Three Dimensional Mapping of Inductive Loop Detector Sensitivity Using Field Measurement TRB Paper 09-0018 by Christopher M. Day Purdue University Thomas M. Brennan Purdue University Matthew L. Harding Purdue University Hiromal Premachandra Purdue University Allen Jacobs Reno A&E Corresponding author: Darcy M. Bullock Purdue University 550 Stadium Mall Dr West Lafayette, IN 47906 Phone (765) 496-7314 Fax (765) 496-7996
[email protected] James V. Krogmeier Purdue University James R. Sturdevant Indiana Department of Transportation
November 11, 2008 Word Count: 3446 words + (14 x 250 words per Figure or Table) = 6946 words
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ABSTRACT Inductance loops continue to be the most widely used sensing device for vehicle detection. There are several different loop geometries that are commonly used, but little technical design literature quantifying their field of detection and sensitivity. This paper presents three-dimensional maps of loop response sensitivity based on field measurements using loops installed in asphalt. Loop response was characterized for different metal objects at various heights from the pavement surface. Sensitivity maps were generated for 6-foot circular, 6-foot octagonal, 20-foot octagonal, and 20-foot quadrupole loops. Based upon the field observations, the paper concludes the claims of increased vehicle sensitivity for quadrupole loops first published in the 1970s are inaccurate for most vehicles and quadrupoles are in fact less sensitive than comparatively sized rectangular loops.
BACKGROUND Inductive loop detectors (ILDs) have been in use since the early 1960s, and have remained the most common type of traffic sensor despite the emergence of competing technology. A great deal of work has been published on ILDs discussing their operation (1, 2, 3), and applications in performance measure calculation (4,5,6), freeway speed estimation (7), freeway travel time estimation (8,9), and vehicle identification (10,11,12). There are few articles in the literature that describe how detection fields vary with geometry and sensitivity. Hamm and Woods (13) published a study in which the detection areas of loops were characterized at different sensitivity settings. The focus of this report was on factors such as pavement condition, depth of placement, and number of turns, rather than the geometry of the detection area. However, Hamm and Woods provide an example of how the detection zone of a particular loop geometry varies by different sensitivity settings. Kidarsa et al. (14) used a MATLAB simulation to characterize the response of ILDs to bicycles and to describe the shape of the detection zone in three dimensions. The methodology and data representation employed in this study are similar to those of these previous papers, but our objective is to document the loop response in three dimensions using field data.
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THEORY OF LOOP RESPONSE TO A METAL SURFACE The following analysis was adapted from the Traffic Detector Handbook (1). Loop sensitivity S is given by S=
∆L Lnv − Lv = L Lnv
,
Equation 1
where the notation L refers to an value of inductance, with Lv and Lnv referring to the loop inductance with and without the presence of a vehicle above the loop respectively. Loop sensitivity can also be stated in terms of the surface area of the metal vehicle body as well as the distance between the loop and the vehicle body. When a vehicle is brought into proximity with an inductive loop, it behaves as an air core transformer1, as shown in Figure 1. The surface of the vehicle undercarriage is modeled as a shorted loop. The sensitivity of such a system is given by S=
M2 LL LV
,
Equation 2
In this equation, the terms LL and LV represent the self-inductance of inductive loop detector and the vehicle body respectively. The coupling or mutual inductance M between the loop and the vehicle body can be expressed as M=
µ 0 N L AV FL d
,
Equation 3
where µ0 is the permeability of free space, NL is the number of turns in the loop, AV is the surface area of the vehicle parallel to the loop surface area, FL is a constant that adjusts for the impact of nonuniform magnetic flux, and d is the distance between the vehicle and the loop. The self-inductance LL of the inductive loop detector is given by LL =
µ 0 N L2 AL FL lL
,
Equation 4
where NL is the number of turns in the loop, AL is the surface area of the loop, l L is the circumference of the loop, and the other terms are the same as in Equation 3. For the vehicle body, the self-inductance LV is given by
1
An air core transformer is a transformer in which the coils are wrapped around air (actually a hollow tube in an actual device) rather than ferrite.
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LV =
µ 0 AV FV lV
,
Equation 5
where FV is similar to the term in Equation 3, AV is the surface area of the vehicle as before, and l V is the effective circumference of that area modeled as a shorted loop. A synthesis of the above three equations yields the following expression of loop sensitivity: S=
AV l L l V FL . AL d 2 FV
Equation 6
With this, we have stated the expected impact of numerous parameters on the loop sensitivity. In particular, note the inverse square relationship between sensitivity and distance d. The response of the loop should drop sharply as the distance of a metal object from the loop surface is increased. The response of the loop is also a function of the ratio of the surface areas of the loop (AL) and of the vehicle body (AV). When AL is larger than AV, the loop response is weaker because the region where currents can be induced is small. As AV increases, the sensitivity increases, within a practical limit. If an infinite plane of metal existed parallel to the loop surface, only a local region of it would feel the inductance and AV would be limited to that area. The reason for this is that the influence of the loop decreases by an inverse square of the distance. One possible approximation for the maximum practical value of AV is AL. It is not the objective of this paper to refine the model, but rather to show that we expect the loop response to increase as a greater portion of the loop surface area is covered by the vehicle surface area (i.e., as AV/AL tends to unity). Loop detectors do not directly measure ∆L/L, but rather the more easily measured quantity ∆f/f, the relative shift in the oscillating frequency of the loop. Depending on the loop amplifier, frequency shifts or period shifts may be measured. This quantity relates to ∆L/L by the following formula (14): S=
∆L 1 ∆f 1 (fv − f nv ) . = = L 2 f 2 fnv
Equation 7
Figure 2 shows traces in ∆L/L values sampled over time as a passenger passed over an octagonal ILD. The three traces correspond to various paths taken over the detector area by the vehicle. The strongest response is for the vehicle traveling along the center line of the loop; this is where the maximum amount of detector surface area was covered by the vehicle. The peaks in the traces correspond to the points where the vehicle passed by the center point of the loop. This would also correspond to the moment when the amount of loop area covered by the vehicle is maximized. This response is as predicted by Equation 6.
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METHODOLOGY Figure 3(a) shows a picture of the test bed, showing the four loop geometries examined in this study: • • • •
6 ft × 6 ft (1.8 m × 1.8 m) octagonal (shown as L1, L2), 6 ft round (L3, L4), 20 ft (6.1 m) octagonal (L5), and 20 ft quadrupole (L6).
The loops were placed in recently set asphalt by conventional saw cuts. The pavement was less than one year old at the time of the study, with no water ponding or pavement damage known to have occurred. Figure 3(b) shows a wiring diagram of the test bed. Two probes were used to measure ∆L/L values at various positions above the inductance loops, simulating the presence of a vehicle body at a fixed height above the pavement: • •
4 ft × 12 ft (1.2 m × 3.6 m) galvanized steel sheet 4 ft × 12 ft anodized aluminum sheet
Different metal probes were used to examine the effects of metal type on the loop response. Different types of metals are known to elicit different response from metal detecting devices (15), particularly when ferrous and nonferrous metals are compared. The test apparatus is illustrated in Figure 4. A wood frame was used to prevent the sheet from bending or warping. A gantry made of nonmetal components controlled the height of the probe. With the height adjusted, the probe was moved across transverse sections of the loop. Values of ∆L/L were recorded at 6-inch (15.2 cm) intervals along the transverse section lines starting from the center of the loop. This was repeated at various heights starting from the pavement surface moving upward in 6-inch increments. Several such traces were measured along different cross sections of the loop, as shown in Figure 5. For the 20-foot loops, traces were taken at the centerline, edge line, 60 inches (152.5 cm) inside the edge, 12 inches (30.5 cm) inside the edge, and 12 inches outside the edge. The 6 foot loops used the same traces, except of course for the 60 inch offset trace. Assuming symmetry along the longitudinal and center transverse axes of each loop, ∆L/L values were mapped for one quadrant and then mirrored across each axis. Test traces in the other quadrants validated the assumption of symmetry. In a typical field installation, loop amplifiers tune out persistent changes in sensitivity caused by introduction of a metal object into the environment (such as a parked vehicle). The ∆L/L values were recorded using a Reno A&E loop amplifier which was modified to not tune out the presence of the metal probe
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during measurement. The ∆L/L values were used to generate the plots of sensitivity presented in the next section. To give context to the ∆L/L values, we present the response of each loop type to different vehicles in Table 1. The passenger car, although smaller than the pickup truck, was closer to the ground and drew a stronger response from the loops, except for the rectangular loop, for which the truck was slightly stronger. Table 2 gives the sensitivity levels of Reno AE and EDI detector cards. Both the car and the truck would have been detected at even the lowest sensitivity levels of both detector cards. Heavier vehicles such as the front end loader and dump truck had larger metal surface areas, but were situated higher above the pavement. As a result, the reported ∆L/L values were lower. Bicycles have the lowest sensitivity of all the vehicles tested. Bicycle wheels have a much smaller metal composition but it is situated very close to the pavement surface. They are virtually undetected at the center of the loops (except the quadrupole loop, where there is a loop wire present), and produce a weak response when situated over the loop edge.
RESULTS OF FIELD MEASUREMENT Figures 6 and 7 show cross sectional traces across the center of the loops, with traces shown for steel and aluminum sheets at 12, 24, and 36 inches from the pavement surface. Figure 6(a) shows traces for the quadrupole loop; Figure 6(b) for the rectangular loop; Figure 7(a) for the octagonal loop; and Figure 7(b) for the round loop. Figure 8 shows superimposed traces of the response of all four loop geometries to the galvanized steel probe at 12 inches above the pavement. It should be noted that although variation in sensitivity was observed within the boundaries of the loops, there was virtually no difference in detector sensitivity outside the loop perimeters. As expected, we confirmed a consistent decrease in loop response with increasing distance from the pavement. Aluminum produced a slightly weaker response than steel, but the difference was only noticeable when closer to the pavement. In order to document the low end of the sensitivity range, probe heights of 12 inches and above are shown. If probe heights of 6 inches are used, the peak ∆L/L values exceed or are similar to the values for the passenger car and pickup truck in Table 1. At heights greater than 12 inches, there was little difference between aluminum and steel. The response in terms of ∆L/L was significantly lower than that of the passenger car and pickup truck (see Table 1), particularly at 24 and 36 inches above the pavement. Across the center cross section trace, we tended to observe the strongest response when the metal probe was positioned at the center of the loops, except for the quadrupole loop, where the response was strongest when between the center and edge loop wires. This is because at the center point, the amount of metal surface area directly above the loop was at maximum. If a vertically aligned probe (such as a bicycle wheel) had been used, the peak would likely have been observed above the loop wires. Using a metal sheet approximates the footprint of 11/11/2008
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a vehicle body and this study confirms the strongest response when the vehicle is aligned directly above the loop. The octagonal and round loops responded similarly, with a notable variation being the greater difference between response to aluminum and steel from the round loop (Figure 7). In general, the response of the octagonal loop was slightly stronger than that of the round loop (Figure 8). At 12 inches, the rectangular loop was considerably less sensitive than the 6 foot loops, but as the height was increased, the difference in sensitivity became less prominent. At 36 inches, the ∆L/L response of rectangular, round, and octagonal loops were comparable. The quadrupole loop was found to be the least sensitive of all. The 20 ft loops exhibited a weaker response because the loop area AL was much larger than that of the 6 ft loops. If multiple 6 ft loops were used to form a wider detector area, the magnitude of their response would have been similar. Three-dimensional maps of loop sensitivity to the steel sheet at 12 inches above the pavement are shown in Figures 9 and 10. Figure 9 (a) contains the map for the quadrupole loop; Figure 9(b) for the rectangular loop; Figure 10(a) for the octagonal loop; and Figure 10(b) for the round loop. The “direction of vehicular travel” noted in these graphs represents the direction in which the longer edge of the metal probe was aligned. The three dimensional figures illustrate features of loop response consistent with what was observed in the cross sections. The response is strongest when the probe is centered above the open areas of the loops, and decreases as it is moved away. As mentioned before, this is where the amount of loop surface area covered by metal is at its greatest. Among the different cross section traces along the longitudinal axes of the 20-foot loops, there is not much difference in the sensitivity until the edge. As for the 6-foot loops, the three dimensional images do not reveal radial symmetry. Instead, the shape of the curve is elongated along the direction of vehicular travel. This is a consequence of the shape of the metal probe. The probe covered almost the entire surface area of the loop when positioned at the “north” edge whereas only about half of the loop was covered when positioned at the “east” edge. If we had used a smaller, symmetric probe we would have observed radial symmetry in these loops. However, the probe used in this study is intended to simulate a vehicle body. Figure 11 shows contour maps of the response of the four types of loops to the galvanized steel sheet at 24 inches from the pavement. The quadrupole loop is shown in Figure 11(a), the rectangular loop in Figure 11(b), the octagonal loop in Figure 11(c), and the round loop in Figure 11(d). In these graphs, the response is mapped in terms of detector sensitivity. We have used the Reno AE sensitivity levels because they are on the same order of magnitude as the variations among point measurements in our observations. Table 2 gives the ∆L/L values associated with each sensitivity level. In addition to the nine sensitivity levels, an additional line is shown to indicate where the loop response falls to zero, as calculated in the MATLAB model used to generate the contours. These plots indicate what regions at 24 inches above the loop are detectable at various sensitivity levels using the test probe. The shapes of the
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plots are similar to the three dimensional plots discussed previously, with the most responsive regions being at the center of the loops. The quadrupole loop is the least sensitive, being completely unable to detect the steel sheet at 24 inches at sensitivity lower than 3. The sensing range drops off sharply with distance from the loop edges. The rectangular loop is more sensitive, and the detection ranges of the loop at each sensitivity level are larger than those of the quadrupole loop. The octagonal and round loops have very similar contour plots. The width of the detection ranges are greater than those of the rectangular loop. The 1976 patent (16) of the quadrupole loop claimed that the loop design would reduce false calls from adjacent lanes, provide better detection of small vehicles, and improve uniformity of loop sensitivity over the detection area. The patent provided a diagram of magnetic field strength across the cross section of the loop, as shown in Figure 12. The strength of the magnetic field was expected to be weakest above the center in the case of the rectangular loop (Figure 12a), and strongest above the center wires in the case of the quadrupole loop (Figure 12b). While these expectations of magnetic field strength are correct, the results presented in this paper demonstrate that such a setup does not necessarily translate into a more sensitive detector. Our observations reveal trends in the loop sensitivity contradictory to the expectations displayed in Figure 12. Although the magnetic field directly measured at a point above the center wire of the quadrupole loop is certainly stronger than at the same point above the rectangular loop, the overall inductance response is weaker because the quadrupole loop does not couple as well with the metal probe. Further investigation is needed to explain why, but we hypothesize that the reason for this is that the weaker magnetic field above the loop perimeter leads to a decrease in induced current and therefore of sensitivity. In addition, our observations suggest that the likelihood of false calls originating from vehicles above adjacent lanes is not lower for a quadrupole loop than for a rectangular loop. The shape of the sensitivity plots outside the loop perimeter (Figure 8) are highly similar.
CONCLUSION This paper presented three dimensional maps of ILD response of four common loop geometries to aluminum and steel objects situated at different heights above the pavement. Although these results represent a very specific set of conditions, a mapping of loop response in three dimensions has not previously been executed in terms of ∆L/L values. This tabulated data provides the following loop design insights: •
Vehicles with high ground clearance (such as trailers) present challenges for accurate detection because loop sensitivity decreases by the inverse square of the distance (Equation 6) between the vehicle undercarriage
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•
•
• •
• •
and the loop face. Although heavy vehicles are more massive, smaller vehicles are more easily detectible because they are closer to the ground. Generally, there was negligible difference in the loop response to the aluminum and steel probes. Even when the probes were 12” above the pavement, the response difference was barely visible on the sensitivity plots shown in (Figure 6, Figure 7). Although sensitivity decreases with vertical distance from the pavement, the overall shape of the sensing range remains the same(Figure 6, Figure 7). 6-foot octagonal and 6-foot round loops had very similar response (Figure 7). Quadrupole loops were less sensitive overall than rectangular loops of similar size(Figure 6). This was true for both the test probe, and several different types of large vehicles that were driven over the loops(Table 1). This finding runs contrary to the claim that quadrupole loops are more sensitive for vehicle detection.. The quadrupole loop had lower sensitivity along its central axis, which was where sensitivity was expected to be greatest (Figure 6).. The field sensistivity maps show no evidence that quadrupole loops are less susceptible than rectangular loops to false calls from vehicles in adjacent lanes(Figure 6, Figure 8).
The outcomes of this study are applicable to the design of ILDs for detection of vehicles with large clearance areas. Accurate presence detection of heavy trucks with large spans between axles is one such application. Another would be the detection of wooden buggies, which have few metal components sitting relatively high above the pavement surface. The methods presented in this study may also be used to map the sensitivity of other ILD geometries for a wide range of applications ranging from the detection of aircraft during ground maneuvers to the detection of smaller metal objects passing through a given space.
ACKNOWLEDGMENTS This work was supported by the Joint Transportation Research Program administered by the Indiana Department of Transportation and Purdue University. The contents of this paper reflect the views of the authors, who are responsible for the facts and the accuracy of the data presented herein, and do not necessarily reflect the official views or policies of the Indiana Department of Transportation. These contents do not constitute a standard, specification, or regulation.
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REFERENCES 1. Klein, L.A., D.R.P. Gibson, and M.K. Mills. Traffic Detector Handbook. FHWAHRT-06-108. Federal Highway Administration, U.S. Department of Transportation, 2006. 2. Mills, M.K. “Self Inductance Formulas for Multi-Turn Rectangular Loops Used with Vehicle Detectors,” 33rd IEEE VTG Conference Record, IEEE. 1983. pp. 64– 73. May 1983. 3. Mills, M.K. “Self Inductance Formulas for Quadrupole Loops Used with Vehicle Detectors,” 35th IEEE VTG Conference Record, IEEE. 1985. pp 81–87. May 1985. 4. Smaglik, E.J., D.M. Bullock, and A. Sharma, “A Pilot Study on Real-Time Calculation of Arrival Type for Assessment of Arterial Performance,” ASCE Journal of Transportation Engineering, Vol. 133, No. 7, pp.415–44, July 2007. 5. Day, C.M., E.J. Smaglik, D.M. Bullock, and J.R. Sturdevant, ”Quantitative Evaluation of Actuated Versus Nonactuated Coordinated Phases,” Transportation Research Board, Paper ID: 08-0383, submitted July 2007, revised October 2007, in press. 6. Bullock, D.M., C.M. Day, and J.R. Sturdevant, ”Signalized Intersection Performance Measures for Operations Decision Making,” Institute of Transportation Engineers Journal, in press. 7. S. Park and S. G. Ritchie, “An Innovative Single Loop Speed Estimation Model with Advanced Loop Data. In Proceedings of the 85th Annual Meeting of the Transportation Research Board, January 21-25 2007, Washington, DC. 8. D. J. Dailey, “Travel-Time Estimation Using Cross-Correlation Techniques,” in Transportation Research Part B, Vol. 27B, No. 2, 1993, pp. 97–107. 9. J. Kwon, B. Coifman, and P. Bickel, “Day-to-Day Travel Time Trends and Travel Time Prediction from Loop Detector Data,” Transportation Research Record, #1717, TRB, National Research Council, Washington, DC, pp. 120–129. 10. B. Coifman, “Vehicle Reidentification and Travel Time Measurement in RealTime on Freeways Using the Existing Loop Detector Infrastructure,” presented at 77th Annual Meeting of the Transportation Research Board, Jan. 11–15, 1998, Washington, D.C.
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11. C. Sun, S. G. Ritchie, K. Tsai, and R. Jayakrishnan, “Use of vehicle signature analysis and lexicographic optimization for vehicle reidentification on freeways,” in Transportation Research Part C, Vol. 7, 1999, pp. 167–185. 12. Ndoye, M. V. Totten, B. Carter, D.M. Bullock, and J. Krogmeier, “Vehicle Detector Signature Processing and Vehicle Reidentification for Travel Time Estimation,” Transportation Research Board, Paper ID: 08-0497, January 2008. 13. Hamm, R.A. and D.L. Woods. “Loop Detectors: Results of Controlled Field Studies.” ITE Journal Vol. 62, No. 11, pp. 12–16, 1992. 14. Kidarsa, R., T. Pande, S.V. Vanjari, J.V. Krogmeier, and D.M. Bullock, “Design Considerations for Detecting Bicycles with Inductive Loop Detectors," Transportation Research Record, #1978, TRB, National Research Council, Washington, DC, pp. 1-7, 2006. 15. Krznaric, S. and J.A. Gatto, “Electromagnetic Properties of Ferrous and Nonferrous Metals,” In American Institute of Aeronautics and Astronautics 37th Structural Dynamics and Materials Conference, Salt Lake City, Utah, April 18-19, 1996. 16. Koerner, S.J., “Inductive Loop Structure for Detecting the Presence of Vehicles Over a Roadway,” U.S. Patent 3,984,764, Oct. 5, 1976.
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Vehicle Body
AV
Induced Current lV
L1 Vehicle
Induced Current
M21
d
Loop Current
Loop Detector L2
NL
Loop Current
AL lL
Magnetic Flux
Loop Detector
(a) Electrical model
(b) Physical model
Figure 1. ILD-vehicle interaction modeled as an air core transformer.
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8
7
Loop Sensitivity ∆ L/L
6
5
4 Vehicle traveling on loop centerline
3
Vehicle traveling on loop edgeline
2
1
0 100
Vehicle traveling 2 ft outside of loop edgeline
150
200
250
300
350
Number of Samples
Figure 2. Example loop detector traces as a vehicle passes over the center of the loop.
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L1
L2
L3
L4
L6
L5
(a) Photo of test bed.
L1
L2
L3
L4
L6 L5
L1 L2 L3 L4 L5 L6
Lead-in terminals
(b) Electrical diagram.
Figure 3. Loop detector test bed.
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2" PVC 12"x12" Engineering Joist 2"x4"
8'
12'
1.92'
(a) Drawing of the gantry used to control the height during measurements.
(b) Picture of test in progress using an anodized aluminum sheet. Figure 4. Testing apparatus.
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144 120
Edge +12 Edge Line Edge –12
72
Reference Point
96
Edge –60
48 24 0
Center Line
–24 Center Horizonal Offset –48
Edge –60
–72 –96 –120 –144 –120
Edge –12 Edge Line Edge +12
–96
–72
–48
–24
0
24
48
72
96
120
Figure 5. Loop traces.
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Table 1. Loop detector response for different vehicles and loop geometries. Vehicle Type Passenger Car (Mitsubishi Gallant) Pickup Truck (Chevrolet Silverado) Front End Loader 2-Axle Dump Truck Bicycle (Loop Edge) Bicycle (Loop Center)
∆L/L Value 20 ft Quadrupole
Clearance (inches)
6 ft Round
6 ft × 6 ft Octagonal
9
7.42
7.72
2.52
5.09
16
5.38
5.52
1.31
5.25
>24
N/A
N/A
0.6
1.67
>24
N/A
N/A
0.561
2.56
On Pavement
0.193
0.241
0.072
0.171
On Pavement
0.02
0
0.264
0.003
20 ft Rectangular
Table 2. Correspondence of sensitivity levels to ∆L/L values. L/L (percent) 2.56 1.28 0.64 0.32 0.16 0.08 0.04 0.02 0.01 0.005 0.0025
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Reno AE Sensitivity Level 1 2 3 4 5 6 7 8 9
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EDI Sensitivity Level 1 2 3 4 5 6 7 8 9 -
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2.5
2.0
Steel at 12"
∆L/L (%)
1.5 Aluminum at 12"
1.28
Similar response for steel and aluminum at 24"
1.0
A
A
0.64
Aluminum at 36" (no response for steel)
0.5 0.32 0.16 0.08
0.0 72 66 60 54 48 42 36 30 24 18 12
6
0
6
12 18 24 30 36 42 48 54 60 66 72
Centroid Horizontal Offset (in.)
(b) Cross section A-A.
(a) 20 ft quadrupole loop. 2.5
Steel at 12" 2 Aluminum at 12"
∆L/L (%)
1.5 Similar response for steel and aluminum at 24"
1.28
B
B
1 Similar response for steel and aluminum at 36"
0.64
0.5 0.32 0.16 0.08
0 72 66 60 54 48 42 36 30 24 18 12
6
0
6
12 18 24 30 36 42 48 54 60 66 72
Centroid Horizontal Offset (in.)
(d) Cross section B-B.
(c) 20 ft rectangular loop. Figure 6. Response of quadrupole and rectangular loops to different metals at various heights.
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4.0 Steel at 12" 3.5 Aluminum at 12" 3.0 2.56
∆L/L (%)
2.5 Similar response for steel and aluminum at 24"
2.0
C
C
1.5 1.28
Similar response for steel and aluminum at 36"
1.0 0.64
(b) Cross section C-C.
0.5 0.32 0.16
0.0 72 66 60 54 48 42 36 30 24 18 12
6
0
6
12 18 24 30 36 42 48 54 60 66 72
Centroid Horizontal Offset (in.)
(a) 6 ft × 6 ft octagonal loop. 4.0
3.5
Steel at 12"
3.0 Aluminum at 12" 2.56
∆L/L (%)
2.5 Steel at 24" Aluminum at 24"
2.0
D
D
1.5 1.28
Aluminum at 36" 1.0 Steel at 36"
0.64
(d) Cross section D-D.
0.5 0.32 0.16
0.0 72 66 60 54 48 42 36 30 24 18 12
6
0
6
12 18 24 30 36 42 48 54 60 66 72
Centroid Horizontal Offset (inches)
(c) 6 ft round loop.
Figure 7. Response of 6-foot octagonal and round loops to different metals at various heights.
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4.0 6 ft x 6 ft Octagonal 3.5
6 ft Round 20 ft Rectangular
3.0
20 ft Quadrupole 2.56
∆L/L (%)
2.5
2.0
1.5 1.28
1.0 0.64
0.5 0.32 0.16
0.0 72 66 60 54 48 42 36 30 24 18 12
6
0
6
12 18 24 30 36 42 48 54 60 66 72
Centroid Horizontal Offset (in.)
Figure 8. Comparison of loop response to galvanized steel at 12 inches above the pavement. Note that the 6 ft loop traces represent the sensitivity of a single loop; multiple loops in series would have an overall lower sensitivity.
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12 -12
24
36
48
60
72
84
132 120 108 96
0
-24 -36 -48 -60 -72 -84 -96 -108 -120 -132
∆L/L (Percent)
2.5
1.5-2.0
2.0
1.0-1.5
1.5
0.5-1.0
1.0
0.0-0.5
0.5
Direction of Vehicular Travel
0.0 72 60 48 36 24 12 0 12 24 36 48 60 72
Horizontal Offset (Inches)
(a) 20 ft quadrupole loop.
-60
12 -12
24
36
72
84
132 120 108 96
48
0
-24 -36 -48 -60 -72 -84 -96 -108 -120 -132
2.0-2.5
∆L/L (Percent)
2.5
1.5-2.0
2.0
1.0-1.5 1.5
0.5-1.0 0.0-0.5
1.0
Direction of Vehicular Travel
0.5 0.0 72 60 48 36 24 12 0 12 24 36 48 60 72
Horizontal Offset (Inches)
(b) 20 ft rectangular loop. Figure 9. Three-dimensional plots of inductance response to the galvanized steel sheet elevated 12 inches from the pavement.
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36
48
24 12 0 -12 -24 -36
3.5-4.0
∆L/L (Percent)
-48
3.0-3.5
4.0
2.5-3.0
3.5
2.0-2.5
3.0
1.5-2.0
2.5
1.0-1.5
2.0
0.5-1.0
1.5
0.0-0.5
1.0 0.5 0.0 72 66 60 54 48 42 36 30 24 18 12 6 0 6 12 18 24 30 36 42 48 54 60 66 72
Horizontal Offset (Inches)
Direction of Vehicular Travel
(a) 6 ft × 6 ft octagonal loop.
36
48
24 12 0 -12 -24
3.5-4.0
-36
3.0-3.5
∆L/L (Percent)
-48 4.0
2.5-3.0
3.5
2.0-2.5
3.0
1.5-2.0
2.5
1.0-1.5
2.0
0.5-1.0
1.5
0.0-0.5
1.0 0.5 0.0 72 66 60 54 48 42 36 30 24 18 12 6 0 6 12 18 24 30 36 42 48 54 60 66 72 Horizontal Offset (Inches)
Direction of Vehicular Travel
(b) 6 ft round loop. Figure 10. Three-dimensional plots of inductance response to the galvanized steel sheet elevated 12 inches from the pavement.
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Paper revised from original submittal.
125
100
100
75
75
Longitudinal Position (Inches)
Longitudinal Position (Inches)
125
50 25 0 –25
7 0
4
0 7 4
–50 –75
50 25 0 –25 –50
–125
–125 0
25
7
50
20 10 0 –10 –20 1
4
1
7 0
–40 –50 –60
–40
–20
0
20
40
60
Longitudinal Position (Inches)
Longitudinal Position (Inches)
30
4
0
25
50
(b) 20 ft rectangular loop.
40
7
–25
Horizontal Position (Inches)
(a) 20 ft quadrupole loop. 50
0
7
–50
Horizontal Position (Inches)
–30
4
4
–75 –100
–25
1 1
–100
–50
7
7
50 40 30 20 10 0 –10 –20
0
7
4
1
–40
–20
1
4
20
40
7
0
–30 –40 –50
Horizontal Position (Inches)
(c) 6 ft × 6 ft octagonal loop.
–60
0
60
Horizontal Position (Inches)
(d) 6 ft round loop.
Figure 11. Contour plots of inductive response to the galvanized steel sheet at a height of 24 inches from the pavement surface.
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Paper revised from original submittal.
(a) Rectangular loop.
(b) Quadrupole loop.
Figure 12. Plots of magnetic field strength for loop geometries, from the 1976 quadrupole loop patent (16).
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Paper revised from original submittal.
