Bucka's Earth Rotation Experiment

[LMR]

Surfing the Internet I found an interesting and easy experiment to check Earth rotation. A German scientist invited it in 1940s.

There is a rod (any material), the length is about 1.5 meters and it can freely rotate around a horizontal axis which is in a frame. The frame can rotate around a vertical axis freely.

The principle is simple: conservation of angular momentum.

MOI - a moment of inertia
L - angular momentum of the rod
I - a moment of inertia of the rod
w - an angular speed of the rod

L = I * w (by definition)

If the rod (and the frame of course) rotates with Earth, they have angular momentum.

What if we change (decrease) MOI (I) in 10000 times? Well, due to the conservation of angular momentum (L), angular velocity (w) is gonna increase 10000 times.

If w is 0 (Earth does not rotate) it will stay 0. (0 * 10000 = 0)
If w is not 0, it will be 10000 times bigger than 1 rotation per day (2*PI/86146) and the frame will start to rotate counterclockwise (in the Northern hemisphere and clockwise in Southern hemisphere).
The rotation speed of the frame depends on your latitude (the close to a pole, the bigger rotation will be).
No effect on the Equator btw.

The longer a rod is, the better (minimum 1.5 meters). The less radius it has, the better.

Here I put my excel file with calculations and more experiment information (in attachments)

A visual demonstration (external site): link

Right now I live in apartments and I do not have any change to fulfill this experiment. But it is very easy to commit. Well, share your results if you please.


@Mick West what do you think about this experiment? Your opinion is important to me.

Source:

• Book link Schiller, Motion Mountain, page 145.
• H. Bucka, Zwei einfache Vorlesungsversuche zum Nachweis der Erddrehung, Zeitschrift für Physik 126, pp. 98–105, 1949, and H. Bucka, Zwei einfache Vorlesungsversuche zum Nachweis der Erddrehung. II. Teil, Zeitschrift für Physik 128, pp. 104–107, 1950

 

[Mick West]

There is a rod (any material), the length is about 1.5 meters and it can freely rotate around a horizontal axis which is in a frame. The frame can rotate around a vertical axis freely.

You say "any material", but your source says: "massive metal rod"

Assuming this actually works, I suspect it needs to be massive in order to overcome friction.

I don't really understand the experiment though? How exactly do you start it? What exactly will happen? Why is there a rope in one diagram, and a mirror in the other, and then no rope of the right hand side?

 

[Mick West]

Ah, I guess you have to cut the rope to start it, the rod rotates to the upright position, and the motion of the earth somehow translates that to spin around the vertical axis.

German paper attached

 

[Trailspotter]

A much simpler device, the Foucault pendulum, was the first experiment to give simple, direct evidence of the earth's rotation
https://en.wikipedia.org/wiki/Foucault_pendulum

 

[Mick West]

A much simpler device, the Foucault pendulum

Simpler perhaps, but difficult to set up in my garage. A smaller and quicker experiment would be interesting.

 

[Trailblazer]

Ah, I guess you have to cut the rope to start it, the rod rotates to the upright position, and the motion of the earth somehow translates that to spin around the vertical axis.

German paper attached

Yes, you beat me to it. https://de.wikipedia.org/wiki/Hans_Bucka

You start with the rod in the horizontal direction, rotating with the Earth. You cut the rope and then the rod falls vertical and the existing angular momentum now acts over a much smaller radius, so the rate of rotation should increase and become visible. I think!

The mirror is presumably to reflect a beam of light and make small rotations more visible.

 

[Trailblazer]

I can't find any videos of this experiment in operation. You'd think if it was that quick, easy and apparent, that it would be better known.

 

[LMR]

@Mick West Yes, of course, the more mass object has, the better (more kinetic energy).

 

[Mick West]

I can't find any videos of this experiment in operation. You'd think if it was that quick, easy and apparent, that it would be better known.

Is suspect the setup required to get to that stage is a bit fiddly. The paper describes a lot of faffing around getting it level and using an electromagnet.

 

[LMR]

Does excel file calculations work? Because I used formula commands not in English.

Yes, you beat me to it. https://de.wikipedia.org/wiki/Hans_Bucka

You start with the rod in the horizontal direction, rotating with the Earth. You cut the rope and then the rod falls vertical and the existing angular momentum now acts over a much smaller radius, so the rate of rotation should increase and become visible. I think!

The mirror is presumably to reflect a beam of light and make small rotations more visible.

The rotation speed is about 25+ degrees/second. It would be visible without any mirrors

Is suspect the setup required to get to that stage is a bit fiddly. The paper describes a lot of faffing around getting it level and using an electromagnet.

It is a different experiment in your link, not the one in the topic. Well anyway, somebody can try it.

 

[Mick West]

I don't think it would make that compelling a demonstration. It's magnifying a very small angular velocity, so how do you prove that you did not induce that initial tiny angular velocity upon release?

 

[LMR]

I don't think it would make that compelling a demonstration. It's magnifying a very small angular velocity, so how do you prove that you did not induce that initial tiny angular velocity upon release?

It is about 25-30 degrees per second. Not small. That is why we need a rope. You do not launch it with hands, you burn the rope and the rod will go down itself. No external torque.

What about excel file? Does it work (calculations?)

 

[Trailblazer]

The rotation speed is about 25+ degrees/second. It would be visible without any mirrors

I meant to detect any movement in the initial phase, when the rod is horizontal. It must be there for something!

Edit: although the diagram's in Bucka's paper don't seem to include a mirror.

 

[deirdre]

It must be there for something!

Challenge 270, page 145: The metal rod is slightly longer on one side of the axis. When the wire keeping it up is burned with a candle, its moment of inertia decreases by a factor of 104 ; thus it starts to rotate with (ideally) 104 times the rotation rate of the Earth, a rate which is easily visible by shining a light beam on the mirror and observing how its reflection moves on the wall.

 

[Mick West]

The earth rotates once a day, or 1/(24*60) rpm, 104 times that is 0.07 rpm

What if we change (decrease) MOI (I) in 10000 times? Well, due to the conservation of angular momentum (L), angular velocity (w) is gonna increase 10000 times.

Where are you getting 10,000? The would require the rod to have a length 10,000x the diameter, no?

 

[deirdre]

Where are you getting 10,000?

i think from my photo posted above your comment. my text didnt translate well. it says 10 to the 4 power.

what is a gyroscope torque?
I'm trying to translate Bucka's paper Part 2.
https://vdocuments.mx/zwei-einfache-vorlesungsversuche-zum-nachweis-der-erddrehung-ii-teil.html

Spend the amount of the angular momentum that is present without the use of the gyroscope torque. There is the possibility to adjust the axis of rotation easier than I described

 

[Mick West]

Something does not make sense here. If the blue rod is pivoting on the yellow pivot then it will swing back and forth - but your diagram and animation seem to suggest it just moves to an upright position.

 

[LMR]

Something does not make sense here. If the blue rod is pivoting on the yellow pivot then it will swing back and forth - but your diagram and animation seem to suggest it just moves to an upright position.

It is unbalanced just a little. The longest part will go downright and the little part will go upright.

Yes, ~10000 times, the calculations are in excel file. That is why we need a thick rod. In the vertical position, it has a very low moment of inertia. (relative to a vertical axis of angular speed)

m - mass of the rod
r - radius of the rod (half of the diameter)
l - length of the rod

Difference = Horizontal MOI/Vertical MOI.

Let m = 3 kg, r = 0.006 m, l = 1.5 m, then a ratio between them will be:
Wolfram alpha calc

 

[Mick West]

It is unbalanced just a little. The longest part will go downright and the little part will go upright.

And why exactly would it stop in the vertical position?

 

[LMR]

And why exactly would it stop in the vertical position?

A little friction + low torque (it is unbalanced just a little).

 

[Trailblazer]

It seems to me it might work better with a "backstop", like a horizontal wire to catch the top part of the rod when it reaches the vertical position and stop it from carrying on through?

Although that might introduce more vibration and make the whole thing wobble around too much.

 

[deirdre]

it just moves to an upright position.

the last bit of your paper in post #3 says (according to my non German keyboard and google translate):

Versuch 2. Die Seilbremse wird gelost. Der Stab pendelt periodisch um die horizontale Drehachse A. Durch Drehen des Torsionskopfes wird vor dem Auslosen des Pendelns eine Anfangstorsion so vorgegeben, dab beim erstein Durchgang durch die senkrechte Lage der Ausschlag infolge der Erdrotation gerade durch dieses Torsionsmoment kompensiert wird. Aus Pendelschwingungsdauer und dem anfanglich vorgegebenen Drehmoment ergibt sich die Winklegeshwindigkeit der Erddrehung.

Attempt 2. The rope brake is released. The rod oscillates periodically about the horizontal axis of rotation A. By turning the torsion head before the triggering of the pendulum an initial torsion is set so that when first pass through the vertical position of the rash due to the earth's rotation is compensated just by this torsional moment. From the pendulum oscillation period and the initially specified torque, the angular velocity of the earth's rotation results.


Ich danke meinem Lehrer, herrn Kersten, fur sein großes Interesse an der beschriebenen Versuchsanordnung, fur viele anregende Diskussionen sowie einige Verbesserungvorschlage. Er hat die Versuche in seiner Vorlesung wie bei anderen Gelegenheiten vorgefuhrt.

I thank my teacher, Mr Kersten, for his great interest in the experiment described, for many stimulating discussions, and some suggestions for improvement. He has performed the experiments in his lecture as well as on other occasions.

https://www.metabunk.org/attachments/bucka1949-pdf.35593/

 

[Antrax]

Sorry if this off topic, but apparently it is possible to greatly reduce the size of a Focault's Pendulum as described in the following paper. Whether this is simpler to perform as Bucka's experiment is a different question though:

"A Short Foucault Pendulum Free of Ellipsoidal Precession"

A quantitative method is presented for stopping the intrinsic precession of a spherical pendulum
due to ellipsoidal motion. Removing this unwanted precession renders the Foucault precession due
to the turning of the Earth readily observable. The method is insensitive to the size and direction
of the perturbative forces leading to ellipsoidal motion. We demonstrate that a short (three meter)
pendulum can be pushed in a controlled way to make the Foucault precession dominant. The method
makes room-height or table-top Foucault pendula more accurate and practical to build.

https://arxiv.org/abs/0902.1829

 

[Mick West]

I did a simple build of the Bucka experiment with an aluminum tube and some fishing line.

Source: https://youtu.be/kRItQBI2pS0


After I burned through the line (you can see it initially seeming to contract from the heat) the rod swung up, and the pivot rotated. However, it seemed to initially slowly move in the opposite direction than suggested in the diagrams. i.e. it rotated clockwise (viewed from above). When the rod became vertical there was a spring in the counter-clockwise direction, but that seems to be from some interference (the rod hitting the line).

First impressions are that this seems like a fiddly experiment, with a lot of potential to introduce movement into the system. A "massive" rod would probably be needed to overcome this, and would hence need a quite solid frame to support it. Building such a thing would be an interesting challenge, but is not in my immediate future.

 

[LMR]

@Mick West thanks, I guess the frame should be solid.

 

[Mick West]

@Mick West thanks, I guess the frame should be solid.

Solid and light, so as not to contribute too much to the moment of inertia.

 

[Mendel]

I just read through the German paper, and in the light of the preceding discussion, here's what I found:

The Frame needs to be light, ideally just wires, and the spacer. Fishing line might be too elastic? There's an adjust built into the spacer to tighten one of the vertical so that the axis can be adjusted to be horizontal, and in fact it is at that stage that Bucka suggests using a sheet of paper as air brake to stop the support frame from spinning as wildly as you have observed (the procedure involves letting the rod swing freely and adjusting the axis so that the jump on the backswing is oriented the same as in the other direction.).

The top wire supporting the contraption is actually a torsion scale, which was familiar to me from the Cavendish experiment (hence the mirror). Once the axis is adjusted (and points N/S), and you know the exact rest position of the scale, the brake is tightened (there is a friction brake acting on the axis) such that the rod swings to vertical and stays like that. The torsion wire then oscillates, and from the periods of oscillation for the now vertical rod and the horizontal rod (determined separately) you compute the Foucault rotation.

For the second experiment you try to eliminate the jump that occurs as the rod goes to vertical by turning the torsion wire, adding some tension; if you adjust it just right, the device stays stationary as the rod goes vertical, and after you do the measurement from the reverse swing, you can compute the angular velocity from the tension. This is more accurate than observing the oscillation, since it's easier to observe if the frame stays at rest or not.

I can't say I've fully understood the physics, but the main principle seems to be to measure the angular momentum with a torsion scale.

Buckas original rod weighed more than 10kg; it was a brass rod with a bit of lead poured into each end.

Using a burn thread connected to the support to hold the rod up serves the dual purpose of introduing no external momentum on release, and to keep the torsion wire vertical.

So with the fiddliness and physics involved, not exactly an experiment for the common man, but if you know what you're doing, seems simpler to achieve and quicker to demonstrate than a Foucault pendulum.

 

[Mick West]

So with the fiddliness and physics involved, not exactly an experiment for the common man, but if you know what you're doing, seems simpler to achieve and quicker to demonstrate than a Foucault pendulum.

I think the question here would be if it's possible to fiddle the experiment the wrong way. It seems like there's lots of steps needed to get it just right - but how is an observer to know it's just right?

 

[deirdre]

I just read through the German paper

Can you read this paper? https://vdocuments.mx/zwei-einfache-vorlesungsversuche-zum-nachweis-der-erddrehung-ii-teil.html

 

[Mendel]

I think the question here would be if it's possible to fiddle the experiment the wrong way. It seems like there's lots of steps needed to get it just right - but how is an observer to know it's just right?

Well, it's good if it works without any undue jerks. Probably needs a youtube tutorial. ;-P

@deirdre The second part was written almost two years later. First Bucka outlines a method to enhance the effect. In the original, that axis is oriented N/S to eliminate the gyrocompass effect, but here he has computed its size and uses the effect to adjust the axis to level more easily, and also as a third method to compute the Earth's rotation.

Then he answers some letters he's received, and shares some tips and tricks: Use a glass box to eliminate air currents (the bane of any torsion scale). Don't connect the wires directly to the axis, use two small metal strips as connectors. Set the brake such that the rod is vertical before the torsion scale has reached the maximum amplitude. With the second method, let the rod swing a bit beyond vertical, and do several measurements; Bucka orginally thought this would be more exact than his first method, but he was mistaken (20% error on both).

He then spends the rest of the paper describing actually doing the experiment and gives his measurements.

His closing remark says:

Zum Schluß möchte ich bemerken, dab die Fehlerquellen für diese Vorlesungsversuche nicht weniger groß sind als beim FOUCAULTschenPendelversuch, und daß deshalb brauchbare Ergebnisse nur bei großer Sorgfalt der Versuchsführung erreicht werden können.

"Finally, I'd like to remark that the sources of possible error for these lecture experiments are just as great as with Foucault's pendulum, and therefore useful results can only be obtained if the experiment is performed with great care."

If you want to actually make this Bucka apparatus, I can have a go at producing a more complete translation.

I am attaching the file you linked, that service requires a 120s focused wait to download.The OCR is atrocious.

 

[Mendel]

I think the question here would be if it's possible to fiddle the experiment the wrong way. It seems like there's lots of steps needed to get it just right - but how is an observer to know it's just right?

Ok, I am not sure I understood your question correctly the first time. Are you asking if we can tell from a video whether the device has been adjusted correctly?

There are criteria for getting the steps right:
* find the neutral position of the torsion scale (let it swing with the rod fixed, figure the center of oscillation) and use it
* adjust the axis to horizontal (swing the rod freely, if the axis is too tilted it jerks both ways on consecutive swings)
* the actual measurements should be ok, method one requires timing the first oscillation? and method two requires using a correct starting torque so that the apparatus compensates exactly for the momentum

If you use it just as a demonstrator, without wanting to measure anthing, the fact that it turns/jerks at all when the rod becomes vertical should be enough of a conundrum for any FE observer: there is no reason for the apparatus to do that unless it already has angular momentum in the horizontal plane (horizontal axis tilted, torsion not at neutral). The rod must be made to swing very vertically, and the jerk of axis makes must be in the same direction both times (if it is N/S oriented) (fore-swing and back-swing), because jerking caused by axial tilt would be reversed as the rod reverses its swing. If you start it from free-hanging with the burning thread, that demonstrates it is at torsion neutral when it doesn't move while the thread burns.

 

[Mick West]

I think if flat earth fold can rationalize a ship going over the curve as "perspective" then they are just going to see this as a magic trick.

Still, it would be interesting to replicate.

 

[Mendel]

I'm not sure if this is the right place to post, but since Bucka mentions that during calibration, this effect also happens, and it's been at the back of my mind ever since: how are the chances of putting together a homebrew gyrocompass? I'm a bit unclear on the concept, but apparently if you restrain one axis of freedom of a spinner, then it will try to orient its axis (precess) parallel to the Earth axis, which eliminates residual torque. This concept has been used forever in naval navigation, these gyrocompasses are probably on many ship's bridges. Building a homebrew device that is able to find North without electricity or magnetism should be a pretty convincing demonstration of the spinning globe, right?

 

[OTACHI]

Those kind of experiments don't work with flat earth people,they will claim it's detecting the aether.

 

[Guillermo E. Mulvihill]

If w is not 0, it will be 10000 times bigger than 1 rotation per day (2*PI/86146) and the frame will start to rotate counterclockwise (in the Northern hemisphere and clockwise in Southern hemisphere).

Why 86146? 24 hours * 60 min * 60 sec = 86400.

 

[Guillermo E. Mulvihill]

Why 86146? 24 hours * 60 min * 60 sec = 86400.

if you consider the value of 23 hours 56 min and 4 sec (wikipedia), results 86164 sec.

 

[JFDee]

24 hours * 60 min * 60 sec = 86400

That's the time for a full day rotation (noon to noon) which is slightly more than 360° - because of earth's orbit.

The shorter value (23 hours, 56 min and 4 sec) is the duration of one 360° rotation.

 

[Mendel]

Those kind of experiments don't work with flat earth people,they will claim it's detecting the aether.

The aether would only affect light, not mechanics, if it existed.

 

[Guillermo E. Mulvihill]

That's the time for a full day rotation (noon to noon) which is slightly more than 360° - because of earth's orbit.

The shorter value (23 hours, 56 min and 4 sec) is the duration of one 360° rotation.

@JFDee But if you consider the value of 23 hours 56 min and 4 sec (wikipedia), results 86164 sec, not 86146 sec.