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Why are umbrellas specifically in black? Of course we do have colored ones, but black is the majority. Is there any scientific reason behind it?

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I'm in Japan. Here vast majority of umbrellas are white or transparent. –  qubyte Feb 19 '12 at 14:06

1 Answer 1

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Physics answer

A black body at a temperature T, area A (on either side) will radiate heat by: $$\dot{Q}_{radiated ,downwards}=\sigma A T^4$$. If incident radiations are of power $P$, then $$\dot{Q}_{body}=mc\frac{dT}{dt}=P-2\sigma AT^4$$ (the 2 comes into place because it radiates in both directions)

We can integrate this if we want, but we mainly want to qualitatively analyse it. From this equation, we can see that as time passes, temperature will increase to an equilibrium value ($T_{eq}=(P/2\sigma A)^{1/4}$). I am assuming that $P>2\sigma A T^4$ in this analysis (I've never seen an umbrella that feels hotter than direct sunlight). At this equilibrium value, you will receive heat $\sigma A T^4$, i.e., $\frac{P}{2}$.

For a non-black umbrella, assuming no transmitted heat, we have $e=a=1-r$ (coefficient of emission,absorption and reflection respectively). Out of incident heat power $P$, $aP$ is absorbed. The body radiates heat on either face as $e\sigma AT^4=a\sigma AT^4$. So we have $$\dot{Q}_{body}=mc\frac{dT}{dt}=aP-2a\sigma AT^4$$. From this, we get the same value of equilibrium temperature as for a black body. But, radiated heat power is $eA\sigma T^4$, so it will radiate less heat than the black umbrella onto you (Since both $T=T_{eq}$ are the same).

So paradoxically, we get that a black umbrella is the worst thing to use on a sunny day.

IMHO

Black seems to be the majority because of a cultural bias. I'm assuming you're from India (by looking at your name). Since India was once a British territory, we can trace the use of black umbrellas back to the Brits. The Brits used to use black because black was considered formal attire (Black suits are actually the most uncomfortable from the physics point of view). This must have proliferated to India (Most British traditions have). Umbrellas before the British must've been colorful (See the painting here). If you take a look at Japanese umbrellas, they're all colorful. So black is really not the majority worldwide.

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Since a black umbrella absorbs all light the fabric will get hotter than a white umbrella. So the black umbrella will radiate more infrared heat onto the user. –  FrankH Feb 18 '12 at 6:41
    
Yeah.. I'll add this to the answer. I sort of saw the radiation tag and wrote that part of the answer without thinking too much.. –  Manishearth Feb 18 '12 at 7:02
    
Love the historic explanation :) How true, or atleast how realistic! –  Greenhorn Feb 18 '12 at 7:08
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I would add that it is a useful color for all social occasions, particularly in a country where it rains most of the time. I remember having a problem going to a funeral with a colored umbrella, I chose to get wet.One does not take red to funerals. Women have the all purpose "little black dress" too. –  anna v Feb 18 '12 at 7:13
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Rather than writing "Edit: This is wrong...." it would be much better if you actually remove the wrong part from the answer entirely and replace it with the right information. –  David Z Feb 18 '12 at 21:04

protected by Qmechanic Sep 2 '13 at 10:23

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