The Coriolis Effect, the Foucault Pendulum, and the Flat-Earth Movement

Nevertheless, I will once again take up the subject in an attempt to straighten out flat-earthers’ thinking about the Coriolis effect.

The Coriolis effect is evidence that the earth spins. Because flat-earthers frequently demand evidence of the earth’s rotation, I included discussion of the Coriolis effect on pp. 181–187 of my book, Falling Flat: A Refutation of Flat-Earth Claims. Since publishing the book last year, I have come to a greater realization of how deeply flawed flat-earthers’ comprehension of the Coriolis effect is. It might help if they bothered to read my book. It’s only fair, since I’ve read and listened to plenty of their material. Nevertheless, I will once again take up the subject in an attempt to straighten out flat-earthers’ thinking about the Coriolis effect.

It probably will help to begin with a demonstration of what the Coriolis effect is. Suppose that you are seated on a playground merry-go-round, about halfway between the center and the edge. Further suppose that the merry-go-round is turning at a constant rate in the counterclockwise (CCW) direction as viewed from above. If you were to roll a ball toward the center of the merry-go-round, you would see the ball’s path would curve toward the right, missing the center of the merry-go-round. If you turned around and rolled the ball toward the edge, away from the center, you again would see the ball’s path curve toward the right. However, note that since you have turned around, the second deflection is opposite to the first deflection—the first deflection was in the direction of rotation of the merry-go-round, while the second deflection was opposite the rotation.

Now consider a person not on the spinning merry-go-round, say, a person perched in a tree overhead. He would disagree with what you saw. He would see the ball move along a straight path in either case. Finally, repeat the experiment while the merry-go-round is not rotating. You and the observer in the tree would agree on what happened: the ball would move on straight paths with no deflection. What is going on?

Take 1

There is more than one way to understand the Coriolis effect, so let’s start with a simple approach. The merry-go-round spins as a rigid object. This means that parts of the merry-go-round maintain relative positions with respect to one another as it spins. We would say that all parts of the merry-go-round rotate with the same angular velocity. The units of angular velocity usually are radians/second, but we could use other units, such as degrees/second, rotations/second, or rotations per minute. On the other hand, parts of the merry-go-round do not move around the axis of rotation at the same linear velocity. There are various units we could use for linear velocity, but meters/second or feet/second would make the most sense. From experience, you know that the edge of the merry-go-round will have the greatest linear velocity, while the very center of the merry-go-round will not have any linear velocity (it will be zero). There is an expression that relates linear velocity, v, to angular velocity (measured in radians per second), ω (omega), to the radius, r:

Notice that this equation agrees with the observation that the linear velocity is zero at the center (where r = 0), and the velocity is maximum at the edge of the merry-go-round (where r is the greatest). Also notice that the direction of the linear velocity is perpendicular to the direction of the radius.

When seated halfway from the center, r is half the maximum radius, so the linear velocity there is half the maximum linear velocity at the edge. Suppose that the edge of the merry-go-round is moving with a linear velocity of 2.0 feet/second in the CCW direction. Thus, a point midway between the center and the edge would be moving 1.0 feet/second. If you rolled a ball from that point toward the center, the ball would continue moving 1.0 feet/second perpendicular to the direction toward the center, but the center of the merry-go-round is not moving at all. Therefore, the ball will appear to veer to the right of the center of the merry-go-round. Now suppose you roll the ball the opposite direction, toward the edge. Since the edge is moving at 2.0 feet/second rather than the 1.0 velocity of the ball, the ball will appear to veer to the right, falling behind the rotation of the point on the edge to which it originally was projected. On the other hand, the person in the tree would see the ball move in a straight line in either case. But the directions of motion that the person in the tree would see are not along the direction of the radius of the merry-go-round

We can use this example to understand how the Coriolis effect works on the spinning globe earth. Objects on the equator are moving nearly 1,040 mph eastward to complete one rotation per day. Meanwhile, objects at the poles aren’t moving at all. Intermediate latitudes undergo circular motion around the earth’s axis, varying from 1,040 miles on the equator to zero mph at the poles. This is because the distance from the earth’s rotation axis depends upon latitude. For a given latitude, φ, the distance, r, from the rotation axis is given by

where R is the earth’s radius (4,000 miles). The linear velocity of rotation, v, at a latitude, φ, is given by

.

For instance, where I live at 39° N latitude, we move nearly 810 mph eastward. If an airmass in the Northern Hemisphere moves from a lower latitude toward a higher latitude (moving northward), the air mass encounters land that is not moving toward the east as fast as it is. Therefore, from the perspective of the earth’s surface (and observers on the earth), the air mass turns rightward (toward the east) as it moves northward. However, from the perspective of an observer above the earth and not sharing in the earth’s rotation, the air mass moves in a straight line. On the other hand, if an airmass in the Northern Hemisphere moves from a higher latitude to a lower latitude (moving southward), it will deflect to the right too, but this will be in the westward direction.

Meanwhile, air masses in the Southern Hemisphere will deflect the opposite direction, toward the left. This means that air masses traveling toward the equator will deflect to the west (as in the Northern Hemisphere), and air masses moving away from the equator will deflect to the east (as in the Northern Hemisphere).

Effect on Weather and Climate

Many people mistakenly think that the Coriolis effect alone explains the rotation of storm systems, such as hurricanes, winter storms, and tornadoes. However, there is another factor involved that I shall discuss shortly. What the Coriolis effect directly affects is the prevailing winds at various latitudes. In the tropics, concentrated sunlight heats the surface, and the heat is transferred to the air. Heated air is more buoyant, so it rises. As the air rises, it cools, and water condenses in the form of rain. This is why rain forests are so prevalent in the tropics. The air at ground level must be replaced, so air is pushed in from higher latitudes. The Coriolis effect deflects the inrushing air toward the west, so in the tropics the prevailing winds are from east to west. These are called the trade winds because, before the development of powered ships, sailing ships took advantage of the trade winds on their voyages.

After the rising air in the tropics reaches several miles altitude, it moves away from the tropics toward the subtropics. The air eventually descends back to the ground, where at least part of the air returns to the tropics in the form of the trade winds. However, some of the air travels away from the tropics to more temperate latitudes. These winds are deflected west to east. We call these the prevailing westerlies, which are the dominant winds in the temperate latitudes. At the poles there is another downdraft of air. As this air returns toward lower latitudes, the Coriolis effect deflects them east to west, the same direction as the trade winds. Therefore, the Coriolis effect is responsible for three distinct wind directions that depend upon latitude

Organized storm systems, such as hurricanes, have an additional factor.

Organized storm systems, such as hurricanes, have an additional factor. At ground level, organized storm systems have low pressure at their centers. Higher pressure elsewhere forces air toward the low pressure. In the Northern Hemisphere, the Coriolis effect causes the inrushing air to deflect to the right, regardless of whether the air is moving northward or southward toward the low pressure. However, there still is the low pressure at the surface in the center of storms, with higher pressure outside. This high pressure continues to force the deflected air back toward the centers of storms, resulting in a CCW rotation around the storm centers. What happens with high-pressure systems in the Northern Hemisphere? At ground level, air moves away from the high pressure. The Coriolis effect deflects the air movement to the right, resulting in clockwise (CW) rotation around high-pressure systems.

Meanwhile, in the Southern Hemisphere the Coriolis deflection is to the left rather than to the right. Consequently, low-pressure systems, such as hurricanes, spin CW, opposite to the direction large storms spin in the Northern Hemisphere. Likewise, high-pressure systems in the Southern Hemisphere spin CCW, the opposite direction of their Northern Hemisphere counterparts. This direction of rotation is strictly observed by all low pressure and high-pressure systems. This is due to the relatively large size of these systems. Locally, the Coriolis effect is very weak, but when that small effect is multiplied over large distances, the Coriolis effect is very pronounced. Tornadoes are low-pressure systems, so they tend to spin the same direction as large organized storms in their respective hemispheres. However, because tornadoes are so small, they occasionally (about 2% of the time) violate the general rule. It is important to emphasize that over very short distances, the Coriolis effect is very small. The Coriolis effect generally manifests itself only over relatively large distances where its local tiny effect is multiplied over great distance.

This brings up another question: is it true that sinks and toilets in the Northern Hemisphere spin CCW as they drain, while sinks and toilets in the Southern Hemisphere spin CW as they drain? Yes, and no. Across the dimensions of sinks and toilets, the Coriolis effect is very feeble. It is extremely difficult to pull a plug in a sink or for the flush of a toilet not to impart a small circular motion that more than swamps the Coriolis effect. In fact, it is relatively easy in most sinks and toilets to impart a direction of spin so that upon pulling the sink plugs or flushing the toilets, the water will follow the imposed direction. If all other factors can be eliminated, then sinks and toilets in the Northern Hemisphere will tend to spin CCW while sinks and toilets in the Southern Hemisphere tend to spin CW. However, it is difficult to eliminate all other effects.

Are aircraft subject to the Coriolis effect? Yes. However, remember that the Coriolis effect is very feeble locally, and it becomes noticeable only when multiplied over great distances. Unlike air and ocean currents, a pilot or autopilot continually makes changes in an aircraft’s flight path to compensate for many factors, such as turbulence and shifting winds. These corrections greatly exceed the feeble Coriolis effect. Are bullets affect by the Coriolis effect? Yes, but given their relatively short range, the deflection is very small and so is swamped by other factors, such as shifting winds. However, in firing long-range guns, such as those found on warships, the Coriolis effect must be considered.

Take 2

The first explanation of the Coriolis effect given above was more by way of example. When an object on a rotating platform moves to a different radius of rotation, there is a deflection of the object as seen from the rotating platform. While this is a good explanation, it doesn’t quite get to the physics of what is going on. Linear momentum is the product of an object’s mass and velocity. If no net force acts on a body, then the body’s linear momentum is conserved. This was underlying the principle of the relatively simple explanation of the Coriolis effect given above. While essentially correct, conservation of linear momentum is more applicable in non-rotating situations. However, the rotating case is a bit more complicated.

In rotating systems, one ought to consider torques and angular momentum. A torque is the product of a force and the radius that the force acts about. Consider a wrench turning a tightly held bolt. One could increase the torque either by exerting more force or by increasing the radius by lengthening the handle of the wrench. Angular momentum is the product of angular velocity and an object’s moment of inertia. For a small mass, the moment of inertia can be approximated by object’s mass times the square of the radius of the object’s motion. We can write this in equation form as

where L is the angular momentum, and m is the object’s mass. A torque is required to change an object’s angular momentum. If no net torque acts on a body, then its angular velocity remains the same. Since there is no net torque acting on the ball on the merry-go-round in the example above, the ball’s angular momentum is conserved. Therefore, as r changes, ω must change in the opposite sense. That is, if r decreases, then ω must increase and if r increases, then ω must decrease. Keep in mind that if the merry-go-round is rotating at a uniform rate, then its angular velocity remains the same. But since the ball’s angular velocity must change as its distance from the center of the merry-go-round changes, then the ball must deflect with respect to the merry-go-round. How will it deflect? If the ball is rolled toward the center of the merry-go-round, its radius of motion decreases, which means that its angular velocity must increase. Therefore, the ball will appear to deflect in the direction of rotation of the merry-go-round. Conversely, if the ball is rolled away from the center, the ball will deflect opposite the direction of rotation. This is what we observe.

Take 3

But there is a better way of looking at the situation. Newton’s three laws of motion describe the world around us extremely well. For instance, Newton’s first law of motion says that if there is no net force acting on an object, the object will remain at rest or continue moving in a straight line. Newton’s second law states that when a net force acts on an object, the object will accelerate in direct proportion to the force and inversely proportional to the object’s mass. Newton’s laws of motion must be slightly adapted to the rotational case. We intuitively understand these things, even if we may not fully comprehend the description of Newtonian mechanics. Furthermore, it doesn’t matter what frame of reference we use to observe these things, as long as the reference frame we use is not accelerating. This last point is a key part of physics. What is a frame of reference? This video helps explain frames of reference. For instance, a very good explanation of the Coriolis effect is found in this video starting around 17:00.

What about a reference frame that is accelerating? Newton’s laws don’t quite work out as well in accelerating reference frames. For instance, a person aboard an airplane that is accelerating for takeoff will notice that everything in the cabin seems to be “falling” toward the back of the airplane in addition to falling downward. Certainly, anything loose that easily moves (such as a flight attendant on a pair of roller skates in the aisle) will fly down the aisle and slam into the back of the cabin. Of course, to prevent this, flight attendants and passengers are required to be seated with seat buckles fastened and all items stored during takeoff. Passengers in their seats feel pushed back into their seats. Since Newton’s laws of motion require such accelerations be caused by forces, what is the mysterious force that is shoving objects toward the rear of the airplane? To an observer at rest outside the airplane, there is no mysterious force. If there were a flight attendant on a pair of roller skates in the aisle, the person outside the plane and looking through the windows would see the flight attendant as motionless with the airplane accelerating around her.

Who is seeing the situation properly? It is the person motionless outside the plane. People inside the plane see objects accelerate with no force causing the acceleration. This violates Newton’s first law of motion. Physicists say that the observer at rest outside the airplane is in an inertial frame of reference, while the passengers aboard the airplane are in a non-inertial reference frame. An inertial reference frame is a frame of reference that is not accelerating, while a non-inertial reference frame is a frame of reference that is accelerating. This doesn’t mean that an inertial frame is not moving. A reference frame that is moving with constant velocity is not accelerating, so it is an inertial frame of reference just as much as a reference frame at rest. This difference is very important because Newton’s laws do not apply without amendment in a non-inertial reference frame.

Rotating reference frames, such as a spinning merry-go-round or the spinning earth, are non-inertial reference frames, because any circular motion requires an acceleration. This is because, according to Newton’s first law of motion, an object will move in a straight line if no net force acts upon it. Since circular motion is not straight-line motion, any circular motion requires a centripetal (center-seeking) acceleration. Forces cause accelerations, so the force responsible for a centripetal acceleration is often called the centripetal force. For an object whirling around on the end of a string, it is tension in the string that provides the centripetal force. For the moon orbiting the earth, it is the earth’s gravity that provides the centripetal force. For the merry-go-round and the earth, it is the internal structure of either that provides the centripetal force. For objects on the merry-go-round, it is friction between the objects and the merry-go-round that keep them there. For passengers on the spinning merry-go-round, it may be their holding onto a part of the merry-go-round that keeps them aboard. On the rotating earth, a portion of a person’s weight provides the centripetal force required to keep them rotating with the earth.

Consider an automobile going around a curve or turn. It is the force of friction between the tires and the road that provides the centripetal force necessary for the car to make the turn. Meanwhile, occupants inside the car find themselves slung toward the outside of the turn. Objects sitting on a seat may slide toward the outside of the turn. We attribute these effects to centrifugal force. But what causes centrifugal force? It appears to be a force that magically appears whenever we round a curve or turn. Suppose that the automobile is a convertible with the top down and that there is a lineman working in a bucket truck above the car. He won’t see this magical centrifugal force at work. Rather, he will see objects on the seat continue to move forward in a straight line in accordance with Newton’s first law of motion as the automobile turns, unless there is sufficient friction between the objects and the seat to compel the objects to turn along with the car. That slinging sensation that occupants of the car feel is caused by their bodies sharing the centripetal acceleration of the car while their bodies are compelled otherwise to continue moving in a straight line. The centripetal force for the occupants to share in the automobile’s centripetal acceleration is a combination of friction between them and the seats, holding on to parts of the car’s interior, and shoulder restraints and lap belts. Again, when viewed from an inertial reference frame, there is no centrifugal force. Centrifugal force is a fictious force that we must make up if we are within a rotating (non-inertial) reference frame to explain what we see.

Sometimes people call the Coriolis effect the “Coriolis force,” but this is incorrect. There is no force that causes moving air masses to deflect on the spinning earth. Rather, it is the effect of viewing things within the non-inertial reference frame of the spinning earth. An observer above the earth who is not rotating with the earth will see the situation properly: the air masses move along straight paths. But to observers rotating with the earth, moving air masses moving north or south appear to deflect as they move over terrain that is not rotating at the same speed that they are.

Where Flat-Earthers Go Awry About the Coriolis Effect

In a recent blog, I discussed a particularly vile group of flat-earthers that I called the BB. While there appears to have been a reduction in new flat-earth material on the web of late, the BB panel has been full steam ahead. The BB panelists have discussed the Coriolis effect quite a bit, and their arguments about the Coriolis effect probably will become mainstream among flat-earthers. The problem is that the BB panelists do not understand the Coriolis effect. They cite elementary treatments of the Coriolis effect from textbooks and websites. Using their misunderstanding of the Coriolis effect, the BB panel misinterprets what these sources say. The BB panel then uses their faulty understanding of the Coriolis effect to try to debunk that the earth is a rotating globe. With their improper application of the Coriolis effect, their effort is a straw-man argument.

One of the sources the BB panel frequently cites is Douglas A. Segars’ Introduction to Ocean Sciences. The BB panel quotes two bulleted points (among 8) from p. 481 of this textbook:

When set in motion, freely moving objects, including air and water masses, move in straight paths while the Earth continues to rotate independently.

Because freely moving objects are not carried with the Earth as it rotates, they are subject to an apparent deflection called the “Coriolis effect.” To an observer rotating with the Earth, freely moving objects that travel in a straight line appear to travel in a curved path on the Earth.

In interpreting this quote, these flat-earthers make several errors. Their first error is misunderstanding the meaning of the term “water masses” in the first quoted point. These flat-earthers correctly interpret the “air” preceding “water masses” as the earth’s atmosphere, but they incorrectly interpret “water masses” as clouds and water vapor in the air. The “water masses” refers to large bodies of water on the earth, the oceans. If the BB panel had read more of this textbook that they like to quote, then they would have seen that. For instance, on p. 181 of the most recent edition of this textbook, this statement appears:

First, any body in motion on the Earth, including water moving in currents, is subject to deflection by the Coriolis effect.

The textbook then gives reference to the discussion where the two bulleted points above come from. On the same page, this sentence is found, again with reference to the section where the Coriolis effect is more fully explained:

The deflection occurs because water set in motion by the wind is subject to the Coriolis effect.

On p. 183, this sentence appears, with the same reference back to the more detailed description of the Coriolis effect:

All fluids, including air and water, are subject to the Coriolis effect when they flow horizontally.

There are many such sentences found in this chapter (Chapter 8) about ocean circulation in this textbook. It is clear from the BB panel’s discussion of the Coriolis effect that they do not understand that both gases and liquids are fluids. Since the general property of fluids is that they flow, then both the air and oceans on the earth are “freely moving objects.”

The textbook author could have made clearer what he meant, but I doubt that it ever occurred to him that anyone would so misunderstand his meaning.

The second error these flat-earthers commit is their incorrect understanding of the word independently in the first point of the quotation from the textbook they cite. They interpret this to mean that the air does not rotate with the earth (incidentally, ancient Greeks who insisted on strict geocentrism made a similar argument). If the textbook these flat-earthers quote meant that the air (and oceans) did not rotate with the earth, it would have said so. What the textbook meant is that as air or water moves from one latitude to another, it does not automatically lose the linear velocity of rotation that it originally had. Instead, fluids in motion on the earth’s surface maintain their original linear velocity due to rotation independently of the linear velocity of the regions of the earth’s surface that they happen to travel over. I will grant that the textbook author could have made clearer what he meant, but I doubt that it ever occurred to him that anyone would so misunderstand his meaning.

The flat-earthers’ third mistake builds upon their second error. When they see the phrase “freely moving objects are not carried with the Earth as it rotates” at the beginning of the second bulleted point they quote, they assume once again that the freely moving objects do not rotate at all with the earth. As I’ve already explained, this is not the author’s intended meaning. Rather, the author meant that objects moving freely across the earth continue with their linear velocity due to rotation regardless of the rotational linear velocity of the terrain over which they move. What is an object that doesn’t move freely across the earth? Trains are constrained by the rails they travel on, so they don’t move freely across the earth. The same is true of automobiles moving along highways. Friction between the road and tires prevents them from moving freely.

The BB panel draws upon other brief discussions of the Coriolis effect that describe the earth rotating underneath moving objects. For instance, the CK-12 Foundation began in 2007 to provide web-based STEM educational resources for primary and secondary education in the United States. Here is part of what their page about the Coriolis effect says:

The Coriolis effect causes the path of a freely moving object to appear to curve. This is because Earth is rotating beneath the object. So even though the object’s path is straight, it appears to curve.

Notice the use of the term “freely moving object” that flat-earthers are inclined to misunderstand. But also notice the second sentence: “This is because Earth is rotating beneath the object.” While technically true if properly understood, it may be a poor choice of words because some people may misunderstand it. This statement does not mean that objects in motion in the air do not share in the earth’s rotation. Rather, as I’ve stated several times, it means that these moving objects continue to move with the rotational velocities they had when they began moving across the earth’s surface and not the rotational velocity of the terrain over which they move. In that sense, the ground beneath these moving objects is rotating at different linear velocities (though the object and the ground have the same angular velocity).

Deliberate Mischaracterization?

With these misunderstandings in hand, the BB panel blithely sets out to prove that the earth does not rotate. They begin by mischaracterizing the Coriolis effect. The BB panel reasons that since freely moving objects rotate independently of the earth and that the earth rotates under freely moving objects, then freely moving objects do not rotate at all. They then argue that if this is true, then any object that becomes airborne will appear from the earth’s surface to speed away westward from the launch point with whatever rotational speed the ground at a given location has. For example, the BB panel says that a drone launched from the equator will not hover over the launch point but will sail away westward at nearly 1,040 mph. Another example they give is that a flight from Charlotte, NC, to Los Angeles, CA, won’t take very long at all. The two cities are near latitude 35°, where the rotational velocity ought to be about 850 mph. If one adds 600 mph as an airplane’s airspeed, then the airplane ought to travel 1,450 mph with respect to the earth. With the airport to airport distance being 2,125 miles, then the flight ought to take about 1 ½ hours, not the usual 4 ½ hours. The BB panel further argues that a hot air balloon could make the trip in only three hours by rising above the ground and waiting for Los Angeles to rotate over.

Obviously, there is something wrong here. Flat-earthers would agree, saying that the problem is the assumption that the earth rotates is false, thus proving that the earth doesn’t rotate. However, there is a much better answer. Flat-earthers assume that when an object becomes airborne it instantly loses all horizontal momentum. But this would require a horizontal force (never mind the fact that such a force would require some time to achieve this loss of all momentum in objects that take off from the ground). Newton’s first law of motion states that absent a net force, a moving object will continue to move in straight-line motion. When a drone or balloon ascends from the earth, there is no net horizontal force (except for any wind). Therefore, the drone or balloon will maintain its eastward rotational velocity that it had before taking off. Since the ground has this same velocity, there will be no net motion between the balloon or drone and the ground (again, ignoring any wind). Nor will airplanes magically lose their rotational motion as they take off. If they did, it would be a gross violation of the conservation of linear momentum, as well as Newton’s first law of motion.

It is very easy to test the reality of Newton’s first law in this matter. Try flipping a coin vertically so that the coin travels upward two feet. It will take the coin ¼ second to rise the two feet, and it will take another ¼ second for the coin to fall the two feet back to your hand, for a total flight time of ½ second. Now repeat this experiment inside a vehicle traveling at a uniform velocity of 60 mph. It is very important that the vehicle does not accelerate during the experiment. You will find that the result will be the same as when you were stationary: the coin will spend ½ second aloft before returning to your hand, moving only in the vertical direction from your perspective. This is because both experiments were done in inertial reference frames, and, as I mentioned before, physics is the same in all inertial reference frames. But during that ½ second, the vehicle would have moved forward 44 feet. If flat-earthers were correct in their assertion about motion, the coin would have flown backward 44 feet from the perspective of a passage in the vehicle. Since this is not what we observe, flat-earthers must be wrong about this. By the way, an observer standing outside the vehicle would see the coin travel along a parabolic path, with height two feet and length 44 feet. This parabolic path transforms back to the straight up-and-down motion that the person in the vehicle sees. This is because both observers are in inertial reference frames.

Flat-earthers usually respond by pointing out if you did the moving experiment on a flat-bed truck, the coin would sail backward. But what flat-earthers fail to realize is that the backward motion of the coin in this case is caused by wind resistance. Wind resistance is a force, so once it is invoked, we are now in the realm of Newton’s second law, which describes the acceleration that occurs when a net force acts on a body. There is no wind resistance with the rotating earth.

This sort of buffoonery makes me think the BB panel (along with many other flat-earth leaders) are not serious about the earth being flat but are arguing for it for their amusement.

At this point, the BB panel usually howls with laughter and derision. They go back to their quotes about the Coriolis effect, hammering home their argument that “the earth rotates underneath things.” With their skewed understanding, they think this means the earth’s atmosphere must not rotate with the earth. In fact, I’ve heard members of the BB panel ask guests on their YouTube show if the atmosphere rotates with the earth. If the guest responds affirmatively, the laughter starts again, with mentions of wind. But it is silly to think that the concept of the atmosphere rotating with the earth cannot allow for relative motions within the atmosphere, aka, wind. This sort of buffoonery makes me think the BB panel (along with many other flat-earth leaders) are not serious about the earth being flat but are arguing for it for their amusement.

Notice that in pursuing their argument, flat-earthers want to apply the Coriolis effect to stationary objects, such as drones and balloons. However, the definition of the Coriolis effect makes it clear that the Coriolis effect affects only moving objects. This little fact seems to have escaped the notice of flat-earthers. To insist that the Coriolis effect applies to stationary objects, such as balloons and hovering drones, displays flat-earthers’ fundamental misunderstanding of the Coriolis effect.

This misunderstanding of the Coriolis effect is displayed in another way. One member of the BB panel rightly points out that the Coriolis effect requires two reference frames, one inertial and the other non-inertial. He correctly points out that the non-inertial frame is the spinning earth, but he misidentifies the inertial frame as the earth’s atmosphere. Since the atmosphere, on average, rotates with the earth, this is false. As I’ve explained above, the inertial frame is one that does not rotate with the earth. Presumably, this inertial frame would be above the earth and the atmosphere.

In another display of their ignorance, the BB panel points to images of hurricanes, showing the CCW rotation in the Northern Hemisphere and the CW rotation in the Southern Hemisphere. They state that the Coriolis effect is an “apparent deflection,” while the rotation patterns of hurricanes are very real. Ergo, the rotation of hurricanes can’t be due to the Coriolis effect. Once again, these flat-earthers have misunderstood what is meant by “apparent deflection.” The deflection is real enough within the non-inertial reference frame of the rotating earth. It is called an “apparent deflection” because there is no force that causes it, but rather it is a result of observing things in a non-inertial reference frame. Furthermore, the rotation patterns of hurricanes are not caused by the Coriolis effect alone. As I previously explained, there is the force due to air pressure differences that exist on the earth’s surface. It is these two factors that produce the characteristic rotations of hurricanes. Before moving on, it is important to point out that flat-earthers generally do not offer any reason why hurricanes and other large weather systems behave this way on a flat earth. When properly understood, the Coriolis effect is strong evidence that the earth is a rotating globe.

The Foucault Pendulum

In 1851, Léon Foucault provided the first direct evidence that the earth rotates. This is so important that I discussed it on pp. 179–181 of Falling Flat. The BB panel sometimes mentions the Foucault pendulum when they talk about the Coriolis effect. They apparently think that the Coriolis effect is responsible for the precession of the Foucault pendulum. It isn’t.

The Foucault pendulum has a massive bob attached to a very long wire. When pulled to one side from its vertical equilibrium position and let go, the pendulum bob will swing back and forth with a regular period of oscillation. The swing defines a plane of oscillation. With its long wire and heavy bob, the Foucault pendulum will swing for a long time before wind resistance and frictional dissipation in the pivot and wire slow it to a stop. It is very important that the pivot at the top of the pendulum be free to spin in the horizontal direction. Most pendula do not have this feature, instead constraining their bobs to swing in only one plane. When not encumbered in this way, the plane of a Foucault pendulum will precess, or turn, at a rate of

where T₀ is the sidereal day (23 hours, 56 minutes) and φ is the latitude.

Why does the Foucault pendulum precess? The only forces acting on the bob are the downward force of gravity and the tension in the wire. Since the tension is along the wire and the wire is in the plane of the oscillatory motion, the magnitude and direction of the tension continually changes. On one side of the equilibrium position, there is a component of the tension toward the equilibrium position. On the other side of the equilibrium position, the tension has a component in the other direction, again toward the equilibrium position. It is linear momentum and this restoring force acting toward the equilibrium position that keeps the pendulum swinging. Since the direction of the component of the tension changes back and forth, the average net force on the bob throughout an entire cycle is zero. Hence, while the bob moves back and forth, the bob otherwise remains stationary. This is key, because as I discussed above, the Coriolis effect only affects objects that move, and then only objects that move some appreciable distance. Therefore, the Coriolis effect cannot cause the Foucault pendulum to precess.

The reason the Foucault pendulum precesses is conservation of angular momentum. Since the tension in the wire is along the radius of the bob’s oscillatory motion, it provides zero torque on the pendulum. The weight of the bob (due to gravity) produces a torque that is perpendicular to the plane defined by the swing of the pendulum. However, throughout one half of the oscillatory cycle, the torque is in one direction while it is opposite that direction in the other half of the cycle. Therefore, on average there is no net torque on the pendulum. With no net torque, angular momentum is conserved. Angular momentum has direction perpendicular to the plane of the oscillation, so in the absence of any torque, the plane will remain fixed in space. Therefore, if the earth does not rotate, then the plane of the oscillation of the Foucault pendulum will remain fixed. However, if the earth rotates, then the plane of the Foucault pendulum will appear to precess to a person in the non-inertial reference frame of the earth. The derivation of the precession period above is beyond the scope of this article. Many advanced mechanics textbooks will explain in detail how this is done. By the way, the device in most pendula that constrains the plane of oscillation provides a small torque that causes the plane to move (as viewed from an inertial reference frame). That is why most pendula do not exhibit precession, and much care must be taken to remove this constraint when building a Foucault pendulum.

How are the Coriolis effect and the precession of a Foucault pendulum different? Both result from observing things in a non-inertial reference frame. Both the Coriolis effect and the Foucault pendulum are due to conservation of angular momentum. However, the Coriolis effect acts only on objects that travel considerable distance over a rotating frame of reference. Since a Foucault pendulum does not move any distance, it is not subject to the Coriolis effect.

Conclusion

The very inaccurate manner with which flat-earthers handle the Coriolis effect and the Foucault pendulum is typical of those in the flat-earth movement. The BB panel does not understand physics at all. Both the Coriolis effect and the Foucault pendulum are direct evidence that the earth rotates. It is no wonder that flat-earthers oppose both, because if they were to accept the reality of either, it would directly disprove their belief in a flat, stationary earth.