Medium Distance Measurement With Homemade Linear Resistor

There are a number of methods for measuring distance that differ in terms of maximum detectable distance and accuracy :

1. Ultrasonic sensors such as the HC SR04 can measure distances up to 10 metres with an accuracy of a few centimetres.
2. The IR detector and its associated detector can be used to assess distance from few centimetre when connected to an operational amplifier in comparator mode.
3. Another IR system, such as the CNY 70 , can give distances of less than 5mm with a fairly good accuracy of close to 0.5mm.
4. For very short distances, such as those required for microscopy or optical measurements, the sensor works on the principle of magnetic field variation. With magnetic sensors such as [TTL173C], we can measure distances as small as hundreds of microns.

In this context, distances close to 1 to 30 cm cannot be estimated with a simple sensor. However, in the context of manufacturing equipment for measuring viscosity and settling time, we needed a good approximation (in the magnitude of mm) of a distance between 10 and 20 cm. So we built this homemade sensor to measure distances of about ten centimetres. 

The concept is to use the conductivity of pencil lead. Pencil lead doesn't contain actual lead but is a non-toxic blend of graphite, clay and more or less 5% of wax for lubrification. The harder the grade, the less graphite it contains. The figure below illustrates the relationship between lead hardness, pencil grade and graphite weight percentage [1, 2]

The graphite is the conductive material that supports the linear resistor we make. We use a sheet of paper (A4 or A3 depending on your needs and the distance to be measured) and a 6B pencil lead:

First we draw a black stripe on the paper with the 6B pencil at the desired distance. Several passes are necessary to achieve sufficient conductivity (picture 1). A 1 cm strip is cut with a cutting machine. This strip can be used to make initial measurements and validate the concept (picture 2). The strip is then positioned on the final support. This is a polypropylene tube. The conductive tape is fixed by means of adhesive and is held in place during the setting time by means of a woollen thread (picture 3). The final assembly, with two connectors separated by a distance (d), makes it possible to measure the resistance obtained (picture 4).

We carried out two tests to validate the concept and assess the accuracy of this sensor. In the first test (number 1 in blue in the graph below) we did not use a lot of pencil deposit, making only two passes. In the second (number 2 in red in the graph below), we forced the amount of pencil deposited by making at least 4 passes. Resistivity measurements have been made randomly three times per distance.

In both cases there is a linear relationship between the distance (d) and the resistance. The slope of the linear equation between distance and resistance depends on the amount of graphite deposited. The higher the graphite deposit, the lower the slope : 1.2 in the first case, 0.52 in the second.

In the second case, we are continuing the investigation. This will enable us to assess the accuracy of this sensor. To do this, we studied the probability distribution of the gap, which is the difference between the measured resistance and the theoretical value given by the equation.

These gaps are representative of the error due to variation in the amount of graphite deposited and the error in the measurement of the distance (d). The gap distribution is not a Gaussian distribution. Alternatively, the cumulative probability for the gap value (±d) gives a fairly good assessment of the probability of being 68% or 95% confident (similar to 1 standard deviation and twice the standard deviation for a Gaussian distribution).

The distance is assessed at the interval of +0.35 cm for a confidence level of 68%. The distance is assessed at the interval of +0.70 cm for a confidence level of 95%. In fact, 68% is more than enough for this sensor, and the higher the distance measurement, the higher the accuracy, thanks to a fixed inaccuracy of 0.35 cm.

Further reading : « 100 Sensors In Action, Electronic For Chemists » - Gérard Bacquet- SciencExpert Edition - 2024

[1] M. C. Sousa and J. W. Buchanan: ‘Observational models of graphite pencil materials’, Computer Graphics Forum,2000,19, (1), 27–49

[2] pdf here : https://www.semanticscholar.org/paper/Observational-Models-of-Graphite-Pencil-Materials-Sousa-Buchanan/24572b411e43eac33ad1fc4233e5b00c8019d3d7