## I’m back, and it’s raining cats and dogs

*Yes, I know. This blog hasn’t been looked at from the inside for three months now. What can I say? I decided to leave off blogging for a bit since I moved. Now I’m back, and it’s raining here.*

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So it’s been raining in Manila for a week now, but the weather hasn’t been that consistent. It starts off perfectly sunny in the morning, and continues to be quite fine up to the late afternoon. It starts to rain, and rain heavily at that, when I’m in the middle of my commute home. Of course, this is orders of magnitude better than having it rain all day I suppose, but I can’t help but feel betrayed by the weather when I have to step out of a jeep and walk a hundred meters or so and the water is seeping up my pants.

Also, if you’re a short person with an umbrella, and you stick too close to me while holding your umbrella low over your head making the edge poke at the nape of my neck over and over again, I *will *spend the rest of my walk plotting a horrible future for you. I won’t do anything, for sure, but if thoughts could kill… Well, anyways, I digress…

Two days ago (from the time of my writing this), I was yet again walking through the pouring rain and I thought about the expression “It’s raining cats and dogs”. And just as trains of thought often lead to the most bizarre places, I wondered what it would look like if it actually rained cats and dogs.

Well, first of all, cleanup would be a mess. All those bodies going splat would ruin everybody’s day. Not to mention that the terminal velocity for a falling cat or dog is probably big enough to damage property and cause serious injuries on impact. But how many cats and dogs would rain if it were raining cats and dogs? In short, if it rained as much cats and dogs as the amount of water that usually falls during heavy rain, how many cats and dogs would that be? That is where the maths come in, because I totally geeked out and computed it.

First of all, we have to imagine the ratio of dogs vs. cats that would be raining down. The term cats AND dogs makes it easy to think that it would be 50/50. But 50/50 of what? Would it be a ratio of count, such that one dog falls for every cat that falls; or would it be a ratio of amount, such that the same amount of cat (either volume or mass) falls for every amount of dog? If we choose the second option, that would mean that more cats would fall that dogs, because there’s certainly more dog stuff in a dog than there is cat stuff in a cat. Personally, I like to imagine that they should be calculated using a 1:1 ratio on amount. It just seems more natural to me. That’s why I’m going to try calculating using that assumption.

The first thing to do is to find out how much water actually falls to the ground during the type of rain that is said to be “raining cats and dogs”. Since we are interested in finding out what the fall of cats and dogs would look like, it would be more appropriate to use rate or rainfall rather than total amount of rainfall. This is usually expressed in terms of milimetres of rain per hour. One milimetre of rain per hour means that, on a flat solid surface of a container, the water level rises to one milimetre per hour. If I want to find out how much water (in volume) falls in an area of ground per hour, here’s what I’m gonna do:

In a square metre of ground area, a milimetre of rain falls per hour. That means that after that hour, there will be a film of water one milimetre high and in an area of one square metre.

Let :

V = volume

A = area

t = time

The rate of rainfall is the volume of water that falls in an area for a specific time. For rainfall measured one milimetre per hour, a total of 1 m^{2} film of water 1 mm thick falls to the a 1 m^{2} area of ground every hour. If I convert that into litres, that’s 1 L or water falling into a 1 m^{2} area of ground per hour.

Next, I decided to use mass for the falling dogs and cats, instead of volume. I *wanted *to use volume as it seemed the more natural thing to use. However, google doesn’t seem to know the average volume of a cat or dog, so I used mass, for which the information was really available. I think people are too afraid to dip cats in water and do the water displacement method, and dogs are probably too heavy to dip anyway. It’s an interesting gap in our understanding though, so somebody out there ought to measure the volume of these animals.

Anyways, since we are using mass, we will have to convert the volume of falling rain into mass. Since the density of water is 1000 grams per litre, a milimetre of rain per hour is equal to 1000 grams of water an hour.

In terms of finding out how many cats and dogs that is, I cooked up an equation for that:

Let:

g= mass

n = number

c = cat

d = dog

As per our assumption, **g**_{c }= **g**_{d}. Therefore:

That means that half the mass of rainfall is converted into dog, and half into cat. To find out how many cats or dogs that is, simply divide that with the average mass per cat (or dog)

Now wikipedia informs me that heavy rain is usually within 10 to 50 milimetres per hour, so let’s assume that our heavy rain is at 30 milmetres per hour. Since 1 mm per hour is equal to 1 g/m^{2}•hr, that equals to 30 L of water per hour per square meter, or 30000 g/m^{2}•hr.

For the other necessary values, I googled around and found out that a medium-sized cat should be around 4500 grams, and a medium-sized dog is about 17000 grams. So:

And,

So there you have it. 3 cats and 1 dog would fall per square metre of ground per hour. That’s quite a lot, actually. If you think about it, a square metre of ground isn’t really that big. Just imagine, in a 10 m x 10 m plot – that’s already 100 m^{2} – 333 cats and 88 dogs would be falling on that area per hour, more than 5 cats and 1 dog per minute.

And just think, all those cats and dogs probably won’t look pretty when the land. Think of the gruesome mess that would look like on the roads! Roadkill stew, anyone? Yikes. Not to mention the rotting bodies becoming a public health concern as authorities become too overwhelmed to clean up all that mess in time. It’s a good thing it’s just an expression though. Still, it’s fun to think about these things once in a while.

Oh, and if you wanted to check out how many cats and dogs would fall off it we used a count ratio for dog:cat rather than mass, click on this link.

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PS: sorry about the blue borders on the equations. Template boo-boo I’m afraid.

This post is brought to you by my triumphant return to blogging… hopefully.

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