Blowing machine

[Tunborough]

Calibrators followed by 130 mm tubing: Ke = 0.12

Is all the calibrators giving the same Ke? So you have the pressure loss down a calibrator modelled adequately? I may have missed that earlier.

Yes, the "known" parameters Kb and Kdw, mostly Kdw, are sufficient to model the differences between the calibrators, which is no small feat. Unfortunately, as we can see with the old Gen and the Feadog, they aren't (yet) sufficient to model the differences between whistles.

A question to Terry ... Fresh out of the mold, both heads would have a dimple or concavity in the fipple under the windway exit. Has the concavity been filled in on any of the sample whistles?

[david_h]

@ Tunborough. Thanks. I was adding the last paragraph, indicated **, to my post above as you were posting.

[Tunborough]

** there are results from Q and P measurements on all members of a consort of recorders on pages 9, 10 and 11 of the paper linked on this page https://www.researchgate.net/publicatio ... of_the_Jet (can't link the PDF directly). Apart from the odd wayward point nothing to indicate any change in the mechanism of flow over the range of an instrument. Figure 1 on page 3 suggests that a curved floor and roof of the windway is standard on a recorder. I think that suggests that oddities in Terry's data (variable resistance on one whistle) are probably due to the flowmeter and maybe some sort of correction could be worked out. That's what I suggested the zero length calibrator for but if Tunborough has the modelling of the calibrator windways sorted out it may not be needed.

That's a very interesting paper that I hadn't seen before. Figure 6 makes me squirm; if I'm reading it right, it suggests our square-law relationship isn't perfect and breaks down entirely at low flows. They give the full details of the windway geometry, so if I can tease out the numbers behind Figure 6, I can plug them into my model and see what shows up.

[david_h]

Figure 6 makes me squirm; if I'm reading it right, it suggests our square-law relationship isn't perfect and breaks down entirely at low flows.

I eyeballed a few points on one of the lines and its not too bad away from low levels. They do say "When the mouth pressure increases, the flow tends to behave with the Bernoulli’s law, as observed by ..." I have been dipping into papers available open access online and several go straight to Bernoulli without any experiment. There are things that we know to be an issue that they haven't considered - and they may have instrumentation issues as well. The reason I was using Q - sqrt(P) plots was to look for things that might be significantly different from the simple straight line that Bernoulli and other losses would predict. Terry's data do look like a square law relationship except at low flows where we suspect the flow meter.

I was interested in the observation that by design resistance was related to fingering rather than pitch to ease players moving between instruments. Handy that Bernoulli's equation is independent of aperture.

I keep being distracted into flute acoustics and that paper came up in a search related to that.

[Terry McGee]

A question to Terry ... Fresh out of the mold, both heads would have a dimple or concavity in the fipple under the windway exit. Has the concavity been filled in on any of the sample whistles?

Both heads are as original - big cavities under the windway in both.

[Terry McGee]

- is the upper PTO far enough away from the whistle/calibrator connector that pressure losses just outside the windway entrance are not missed? (does moving it make a difference?)
- is the upper PTO so far away from the whistle/calibrator connector that pressure losses in the tubing need to be included in the model? (ditto)

The Whistle Connector tube is about 110mm long, with the PTO 40mm up from the end where the head plugs in. The beak probably penetrates about 10mm into the tube, so the PTO would be about 30mm upstream. Happy to try greater and shorter distances if you'd like to suggest them. An easy one would be to reverse the tubing, which would give us about 60mm upstream. But would also mean that the expansion zone above the PTO was reduced by 30mm in length. I have heaps of this tubing, so no concerns about using more.

[Terry McGee]

I think I mentioned further up somewhere that I had made a 12.7mm bore whistle from scratch. In Delrin, along the lines of the three-part Sindt style head.

When first made, with a parallel ceiling and floor in the windway, it needed more pressure than I liked, so I sanded down the top of the block rather crudely on the bench belt sander to give some taper. Hard to do well, given the curved surfaces involved. I'd also made the window length a bit big. It played OK, but not really well.

So yesterday I made a new block and cover, and this time milled the top of the block to get the taper more uniform across and along. Comparing it with the Killarney and Tweaked Mellow D, I feel it now lies well between them. So just mentioning that, in case at some point we want to make or modify a head to test a theory, rather than trying to fit the theory around our old relics!

[Terry McGee]

So today, I did the same but with my previously made 13.5mm bore whistle, McGee #3. It too had been "voiced" haphazardly on the bench belt sander, and was too aggressive to be enjoyable. And exascerbated by too long a window. So, again, I made a new cover and block to start again on the voicing.

And I thought to take some measurements along the way. I milled the top of the block in the mill, with the Dividing Head set at 1º to horizontal. That meant I would be removing a smidge more at the tip of the beak than at the window. I approached the milling of the top of the block cautiously, so we could follow progress. The three phases are no milling, milling about 2/3 of the length, so not touching the block at the window end, milling the full length. As you can see below, the "Resistance" drops as we go along.

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McGee #3 new block and cover, no voicing			
Flow	MM(H20)	√A/P	Resistance
5	6.5	2.55	0.51
10	24	4.90	0.49
15	51.5	7.18	0.48
20	90	9.49	0.47
			
Average Resistance			0.49
			
			
McGee #3 new block and cover, milling for 2/3 of windway			
Flow	MM(H20)	√A/P	Resistance
5	5	2.24	0.45
10	20.5	4.53	0.45
15	44.5	6.67	0.44
20	78.5	8.86	0.44
			
Average Resistance			0.45
			
			
McGee #3 new block and cover, milling for all of windway			
Flow	MM(H20)	√A/P	Resistance
5	4.5	2.12	0.42
10	19	4.36	0.44
15	39.5	6.28	0.42
20	69	8.31	0.42
			
Average Resistance			0.42

Then I thought it would be good to compare it with another 13.5mm head, the Soodlums Mellow D. And also to answer Tunboroughs question about can we detect any change in pressure if the cavity inside the head is filled. Because of the changes to the setup mentioned recently, I retook those measurements:

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Mellow D Unpacked head cavity			
Flow	MM(H20)	√A/P	Resistance
5	6	2.45	0.49
10	22	4.69	0.47
15	46	6.78	0.45
20	83.5	9.14	0.46
			
Average Resistance			0.47
			
			
Mellow D Packed head cavity			
Flow	MM(H20)	√A/P	Resistance
5	5.5	2.35	0.47
10	21	4.58	0.46
15	45.5	6.75	0.45
20	83.5	9.14	0.46
			
Average Resistance			0.46

Because of the shapes of the beaks I had to go for a larger whistle connector tube for the McGee, then went back to the usual one for the Mellow D. Then I got a bit nervous - will the bigger tube throw in some more confusion? So I put the bigger tube back, and packed out the Mellow D beak with mirror tape to fill the hole. Doesn't look like the results were much affected:

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Mellow D Packed head cavity in bigger Whistle Connector tube			
Flow	MM(H20)	√A/P	Resistance
5	6	2.45	0.49
10	21	4.58	0.46
15	46	6.78	0.45
20	81	9.00	0.45
			
Average Resistance			0.46

[david_h]

Here's hoping Tunborough hasn't already done this. Blowing pressure and flow for a consort of recorders. Data from Blanc and others 2010.

Above 25 Pa (~2.5mm H2O) there is a pretty good square law relationship, with some departures that may be of interest. Excluding the zero point straight line fits of Q vs sqrt(P) have intercepts on the sqrt(Pa) axis for the sopranino, soprano, alto, tenor and bass of 3.3, 2,9, 2.8, 2.6 and 2.7 Pa. So whatever is happening at the bottom of the range it seems consistent.

I think it is a chromatic scale on each instrument but there are a few points missing at the low end because the graph is cluttered.

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Blowing  pressure and Flow data (first two numeric columns) from  Figure 6 of  Blanc F., Fabre B., Montgermont N., De La Cuadra P., Almeida A. 2010,
Scaling of flute-like instruments : an analysis from the point of view of the hydrodynamic instability of the jet


Recorder,Pa,m3/s/10000,sqrt(Pa),mmH2O,sqrt(mmH2O)
Sopranino,0,0.000,0.000,0.000,0.000
Sopranino,28,0.163,5.249,2.809,1.676
Sopranino,41,0.249,6.420,4.203,2.050
Sopranino,58,0.332,7.630,5.937,2.437
Sopranino,82,0.411,9.068,8.384,2.896
Sopranino,82,0.411,9.068,8.384,2.896
Sopranino,107,0.501,10.335,10.891,3.300
Sopranino,135,0.583,11.600,13.720,3.704
Sopranino,166,0.664,12.875,16.902,4.111
Sopranino,204,0.749,14.282,20.800,4.561
Sopranino,234,0.826,15.300,23.871,4.886
Sopranino,234,0.826,15.300,23.871,4.886
Sopranino,301,0.914,17.345,30.676,5.539
Sopranino,324,1.000,18.011,33.078,5.751
Sopranino,369,1.086,19.215,37.649,6.136
Sopranino,410,1.165,20.255,41.835,6.468
Sopranino,518,1.332,22.762,52.831,7.268
Sopranino,624,1.499,24.988,63.672,7.979
Sopranino,751,1.666,27.398,76.544,8.749
Sopranino,860,1.835,29.326,87.695,9.365
Sopranino,1004,2.000,31.690,102.407,10.120
Sopranino,1190,2.168,34.491,121.309,11.014
Sopranino,1354,2.335,36.798,138.080,11.751
Sopranino,1506,2.498,38.805,153.547,12.391
Sopranino,1747,2.663,41.797,178.136,13.347
Sopranino,1855,2.830,43.067,189.132,13.753
Sopranino,2179,3.016,46.679,222.187,14.906
Soprano,0,0.000,0.000,0.000,0.000
Soprano,19,0.166,4.352,1.931,1.390
Soprano,29,0.255,5.380,2.952,1.718
Soprano,49,0.339,6.972,4.957,2.226
Soprano,63,0.422,7.959,6.460,2.542
Soprano,80,0.502,8.937,8.145,2.854
Soprano,98,0.589,9.922,10.038,3.168
Soprano,118,0.671,10.842,11.987,3.462
Soprano,143,0.807,11.945,14.549,3.814
Soprano,165,0.837,12.855,16.850,4.105
Soprano,193,0.919,13.883,19.653,4.433
Soprano,219,0.999,14.803,22.345,4.727
Soprano,252,1.085,15.860,25.648,5.064
Soprano,282,1.170,16.780,28.711,5.358
Soprano,316,1.255,17.770,32.201,5.675
Soprano,344,1.336,18.542,35.059,5.921
Soprano,385,1.419,19.616,39.236,6.264
Soprano,423,1.505,20.567,43.133,6.568
Soprano,462,1.588,21.490,47.092,6.862
Soprano,500,1.667,22.370,51.027,7.143
Soprano,546,1.756,23.373,55.705,7.464
Soprano,594,1.835,24.375,60.586,7.784
Soprano,685,2.002,26.179,69.884,8.360
Soprano,795,2.170,28.191,81.040,9.002
Soprano,903,2.333,30.048,92.066,9.595
Soprano,1000,2.504,31.621,101.959,10.097
Soprano,1189,2.667,34.484,121.257,11.012
Soprano,1312,2.834,36.217,133.748,11.565
Alto,0,0.000,0.000,0.000,0.000
Alto,70,0.667,8.377,7.156,2.675
Alto,129,0.999,11.378,13.201,3.633
Alto,205,1.331,14.323,20.918,4.574
Alto,297,1.667,17.240,30.308,5.505
Alto,406,2.002,20.150,41.404,6.435
Alto,530,2.336,23.014,54.009,7.349
Alto,665,2.670,25.780,67.771,8.232
Alto,821,2.996,28.645,83.671,9.147
Alto,993,3.336,31.517,101.291,10.064
Alto,1388,3.999,37.262,141.583,11.899
Alto,1830,4.663,42.778,186.600,13.660
Tenor,0,0.000,0.000,0.000,0.000
Tenor,15,0.233,3.821,1.489,1.220
Tenor,20,0.335,4.517,2.080,1.442
Tenor,35,0.497,5.934,3.591,1.895
Tenor,51,0.666,7.167,5.238,2.289
Tenor,66,0.834,8.135,6.749,2.598
Tenor,86,1.002,9.258,8.739,2.956
Tenor,108,1.168,10.378,10.983,3.314
Tenor,130,1.334,11.399,13.249,3.640
Tenor,158,1.500,12.551,16.063,4.008
Tenor,186,1.670,13.656,19.015,4.361
Tenor,252,2.000,15.868,25.675,5.067
Tenor,322,2.332,17.958,32.883,5.734
Tenor,407,2.669,20.165,41.464,6.439
Tenor,501,2.998,22.381,51.076,7.147
Tenor,597,3.334,24.427,60.846,7.800
Tenor,714,3.664,26.718,72.791,8.532
Tenor,837,3.996,28.932,85.354,9.239
Tenor,961,4.332,30.999,97.986,9.899
Tenor,1090,4.662,33.018,111.167,10.544
Bass,0,0.000,0.000,0.000,0.000
Bass,3,0.162,1.671,0.285,0.533
Bass,28,0.416,5.321,2.888,1.699
Bass,35,0.503,5.914,3.567,1.889
Bass,43,0.580,6.580,4.415,2.101
Bass,47,0.667,6.829,4.755,2.181
Bass,61,0.748,7.814,6.226,2.495
Bass,67,0.837,8.161,6.792,2.606
Bass,81,0.913,9.002,8.263,2.875
Bass,88,1.002,9.365,8.942,2.990
Bass,109,1.170,10.442,11.118,3.334
Bass,133,1.339,11.529,13.553,3.681
Bass,160,1.502,12.640,16.293,4.036
Bass,190,1.668,13.771,19.337,4.397
Bass,222,1.833,14.915,22.685,4.763
Bass,293,2.170,17.130,29.923,5.470
Bass,328,2.336,18.118,33.474,5.786
Bass,370,2.499,19.237,37.736,6.143
Bass,413,2.674,20.319,42.100,6.488
Bass,458,2.833,21.393,46.666,6.831
Bass,551,3.169,23.477,56.204,7.497
Bass,595,3.338,24.392,60.669,7.789
Bass,649,3.500,25.470,66.148,8.133
Bass,704,3.663,26.541,71.831,8.475
Bass,756,3.835,27.499,77.107,8.781
Bass,817,4.004,28.581,83.297,9.127
Bass,868,4.167,29.456,88.472,9.406
Bass,983,4.498,31.354,100.243,10.012
Bass,1319,5.310,36.324,134.540,11.599

Sorry, should have put a l/min column in there.
And no, I didn't measure them all off with a ruler.

[Tunborough]

Here's hoping Tunborough hasn't already done this. Blowing pressure and flow for a consort of recorders. Data from Blanc and others 2010.

...

And no, I didn't measure them all off with a ruler.

This is terrific, David. I started to pick out a few points, but this is far beyond what I could do. I'll plug these into my model.

How did you get these numbers?

[david_h]

How did you get these numbers?

Scaled the image of Fig 6 into CAD software, clicked a point onto the symbols for each recorder and exported the coordinates.

Unless I've got my units wrong the resistance is a lot higher than the D whistles. I guess that could be for genres of music with longer phrases than your average reel.

[david_h]

Looks like blowing machines for air reed research is a long story. My distraction into flute acoustics led me - via Terry's web site - to John Gunn "Art of Playing the German Flute" c.1793 where we find:

Hence it will follow, that whatever additional acutenefs any found may acquire, muft be produced by fome caufe that increafes the velocity of the air, modified into found; and that a diminution of fuch velocity, will, on the contrary, make the found flatter or more grave. On this principle it was, that the ingenious M. Vaucanfon produced the lower tones, the octaves, the double octaves, in his automation figure, or mechanical flute-player: the wind that was conducted, through the aperture or lips of the figure, into the flute, was, for the lower or graver founds, impelled by a bellows that acted with the weight of one pound; for the firft octaves, by a bellows acted on by a two-pound weight; and the double octaves were produced by a bellows acting with a weight of four pounds.

[Terry McGee]

How did you get these numbers?

Scaled the image of Fig 6 into CAD software, clicked a point onto the symbols for each recorder and exported the coordinates.

Heh heh, Data Scavenging in style!

Unless I've got my units wrong the resistance is a lot higher than the D whistles. I guess that could be for genres of music with longer phrases than your average reel.

And remember those data are for Sopranino recorders, equivalent to our whistles in high G (xxx xxx = G5). So tiny windways.
The nearest equivalent to our treble D whistle would be the Descant recorder ((xxx xxx = D5).

D'uh, edited to say I didn't scroll down the list to see you've included all the sizes of recorders. And what I called the Descant is the "Soprano" on the data given. Is the Soprano resistance higher than the typical Treble D whistle? Windway length in recorders tends to be greater than in whistles.

[Terry McGee]

Remember the lady who brought in the 2 Coomber Treble recorders for a cleanup last week? She brought in her Saunders Treble yesterday. Joanna (Jo) Saunders is a highly regarded Melbourne recorder maker who trained under the late Fred Morgan. The late Michael Grinter, Irish flute maker, was also one of Fred's trainees. I visited Fred in his Melbourne workshop back in the seventies.

The owner commented that the resistance seemed higher, so I measured both.

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Coomber Treble			
L	H(L)	W	Area
0	1.62	13.86	22.4532
6.6	1.575		
15.85	1.53		
21.7	1.48		
31.7	1.375		
57.83	1	12	12
			17.2266
			
Saunders Treble			
L	H(L)	W	
0	1.34	13	17.42
4.7	1.29		
29.9	1.185		
55.44	0.85	11.9	10.115
			13.7675

So, quite a reduction in cross sectional area between them.

[trill]

I've been diverted for a while, but have been simmering flowmeters on the back burner.

Question: If the flowmeter has relevant errors, how will those errors manifest ?

Answer: in trying to reconcile the model(s) and the measurements.

Here are some options:

Low cost, but no specs or provenance:


https://eoutlet.2023shoponline.com/cont ... price&id=2
$28. But hey, it's digital ! Much easier on Terry's eyes ! Says "Thermal Mass. . .", so probably MEMS.
(but seriously, folks . . .)


Similar to current, but calibrated for air and with a much more uniform scale:



https://www.dakotainstruments.com/air-f ... s-fittings
$68 with needle valve, 50lpm.
+/- 5% of full-scale.


And finally, some modern meters with data sheets:



The Omega is too rich for my blood, even with cost sharing.

My favorite is:
https://www.digikey.com/en/products/det ... A/11657803

I have a query into the mfr to see if they have a distributor in Australia. Would be nice to avoid + $100 shipping.