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For Whom the Tubular Bells Toll

If you are a whizz at waveforms vis-à-vis bells of a totally tubular persuasion, then any light you can shed on this subject would be very gratefully received.

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If you are a regular reader of my columns (in which case you are obviously a person of discernment and distinction), you will doubtless recall my waffling on more than one occasion about my chum Paul Parry. This “Maker’s Maker” is the founder of Bad Dog Designs in the UK, where he specializes in creating bespoke Nixie tube clocks with a steampunk aesthetic. One of Paul’s constructions that has really sparked my imagination is called the Symphony. In addition to boasting two 6-digit Nixie tube clocks, the Symphony also flaunts a form of Tubular Bells comprising 32 pipes. Just to refresh our memories, this video shows an early incarnation of the Symphony playing part of Bach’s Toccata and Fugue.  
I keep on coming back to this video and — every time I watch it — I think, “I would love to have something like this to play with.” I was chatting with Paul a few days ago about “this and that,” as part of which I posed some probing questions.
My interpretation of Paul’s early Symphony striker mechanism drawing (Click image to see a larger version — Image source: Max Maxfield)
First, Paul noted that the note associated with each pipe is a function of the length of the pipe, the diameter of the pipe, the thickness of its walls, and the material from which the pipe is made. I assume temperature is also a factor because the pipes will expand and contract. I wonder if barometric pressure also comes into play. Paul also mentioned that, in the case of the Symphony, he used copper pipes, which ring with relatively high-pitched notes. He suggested that if I were to do something like this, then I might consider using something like steel pipes, which are harder to work with, but which have a lower frequency. I just recreated one of Paul’s early drawings for a Symphony striker (above right). Paul tells me he’s using HCNE1-0530 solenoids, which — from what I read on various eBay pages — are rated at 12 V, 300 mA, and have a stroke length of 10 mm (if you know of any devices that are cheaper or more appropriate for this task, please let me know in the comments below).
Symphony 4-striker module Mark II (Click image to see a larger version — Image source: Paul Parry)
Of course, this image is not to scale. Also, although the solenoid’s stroke length is 10 mm, Paul says that the tip of his striker moves only 2 to 3 mm. Paul continued, “Timing-wise, you only apply power to the solenoid for 20 to 40 ms. You kill the power as soon as the solenoid starts to move, otherwise it will draw anything up to 2A! When you’ve got 32 of them, like in the Symphony, that’s a lot of power. As a result, the playback is limited to no more than six simultaneous notes.” Paul went through several iterations of his design, eventually ending up with a 4-striker module (he used eight such modules to drive the Symphony’s 32 notes). One of the characteristics of Paul’s striker is that it converts the linear motion of the solenoid into the rotational motion of the striker (observe that I’ve drawn the Paul’s pipe horizontally because it makes things easier to display in the column — in reality the whole assembly would be rotated 90° so that the pipe is orientated vertically). I’ve been thinking about this, and it strikes me (no pun intended) that — since the tip of the striker requires only 2 to 3 mm of motion — it should be possible to dramatically simplify things so as to use only the linear motion of the solenoid.
My version of a striker mechanism using linear motion only (Click image to see a larger version — Image source: Max Maxfield)
My drawing of this reflects a bird’s eye view looking down on top of the vertically mounted pipe, because this makes it easier to see how things work. There would be additional bits and pieces — like something to guide the striker — but nothing too complex. I’ve not discussed this with Paul yet, so I’m looking forward to hearing what he thinks. Another idea that’s rattling around my noggin is that Paul mounted his Pipes side-by-side, but I was thinking about mounting mine in a circle, with my solenoid strikers radiating out from the center like the spokes on a wheel, thereby resulting in a table-standing model. Do you recall my mentioning the fact that the Symphony features two 6-digit Nixie tube clocks? As you can see in the picture below, the left-hand clock displays the time in Crief, while the right-hand clock reflects the time in Tye Green.
Close to the finish (Click image to see a larger version — Image source: Paul Parry)
Crieff (Scottish Gaelic: Craoibh, meaning “tree”) is a Scottish market town in Perth and Kinross, while Tye Green is a village in the civil parish of Cressing and the Braintree district of Essex, England. The Scottish guy who commissioned this clock currently hangs his hat in Tye Green, but his father lives in Crieff, hence the two clocks. What? Yes, of course they show the same time. Why wouldn’t they? Scotland and England are in the same time zone. What’s your point? Sad to relate, I think a lot of the valuable information Paul gave me “went in one ear and out of the other,” as it were. Even worse, I’ve suddenly realized that I’m a bit “fluffy around the edges” when it comes to acoustic resonance. I’m sure that Paul told me that his strikers hit the pipes about 1/3 of the way along their length. Initially this seemed to make sense to me, because I was looking at the Wikipedia page on acoustic resonance, which shows some interesting animated wave representations. Based on these, I initially assumed that if you hit the pipe 1/3 of the way along its length it would ring with its third harmonic (it seemed to make sense at the time). However, I subsequently realized that the diagrams in the Wikipedia are associated with pipes that are closed at both ends. The Wikipedia goes on to say that, “In cylinders with both ends open, air molecules near the end move freely in and out of the tube. This movement produces displacement antinodes in the standing wave. Nodes tend to form inside the cylinder, away from the ends. In the first harmonic, the open tube contains exactly half of a standing wave (antinode-node-antinode).” Furthermore, as seen in this video, Paul’s strikers all hit their corresponding pipes the same distance from the end. So now I’m back to thinking that each pipe rings with its own fundamental tone, irrespective of where you strike it. Having said this, it would seem to make sense to me that the optimum strike zone was in the middle of the pipe if that pipe is somehow restrained close to its ends, or at the bottom end if the pipe is dangling from a string attached to its top end.
Yet another source of interesting facts comes from an Instructables article on building a Copper Pipe Glockenspiel. I have to say that this is a great article, not the least that it notes “there are two nodes, 22.4% of the way in from each end, that stay put, and the pipes vibrate around them, the ends going up when the middle goes down, and vice versa. The pipes will sound the best when they are flexibly supported around the nodes.” This ties in with the Wikipedia’s pithy comment that “nodes tend to form inside the cylinder, away from the ends.” I’m not sure why the magic number is 22.4% of the way in from each end, I would have been much happier if it were 25%, but I’ll take what I can get. I fear I’m going to have to drop in The Home Depo this coming weekend, purchase a length of copper pipe, and perform some experiments. In the meantime, if you are a whizz at waveforms vis-à-vis bells of a totally tubular persuasion, then any light you can shed on this subject would be very gratefully received.

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Paul Parry

Many thanks for documenting this up!
Be very careful once you go to Home Depot.. once you get one pipe to strike and produce the correct note, there is a very strong desire to then make another with a different note, and then another so you can play a tune.
You then notice they then sell a 1″ diameter pipe….

Paul Parry

On a side note, I later discovered a solenoid that has a plunger that extends through the body, so as it pulls in on the one end, the other end flies out and that could have struck the pipe directly.. not much ‘theatre’ with that though!

Aubrey Kagan

Max

It is possible to reduce the current consumption of a solenoid after it has “struck”, so you can use a small fraction of the power to keep it energised. In one of my experiments I managed to reliably reduce the power to less than 10%.

See my blog

Saving power with relays and solenoids
https://www.embedded.com/saving-power-with-relays-and-solenoids/

Also remember to read the comments.

The PWM method is the simplest, but getting the driver to operate at above sonic frequencies is difficult. So it is likely to introduce audio depending on the mechanical construction of the solenoid- perhaps you can damp it, but I fear you will need to used one of the other methods.

P.S. I see that Paul has no need to maintain the solenoid in an energised state, so I guess all the above is hot air!

Elizabeth

I have a couple wind chimes made of tuned metal tubes. The tubes are supported an inch or so from the top end with strings and struck closer to the opposite end by a wooden disk. There isn’t a fixed relationship that I can see in terms of percentage of length for either the string or disk placement since the tubes are different lengths.

This type of wind chime is reasonably common so I’m sure there are instructions for tuning somewhere on the internet…

PeterTraneus Anderson

If you’re using steel tubes, you could hang coils loosely by their wires close to the tubes. Energize a coil to make the coil hit the tube. Unrelatedly, push-pull solenoids should work well. You may want a soft pad on the tip of the plunger hitting the tube.

Elizabeth

I was actually thinking of something similar except with a fixed coil and moving tube.
And, yes a pad on the tip of the solenoid hitting the tube would be good. Not too soft though or the sound might get muffled.

Elizabeth

Close your eyes, take a deep breath and repeat after me “I do NOT need another project” repeat until the desire goes away or you find yourself with parts in hand. I recommend opening your eyes before starting construction.

Let me know if this works any better for you than it has for me. LOL

PeterTraneus Anderson

If you excite the coil with a fast pulse or with the steel tube’s resonant frequency, you might not need to physically contact the tube at all. Extend this to a flat steel plate, and we’ve reinvented the headphone.

David Ashton

Nice diagrams as always Max, but what’s a solanoid?

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