Blowing machine

[trill]

. . . I settled on the old Generation head. . . Here are its vital statistics:

So, Terry, using your test results for pressure, flow and windway-exit area, a "discharge coefficient" was derived. This presumes a model from Bernoulli's equation.

Here is plot of the results:



There are some caveats:
1) The derived coefficients are unrealistic. They are greater than 1. (1.03, 1.06, 1.09).
2) I don't know why yet. Could be measurement error, could be derivation error. I'll dig into it.
3) The 3 lines are for each of those 3 values.
4) your test data is shown as the blue diamonds.

It's a first look at the effect of exit area on flow.

. . . Doesn't the relationship between pressure and flow (e.g. the constant in Bernoulli's equation) vary with overall windway geometry as well as final exit area? . . .

That was the idea I wanted to test. Using Terry's data from other whistles, we can check. After I run down the discharge coeffieicnts.

[david_h]

903Hz is A6+45cents, we shouldn't have to note both. I do have an app which translates but I also don't want to have to enter the data and transfer the answers. It would be nice to have a column in the spreadsheet to enter either of these data, and for the spreadsheet to automatically fill in the next column with the other form of data. Probably easier to log Frequency and calculate Pitch?

From something I prepared earlier. Unless I have added any typos by substituting for the cell references the below seems to work

Code: Select all

From Excel [2002 version!] functions. Replace the bit in angle brackets (and the brackets) with the cell reference for wherever you put the named values calculated on the left.

Hz in the first equation is your measured frequency. 16.3516 is the frequency of C0.

Piano cents  =INT(1200*LOG(<Hz>/16.3516,2)+0.5)
Octave number=INT(<Piano cents>/1200)
Scale semitone=INT(MOD(<Piano cents>,1200)/100+0.5)
Note name =MID("C C#D D#E F F#G G#A BbB !!",1+<Scale semitone>*2,2)
Delta cents=MOD(<Piano cents>,1200)-100*<Scale semitone>

Cobbling them together into one string with text functions (getting rid of the untidy spaces in the note names) is left as an exercise for the reader.

If you test this by putting in 903Hz it gives A5 not A6 - as does s8tuner.exe when I blow it.

I haven't done the stats but given the scale precision of Terry's flow measurement I think we can regard Flow vs SQRT(P) as a straight line through the origin and use the slope of a line fitted to that as a single figure for resistance. I still think we need several values as for the Generation so we can keep looking for a departure from linearity.

[Terry McGee]

Ooops, sorry, silly me. I'm trying to get used to the notion that bottom D (on a treble D whistle) is D5, compared to D4 on a flute. So I automatically put my example up an octave! D'uh!

[Tunborough]

I tried the air speed model posted at viewtopic.php?p=1259223#p1259223 on Terry's new data for the Mellow D, Killarney, McGee #3, and old Gen. The results were disappointing, to say the least. For the Feadog, I get very similar results for air speed from the air flow and the pressure. For all of the others, the pressure predicts an air speed much lower than the air flow does; for the old Gen, the pressure predicts an air speed that's not much more than half what I would like to see.

- a proposed approach to defining and measuring resistance
<snip>
- confirmation that we don't really need to measure pressure and flow, apart from perhaps at the outset to identify their relationship (the resistance) of the whistle-under-test
<snip>
- being able to calculate Resistance from the physical data

Unfortunately, the resistance from your definition depends on the air density, which means it would vary with temperature, elevation, and maybe humidity, and even the size of your "mouth" tube where you're measuring the pressure. The resistance you calculate at sea level in summer won't agree with the resistance I calculate at 300 m up in winter. That first set of equations was an attempt to account for all of the physical data, including air density. Unless you can think of something that changed between test runs on different whistles, I have to go back to my scratch pad. I'm using only measurements at the windway exit. Maybe the additional windway profile information that you've measured will help get more consistent results.

[Tunborough]

Hmmm, in my 10 tubes in, 1 tube out thought experiment, continued long after bedtime last night, I realised that opening up the additional 9 tubes would send water levels scooting up the out tube, even at balance. Might need to rethink that one!

That won't happen. You don't get any "gain" from the multiple tubes. Instead of one side going down 5 mm and the other side going up 5 mm, the 10 tubes go down 0.91 mm each, and the outlet tube goes up 9.1 mm, so instead of doubling, you multiply your measurement by 1.1. With a very large reservoir, the reservoir goes down hardly at all, so you only need to measure the outlet height.

To get something like gain, you need one of these (clickable image).

[david_h]

Unfortunately, the resistance from your definition depends on the air density, which means it would vary with temperature, elevation, and maybe humidity, and even the size of your "mouth" tube where you're measuring the pressure.

So that's another four readily available things, plus barometric pressure, to record for each set of measurements. I think I would add at least one measurement on the IASoWR when Terry has machined it.

[Tunborough]

The results were disappointing, to say the least.

I was reading the tables wrong. I didn't realize that the first column of the pressure/flow table was the half-height measurement, and the second column was the full-height pressure. With that correction and a Darcy friction factor fD of 0.03 instead of 0.04, I get much better results. For the old Gen, the air speed from pressure is still 20% lower than for the flow, for McGee #3 it is about 10% lower. For the other whistles it is mostly within about 5%.

For the old Gen, Bernoulli suggests that 226 mm H2O pressure shouldn't be able to push more than 28.7 L/min through a 1 mm by 7.85 mm opening, not 30 L/min. Could there be something off in the old Gen measurements?

[Terry McGee]

The results were disappointing, to say the least.

I was reading the tables wrong. I didn't realize that the first column of the pressure/flow table was the half-height measurement, and the second column was the full-height pressure.

Sorry, my fault for sloppy column labelling. These are the kind of things that show up in the system development phase. I've edited the Do-List (above) to include: "I need to go through the spreadsheets, making the records of various whistles consistent in format, to avoid misinterpretation."

With that correction and a Darcy friction factor fD of 0.03 instead of 0.04, I get much better results. For the old Gen, the air speed from pressure is still 20% lower than for the flow, for McGee #3 it is about 10% lower. For the other whistles it is mostly within about 5%.

I think 5% is pretty encouraging, given the crudity of the measurement systems. I think ignore the McGee #3 until I do the tapering more assiduously!

For the old Gen, Bernoulli suggests that 226 mm H2O pressure shouldn't be able to push more than 28.7 L/min through a 1 mm by 7.85 mm opening, not 30 L/min. Could there be something off in the old Gen measurements?

There could well. I spent a bit of time tightening up connections to reduce the chance of leaks. I think that is a real risk and I might need to develop a testing procedure for that! Then re-run the Old Gen. Slightly different results, but probably within measurement error. Here we go:

[Edited to try to improve readibility]

Code: Select all

Old Generation Revisited			
Mano/2	MM(H20)	√AirP	Flow
118	236	15.4	30
56	112	10.6	20
13.5	27	5.2	10
0	0	0.0	0
		
Resistance	SQRT(P)/Flow	0.529150262212918

(Note I've given the first column a label to reduce confusion! And changed the other labels to avoid spaces. Any better suggestions?)

Would there be any point in making and testing a Reference Windway? I imagine a 25mm length of Delrin rod that couples nicely into my feed tube, with say a 4mm diameter hole through it. Or a Reference Orifice? Or whatever....

[Terry McGee]

Indeed, would the world be ready for a square Low Whistle? That would put it within the scope of people equipped for linear woodwork, but lacking a lathe. Sorry, Dear Reader, your range of excuses is evaporating.

There’s nothing new with that: https://www.recorderhomepage.net/a-roun ... recorders/

Indeed. Many years ago, I got a phone call out of the blue from a chap down in Victoria. He was a bassoon player and teacher, and lamented that so few people were taking the instrument up, because of the enormous costs of even a cheap one. And the cheap ones were rubbish. He wondered if I had any thoughts on how to make a cheap but serviceable bassoon. When you come to look at it, you realise what he was up against. Massive chunks of wood to be bored and reamed to taper. I thought for a minute while we were chatting, and then said "of course, it doesn't have to be round". The phone went quiet for a few moments, and then he made his excuses and slipped away. Odd, I thought.

A few months later, he called again, and asked would I like to hear the bassoon he had made. He played it over the phone. It sounded fabulous, and he thanked me profusely for giving him the idea it could be square. Later he sent images, and he'd managed to make it look great too. He'd rounded off the corners on the outside, so you didn't really notice it was essentially square.

Definitely worth thinking about for low whistles. Not good for flutes because the vacillating air column starts off life being transverse, and spirals to being longitudinal. It wouldn't enjoy the corners up in the head.

[Tunborough]

The new measurements improve the picture a little, but only slightly. For those keeping score at home, here is the table of numbers so far.

Code: Select all

Whistle 	h	w	L	Flow, L/min	P, mm H2O	v from flow, m/s	K	v from P, m/s	Ratio
Feadog Mk 1	1.5	8.23	24.8	40		252		54.00			1.293	56.59		1.048
Feadog Mk 1	1.5	8.23	24.8	30		136		40.50			1.293	41.57		1.026
Feadog Mk 1	1.5	8.23	24.8	10		14		13.50			1.293	13.34		0.988
Killarney	1	7.23	25.6	30		340		69.16			1.437	62.35		0.902
Killarney	1	7.23	25.6	20		180		46.10			1.437	45.36		0.984
Killarney	1	7.23	25.6	10		50		23.05			1.437	23.91		1.037
Mellow D	1.28	8.17	28.66	30		170		47.81			1.388	44.85		0.938
Mellow D	1.28	8.17	28.66	20		82		31.87			1.388	31.15		0.977
Mellow D	1.28	8.17	28.66	10		25		15.94			1.388	17.20		1.079
McGee #3	1.33	7.63	24.24	30		150		49.27			1.321	43.19		0.877
McGee #3	1.33	7.63	24.24	20		72		32.85			1.321	29.93		0.911
McGee #3	1.33	7.63	24.24	10		18		16.42			1.321	14.96		0.911
Old Gen 	1	7.85	24.79	30		236		63.69			1.419	52.27		0.821
Old Gen 	1	7.85	24.79	20		112		42.46			1.419	36.01		0.848
Old Gen 	1	7.85	24.79	10		27		21.23			1.419	17.68		0.833

We're hoping for a ratio of 1 between the two calculations of the air speed, v. Mixed results so far, I'd say.

Would there be any point in making and testing a Reference Windway? I imagine a 25mm length of Delrin rod that couples nicely into my feed tube, with say a 4mm diameter hole through it. Or a Reference Orifice? Or whatever....

That's not a bad idea. We've got several different long, low, wide windways, all with some degree of taper. A short, fat, round windway with no taper might tell us something else, and a 5 mm hole, 10 mm long would qualify. And a longer, round windway, say a 4 mm hole, 30 mm long.

[Terry McGee]

OK, results with the two calibrators requested:

Code: Select all

30 x 4mm Calibrator				
Mano/2	MM(H20)	√A/P	Flow	Resistance
163.5	327	18.1	40	0.45
85	170	13.0	30	0.43
39.5	79	8.9	20	0.44
9.5	19	4.4	10	0.44
				
				
10 x 5mm Calibrator				
Mano/2	MM(H20)	√A/P	Flow	Resistance
52.5	105	10.2	40	0.26
27.5	55	7.4	30	0.25
13	26	5.1	20	0.25
2	4	2.0	10	0.20

Note that rather than giving a single Resistance figure for each device, I've changed it to give one for each flow rate.

Now all we need to do is make the Resistance figure more real world!

[trill]

. . . Unfortunately, the resistance from your definition depends on the air density, which means it would vary with temperature, elevation, and maybe humidity . .

Some notes from today, pondering explanations for our mismatches . . .

1) As mentioned by Tunborough, air density is a factor. Myself, I began with a simple "nominal" number: 1.22kg/m^3.

Well, here's a site done by some authentic-sounding techo-os: https://www.omnicalculator.com/physics/air-density

I plugged in Malua Bay current condx, and got:



There's 5% right there.

2) I'm wondering about "floating ball" flow-meters. I've seen them in hospitals. They're used for pure oxygen. Our cases are "air", which is 70% N2. So, in my spare time, I'd like to compare density + viscosity of N2 and O2. Maybe some manufacturer has a web-page showing different meters for air or oxygen. Another "spare time" item.

3) I'm wondering about sensor accuracy. In the one case I have examined so far ("old Gen"), I was expecting Cd to drop steadily with increasing flow. What I got was ups+downs.

4) Bonus for today: There's a connection between "whistle resistance", "discharge coefficient", and "exit area". It looks like this:

WR = sqrt(rho/2)/(Cd*A)

Note the influence of A. Exit area is a primary driver of resistance. Cd is a single-number representing the losses not included in Bernoulli's lossless exchange of pressure + kinetic energy (potential energy, too, but omitted assuming we're holding the whistle horizontal ).

I like WR because it's a direct indicator of what a player experiences. It's a number for "backpressure". Personally, I love backpressure. Allows long passages without breaths.

One thing that Cd brings is visibility into the role of windway-exit-area in backpressure: direct inverse proportion. So, anyone interested in "making" . . .

More when I get to it. . .

[Terry McGee]

Now surely it can't be as simple as just windway exit area? With no effect from the length and profile of the rest of the windway?

For example, if I were to make a calibrator that was 30mm long, had an exit hole of 4mm diameter for the last 1mm of length, but had the rest of the length bored out to 10mm, wouldn't we expect it to show less resistance than the one I've just tested that is 4mm all the way?

And if I took that new calibrator and reversed it so that we now had an entry diameter of 4mm and an exit diameter of 10mm, we wouldn't expect to see the resistance of a 10mm exit, would we? Would we expect to see the same as when it was not reversed?

On the nature of gas intended to be used with this flowmeter, there are no indications on it. Not very helpful, I know! I notice that they are sometimes called Rotameters, and sometimes Variable Area Flow Meters. Mine bears the name SHLLJ. And there's a sticker on the side which says chinway.com. Possibly the dealer?

[stringbed]

It's a number for "backpressure". Personally, I love backpressure. Allows long passages without breaths.

Now surely it can't be as simple as just windway exit area? With no effect from the length and profile of the rest of the windway?

Speaking yet again from the perspective of an erstwhile day-job voicer of duct flutes, and applauder of the present effort at plugging numbers into the study and application of that process —

The Rottenburgh recorders were delivered to the voicers with radially arched, axially flat windways. Among the routine subsequent actions was adding a varying degree of concavity along the length of the windway’s ceiling. It began at its midpoint and was worked toward the inner edge of the chamfer, the latter first having been cut to its full extent. The axial arching had a few purposes and one of its consequences was a reduction in the instrument's resistance — making it "easier blowing" in the workshop vernacular.

The assumption was that it increased the angle of the windway toward its exit, without increasing the size of its entrance. This had no effect on the measured air pressure in the player's mouth but the increase in flow was perceptible in terms of how long a lungful of air would last. I suspect that there would be some rough and ready method for recording that interval but Terry's nascent coefficient of resistance is more purposeful. The experience noted in the preceding paragraph supports his skepticism about the windway exit area providing a sufficient basis for that calculation.

I'd also like to question the utility of the term "backpressure" as a synonym for "resistance." Pressure is a measurable quantity that we are expressing as the difference between that at the entrance to the windway and ambient atmospheric air pressure. The term backpressure implies that there is a second such quantity exerting a corresponding force in the opposite direction. Unless we can demonstrate that the pressure in the window differs from that of the atmosphere, it might be a good idea to stick to the term “resistance" and avoid backpressure altogether.

[david_h]

2) I'm wondering about "floating ball" flow-meters. I've seen them in hospitals. They're used for pure oxygen. Our cases are "air", which is 70% N2. So, in my spare time, I'd like to compare density + viscosity of N2 and O2. Maybe some manufacturer has a web-page showing different meters for air or oxygen. Another "spare time" item.

I had also been thinking about Terry's flow meters, but in the context of Tunborough's comments about air density (temperature, humidity etc). Those metres are probably calibrated assuming only small changes in working pressure with flow rate. If in Terry's setup his valve is on the input side of the gauge then higher flows are measured at higher pressure, so with denser air. If on the outlet side then does the reservoir pressure change as it gets to needing another pump? Either way is it doesn't seem to be causing a departure from linearity with sqrt(P) but as something similar is happening at the windway I wonder if the slope of that line could be wrong. When getting to those last few percent departure from the model these things may matter, if only by adding noise to the measurements.