How to detect yellow school bus from 100 to 200 yards away?
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First some kind of optics (old binoculars or a telescope) that you would aim along the travel path of the bus. Then at the focal point of this you put a color light sensor (like this one) connected to a microncontroller (like the Arduino or PICAXE), and wire it up to your bell or whatever. Then you need to make sure that it's protected from the elements. After you've got all that you'd need to take time to calibrate it. This will be very tricky since it would need detect the yellow of the bus on both sunny and cloudy/rainy/foggy/snowy days. But also not detect the yellow of, for example a truck illuminated by a yellow sunrise, or a tree in the background who's leaves are turning yellow, or a DHL truck.
You could minimize the calibration problems by hooking it into a real-time clock and write a schedule for it so it only looks for a bus it at certain times and days of the week. In addition you could add an ambient light, a moisture sensor and a temperature sensor to check the light and rain/snow levels and adjust the color sensitivity accordingly. Heck, while you're at it, you could put a whole weather station out there, and add a switch to tell you when the mail has gone as well.
Depending on how far away your mail box is from the house, either you'd need to run wires (for power and to ring your bell) or or hook it up via batteries and probably a solar cell and then communicate with the base station in your home with some kind of wireless solution. And hope no one steals it.
Or you can get ready for the bus ahead of time. (But it would be totally cool to see a weather station/bus/mail detector out at the end of someone's driveway.)
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