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Episode 161 - Water on Earth: Coriolis and Tides

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Recap: Inspired by one of the longest-running primetime television shows in history, and frustration with late-night radio hosts pretending they can Science, this episode addresses two common misconceptions about the forces from and on water on our planet and their effects on human scales. I first discuss whether Coriols makes toilet bowls swirl in opposite directions in opposite hemispheres, and then whether the moon's tides are strong enough to affect the water in your body.

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Episode Summary

Claim: The first water-related topic for this episode is a simple science issue that I re-learned wrong in The Simpsons, when we learned that toilets flush in different directions in different hemispheres. My grandmother also told me in the 1990s that when she visited Africa with a tour group, they went to the equator, and they were shown that north of the equator, a bucket of water with a hole in the bottom drained counter-clockwise, it drained clockwise south of the equator, and it just drained straight through when they were on the equator. At the time, I imagined the equator as a thick red line going through the area just like on the globe we had at home. What these two claims have in common is a very common misconception about the Coriolis Effect, also sometimes known as the Coriolis Force. How it works and to what it applies is one of the more common misunderstandings about how bodies of water behave on our planet. So, the first part of this episode is a primer on the effect and to what it really applies, so that you, too, can be the stick-in-the-mud at parties.

Background

First off, the Coriolis "force" is not a real force -- in physics, it's called a "fictitious force" because it's not real. What do I mean by that ...

In physics, per Newton's First Law, an object will maintain a constant velocity (even if that velocity is zero) unless acted upon by a force. So a force - a real force - is something that can change an object's motion.

A fictitious force is something that we invent to describe the appearance of a change in an object's velocity, when in reality, that object's velocity has not changed in its own reference frame. We call its own reference frame the "inertial reference frame." That just comes from the idea of inertia, or the tendency for an object to maintain its own motion. See, these things do tie together.

Probably the most common example of a fictitious force is centrifugal force. If I'm in a car and moving in a straight line, and I turn the car to the left, I'm going to feel the car pushing me from the right. Because of Newton's Third Law, if the car is pushing me from the right, I'm pushing on it from the left to the right.

Me pushing on it in the equal and opposite direction is a pseudo-force, or fictitious force -- in this case, centrifugal force. My body wants to follow Newton's First Law and keep going straight. The car is acting upon my body to push it to the left, and so in physics, we create a fictitious force called the centrifugal force to explain how it seems as though I'm pushing outwards, away from the direction of the turn. Centrifugal forces only exist in the rotating reference frame. In the inertial reference frame, there is no force going on. But if we want to use basic, classical mechanics to describe my motion from the rotating or turning reference frame, we have to create a new force.

The same is true for the Coriolis Force, though the Coriolis Force or Effect is almost always described with systems on the scale of a planet.

To understand the Coriolis Effect, I had to pause here and read several examples because I was getting it the opposite of how it works. For me, the example that works is one of those playground spinny things where the goal is to make everyone dizzy and see who's the last one standing. But they can also be used to demonstrate the Coriolis Effect.

Let's say you have a quadcopter and you have a camera aimed straight down at the center of the spinny thing and have signed consent forms from everyone who's being imaged. You have one person in the middle. You have another person at the 12:00 position. Someone else starts to spin it counter-clockwise, so to the right from the person at the 12:00 position. That person at the 12:00 position has a helmet with a GoPro on it and is recording.

Once you get it spinning and you maintain a constant rate of spin, and the person who started at the 12:00 position reaches there again, they roll a ball to the person in the middle. That person in the middle catches it.

After you thank everyone and buy pizza for participating in your experiment, you get home and look at your footage. From the quadcopter's vantage point, straight up, the inertial frame, the ball appears to simply go straight down, from the 12:00 position in a line that would take it to the 6:00 position but is interrupted by the person in the middle who catches it.

Now you look at the GoPro footage. From the rotating position of the initial roller, the ball does not go in a straight line. It instead curves to their left, away from the direction of rotation, and then curves back to the middle to reach the catcher.

I'm going to link to that venerable source of all that is True, Wikipedia, in the shownotes which I encourage people to look at because it has lots of examples both explained verbally and in pictures, including this one, which is the "Tossed ball on a rotating carousel."

But to put that example perhaps more succinctly, the moving object is going to move in a straight line from the inertial reference frame.

BUT, in the rotating reference frame, it will appear to deviate, moving in a direction away from the direction of motion. If the rotating reference frame is rotating counter-clockwise, that means it will deviate clockwise, or to the right if you're looking from above. If rotating clockwise, then it will deviate to the left if you're looking from above.

The amount of the deviation will be more if the reference frame is rotating faster. That means the deviation is stronger as you get closer to the equator, because it's moving faster than right next to either pole.

It also means that large-scale patterns of stuff that acts like a fluid on the planet will rotate COUNTER-clockwise in the northern hemisphere and CLOCKWISE in the southern hemisphere. That's why hurricanes or typhoons or cyclones or twisters or tornadoes or other spinning storms and synonyms for them will rotate counter-clockwise in the northern hemisphere and clockwise in the southern hemisphere.

The only time the Coriolis Force is zero is when the velocity of an object is parallel to the axis of rotation. So on Earth, that happens if an object is on the equator and moving north or south. But as soon as it gets off the equator, that infinitesimal point on the surface, Coriolis will start to kick in.

To What Does the Coriolis Force Not Apply?

So, was my grandmother right? Was The Simpsons right? Well, it's complicated but not.

From a physics standpoint, no, neither were correct. The reason is that the Coriolis Force is rather weak as fictitious and real forces go. While it's always there, or the effect is there, it simply doesn't apply much in our daily lives because it's drowned out by everything else.

For example, if I fill a bowl with water, the residual motions of all the water molecules within it from me filling it is going to be huge relative to any Coriolis Force. Same thing goes if I fill a bathtub, or a pool.

If I were to drain any container of water out the bottom, the shape of that hole and all its imperfections - either designed or not - is going to dominate by many powers of 10 over the amount of any rotational effects that would be caused by the Coriolis Force.

In a toilet bowl in particular, there are usually jets of water that are aimed at an angle - to the left or to the right - along the top of the bowl such that when you flush, it has a larger chance of dislodging material and moving it down the drain. Those jets' directions are what will cause the water in the toilet bowl to spin either clockwise or counter-clockwise, or, if you're special, those jets are straight down and there may be no rotation at all.

As for my grandmother's experience? If it really happened, it's very likely that the guide just swished the water in the correct direction at the start to get it to rotate the correct direction for the location north or south of the equator, and didn't when on the equator. It may not even have been intentional, but rather the ideomotor effect that we hear about so often in skepticism with things like Ouija boards and dowsing.

Claim: Another factor that has a minimal effect in small bodies of water is the next topic of this episode: Tides. In the crossover episode with The Reality Check podcast, Episode 157, Cristina addressed the general idea of lunacy, that the full moon has an effect to generally make people more agitated, such that emergency room visits spike as do crimes. That's not true, as she pointed out. I also talked about whether the phase of the moon correlates with earthquakes back in Episode 50 -- it doesn't. But, there are yet more claims that we can talk about, and one that I'm surprised I haven't covered before: The claim that because humans are "mostly" water, and the moon creates tides in water, the moon affects us, too.

Background

The necessary background to analyze this claim is similar to Coriolis: An understanding of the tidal force. Just as Coriolis is a fictitious force, tidal force is also not really a force in and of itself, instead it's a secondary effect from the force of gravity.

Put in my own words, succinctly, the tidal force is the difference in the force of gravity on one side of an object to the other side of the object.

Understanding tides is another case of understanding frames of reference. Let's go from Earth's reference point and ignore everything else's effect on it and the moon. Newton's universal law of gravitation states that the force of gravity is proportional to the distance between two objects, squared. In particular, the closer you are, the stronger the effects, so it's an inverse-square law.

That means that if we set the force from gravity on an object on another object a certain distance away as 1, if you double that distance, the force of gravity is quartered, it's only 25% as strong. If you triple the distance, gravity is only 1/9 as strong. Quadruple, it's 1/16th, and so-on.

In that thought experiment, if you're paying attention and thinking about this in your head, you probably thought of those values as applying evenly to each object. The thing about tides is that they don't: You have to consider the fact that all objects have a certain size to them.

That means that while we can give a value for the gravitational force between Earth and the moon, that value is, in fact, a little different for the point on the moon that's closest to Earth versus the point on the moon that's farthest away from Earth. The point that's closest experiences a stronger pull, and the point farther away experiences a slightly less strong pull.

From Earth's reference point, it's still pulling on all parts of the Moon, just slightly less on the farthest side. But the moon's pretty strong and it can handle it, though it does flex a little bit as a result.

But if we shift to the moon's vantage point, such that our reference point is at the center of the Moon, the part of the moon that is closest to Earth is pulled towards Earth, and the part farthest away from Earth is "pulled" in the other direction. The top and bottom also get pulled a little towards the center of the moon.

To reiterate, all of the moon is still pulled towards Earth, it's just pulled by different amounts, such that it's often easier to think of tides from the reference point of the body experiencing the tides.

To think about it another way, consider the moon's effects on Earth. Newton's Third Law, for a second time in this episode, holds that when one body exerts a force on another, that other body will exert an equal and opposite force on the first body. So Earth causes a gravitational force on the moon, meaning the moon causes a gravitational force on Earth.

And, because Earth is a reasonably sized planetary body, the side facing the moon will experience a stronger gravitational pull than the side facing away from the moon. All of Earth gets pulled to the moon, it's just that the closest part gets pulled more.

And, that's why we see ocean tides. If everything were perfectly aligned, then the water on the side of Earth that faces the moon will be pulled towards the moon more than the land below it, while the water on the opposite side of Earth will experience less gravitational pull towards the moon than the land below it so it will effectively "stay put."

Explained a bit differently, if we shift reference frames again so we're looking at the Earth-Moon system as an outside observer, let's put Earth on the left and the Moon on the right. The water facing the moon gets pulled a lot towards it, the land underneath it gets pulled somewhat towards the moon, and the water on the other side of Earth gets pulled just a little towards the moon.

That's why we have two tides roughly each day on Earth: You get a high tide when you're facing the moon and you get a high tide when you're facing in the opposite direction from the moon. That anti-moon tide is almost like the water being "left behind" as the ground underneath it is pulled towards the moon.

Now, I've simplified the explanation quite a bit. For example, Earth's tides are actually ahead of the moon due to Earth's rotation. Incidentally, this pulls the moon forward in its orbit, giving it more energy, and that's why it's steadily receding from the planet AND Earth's rotation is slowing down, such that in 1-2 billion years we will likely be a tidally locked system, like Pluto and Charon, where the same side of each body constantly faces the other.

Also, something I didn't mention is that Earth's crust also flexes due to the moon's tidal effects, but because rock is much stronger than water, we notice the water but don't notice the ground underneath us shifting very, VERY slightly.

Another simplification is that I told you to ignore every other solar system body. We experience tidal effects from everything just as we experience them from the moon. But none-so-much as the moon. The sun is the next-largest factor, and it's only 45% of the moon's tidal effects. But, when it's a new or full moon, those can add up and give us larger than normal tides called "spring tides," and when they're at right angles to each other, they cancel out a lot and we get weak tides called "neap" tides.

The reason that the sun is such a small effect tidally, even though it's by far the dominant gravitational force on us, again gets back to the root idea of tides being a secondary effect from gravity: What matters is the DIFFERENCE in gravitational force from one side of the body to the other.

Earth and the moon are close, so even though they are much less massive than the sun, the difference in gravitational force from one side to the other is fairly large, in contrast with the sun: The sun's gravitational force on us is very large, but the difference in that force from one side of Earth to the other is relatively small. Same thing goes with Jupiter, Mars, Venus, etc. -- true, they will all cause a tide on us, and we on them, but the effect is super-tiny compared with the dominant one of the moon, and the secondary one of the sun.

Addressing the Claim

That brings us back to the claim that because we're made mostly of water, and the moon produces tides, it must also affect us because it makes tides in our body.

You can easily come up with the answer to this claim by remembering that the amount of a tide is proportional to the DIFFERENCE in gravitational force from one side of the body to another.

Earth is quite large at roughly 12,742 km in diameter. You are quite small, at perhaps 1.7m tall or maybe 0.3 m deep. The difference in gravitational force from one side of you to the other, versus one side of Earth to another, is miniscule.

In fact, I used an online tidal force calculator because I didn't want to do it by hand, and I calculated the tidal force on Earth from the moon. I then calculated it between a human that's 0.3 m deep and weighs 70kg and the moon.

In the first calculation, as an order of magnitude, I got 10^19 Newtons. The unit's not important, just that order of magnitude. In the second calculation, the moon's tidal force on you, I got 10^-10 Newtons. That is a factor of 10^29 difference in tidal force.

The SI or metric system doesn't even have a prefix for that. Best I can do for you is it's 100 exa-giga-times as much, or 100 kilo-tera-tera-times as much.

This is basic physics, understood for over 400 years. The moon's gravitational effect on you is pretty much zero.

And, you can use these online calculators to test the comparison that's often given: A mosquito sitting on your arm has more of a tidal effect on you than the moon. So, put in the moon's mass and distance, put in your mass and radius, and put in a mosquito's mass and distance. I used 70 kg again for a person and a radius of 0.00015 km (15 cm), which I'm guessing at because when I did an internet search for the average depth of a human I got only not-safe-for-work results on the first page, a weight for a mosquito of 0.0000025 kg (2.5 mg), and a distance for the mosquito of 10 cm if it's on my arm and so away from the core of my body.

When I use those numbers, the tidal force exerted on my body from the mosquito is 2x as much as that from the moon.

Wrap-Up

So, there you go: Given pretty well established physical laws, and reasonably straight-forward calculations, there is no way that the moon's tides could possibly affect you. It doesn't matter that your body is around 55-60% water, it wouldn't matter if your body were 99% air as I think some late-night radio hosts might be: it is impossible for the tidal force of the moon to directly affect your body.

The magnitude of the force is simply too small. It's too small in comparison with everything else that is pushing and pulling on your body, like the chair you're sitting in, the truck that just drove past you on the highway, or your boss asking for those TPS reports.

Similarly, while the Coriolis Force is a real fictitious force, and just like tides it technically operates at all scales, your kitchen sink or bathroom toilet bowl is simply too small to show effects from it, just as you don't get high and low tides in your hot tub whenever the moon is an hour from passing overhead or directly under you.

As with many things in life, it's all about moderation, and understanding how much of something is really going to affect you.

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