# Eating one whale every three thousand days?

My current ongoing project, about which I've asked many questions, is about a world in which evolutionarily plausible legendary and folkloric creatures roam the Earth. One such creature is the sea serpent. In my world, sea serpents are giant relatives of moray eels which use constriction to kill their prey, large whales.

Note: pretty much every figure I give below is only roughly so, so just pretend I've put the word "about", "roughly", or "approximately" before every number.

If I assume a grey whale is cylindrical, then it has a diameter of 4 metres, and therefore a circumference of 12 metres. If the serpent is to wrap itself around its grey whale prey 3 times, then it needs to be at least 36 metres long. I'll add 6 metres to account for the head and tail. To decide how wide it would be, I copied the proportions of a different constricting predator, the boa constrictor (who is 40 times longer than he is wide), and concluded that a sea serpent is 1.25 metres thick.

Again assuming a cylinder shape but this time for the predator (which is reasonable given that it's an eel), I calculated a volume of 224 $$m^3$$. A marine animal needs to be roughly as dense as seawater so that they don't sink or float too much, so the sea serpent will have a density of 1020 kilograms / m^3. Now with both volume and density, I can calculate mass, and end up with... 230,000 kilograms. Well above that of a blue whale. Since I've been very rough in my maths, I'll knock off the 30,000 to cut down on mass, but I'm still over blue whale size.

The basal metabolic rate (in kilocalories per day) of an organism is given by $$K \cdot M^{0.75}$$, where K is a constant depending on the kind of organism and M is the mass in kilograms. K for a fish is 10. So, $$10 \cdot 200000^{0.75}$$ gives you 95,000 kilocalories per day. A guy on r/theydidthemath calculated that the total blubber of a large bowhead whale contains 291,000,000 kilocalories, so - therefore - a sea serpent needs to eat a whale once every 3 thousand days (or a liitle more than 3 thousand days, of course, since there'll be more than just the blubber to eat).

Now finally to my question. One whale every three thousand days... sounds like a lot. I mean, for the ecosystem. Is that too much of a blitzkrieg for the local whale populations to handle? Is one whale every three thousand days per sea serpent sustainable for the local ecology?

• Why does it need so much, some snakes eat once a month or less, is this seaserpent constantly exercising as hard as it can or something? Eat the meal, find somewhere quiet to digest for a few weeks, hunt another, makes more sense – Kilisi Mar 3 '19 at 11:51
• @Kilisi It needs so much because it's so damn huge. K is actually the same for reptiles (including snakes) and fish, but the M-value is so big it bloats the result. – SealBoi Mar 3 '19 at 12:02
• "A guy on r/theydidthemath calculated that the total blubber of a large bowhead whale contains 291,000 kilocalories": you definitely want to double check this. A kilogram of fat has some 8,000 kcal; your "guy on r/theydidthemath" is basically saying that a "large bowhead whale", whatever that is, has about 35 kilograms of fat. This cannot be true. (Hint: a human needs about 2,500 kcal per day; we can obviously get those by eating less than one kilogram of food. Second hint: a Big Mac and large fries gets you 1,000 kcal.) – AlexP Mar 3 '19 at 13:23
• @Kilisi - "Nature usually balances somehow in the long term." Well, yes and no. Depends very much on what you mean by "balance". As the saying goes, 99.9% of all the species which have ever existed are extinct. – WhatRoughBeast Mar 3 '19 at 13:32
• The calculations in the linked article are all right. The confusion is with you; the linked article gives 291,240,000 food calories per whale; one food calorie is one physicist's kilocalorie. So it's 291 million kcal per whale, not 291 thousand. You erased three zeros by mistake. Now the snake needs to eat a whale every 3,000 days, which is much more reasonable. – AlexP Mar 3 '19 at 13:39