Additional Math Pages & Resources

Wednesday, September 15, 2010


Here's a question for you. It involves units, and measuring, and judgement. It's math to me.

Q. How do you determine visibility?

Here's the freeway this morning, as I was driving to work. I'd say it was limited visibility. As I got closer to work, it got worse.
Now it wasn't unsafe to drive or anything, but you certainly couldn't see too far. Since I was driving around with my camera, I went looking for other things that would help me determine the range of visibility. Here's what I saw, quite by accident. A giant spider web. About 5 feet across, I'd say.

Can you see it? My camera had a very hard time focusing and I needed to move around until I got a dark tree right behind the web. Is this better?

It was only visible because the mist (which ruined visibility when driving) was clinging to the web strands and then the sun (trying to peek through the mist) glinted off the moisture.

I now repeat my original question. Q. How do you determine visibility?

Here's what I learned from the Mt Washington Observatory website:

Visibility" is a measure of how far you can see in the atmosphere. 
  • In clear air you can see for long distances, maybe tens of miles. This is "good" or high visibility. 
  • In fog (cloud) you may only be able to see objects a short distance away. This is "poor" or low visibility.
  • For scientific purposes, visibility is recorded more precisely in feet or meters. Our visibility detector (model FD-12P) is calibrated for visibilities from ten meters (33 feet) to 50 km (30 miles). The visibility is measured by a light beam that is projected downward inside one of its slanted "arms". Whenever any cloud is present at the location of the instrument, the tiny cloud droplets deflect some of the projected light up into another arm where a sensitive photodetector is housed. The photodetector generates an electrical voltage that is proportional to the amount of light deflected up the tube. This deflected light is proportional to the density of the cloud (i.e., it indicates the number of cloud droplets per cubic centimeter). This  determines the visibility at the location of the instrument. Our photodetector allows a scientist to know at a glance what the visibility was at any time, day or night.
 Did you notice the limited visibility of the preceding paragraph? Can we use the FD-12P gizmo the observatory folks are using? NO. It measures visibility from 10 m to 50,000 m, it doesn't care about color, and it costs $20,000 - so it is not useful to us.

A. We describe atmospheric visibility by stating a distance in yards or meters. Stating the color of the viewed object is not part of the normal process. Notice how everything so far in the blog post is grey or blue or black?


I think seeing a grey car on a misty morning on a concrete highway is much more seeing like a spiderweb, than it is like seeing the outfit I wore today.

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