COMPUTATION OF VEHICLE DECELERATION

The deceleration from the 20-mph stops could be obtained in one of three ways:

(1) indirectly from the fifth-wheel, (2) indirectly from the Labeco instrumentation, or

(3) directly from the on-board accelerometer. Insufficient data were collected by the accelerometer to be reported herein. The deceleration was primarily computed from the fifth wheel data using regression analysis of the linear portion (Region B) of the velocity-versus-time profile (Figure B1).

Appendix B-1

Figure B1. Vehicle velocity data as a function of time during a 20-mph stop (fifth wheel data). The trace in Region B is used for regression analysis and computation of the assumed constant deceleration of the vehicle.

When fifth-wheel data was not available, the deceleration was back-calculated from the Labeco data and assuming that the deceleration profile was similar to the profile shown in Figure B2. The Labeco system is triggered by a sensor placed on the foot brake pedal of the vehicle. As soon as the driver’s foot touches the brake pedal, the distance traveled is recorded by the Labeco instrumentation even though, for a brief period of time, no brake force is developed and the vehicle initial velocity remains unchanged. The distance calculated from the recorded data was estimated to be approximately 3 percent lower than that measured by the Labeco. In Figure B2, region I (of duration T0) refers to the portion of the overall stop for which no change in velocity is seen even though the driver’s foot is in contact with the brake pedal. Region II (of duration T1) corresponds to the portion of the overall stop for which the vehicle starts to decelerate but full brake forces (assumed equivalent to maximum deceleration) are not yet achieved. A linear increase is assumed. Region III refers to the portion of the overall stop for which brake forces are fully applied and assumed constant until the complete immobilization of the vehicle. No in-stop fade of brake forces (and therefore deceleration) is assumed since it was not observed in any of the on-road 20-mph stops. The assessment of the times T0 and T1 is critical. Based on observations of the available data recorded by the fifth-wheel for the two-axle truck, these times were both estimated to be equal to 0.125 second.

Appendix B-2

Figure B2. Assumed profile of the deceleration as a function of time used for computation of stopping distance.

In a similar manner, using T0 and T1 equal to 0.125 second, the stopping distance of the trucks can be obtained from the ratio BFT_OT /GVW measured with the PBBTs. In this case, the deceleration during Stage III is taken as BF_TOT /GVW x g, where g is the acceleration due to gravity (9.8 m/s² or 32.2 ft/s²). This deceleration during Stage III is ultimately the quantity that will be estimated and used in a pictorial display software developed by Battelle to predict vehicle stopping distances from PBBT results. The stopping distances and decelerations (where available) for the nine vehicle configurations are presented in Table B1.

Appendix B-3

 

Table B1. Stopping distances and average decelerations during 20 mph on-road stops.

Conditions					From Labeco						Calculated from fifth wheel data
			Test #	Number of Rep.	Average Stopping Distance normalized to 20 mph (ft)			Average Stopping Distance normalized to 20 mph (ft)			Average Deceleration (g)
					Avg	Min	Max	Avg	Min	Max	Avg	Min	Max
Part 1: Vehicles with Weak Brakes Dry Conditions
3-S2	Laden		1	9	43.0	40.7	45.0	36.8	33.9	43.2	0.39	0.38	0.41
	Unladen		3	3a	50.4	44.7	60.9	45.2	38.7	55.8	0.25	0.25	0.25
				6a	45.4	44.7	46.4	40.6	38.7	42.6	0.36	0.34	0.37
2-Axle	Laden		2	3				38.5	34.9	41.2	0.36	0.34	0.38
	Unladen		4	2				31.4	31.0	31.7	0.42	0.41	0.43
				3	41.5	40.9	42.0	39.7c			0.40c
Part 2: 2-axle vehicle Fully Adjusted, Strong Brakes
2-Axle	Unladen	Dry	5	3	30.3	27.7	31.8	28.9c			0.58c
	1/3 Laden	Dry	6	3	31.2	29.6	32.0	29.8c			0.56c
	2/3 Laden	Dry	7	6b	27.8	26.3	28.3	26.6	24.3	27.9	0.63	0.61	0.65
	2/3 Laden	Wet	8	3	28.8	28.5	29.3	28.2	27.3	28.8	0.60	0.59	0.61
	Unladen	Wet	9	0	n/t	n/t	n/t	n/t	n/t	n/t	n/t	n/t	n/t

n/t -	not tested	.......	not available
a	The 9 replicates are separated due to the improper brake settings during the first round of testing in this condition.
b	A 2nd set of 3 replicate stops was conducted in the 2/3 laden condition during the "wet" test sequence.
	Since these tests were conducted dry, the results are included in the "2/3 loaded and dry" test series.
c	The deceleration is back-calculated from Labeco stopping distances.

 

ROAD STOPS UNCERTAINTIES

For use in enforcement, performance-based regulations to be used with PBBTs must take into account the accuracy and repeatability of the PBBTs, must be based on safety, and must also consider the variations typically found in actual vehicle stopping behavior.

There are three sources of uncertainty to be considered in establishing the allowable window of deviations from the desired minimum stopping capability.

Appendix B-4

1) The stopping distances or the computed decelerations of a given vehicle under identical conditions will vary from stop to stop. Statistically, as the number of samples (replicate tests) increases, the level of confidence in the results increases accordingly. Since only three replicates were conducted, variability observed in the test results was high, and the extremes may not have represented those found in a large number of tests (Table B1). For the 20 mph stops conducted during the round robin, the maximum range of variation of the deceleration (from minimum to maximum) for a given truck configuration (weak and strong brakes) was approximately 10 percent, i.e. ± 5 percent. This type of uncertainties is referred to as “real-life braking variations”.

2) The second type of uncertainty is “data measurement” variations, which are manifest in the range of reported values the PBBT exhibit under controlled (usually static) conditions. These are due to transducer accuracy and/or data manipulation or reduction. The proposed specifications call for ± 2.5 percent on the weight and brake force measurements. When combined, these lead to an approximate ± 5 percent variation on the deceleration (BFTOT/GVW).

3) The third type of uncertainty is introduced by the specific interacttion of the vehicle tested and the PBBT used. These “dynamic” variations can originate from test geometry (design characteristics of trucks such as total number of axles, position of axles, type of suspensions, etc.) and data manipulation (filtering, smoothing, brake force calibration algorithm, etc.), and variability in the way the driver/operator conducts the tests.

Appendix B-5

Brake Forces

COMPUTATION OF REFERENCE BRAKE FORCE FROM TORQUE WHEEL DATA

The calibration check on the torque wheel indicated an accuracy within 0.5 percent. To compute the brake forces from the measured torques, a radius of 19.25 inches was used for the fully laden condition, and 19.6 inches was used for the unladen condition. The accuracy on the radius measurement was approximately 1.3 percent (0.25 inch). Additionally, the variation of the contact geometry due to deflection on the rolls or gripper pads is estimated to contribute to the variation of the radius by 0.5 inch (~ 2.6 percent) for the RDs and 0.25 inch (~ 1.3 percent) for the BTT. No additional geometry factor is expected for the flat plate testers. As such, the total estimated uncertainty in measured torque values is ± 4.3 percent for FPs, ± 5.6 percent for BTTs, and ±6.9 percent for RDs, respectively. On the 3-S2 vehicle, torque data was collected during all tests by a torque wheel installed on wheel 5.

Figure B3 illustrates typical brake force versus time traces as well as the methods used for computing a single value for the brake force from the data. As the vendors’ algorithms for computing brake forces were not all known at the time of this report, three different methods were used to determine brake force data from torque wheel data. For all three PBBT types, method 1 reported the maximum brake force (“Max”) during the test. Method 2 calculated the average of data points greater than 80 percent of the maximum brake force (“0.8 avg”). Method 2 helps average data for which a nominal plateau is reached during the test or for which a spike occurs. However, if a large spike occurs with no filtering, for example, of magnitude 20 % greater than the plateau, then none of the plateau data would be included. Finally, for all PBBTs except FP testers, Method 3 determined the brake force at the time of test termination (“Term”). No averaging of the torque wheel data was performed.

Appendix B-6

Figure B3. Methods for computing the brake force from torque wheel data.

Appendix B-7

REFERENCE BRAKE FORCE DATA

Table B2 summarizes the brake forces reported by the PBBTs (indicated by “Rep.” in the “PBBT” column, standing for “as reported”) and the brake forces obtained from the torque wheel data. Data are presented for laden and unladen conditions.

Table B2. Brake forces (in pounds) for wheel 5 of the 3-S2 reported by PBBTs and computed from the reference torque wheel data (Appendix D).

LADEN CONDITIONS
		Replicate 1				Replicate 2				Replicate 3
		PBBT Rep. 4362	Torque wheel			PBBT Rep. 4369	Torque wheel			PBBT Rep. 4333	Torque wheel
Machine			Max.	0.8 avg	Term		Max.	0.8 avg	Term		Max.	0.8 avg	Term
B&G BTT	6		4690	4241	4690		4646	4182	4646		5330	4812	5330
HTR FP	1	5395	5807	5501	n/a	5343	6068	5773	n/a	5791	7330	6954	n/a
HEKA FP	7	3797	5406	5040	n/a	4563	4999	4624	n/a	4651	5161	4711	n/a
VRTC RD	4	5604	5911	5580	5911	6077	6499	5995	6499	6147	6415	6180	6415
RAI RD-ig	9	5873	6045	5890	5965*	6106	6317	6044	6234*	5850	6290	6089	6001*
RAI RD-p	2	5212	5701	5099	4638†	4892	5398	4805	5157†	4964	5566	4912	5046†
VIS RD	3	4078	4772	4265	4772	2308	2623	2246	2623	2200	2426	2106	2426
HEI RD1	5a	4957	5403	4864	5403	5169	5898	5314	5898	3989	4356	3957	4356
HEI RD2	5b	-----	-----	-----	-----	-----	-----	-----	-----	-----	3937	3491	-----
20mph st.	8	-----	5816	5582	n/a	-----	5779	5507	n/a	-----	5916	5584	n/a
LADEN CONDITIONS
		Replicate 1				Replicate 2				Replicate 3
		PBBT Rep. 1287	Torque wheel			PBBT Rep. 1559	Torque wheel			PBBT Rep. 1597	Torque wheel
Machine			Max.	0.8 avg	Term		Max.	0.8 avg	Term		Max.	0.8 avg	Term
B&G BTT	6		1326	1250	1326		1635	1556	1635		1635	1547	1635
HTR FP	1	1792	1518	1385	n/a	1815	1896	1717	n/a	1684	1792	1630	n/a
HEKA FP	7	1356	1116	1023	n/a	2114	1789	1659	n/a	1691	1411	1294	n/a
VRTC RD	4	1544	1640	1504	1448*	1640	1801	1595	1523*	1592	1914	1769	1689*
RAI RD-ig	9	1601	1737	1535	1631*	1727	1923	1760	1734*	1943	2090	1961	1977*
RAI RD-p	2	1579	1626	1543	1579*	1988	2021	1901	1967*	1767	1915	1770	1785*
VIS RD	3	1426	1585	1378	1585	1520	1635	1415	1635	1466	1793	1544	1793
HEI RD1	5a	1624	1617	1496	1476*	1431	1649	1533	1649	1366	1567	1442	1567
HEI RD2	5b	-----	-----	-----	-----	-----	-----	-----	-----	-----	-----	-----	-----
20mph st.	8	n/a	1519	1389	n/a	n/a	1778	1639	n/a	n/a	1767	1621	n/a

Rep.=reported; Max.=maximum; 0.8 avg=average of data greater than 80% maximum; Term=at test termination.

* Average of last 10 points prior to test termination.

† Test termination prior to the upsurge, as specified on Figure xx11.

Appendix B-8

Vehicle Weights

Table B3. Weights (in pounds) measured using certified scales

Wheel Number	Wheel Position	3-S2 Laden	3-S2 Empty	2-Axle Laden	2-Axle Empty	2-Axle 1/3 Laden	2-Axle 2/3 Laden
1	1L	6,050	5,100	6,000	4,100	4,790	5,310
2	1R	5,850	4,850	5,450	3,700	4,510	4,980
Axle 1		11,900	9,950	11,450	7,800	9,300	10,290
3	2L	9,150	3,000	11,300	4,700	6,940	9,810
4	2R	8,150	2,750	10,050	4,200	6,490	8,870
Axle 2		17,300	5,750	21,350	8,900	13,430	18,680
5	3L	8,400	2,900
6	3R	8,100	2,900
Axle 3		16,500	5,800
Total Tractor		45,700	21,500
7	4L	8,700	2,400
8	4R	8,700	2,050
Axle 4		17,400	4,450
9	5L	7,900	2,350
10	5R	7,800	2,400
Axle 5		15,700	4,750
Total Trailer		33,100	9,200
Total Vehicle		78,800	30,700	32,800	16,700	22,730	28,970

Appendix B-9