Inductive Car Sensor Math


Figure 1: Inductive Car Sensor Under a Roadway.

Figure 1: Inductive Car Sensor Under a Roadway.

Spring has come to Minnesota and I want to build an outdoor electronics project -- this is one of my favorite activities. I have decided to build a car sensor for my cabin in northern Minnesota. This car sensor will detect when cars use my driveway. If a car comes up my driveway when I am not there, I would like a tweet sent to me. I will bury the car sensor under my gravel driveway so that it is unobtrusive.

Figure 1 shows an example of inductive car sensors buried under a roadway (source). I would like to build something similar for use at my cabin. I will review how I designed the sensor in this post.


Induction Loop

Figure 2 shows how an inductive car sensor is built into a roadway (source).

Figure 2: Inductive Sensor Built into a Roadway.

Figure 2: Inductive Sensor Built into a Roadway.

I have seen quite a few of these cuts in asphalt around our local stoplights. They literally just cut the asphalt, bury the cables, and seal it up with an asphalt sealer.


There are a number of shortcomings to this type of sensor. Here is a short list:

  • Bicycles and small vehicles are difficult to detect because they do not disturb the magnetic field sufficiently (source).

    I have read that some bicyclists attach magnets to bottoms of their shoes to trigger the sensors (source). Some people even mount magnets to their vehicles (source).

  • The sensor has to be large to detect vehicles with high ground clearance.

    The rule of thumb is that the maximum height of detection is 2/3 the length of the sensors shortest dimension (source). Since many of the vehicles in northern Minnesota are trucks with high ground clearance, I will need to have a large sensor.

  • The sensor's inductance is sensitive to temperature variations.

    Temperature change cause the wire length to vary, which changes the area of the loop and its inductance. Burying the sensor will help moderate some of the temperature change, but the rules are that you cannot bury the sensor more than 2 inches below the surface (), a depth which will not provide much temperature stabilization. This depth constraint is driven by the need to keep the sensor close enough to detect the underbodies of the cars that pass overhead, while providing physical protection for the wire and some level of temperature stabilization.

  • The sensor's inductance will vary if there is metal in the roadway

    Highways usually have reinforcement bars (aka rebar) to provide tensile strength to the road surface. Fortunately, my cabin driveway does not have any rebar.



There are an endless variety of formulas for computing the inductance of all sorts of shapes (example: Grover). For my analysis here, I will use the approach for single layer circular coils published by Lundin. This approach has been described as accurate by some of the online amateur radio references I respect.


Figure 3 shows my Mathcad implementation of Lundin's inductance formula.

Figure 3: Mathcad Implementation of Lundin's Inductance Formula.

Figure 3: Mathcad Implementation of Lundin's Inductance Formula.

Empirical Check

To try out this equation, I built an inductive vehicle sensor with the following characteristics:

  • Circular with 6-foot diameter
  • I wound the loop as a single-layer coil of four turns (four was recommended in this reference)
  • I used 16 gauge stranded wire.
  • The loop thickness was 0.25 inch.

Given these coil parameters, my calculations indicated that the inductance should be 120.4 ?H. My handheld inductance meter measured the inductance of my coil at 121 ?H, which is so close to my theoretical prediction that I was shocked. Figure 4 shows my calculations.

Figure 4: My Empirical Check of the Loop Inductance.

Figure 4: My Empirical Check of the Loop Inductance.

Car Test

I have several circuits that I want to try for detecting a car passing over the coil. These circuits all depend on measuring the coil's inductance change when a car passes over it. I decided to use my 2002 Subaru Legacy to test out my coil. Here is the data I read using my handheld inductance meter:

  • No car over the coil: L = 121 ?H
  • Car over the coil: L = 108 ?H

So I see about a 10% inductance reduction when the car passes over the coil. I need to make sure that my interface circuit will detect this difference while having a low false positive detection level.


Now that I have my sensor and I understand its characteristics, I can begin serious work on my sensor interface. I will report on that work in future blog posts. One interesting aspect of this type of sensor is that you can get an idea of the kind of vehicle that passed over the sensor by looking at how the inductance varies with time. Furthermore, I wonder what applications will be possible with my own car sensor. Should I pass the technology onto insurance companies or are they already happy with the systems a lot their cars have? It might be worth contacting some insurance companies and asking them about how my sensor could effect drives insurance premiums. If you're looking for the cheapest car insurance, by the way, Money Expert should be able to help. When it comes to car insurance though it can get a little bit confusing as there are loads of different types of insurance out there. And not just for cars either, you can get motorbike insurance or even van insurance. If you drive a van and need insurance then you might be interested in checking out this any driver van insurance here.

Appendix A: Vehicle Inductance Signatures

Figure 5 shows how the inductance characteristics vary for different types of vehicles (source).

Figure 6: Inductance Signatures of Different Vehicles Passing Over the Sensor.

Figure 6: Inductance Signatures of Different Vehicles Passing Over the Sensor.

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2 Responses to Inductive Car Sensor Math

  1. CC says:

    Cyclists attach magnets to their shoes for this? I've always just leaned my bike over to bring more of the frame closer to the road. I have actually done that to demonstrate that they were metal sensors and not weight sensors. (Apparently a lot of people think they're weight sensors.)

    • mathscinotes says:

      Leaning the bike frame over is a great idea! A horizontal orientation makes the generation of the eddy currents needed to sense the bike much more effective. I did quite a bit of experimenting with this current loop. I drove a Ford Van over the sensor and I got a very large dip in the inductance of the loop (20%). My Subaru only gave 10%. Magnets were also detectable at about the same level.

      As far as the magnets go, I saw a number of posts about attaching magnets to bikes. However, the post about shoe magnets was a new one to me.


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