the linearity and continuity of each variable could be checked by allowing it to vary slowly while the other variables were held constant. But in the real world of traffic such experimental control is not possible, and one is largely confined to the passive role of observer. Certainly there is no evidence in the data of non-linearities or discontinuities and if such effects are present in the range of situations so far studied, they are nevertheless too small to figure significantly in the standard errors of the predictive equations. Of course this must not be taken as implying that non-linearities and discontinuities do not exist outside the range of variables studied (e.g., for flows below, say, 200 vehicle/h or speeds above 50 km/h), and it may well be that separate equations are needed to predict traffic noise for these conditions.
6. CONCLUSIONS An equation for predicting kerbside Lio levels in urban streets has been derived, based on measurements at 190 sites in Edinburgh and elsewhere. These measurements were made by using industrial-grade sound level meters and a simple analysis technique. The validity of the equation so obtained has been confirmed by an analysis of 134 measurements made in Sheffield and Rotherham. The provisional equation included a dependence on the index of dispersion, T. Since this is difficult to predict, given our present understanding of traffic, a further equation including only predictable variables was derived by using the Sheffield and Rotherham data. This equation did not include either the index of dispersion, T, or the mean traffic speed, V, and should therefore be easier to use than the provisional equation, but it gives a somewhat higher standard error.
180.
D. GILBERT
Both equations are valid for traffic volumes in the range 1000-2000 vehicle/h and for proportions of heavy goods vehicles ranging from 0 to 3 0 ~ of the total flow. The provisional equation predicts kcrbside L~o levels and may be used for streets where the carriageway width is in the range 6 to 15 metres and speeds are in the range 20-50 km/h. The Sheffield equation (2) predicts L~o levels from kerbside up to 6 metres from the kerb and over pavement. This equation can be applied to streets where the carriageway width ranges from 6 to 14 metres and where the gradient does not exceed 5 ~ . The Standard Error associated with all the derived equations was high. The investigations reported in this paper indicate that the standard error is not significantly affected either by the instrumentation deployed, provided it reaches industrial grade standards and is used carefully, or by the sampling period, provided the survey period is not less than 15 minutes. An examination of the residuals indicated that the standard error was not significantly affected by non-linearities or discontinuities in the 16 variables included in the regression analysis. This examination also showed that the residuals did not vary systematically with any of the 17 other variables, and it was concluded that these did not significantly affect the standard error. It could be argued that the standard errors associated with the derived equations is due largely to vehicle-to-vehicle variations in noise level and variations in acoustic propagation. However, current studies suggest that when sites are chosen with a restricted range of street layouts, then the standard error falls substantially. When a level ofservice term, aggregating several of the variables which had been eliminated as insignificant in the multiple regression, was submitted to the regression analysis, the standard error of the resulting predict.lye equation was markedly lower than that of the equations previously obtained. It was concluded from this that the multiple regression analysis used in this investigation was unable explicitly to detect significant interactions between variables, and that some significant part of the standard error of the predictive equations arises from these interactions. The multiple regression analysis used in the study rejected as insignificant certain variables whose interaction subsequently was found to be significant. It would seem advisable therefore in any further analysis to test for the significance of variable interactions. During this investigation it has become apparent that further work should be undertaken to explore the effect of further divisions of vehicle category, layout variables, and the effect of roughness of flow. In this latter respect, the concepts of index of dispersion and level of service index are potentially useful additions to the field of traffic noise prediction. There are problems, however, associat.cd with estimating values of these variables. In the last analysis, and if we cannot reliably estimate these roughness of flow variables, there may well be a high standard error. But all the evidence suggests that there is still room for improvement to prediction equations for Llo levels associated with urban traffic.
ACKNOWLEDG M ENTS This paper was prepared in the Transport Section, Department of Civil Engineering, Imperial College. It is based on the work of D. H. Crompton and D. Gilbert, assisted for part of the study by L. George. The work described in this paper was started under contract to the Department of the Environment (Supervising Qfficer A. kassiere), and continued under contract to the Transport and Road Research Laboratory (Supervising Officer D. G. Harland).
NOISE FROM ROAD TRAFFIC
181
REFERENCES 1. B. OAKESand M. A. TOMLINSON 1973 Applied Acoustics 6, 319-322. A note on the measurement of traffic noise in congested urban situations. 2. Anon. 1971 Inlperial College of Science and Technology Department of Civil Engineering Report. Prediction of traffic arrival patterns.