Velocity Mapping

The goal of the mapping is to have an idea of how the wind speed in the duct varies with the location. To acheive this mapping, a 2 axis cartesian arm has been built. A pitot attached to the vertical arm is coupled to a pressure transducer. This setup will measure the pressure difference between the total and static pressure. Using the Bernoulli equation, the wind speed can then be derived.

The Setup

The entire setup, like the rest of the intrumentation has been entirely built out of legos. Micromotors are used to move the vertical and horizontal arm. The motors are coupled with rotation sensors which allows to deadrecon the arms positions. The entire instrumentation is controlled by an RCX programmed in Robolab. It is wise to power the RCX with an A/C adaptor instead of batteries, in order to maintain a constant voltage to the sensor. The dataset collected was exported to Matlab for analysis and plotting.

In order to connect the pressure sensor with the RCX, a sensor adaptor needs to be built. This is what the breadboard visible on the picture if for. The sheet of paper is used to try to cover the opening left to allow the vertical arm to slide from one side of the duct to the other. This method is far from perfect...

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The Sensor

The differential pressure tranducer chosen for this setup is the model No 646-1 from Dywer Instrument. It can measure pressure differential ranging from 0 and 250Pa, which corresponds to velocities going from 0 to 20m.s^-1. It also has a reasonnable price (<100$).

As it is a three wire sensor (power supply in, output and ground) an interface needs to be built in order to connect it to the RCX which uses only two wires (the same wire used for supply and output). Electronic components required:
   • 6 diodes
   • 1 22uF capacitor
   • 1 1000ohms resistor
   • 1 breadboard

Wiring diagram:

What the sensor adaptor looks like for this setup (green: ground, red: power in, black: output).

Sensor Calibration

The calibration aims at obtaining a linear relation between the raw value read by the RCX (0 to 1024) to the actual pressure difference. This is done in two steps, a first relation needs to be obtain to correlate the raw value to the output voltage of the sensor. This voltage then needs to be converted to pressure. This information is usually available with the product's documentation. However it is wise to check it as the sensor output may vary with input voltage. Merging those 2 relations will give you the a linear relation between the raw value and pressure.

Here are 2 linear curves obtained with the described configuration:

Acheiving several calibrations enables to obtain graphically the calibration uncertainty: 2.5Pa. Note that this uncertainty is not constant when considering the velocity, this is caused by the square root in the formula relating the pressure to the velocity.

Reading the sensor

The resolution of the sensor can be found using the calibration curve. The pressure that can be actually measured by the sensor when couped to the RCX ranges from 0 to 135Pa for raw values between 450 and 1024. This gives for this configuration a resolution of 0.24Pa.

It is also wise to average multiple readings over a period of time at one location and average them. Taking 10 measurements at one location gives a 95% confidence interval of 0.35Pa, taking 100 redudes this interval to 0.10Pa.

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The Results Obtained

For the plots below, pressure was measured at the intersections of a 21x15 grid represented by the rectangle ABCD on the picture. 10 values were averaged over 1 second at each location.

This is one of the mapping which should be relatively correct. The velocity has been measured highest in the corners, and lowest in the center of the duct. The lower speeds at the top are caused by the opening around the vertical arm.
(Legend: Red: 9.3m.s^-1, to deep blue:8.6m.s^-1)

The following plots show results that had been previously obtained before taking into account some artifacts. These plots my help you identify what may alter the measurements.

The following plot was the first one completed, notice that the velocity measured increases at the bottom the duct. In effect, for this first try, the needed opening for the vertical arm and pitot tube hadn't been covered to prevent the air flow from escaping.

This next example was obtained when the RCX was running on batteries. The velocity measured tends to decrease as we move to the right of the duct, which woud have been very unlikely. This was explained when noticing that the measurements started at the left of the duct and ended to the right. A complete run being relatively long, the RCX would not sustain a constant voltage to supply the sensor, causing the output voltage to decrease as well. That is why the RCX is now powered with an A/C adaptor.

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Downloads

RCX code example: code used to control the 2 arms and log the data. The data needs to be downloaded via the investigator afterward.
Matlab plotting code example: code used to do the plotting, data obtained by the RCX are exported as a text file and imported in Matlab.