Correction

This article refers to:

Whole-body vibration and vertical road profile displacement power spectral density

Article title: “Whole-body vibration and vertical road profile displacement power spectral density”

Authors: Peter Múčka, George Juraj Stein and Peter Tobolka

Journal: Vehicle System Dynamics

DOI: 10.1080/00423114.2019.1595675

Authors have identified incorrect results in their paper. Trend removal of measured acceleration signal in Matlab code was inadvertently not turned on. This caused incorrect and overstated acceleration root-mean-squared values (predominantly on the seat surface). Further, the correct multiplying factors in Eq. (2) should be k_Sx = k_Sy = 1.4 in accordance with ISO 2631-1: 1997 because the vibration on the backrest was not measured. Presented incorrect results of vibration total value a_v in were substantially higher than the correct values. The authors would like to apologise for any inconvenience caused.

The corrected tables and figure are shown below:

Note: Changes are marked with red font.

Table 4. Parameters of regression function a_v = f(C,w,v) (Equation 11) for motorways, 1st and 2nd class roads.

		N	Length (km)	b1	b2	b3	b4	RMSE	R	R^2
All test sections	Ford Transit	661	132.2	0.0468	0.3571	0.5428	−0.0545	0.1642	0.773	0.597
	Hyundai	870	174	0.0154	0.3812	0.7323	0.0071	0.1371	0.780	0.609
	Skoda Citigo	668	133.6	0.0061	0.3965	0.9193	0.1328	0.1263	0.804	0.646
	Skoda Fabia	868	173.6	0.0081	0.3790	0.9494	–0.3476	0.1387	0.789	0.622
	Skoda Octavia	671	134.2	0.0109	0.3637	0.8491	–0.0720	0.1435	0.790	0.624
	Skoda Rapid	657	131.4	0.0046	0.4189	0.9702	0.0607	0.1206	0.818	0.670
	Skoda Superb	706	141.2	0.0121	0.3312	0.6911	0.3829	0.1126	0.754	0.568
	Skoda Yeti	681	136.2	0.0059	0.4252	0.9812	–0.0927	0.1223	0.859	0.737
	Volkswagen Golf Plus	664	132.8	0.0088	0.3689	0.8283	0.1059	0.1210	0.812	0.659
	All vehicles	6446	1289.2	0.0124	0.3744	0.7902	–0.0140	0.1455	0.762	0.580
Motorways	Ford Transit	203	40.6	0.0371	0.2642	0.6215	–0.3282	0.1124	0.581	0.337
	Hyundai	212	42.4	0.0155	0.1756	0.6797	0.1049	0.0873	0.557	0.310
	Skoda Citigo	224	44.8	0.0135	0.3693	0.7557	0.0702	0.0712	0.846	0.715
	Skoda Fabia	94	18.8	0.0375	0.1571	0.5336	–0.0786	0.1026	0.362	0.131
	Skoda Octavia	196	39.2	0.0031	0.3730	1.1851	–0.4389	0.1159	0.720	0.518
	Skoda Rapid	191	38.2	0.0489	0.3353	0.4974	–0.1222	0.0769	0.753	0.567
	Skoda Superb	233	46.6	0.0296	0.3153	0.5575	0.1039	0.0883	0.723	0.523
	Skoda Yeti	201	40.2	0.0710	0.3125	0.4322	–0.0864	0.0805	0.738	0.545
	Volkswagen Golf Plus	210	42	0.0120	0.3231	0.7618	0.0664	0.0658	0.853	0.727
	All vehicles	1764	352.8	0.0472	0.2985	0.5074	–0.0734	0.0978	0.666	0.443
1st class roads	Ford Transit	244	48.8	0.0164	0.3694	0.7810	–0.0172	0.1008	0.874	0.764
	Hyundai	304	60.8	0.0084	0.3444	0.8570	0.0718	0.1022	0.821	0.674
	Skoda Citigo	217	43.4	0.0013	0.4553	1.3113	–0.0803	0.1156	0.878	0.771
	Skoda Fabia	179	35.8	0.0047	0.3241	1.0059	0.0008	0.0778	0.847	0.717
	Skoda Octavia	243	48.6	0.0038	0.4146	1.106	–0.1668	0.0944	0.889	0.791
	Skoda Rapid	236	47.2	0.0017	0.4682	1.2138	–0.0390	0.0703	0.914	0.835
	Skoda Superb	241	48.2	0.0022	0.4508	1.1342	0.1095	0.0935	0.864	0.746
	Skoda Yeti	245	49	0.0045	0.4144	1.0461	–0.0825	0.0810	0.919	0.845
	Volkswagen Golf Plus	230	46	0.0034	0.4051	1.0816	–0.0579	0.0748	0.917	0.841
	All vehicles	2139	427.8	0.0041	0.3951	1.0396	–0.0003	0.1092	0.840	0.706
2nd class roads	Ford Transit	214	42.8	0.0678	0.2985	0.4914	–0.1065	0.2347	0.507	0.257
	Hyundai	354	70.8	0.0099	0.3972	0.8366	0.0219	0.1704	0.692	0.479
	Skoda Citigo	227	45.4	0.0226	0.3141	0.6680	–0.0016	0.1576	0.605	0.365
	Skoda Fabia	595	119	0.0103	0.3719	0.9137	–0.4158	0.1524	0.736	0.542
	Skoda Octavia	232	46.4	0.0189	0.3219	0.7376	–0.0727	0.1922	0.636	0.405
	Skoda Rapid	230	46	0.0035	0.3508	1.0352	0.1848	0.1705	0.692	0.479
	Skoda Superb	232	46.4	0.0232	0.3357	0.5444	0.3127	0.1321	0.603	0.364
	Skoda Yeti	235	47	0.0050	0.3371	1.0578	–0.0797	0.1665	0.784	0.614
	Volkswagen Golf Plus	224	44.8	0.0121	0.3255	0.7775	0.0770	0.1783	0.630	0.397
	All vehicles	2543	508.6	0.0158	0.3396	0.7591	–0.0668	0.1883	0.617	0.381

Table 5. Statistics of vibration total value a_v as a function of vehicle speed and road category for all tested vehicles.

			v (km/h)				C (10^-6 m^3–wrad^w^–1)		w		av (m/s^2)
	N	Length (km)	Min	Max	Mean	Std	Mean	Std	Mean	Std	Mean	Std	P10	P25	P50	P75	P90
Motorways	106	21.2	80	90	85.4	2.7	0.9	0.66	2.6	0.31	0.387	0.113	0.246	0.302	0.388	0.450	0.566
	148	29.6	90	100	95.5	2.9	0.8	0.53	2.5	0.32	0.370	0.107	0.248	0.284	0.345	0.443	0.533
	251	50.2	100	110	105.9	2.7	0.7	0.56	2.4	0.33	0.405	0.130	0.271	0.308	0.371	0.480	0.594
	555	111	110	120	116	2.7	0.7	0.50	2.4	0.32	0.427	0.144	0.280	0.324	0.392	0.490	0.640
	628	125.6	120	130	124.5	2.9	0.6	0.44	2.4	0.30	0.423	0.129	0.284	0.326	0.396	0.488	0.610
	410	82	130	140	134.3	2.8	0.6	0.47	2.4	0.33	0.425	0.123	0.292	0.338	0.400	0.494	0.595
	62	12.4	140	150	142.4	1.6	0.8	0.56	2.5	0.33	0.479	0.140	0.307	0.357	0.475	0.571	0.688
1st class roads	24	4.8	30	40	36.8	2.8	6.4	2.75	2.8	0.20	0.433	0.132	0.296	0.335	0.391	0.488	0.601
	180	36	40	50	46	2.7	5.6	6.51	2.8	0.42	0.43	0.155	0.27	0.327	0.403	0.482	0.666
	271	54.2	50	60	54.6	2.8	4.7	5.73	2.6	0.46	0.454	0.153	0.281	0.339	0.438	0.533	0.677
	260	52	60	70	65.3	2.9	3.5	3.05	2.8	0.42	0.474	0.171	0.281	0.362	0.438	0.549	0.706
	336	67.2	70	80	75.1	2.8	2.8	2.20	2.8	0.35	0.507	0.177	0.311	0.371	0.488	0.607	0.722
	501	100.2	80	90	85.3	2.9	2.3	2.08	2.8	0.33	0.535	0.211	0.311	0.378	0.496	0.646	0.806
	409	81.8	90	100	94.2	2.7	2.0	1.70	2.7	0.29	0.585	0.210	0.354	0.440	0.548	0.698	0.853
	145	29	100	110	103.9	2.7	1.9	1.72	2.7	0.31	0.611	0.279	0.363	0.442	0.545	0.700	0.874
2nd class roads	44	8.8	30	40	37.3	2.5	8.4	5.06	2.7	0.39	0.504	0.150	0.317	0.397	0.490	0.594	0.695
	331	66.2	40	50	45.9	2.9	8.8	5.21	2.6	0.33	0.569	0.184	0.348	0.445	0.545	0.676	0.811
	479	95.8	50	60	54.9	2.9	6.7	3.95	2.8	0.50	0.559	0.178	0.342	0.432	0.541	0.676	0.788
	355	71	60	70	64.7	2.9	5.3	3.29	2.9	0.59	0.574	0.184	0.337	0.420	0.557	0.705	0.816
	465	93	70	80	75.2	2.9	5.0	2.33	2.7	0.54	0.652	0.206	0.378	0.475	0.662	0.792	0.908
	507	101.4	80	90	84.9	2.8	5.3	1.71	2.4	0.39	0.762	0.228	0.415	0.609	0.791	0.914	1.034
	290	58	90	100	94	2.8	5.1	1.60	2.3	0.31	0.853	0.283	0.393	0.696	0.879	1.049	1.213
	82	16.4	100	110	103.2	2.3	4.8	1.25	2.2	0.25	0.799	0.331	0.355	0.479	0.861	1.044	1.230

Table 6. Statistics of vibration total value a_v as a function of ISO 8608 road classes.

			v (km/h)		C(10^-6 m^3-wrad^w^-1)				w		av (m/s^2)
ISO 8608 road class	N	Length (km)	Mean	Std	Min	Max	Mean	Std	Mean	Std	Mean	Std	P10	P25	P50	P75	P90
A	2839	567.8	104.4	23	0	2	0.8	0.50	2.58	0.40	0.413	0.125	0.276	0.322	0.391	0.480	0.581
B	3093	618.6	73.1	18	2	8	4.6	1.59	2.61	0.47	0.635	0.222	0.374	0.466	0.607	0.775	0.933
C	512	102.4	59.1	15.7	8	32	11.9	4.10	2.70	0.31	0.754	0.246	0.481	0.601	0.730	0.882	1.052

Table 7. Percentage of travelled sections in comfort level according to the ISO 2631-1 as a function of road category and vehicle speed.

			av (m/s^2)
	v (km/h)		< 0.315	0.315–0.63	0.5–1	0.8–1.6	1.25–2.5	> 2
Road category	Min	Max	Not uncomfortable	A little uncomfortable	Fairly uncomfortable	Uncomfortable	Very uncomfortable	Extremely uncomfortable
Motorways	80	90	28.4	69.1	12.3	0	0	0
	90	100	35.8	62.5	13.3	0	0	0
	100	110	28.1	63.5	21.2	0.5	0	0
	110	120	20.4	68.7	23.1	1.8	0	0
	120	130	22.1	69.7	22.7	1	0	0
	130	140	16.6	77.6	22.7	0.9	0	0
	140	150	13	68.5	44.4	0	0	0
1st class roads	30	40	16.7	70.8	20.8	0	0	0
	40	50	21.7	67.2	20.6	3.3	0	0
	50	60	16.2	70.1	32.5	3.3	0	0
	60	70	17	67	34.8	6.4	0	0
	70	80	10.4	68.2	45.6	6.8	0	0
	80	90	10.3	61.3	45.3	10.1	0.6	0
	90	100	6.2	57.8	57.8	12.5	1	0
	100	110	4.1	59.2	55.8	13.6	4.1	1.4
2nd class roads	30	40	6.8	68.2	47.7	4.5	0	0
	40	50	4.5	63.1	59.5	10.6	0	0
	50	60	6.9	61.6	57.2	9	0	0
	60	70	4.8	55.2	58	10.4	0	0
	70	80	2.2	41.7	68	23.7	0.4	0
	80	90	2.4	25.4	69.8	47.7	1	0
	90	100	3.1	18.6	52.1	64.8	7.6	0
	100	110	6.1	28	41.5	56.1	9.8	0

Table 8. Percentage of travelled sections in comfort level according to the ISO 2631-1 as a function of unevenness index.

									av (m/s^2)
			C (10^–6 m^3–w rad^w^–1)		w		v (km/h)		< 0.315	0.315–0.63	0.5–1	0.8–1.6	1.25–2.5	> 2
Road category	N	Length (km)	Min	Max	Mean	Std	Mean	Std	Not uncomfortable	A little uncomfortable	Fairly uncomfortable	Uncomfortable	Very uncomfortable	Extremely uncomfortable
Motorways	178	35.6	0.10	0.21	2.26	0.09	120.6	12	61.8	37.1	2.8	0	0	0
	545	109	0.21	0.44	2.40	0.20	120.6	12.4	31.2	67.5	2.4	0.2	0	0
	654	130.8	0.44	0.91	2.43	0.35	117.2	15	12.2	84.1	19	0.5	0	0
	323	64.6	0.91	1.91	2.63	0.38	117.7	15.5	7.7	70.3	62.2	1.9	0	0
	64	12.8	1.91	4	2.61	0.39	112	18.8	7.8	34.4	76.6	10.9	0	0
1st class roads	68	13.6	0.20	0.48	2.57	0.22	88.2	9.2	64.3	34.3	0	0	0	0
	503	100.6	0.48	1.15	2.67	0.32	85.5	14.5	26.5	71.2	12.8	0	0	0
	682	136.4	1.15	2.77	2.79	0.31	80.3	16.5	6.7	76.9	44.9	2.4	0	0
	728	145.6	2.77	6.66	2.72	0.45	70.3	18	2.2	58.1	62.7	13.9	0.7	0
	136	27.2	6.66	16	2.93	0.31	61.5	17.4	5	28.8	64	35.3	5.8	1.4
2nd class roads	13	2.6	0.5	1.15	3.12	0.1	77.4	9.5	7.7	92.3	0	0	0	0
	258	51.6	1.15	2.64	3.30	0.45	68.4	12.3	13.2	80.2	17.4	0.8	0	0
	1315	263	2.64	6.06	2.50	0.47	75.2	17	4.3	44	62.3	27.1	1.1	0
	855	171	6.06	13.93	2.55	0.37	66.4	16.9	0.9	35	71.1	36.5	2.6	0
	102	20.4	13.93	32	2.58	0.21	48.1	6.6	1	33.3	71.6	26.5	0	0

Table 9. Percentage of travelled sections in comfort level according to the ISO 2631-1 as a function of ISO 8608 road classes.

			C (10^–6 m^3–w rad^w^–1)				W		v (km/h)		av (m/s^2)
ISO 8608 road class	N	Length (km)	min	mean	std	max	mean	std	mean	std	< 0.315	0.315–0.63	0.5–1	0.8–1.6	1.25–2.5	> 2
A	2839	567.8	0	0.8	0.5	2	2.58	0.40	104.4	23	22	71.4	20.7	0.9	0	0
B	3093	618.6	2	4.6	1.6	8	2.61	0.47	73.1	18	3.3	50.5	61.5	21.9	1.1	0
C	512	102.4	8	11.9	4.1	32	2.70	0.31	59.1	15.7	1.4	28.8	74.7	36	2.9	0.4

Table 10. Parameters of regression function a_i = f (C,w,v) (Equation 11) for all test sections and vehicles as a function of vibration measuring point and direction.

Measuring point	Direction	Denotation	b1	b2	b3	b4	RMSE	R	R^2
Seat base	x	awBx	0.0305	0.2874	0.4981	–0.6055	0.0643	0.638	0.407
	y	awBy	0.0894	0.2630	0.1960	–0.2515	0.0529	0.709	0.502
	z	awBz	0.0076	0.3904	0.9284	–0.0024	0.1833	0.748	0.559
Seat surface	x	awSx	0.0014	0.3349	0.8193	0.9038	0.0559	0.655	0.429
	y	awSy	0.0246	0.2304	0.2469	0.4053	0.0447	0.534	0.285
	z	awSz	0.0103	0.3920	0.8075	–0.1939	0.1279	0.741	0.549
Seat surface	x, y, z	avSEAT	0.0121	0.3726	0.7633	–0.0070	0.1278	0.759	0.576
Seat surface & seat base	x, y, z	av	0.0124	0.3744	0.7902	–0.0140	0.1455	0.762	0.580

Figure 5. Relation a_v = f(C,w,v) for all vehicles as a function of road category: (a) motorways, (b) 1st class roads, (c) 2nd class roads, (d) all road categories.

Correction of text

Note: Changes are marked with red font.

Table

ORIGINAL TEXT (Page 13, 4^th paragraph):

CORRECTED TEXT:

Acceleration response increased with an increase of a scaling factor b1 and exponents b2–b4. The function (11) parameters (Table 4) for nine test vehicles and all road categories ranged in the intervals: b1 = 0.0211–0.0666, b2 = 0.15–0.2696, b3 = 0.5195–0.7843 and b4 = –0.1607–0.1324, for motorways ranged in the intervals, b1 = 0.0265–0.1, b2 = 0.0825–0.1781, b3 = 0.4205–0.7582 and b4 = –0.1903–0.0877, for 1st class roads, b1 = 0.006–0.0267, b2 = 0.1758–0.2961, b3 = 0.6773–1.046 and b4 = –0.0822–0.0845, and for 2nd class roads, b1 = 0.0089–0.0806, b2 = 0.2046–0.2556, b3 = 0.4886–0.9034 and b4 = –0.1906–0.1837.

Acceleration response increased with an increase of a scaling factor b1 and exponents b2–b4. The function (11) parameters (Table 4) for nine test vehicles and all road categories ranged in the intervals: b1 = 0.0046–0.0468, b2 = 0.3312–0.4253, b3 = 0.5428–0.9812 and b4 = –0.3476–0.3829, for motorways ranged in the intervals, b1 = 0.0031–0.071, b2 = 0.1571–0.373, b3 = 0.4322–1.1851 and b4 = –0.4389–0.1049, for 1st class roads, b1 = 0.0013–0.0164, b2 = 0.3241–0.4682, b3 = 0.781–1.3113 and b4 = –0.1668–0.1095, and for 2nd class roads, b1 = 0.0035–0.0678, b2 = 0.2985–0.3972, b3 = 0.4914–1.0578 and b4 = –0.4158–0.3127.

Table

OROGINAL TEXT (Pages 13-14):

CORRECTED TEXT:

Results in Table 4 may be commented as follows: Total vibration av increased with unevenness index and velocity and increased or decreased with an increase of waviness. Identified value of unevenness index exponent, b2 ∼ 0.25, is lower than theoretical value of unevenness index b2 = 0.5. Identified value of velocity exponent, b3 ∼ 0.6–0.8, is approximately in accordance with theoretical value of b3 = (w–1)/2 in Equation (9) for waviness of processed sections (Table 1). RMSE value was lowest for motorways (0.085) and higher for 1st class roads (0.0979) and 2nd class roads (0.1605).

Results in Table 4 may be commented as follows: Total vibration av increased with unevenness index and velocity and increased or decreased with an increase of waviness. Identified value of unevenness index exponent, b2 ∼ 0.3–0.4, is lower than theoretical value of unevenness index b2 = 0.5. Identified value of velocity exponent, b3 ∼ 0.5–1, is approximately in accordance with theoretical value of b3 = (w–1)/2 in Equation (9) for waviness of processed sections (Table 1). RMSE value was lowest for motorways (0.0978) and higher for 1st class roads (0.1092) and 2nd class roads (0.1883).

Table

ORIGINAL TEXT (Page 15, 11^th line):	CORRECTED TEXT:
Percentile P90 often exceeds a lower bound of expected ‘uncomfortable’ reaction (av = 0.8 m/s2, Table 1) for motorways & v > 110 km/h, 1st class roads & v > 70 km/h, and 2nd class roads & v > 40 km/h.	Percentile P90 exceeds a lower bound of expected ‘uncomfortable’ reaction (av = 0.8 m/s^2, Table 1) for 1st class roads & v > 80 km/h and 2nd class roads & v > 60 km/h.

Table

ORIGINAL TEXT (Page 18–19):

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Table 6 shows the vibration total value av statistics as a function of ISO 8608 road classes. About 44% of processed sections fall in A road class, 48% in B road class and only 8% in C road class. Median values of av increased with ISO road classes (0.626, 0.743 and 0.811 m/s2). Upper quartile av for B road class and median av for C road class correspond to ‘uncomfortable’ level with av > 0.8 m/s2. … Results in Table 7 may be commented as follows: Negligible portion of sections falls in best and worst comfort likely reaction levels, ‘notuncomfortable’, ‘very uncomfortable’ and ‘extremely uncomfortable’. Comfort level ‘fairly uncomfortable’ prevailed with a mean value 79.8% for all roadcategories, then follows ‘a little uncomfortable’ with 43.2%, and ‘uncomfortable’ with22.8%. For motorways (Table 7), ‘fairly uncomfortable’ level slightly increased with a vehiclespeed from 79% to 100% and ‘uncomfortable’ level has increased with a speed from1.2% to 24.1%. Comfort level ‘a little uncomfortable’ was decreased from71.6% to 1.9%. For 1st class roads, ‘a little uncomfortable’ level is decreased with a speed from 83.3%to 17.2%, ‘fairly uncomfortable’ level increased from50% to 86.2% and ‘uncomfortable’increased with a speed from 4.2% to 33.1%. For 2nd class roads, ‘a little uncomfortable’ decreased with a speed from 63.6% to 15.9%, comfort level ‘fairly uncomfortable’ decreased for a speed over 70 km/h and ‘uncomfortable’ level increased from 4.5% to 80.3%. Comfort level ‘very uncomfortable’ increased with a speed from 0% to 15.5%.

Table 6 shows the vibration total value av statistics as a function of ISO 8608 road classes. About 44% of processed sections fall in A road class, 48% in B road class and only 8% in C road class. Median values of av increased with ISO road classes (0.391, 0.607 and 0.730 m/s^2). Upper quartile av for C road class correspond to ‘uncomfortable’ level with av > 0.8 m/s^2. … Results in Table 7 may be commented as follows: Negligible portion of sections falls in worst comfort likely reaction levels ‘very uncomfortable’ and ‘extremely uncomfortable’. Comfort level ‘a little uncomfortable’ prevailed with a mean value 59% for all road categories, then follows ‘fairly uncomfortable’ with 40.3%, and ‘not uncomfortable’ with 13.2%. For motorways (Table 7), ‘fairly uncomfortable’ level slightly increased with a vehicle speed from 12.3% to 44.4% and comfort level ‘not uncomfortable’ was decreased from 35.8% to 13%. For 1st class roads, ‘a little uncomfortable’ level is decreased with a speed from 70.8% to 59.2%, ‘fairly uncomfortable’ level increased from 20.8% to 55.8% and ‘uncomfortable’ increased with a speed from 0% to 13.6%. For 2nd class roads, ‘a little uncomfortable’ decreased with a speed from 68.2% to 28%, ‘uncomfortable’ level increased from 4.5% to 56.1%, and ‘very uncomfortable’ increased with a speed from 0% to 9.8%.

Table

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Table 8 presents the percentage of travelled sections in ISO 2631-1 comfort levels as afunction of road category and unevenness index. Results in Table 8 may be commented as follows: Negligible portion of sections falls in best and worst comfort likely reaction levels, ‘notuncomfortable’, ‘very uncomfortable’ and ‘extremely uncomfortable’. Comfort level ‘fairly uncomfortable’ prevailed with a mean value 83.7% for all roadcategories, then follows ‘a little uncomfortable’ with 44% and ‘uncomfortable’ with22.5%. For motorways (Table 8), ‘fairly uncomfortable’ level slightly decreased with C from91.6% to 87.5% and ‘uncomfortable’ level has increased with C from 1.1% to 60.9%.Comfort level ‘a little uncomfortable’ was decreased from 69.1% to 17.2%. For 1st class roads, ‘a little uncomfortable’ level decreased with C from 88.2% to 20.6%,‘fairly uncomfortable’ level varied only slightly and ‘uncomfortable’ increased from 0%to 47.8%. For 2nd class roads, ‘a little uncomfortable’ decreased with C from 61.5% to 17.5%,comfort level ‘fairly uncomfortable’ slightly decreased with C, and ‘uncomfortable’ levelincreased from 0% to 51.2%.

Table 8 presents the percentage of travelled sections in ISO 2631-1 comfort levels as afunction of road category and unevenness index. Results in Table 8 may be commented as follows: Negligible portion of sections falls in worst comfort likely reaction levels ‘very uncomfortable’ and ‘extremely uncomfortable’. Comfort level ‘a little uncomfortable’ prevailed with a mean value 56.5% for all road categories, then follows ‘fairly uncomfortable’ with 38% and ‘not uncomfortable’ with 16.8%. For motorways (Table 8), ‘fairly uncomfortable’ level increased with C from 2.8% to 76.6% and ‘uncomfortable’ level has increased with C from 0% to 10.9%. Comfort level ‘not uncomfortable’ was decreased from 61.8% to 7.8%. For 1st class roads, ‘not uncomfortable’ level decreased with C from 64.3% to 5%, ‘fairly uncomfortable’ increased from 0% to 64% and ‘uncomfortable’ increased from 0% to 35.3%. For 2nd class roads, ‘a little uncomfortable’ decreased with C from 92.3% to 33.3%, ‘fairly uncomfortable’ increased with C from 0 to 71.6%, and ‘uncomfortable’ level increased from 0% to 26.5%.

Table

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Table 9 shows comfort levels according to ISO 2631-1 as a function of ISO 8608 road classes. Comfort level ‘a little uncomfortable’ decreased from 51.2% to 16.4% and ‘uncomfortable’ increased from 7.4% to 51.2%.	Table 9 shows comfort levels according to ISO 2631-1 as a function of ISO 8608 road classes. Comfort level ‘a little uncomfortable’ decreased from 71.4% to 28.8% and ‘uncomfortable’ increased from 0.9% to 36%.

Table

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The highest scale factor b1 was calculated for the fore-and-aft (x-) direction on the seat surface (awSx) and the vibration total values avSEAT and av. The highest exponent b2 was calculated for the vertical direction on the seat base and seat surface and for the fore-and-aft direction at the seat base (awBx). The highest influence of speed (b3) was observed for the vertical direction at the seat base and surface and longitudinal direction at the seat base.Results in Table 10 may be commented as follows: … Exponent b3 = 0.9285 for vertical direction and seat base and 0.8046 for seat surface indicate approximately linear increase of total vibration with velocity. Total vibration is in some cases more strongly related to waviness. Coefficient b4 = –0.5756 in fore-and-aft direction at seat base indicates decrease of total vibration with increase of waviness.

The highest scale factor b1 was calculated for the transversal (y-) direction on the seat base (awBy). The highest exponent b2 was calculated for the vertical direction on the seat base and seat surface and for the vibration total values avSEAT and av. The highest influence of speed (b3) was observed for the vertical direction at the seat base and surface and fore-and-aft direction at the seat surface. Results in Table 10 may be commented as follows: … Exponent b3 = 0.9284 for vertical direction and seat base and 0.8075 for seat surface indicate approximately linear increase of total vibration with velocity. Total vibration is in some cases more strongly related to waviness. Coefficient b4 = –0.6055 in fore-and-aft direction at seat base indicates decrease of total vibration with increase of waviness.

Table

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The main results of this study were as follows: … Parameters of regression function indicate the difference with theory. Exponent of unevenness index C was substantially lower (∼ 0.25) than theoretical value, 0.5. …  Indication of three comfort levels ‘not uncomfortable’, ‘very uncomfortable’ and ‘extremely uncomfortable’ was very rare for common road categories. Comfort level ‘fairly uncomfortable’ and ‘uncomfortable’ prevailed among comfort reaction categories. About 26% of all processed sections exceed a lower bound of expected ‘uncomfortable’ comfort reaction, and 1.4% exceeds a lower bound of ‘very uncomfortable’ level.

The main results of this study were as follows: … Parameters of regression function indicate the difference with theory. Exponent of unevenness index C was lower (∼ 0.3–0.4) than theoretical value, 0.5. …  Indication of two comfort levels ‘very uncomfortable’ and ‘extremely uncomfortable’ was very rare for common road categories. Comfort level ‘a little uncomfortable’ and ‘fairly uncomfortable’ prevailed among comfort reaction categories. About 13.8% of all processed sections exceed a lower bound of expected ‘uncomfortable’ comfort reaction, and 0.78% exceeds a lower bound of ‘very uncomfortable’ level.

Correction Statement

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