Cat Mathematics: How Many Cats Fit Into the Trunk of a Honda Civic...
Where would the world be without cats and mathematics? For one, the internet probably wouldn't exist. But what do cats and mathematics have to do with each other? Well, follow my logic here: 1) The Internet and it's users are obsessed with cat pictures, cat videos, and cat memes. 2) The internet was created by a bunch of nerds. 3) Nerds tend to both love and be good at math.
Once I realized the connection between cats and mathematics it become obvious that these two seemingly different things were destined to be unified. I suddenly became intrigued and had so many new questions regarding these cute and cuddly creatures. There really is no cooler combination than mathematics and cats. With that said, here are several fun math problems involving our favorite feline friends.
Cat Volume Problems
Cats are slender and flexible creatures that tend to fit into very small or tight spaces. If you've owned any cats in your life then you know exactly what I'm talking about. Domestic cats do come in a variety of sizes and may weigh anywhere from 4 to 30lbs when fully grown. For these math problems we are going to use an average sized domestic cat which weighs in at around 5.5lbs. Assuming a biological density of 66.3 lbs/ft3 the average domestic cat would have a volume of about 0.083 ft3.
If you were to randomly stuff a bunch a of cats inside of a container you would find that there will be plenty of empty space left in the container. This is because cats have an interesting, but cuddly, non-uniform shape. I did some research on the subject of packing ratios and although no one has done an experiment with cats, I've estimated their packing ratio to be about 0.5. For reference, a uniform object like a sphere has a random packing ratio of 0.64, an M&M's is 0.685, and a cube's is 0.78.
Using this information we can easily solve for the number of cats that would fit into a variety of spaces. Below are some example problems
Honda Civic Trunk
First released in 1972, the Honda Civic quickly rose to be one of the worlds most reliable cars. Sales of these vehicles are still going strong and in 2011 Honda released its ninth generation version of the Civic. According to Honda, the modern Civic sedan has a cargo space of around 12 cubic feet. To figure out the number of cats that would fit inside we first have to divide the volume of the Civic trunk by the volume of a cat. So 12 divided by 0.083 is 144.5. Next we multiply this by the cat packing ratio to get the result. So 144.5 x 0.5 = 72 (rounding down). Therefore 72 average domestic cats will fit inside a modern Honda Civic Trunk.
Average American Refrigerator
The average American refrigerator has a storage volume of roughly 22.5 cubic feet (including the freezer). To figure out the number of cats that would fit inside first we have to divide the volume of the refrigerator by the volume of a cat. So 22.5 divided by 0.083 is 271. Next we multiply this by the cat packing ratio to get the result. So 271 x 0.5 = 135 (rounding down). Therefore 135 average domestic cats will fit inside a typical American refrigerator.
Standard Forty-Foot Shipping Container (FEU)
Did you know that 90% of the world's freight is delivered using shipping containers? That's a lot of shipping containers! Although shipping containers come in a variety of sizes, the most common one by far is the Standard Forty-Foot Shipping Container (FEU). Inside a typical 40ft shipping container you will find a maximum capacity of 2261 cubic feet. To figure out the number of cats that would fit inside we first have to divide the volume of the shipping container by the volume of a cat. So 2261 divided by 0.083 is 27,241. Next we multiply this by the cat packing ratio to get the result. So 27241 x 0.5 = 13,620 (rounding down). Therefore 13,620 average domestic cats will fit inside a Standard Forty-Foot Shipping Container.
Construction for the New Orleans Superdome began in 1971 and lasted for 4 years. The stadium is located on 52 acres of land and has an interior space of 125 million cubic feet. To figure out the number of cats that would fit inside we first have to divide the interior volume of Superdome by the volume of a cat. So 125,000,000 divided by 0.083 is 1,506,024,096.4. Next we multiply this by the cat packing ratio to get the result. So 1,506,024,096.4 x 0.5 = 753,012,048 (rounding down). Therefore 753,012,048 average domestic cats will fit inside the New Orleans Superdome.
Cat Area Problems
As we saw with the volumetric calculations, cats actually take up surprisingly little space. Another burning question that I have is how many cats would fit on a standard American football field. The first step to answering this (and similar) questions is to determine the cross sectional area (in the horizontal plane) that a cat physically takes up.
For some reason finding this information online has proven to be very difficult. Therefore, I decided to calculate it myself based on a photograph of a cat. The image below shows a typical cat and its horizontal cross sectional area which I calculated using AutoCAD. The 4-inch wide floorboard was used for scale. Using this image I determined that this particular cat has a cross sectional area of about 178.8in2 or about 1.24ft2.
Now that we have this information it's time to solve some more fun cat problems.
The average U.S. convenience store has a sales area of 2,768 square feet. That's bigger than most American's homes! So exactly how many cats could occupy that floor space? To figure out the number of cats that would fit side by side and end to end in an average American convenience store we have to divide the area of the store by the area of a cat. So 2,768ft2 divided by 1.242ft2 is 2,228 (rounding down). Therefore 2,228 average domestic cats could fit inside a majority of the convenience stores in America.
A standard American football field measures 120 yards long by 53.33 yards wide. The equates to an area of 6399.6 square yards or about 57,596.4ft2. To figure out the number of cats that would fit side by side and end to end on a football field we have to divide the area of the field by the area of a cat. So 57,596.4ft2 divided by 1.242ft2 is 46,373 (rounding down). Therefore 46,373 average domestic cats will fit on a standard American football field.
The Moon's Surface
Although the moon is fairly small compared to Earth, it's much larger than a cat. In fact NASA reports that the surface area of the moon is roughly 14.658 million square miles. So right off the bat we know that it would take a lot of cats to cover the entire surface of the moon. Converting the moon's surface area into square feet and then dividing by the area of a cat yields 329,018,991,304,348 cats. That slightly more than 329 trillion cats!
Feline Terminal Velocity
A falling cat always lands on its feet right? That may be true (most of the time) but the question I want answered is what is a cat's terminal velocity? As it turns out, there is actually a field of study surrounding falling cats (don't worry it's a very small field). Scientists who study this are called Feline Pesematologists. With that said, I'd like to perform my own analysis (on the computer and without real cats of course!)
The formula for terminal velocity is as follows:
Where m is the mass of the falling object, g is the acceleration due to gravity, C is the drag coefficient, ρ is the air's density, and A is the cross-sectional area of the object.
For this physics problem we will need a cats mass, horizontal cross sectional area, and a representative drag coefficient. Problems like this are easier to solve using the metric system so the following parameters will be used to solve the problem:
m = 2.5 kg (5.5lbs)
g = 9.81 m/s2
C = 1.15 (Determined from online research)
ρ = 1.29 kg/m3
A = 0.115m3 (1.242ft2)
Therefore, vterm = sqrt[(2 x 2.5 x 9.81)/(1.15 x 1.29 x 0.115)] which equals 17 m/s. Converting this to miles per hour we get about 38mph. That is one high velocity cat right there!
No cats were harmed in the making of this article. The scenarios presented are not meant to resemble real life events and any similarities to such are purely coincidental.
© 2014 Christopher Wanamaker