Cloud Detection - Part Five

Power output

I would like the heater wire to output approximately 0.3 W per cm; being that the wire needs to be approximately 37.5 cm long to cover the mirror back, the total power output \(P_{out}\) will be the following:

Supply Current

Calculating the supply current is quite straightforward. The supply voltage \(V_{supp}\) will be 9 V, therefore:

Total Heater Wire Resistance

Now we need to know what the resistance of the entire length of the heater wire will be in order to get the correct gauge nichrome resistance wire:

So the wire ideally needs to have an overall resistance of 6 ohms once built. This includes an extra few centimetres at the end on which to solder on a supply and ground wire.

Let's say that the total length \(\ell_{total}\) of the wire will be 45.5 cm ; at that length:

Conclusion

Ideally the nichrome resistance wire will need to be rated at \(\text{13.2 }\Omega \cdot m\). The nearest I could find was 30 SWG (0.315 mm) at \(\text{14.27 }\Omega \cdot m\), which is what I bought in the end.

Thermostatic Control

The basic cycle of thermostatic control for the mirror is set out below:

1. Define the hysteresis variable \(t_{hyst}\).
2. Derive current dew point temperature from a Humidity Sensor \(t_{dew}\).
3. Measure the current temperature of the mirror surface \(t_{mirror}\).
4. Check the state of condition \(t_{dew} \gt t_{mirror} - t_{hyst}\).

If condition 4 is true then apply heat until condition 4 is false. Once condition 4 is true, switch the heat off. \(t_{hyst}\) is there to ensure that there is a buffer between the dew point \(t_{dew}\) and the temperature of the mirror \(t_{mirror}\) in order to prevent rapid switching of the heater circuit transistor.

Electronics

Control of the heater as above is achieved by using the Arduino to run the thermostatic control cycle, having the DS18B20 to measure \(t_{mirror}\) and an externally situated HTU21D to measure \(t_{dew}\). Using these inputs the Arduino controls the base voltage of a TIP120 Darlington NPN transistor. This transistor in turn controls the voltage to the heater wire.

Below is a mockup of how to wire up an Arduino to control the base voltage of a transistor thus controlling the higher power supply to the (in this case) coil. Of course, the coil symbol in the diagram represents the heater.

Arduino with TIP120 High Power Control

Sensor Update

I've had some long time concerns about the humidity sensor I had lined up to undertake the task of determining dew point.

Up until recently I had always considered using a DHT22 (also known as an Aosong AM2302) to do the job, but had always been a little unsure of how well adapted this sensor would be to living outside all the time. My uncertainty about their robustness comes mostly from their build quality which, to be polite about it, is not really the best.

DHT22 Humidity Sensor

I suppose that my main concern is how a DHT22 would fare in a cold and wet environment and potentially have its performance degrade leading to short to medium term reliability issues; longer term, I cannot imagine it lasting at all! I could find no satisfactory manufacturer's documentary evidence as to how waterproof the packaging was. There is a good deal of in depth research here comparing the different humidity sensors (or Hygrometers as he calls them) available on the market, for those that are interested in further reading. The DHT22 has an accuracy of around 5% between 0% and 90% humidity. Above 90% humidity the device performance is a little uncertain; no real world data exists, just what is presented in the datasheet. Additionally, Robert from www.kandrsmith.org indicates a 50% device failure rate over a period of 2 years in his research.

So, research into DHT22 alternatives lead me to the HTU21D module.

HTU21D Humidity Sensor on a Breakout Board

The stats on the HTU21D look much better; as soon as you take a peek at the datasheet, it becomes obvious that this is a much higher quality product than the DHT series sensor. For a start, there is a proper datasheet rather than the token effort offered by the developers of the DHT22. The build looks much more robust too; both the exterior housing and connector pins are very flimsy on the DHT22, whereas the HTU21D is of a clearly better quality and more robust build.

The HTU21D has a version that comes with a PTFE protector on the sensor window which provides the sensor with a degree of protection from the moisture ingress of an outside environment. Rather than the serial interface of the DHT22, the HTU21D provides I²C communications which I prefer.

Calculating the Dew Point

The dew point temperature measurement is derived from air temperature and humidity both of which are supplied by a humidity sensor. The code I use to derive the dewpoint is written by Rob Tillaart, I cannot even remember when or where I found it, but I have found it useful many times. Below is the code that does the business:

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double dewPoint(double celsius, double humidity)
{
  // (1) Saturation Vapour Pressure = ESGG(T)
  double RATIO = 373.15 / (273.15 + celsius);
  double RHS = -7.90298 * (RATIO - 1);
  RHS += 5.02808 * log10(RATIO);
  RHS += -1.3816e-7 * (pow(10, (11.344 * (1 - 1 / RATIO ))) - 1) ;
  RHS += 8.1328e-3 * (pow(10, (-3.49149 * (RATIO - 1))) - 1) ;
  RHS += log10(1013.246);

  // factor -3 is to adjust units - Vapour Pressure SVP * humidity
  double VP = pow(10, RHS - 3) * humidity;

  // (2) DEWPOINT = F(Vapour Pressure)
  double T = log(VP / 0.61078); // temp var
  return (241.88 * T) / (17.558 - T);
}