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Mon, 10 Nov 2008


What's the point of umbrellas? To be effective, their diameter needs to be slightly more than h * sin(ϑ) (where h is your height and ϑ is the angle of the rain from the vertical). So, if rain is falling vertically you need an umbrella with diameter slightly more than* the width of your shoulders. If rain is going horizontally, you need an umbrella slightly wider than you are tall. If rain is coming down at 20° from the vertical, you need an umbrella diameter just over 0.34 * your height, and so on.

Given that rain can subtend any angle from 0 to 90° from the vertical, then unless you wish to be your umbrella supplier's very best friend in the whole world, you need a Very Large umbrella. And yet, no-one carries such a thing. Indeed, I don't think anyone makes such a thing suitable for anyone other than midgets. So we see that every umbrella user has, from the point of view of keeping themselves dry, made the wrong decision. Their partial solutions are no better than what they would achieve by wearing a good coat and a hat.

Unfortunately, their partial solutions come at the cost to everyone else of getting poked in the face by the metal spikes at the edge of the umbrella.

* the value of "slightly more" is a function of ϑ and the shape of the human body. A good approximation would be to assume that a person's width is h/3 and their depth is h/4.

Posted at 22:21 by David Cantrell
keywords: etiquette | maths | rant
Permalink | 2 Comments

You're quite right, but you're overlooking two points:

1. You can tilt an umbrella into the wind, thus creating a larger safe-zone in the 'shadow' of the umbrella, and

2. An umbrella is a lot compacter to carry around when closed than rainproof hat and coat.

Posted by vegiVamp on Tue, 11 Nov 2008 at 13:39:29

Vegivamp's first point is what the formula I gave was about - the trivial example is that in vertical rain I need an umbrella about 2'6" wide, but in horizontal rain I need one about 6'4" wide.

His second point forgets that the convenience of an umbrella-wielder does not out-weigh his duty to not poke peoples' eyes out. Also that umbrellas look stupid.

Posted by David Cantrell on Tue, 11 Nov 2008 at 21:43:33

Sorry, this post is too old for you to comment on it.