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 Post subject: Is it 50LOG10(rpm2/rpm1) or 60LOG10(rpm2/rpm1) ?Posted: Fri May 25, 2007 4:47 pm

Joined: Thu Dec 15, 2005 11:06 am
Posts: 2049
Location: Klamath Falls, OR
Comair and NMB think it's 50LOG10, but what do they know?

Here's the deal: everyone agrees that the energy in flowing air from a fan is proportional to the cube of the velocity of the airflow. This is because of the kinetic energy of the individual air molecules, which is proportional to the square of the velocity, and the number of molecules, which is proportional to the velocity. Multiply the two together, and you get V^3, a number that's easily understood. I like things that are easily understood.

I believe the formula for the noise of a fan at different rpms assumes the CFM, or air flow rate, is linear with rpm. And of course the airflow velocity is directly proportional to the CFM. So, is it 50 or 60? I've said 60 several times in SPCR postings. I'm also a (retired) EE, not an airflow physicist. I did bump up against acoustics once upon a time, but that was because an outdoor datalogger was needed that used low power and hence small batteries. I was the embedded microprocessor systems guy, but the front end was a 1" General Radio electret microphone. So I'm not a complete novice at acoustics, but again, I'm not a physicist.

So why buck Comair and NMB? Because I think they're wrong. Look, let's take that V cubed and break it up into six V^.5s. What I allege is that all of that kinetic energy gets converted to noise by turbulent collision of the moving air column with the ambient air. This means a very simple explanation of where the energy goes. You see, energy can be neither created or destroyed. It can change form, and it does, but it can't disappear. There are no energy magic acts.

My 60LOG10 implies that all six of the V^.5s get converted to noise. We start with kinetic energy and wind up with six dirty, smelly linebackers who need shaves. The other guys say the kinetic energy gets converted into five linebackers (noise) and a cute cheerleader.

The cheerleader is the part of the kinetic energy that doesn't get converted to noise (the dirty smelly linebackers). I want that cheerleader's ID! What did that particular V^.5 get converted into? Now, if 1/6 of the kinetic energy gets converted into something besides noise, then Comair and NMB are right, and 50LOG10 describes the noise level of an rpm change.
--------------------------------

I decided what I had to do was perform a controlled experiment or three (or 17) to measure the change in noise with RPM. I need three things: an SLM, which arrived last Tuesday, a stroboscope, which arrived today (Extech, \$230), and a noise source. The noise source is a fan, a variable power supply, and (for convenience) a digital voltmeter. I have those, and have had them for some time now.

After double-checking the acoustic "rules of the road" with my new SLM, and with the arrival of the stroboscope, I performed two experiments (on different fans), and a variation on one of those two. Results first:

The experiment on the "hot" sleeve-bearing 7-blade 220mm fan that came with an Aplus CS-188AF case yielded 63.09 instead of 50 or 60 as the multiplier. I ran the experiment on that fan twice and came up with the same number each time.

Next, I used a 140mm Yate Loon D14SH-12 as the noise source, a fan rated at 2400RPM and 40dBA. I came up with 62.70 as the multiplier. I changed the distance to the microphone drastically (but nothing else) and came up with the exact same number: 62.70.

Three things are obvious: the results are 4 times closer to my 60 than to Comair and NMB, the results don't match either formula, and yet the two experiments, carefully performed on very different fans, have results that only differ by six tenths of one percent!

It's as if we got the six linebackers all right, but the cute cheerleader's future kid showed up unexpected and unaccounted-for.
------------------------------------

Briefly: I positioned the SLM on-axis of the fan under test, close to the fan (initially 6" for the 220mm fan, 3.5" for the 120mm fan). I wanted to be as high above the ~27.6dBA ambient as possible, so I didn't have to adjust the measured numbers for the noise background.

Then I applied 12V, allowed things to stabilize for >15 minutes, turned on the SLM, and made small adjustments in the microphone distance so the sound level reading was on an even dBA. I read and recorded the dBA and the rpm taken with the new strobe. Then I reduced the voltage on the fan (with a fifteen minute stabilization period) until the SLM read 6dBA less, and recorded the rpm (and for the record, the voltage). That completed the data-gathering portion of one experiment. Now to evaluate the data:

For the 220mm fan, the two rpms were 738.8 and 593.5. The LOG10 of their ratio was .0951, which surprised me. Had I been correct and the multiplier was 60, then the ratio would have been exactly 0.1, and if Comair and NMB were right the ratio would have been exactly 0.12:
60 x 0.1 = 6dBA
50 x 0.12 = 6dBA
but what happened was, a lower .0951 showed up. And then when I repeated the same basic experiment with the noisier Yate Loon, I got almost exactly the same (wrong) number! I even tried a 21" distance to the fan from the SLM, reducing the noise level 10dBA, but it made no change at all in the outcome.

I need to think about this. I need to perform more experiments on different fans at different noise levels. Can any of you identify the cute cheerleader's future kid (the cheerleader herself appears to be absent)?
----------------------------

The Extech stroboscope can (evidently) also serve as a tachometer, which doesn't interest me. It's identical to the Reed stroboscope, which costs \$20 more but is silver instead of black. Everybody knows black stroboscopes are faster, so I got the Extech.

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 Post subject: Posted: Fri May 25, 2007 6:50 pm

Joined: Thu Dec 15, 2005 11:06 am
Posts: 2049
Location: Klamath Falls, OR
I've found the major part of the problem.

It's true that there's an abundance of evidence readily available that the dBA ~ 60LOG10(rpm2/rpm1). At least for fans 120mm & up. My own 2 or 2.5 experiments earlier this afternoon confirmed that 60LOG10 was close, for dBA levels. And all we're interested in here at SPCR is the dBA levels.

But I falsely stated that Comair sez dBA = 50LOG10etc. Comair does no such thing. Comair sez noise - unweighted noise - fits that formula. That formula must have been derived from theoretical considerations, meaning they have the cute cheerleader's locker combination.

There's never been an unweighted noise level measurement posted at SPCR, I'm sure of that. Measurement-class microphones are all condenser microphones, and SLMs with condenser microphones have horrendously high linear-weighted self-noise levels. Maybe MikeC can tell us if his type 1 SLM has a linear weighting available, and if so, what the noise floor is in that mode.

It is true, however, that 60 is a far more accurate multiplier than 50 for dBA measurements - the only ones us folks at SPCR use. So I will resume using 60LOG10 and 18dBA per doubling in my postings, as I had previously. Those numbers aren't exact, but they're close.

The Comair and NMB 50LOG10 isn't close at all for our dBA measurements, the only kind used here at SPCR. Nobody here at SPCR (or elsewhere) should use that formula for dBA calculations.

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 Post subject: Posted: Fri May 25, 2007 11:21 pm

Joined: Tue Feb 13, 2007 7:28 pm
Posts: 1406
Location: USA
Interesting to see your experimental results differ so much from the accepted rule of thumb (60+ vs. 50). This is certainly not a trivial difference as we are talking about exponents here. I'm not sure that the work of others supports your results. Look at the most recent SPCR fan roundup.

Yate Loon D12SM-12
SPL @ 1640 RPM = 32 dBA
SPL @ 880 RPM =20 dBA
50LogX Prediction = delta 13.5 dB
60LogX Prediction = delta 16.2 dB
Actual Result = delta 12 dB

SilenX IXP-74-11
SPL @ 1140 RPM = 26 dBA
SPL @ 820 RPM = 20 dBA
50LogX Prediction = delta 7.2 dB
60LogX Prediction = delta 8.6 dB
Actual Result = delta 6 dB

Enermax UC12EB
SPL @ 950 RPM = 28 dBA
SPL @ 540 RPM = 20 dBA
50LogX Prediction = delta 12.3 dB
60LogX Prediction = delta 14.7 dB
Actual Result = delta 8 dB

In each of these cases, the SPCR result was closer to that predicted by 50LogX and in fact all of them indicate that perhaps even 50 is too high a multiplier. I think that would be explained by the contribution of bearing noise, which may have a different relationship with RPM than air flow and one that further varies with bearing type and implementation. Given that SPCR's results support the 50LogX rule of thumb, perhaps you need to recheck you SPM and/or stroboscope technique for compliance with generally accepted practice.

Please, don't take this as negative criticism. I applaud your desire to learn and willingness to spend your own time and money on experimentation.

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 Post subject: Posted: Sat May 26, 2007 2:20 am

Joined: Mon May 08, 2006 4:36 am
Posts: 497
jessekopelman wrote:
Look at the most recent SPCR fan roundup.
But you have to remember that SPCR's measurements get pretty close to the noise floor at the low end of that (20 dBA is not much over 18-19dBA), so this means that the actual fan noise here is lower, and this error makes the difference smaller than it really is.

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 Post subject: Posted: Sat May 26, 2007 10:50 am
 SPCR Reviewer

Joined: Sun Sep 21, 2003 11:23 am
Posts: 1850
I wouldn't use any of SPCR's 20 [email protected] results in your calculations. They're too close to the noise floor to be wholly accurate.

I should also refer you to the text of the review for the Enermax UC12EB â€” the 28 [email protected] number is skewed on the high side because of a pure tone resonance that is not present at lower levels. I also note that the acoustic behaviour of the Enlobal bearings is ... unusual. Had the measurements been done with the SPL off-axis, I doubt I would have seen any change in the measurements at all.

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 Post subject: Posted: Sat May 26, 2007 10:36 pm

Joined: Thu Dec 15, 2005 11:06 am
Posts: 2049
Location: Klamath Falls, OR
Earlier, I posted some measurements that I took pains to make carefully. I let the fan stabilize for 20 minutes+ upon turnon, and 15 minutes for each new fan voltage, for example. The measurements included RPMs (taken with an Extech stroboscope) and dBA levels (Extech SLM) at 12V and 5V on the fan. The RPMs were 855.4 and 340.7, a ratio of 2.51, LOG10 is .400 (honest, try it!) and 60LOG10 is 23.99. So my 60LOG10(rpm2/rpm1) predicts a 23.99dBA noise level difference.

I also measured the dBA levels at 12V and 5V, and they were 50.48dBA and 26.24dBA (after correcting for the noise floor). That's a difference of 24.24dBA.

So 60LOG10 predicted the dBA difference with an error of 1.05%. Like I said, there is abundant empirical data to support 60LOG10. I just added more empirical data myself!

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 Post subject: Posted: Sun May 27, 2007 1:41 am

Joined: Tue Feb 13, 2007 7:28 pm
Posts: 1406
Location: USA
Devonavar wrote:
I wouldn't use any of SPCR's 20 [email protected] results in your calculations. They're too close to the noise floor to be wholly accurate.

I should also refer you to the text of the review for the Enermax UC12EB â€” the 28 [email protected] number is skewed on the high side because of a pure tone resonance that is not present at lower levels. I also note that the acoustic behaviour of the Enlobal bearings is ... unusual. Had the measurements been done with the SPL off-axis, I doubt I would have seen any change in the measurements at all.

Well, that concern is exactly why I only used the 20 dBA measurements and not anything lower in my examples
Your specific issue with the Enermax is further argument against Felger Carbon's claim that SPL delta should be greater than predicted by the 50LogX rule of thumb.

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 Post subject: Posted: Sun May 27, 2007 2:19 am

Joined: Tue Feb 13, 2007 7:28 pm
Posts: 1406
Location: USA
The problem with using SPCR data is that the fans they test are often relatively low speed and, as such, it is hard to find RPM swings that keep SPL well above the noise floor and at the same time provide a difference between 50LogX and 60LogX that is more than 1 dB (you really need to have the RPM ratio be 1.5 or greater for such results). Looking through the past SPCR fan roundups for good data here is what I came up with:

DELTA AFB0812SH
SPL @ 3790 RPM = 44 dBA
SPL @ 2230 RPM =28 dBA
50LogX Prediction = delta 11.5 dB
60LogX Prediction = delta 13.8 dB
Actual Result = delta 16 dB

ACT-RX FD1212-A2060E
SPL @ 2440 RPM = 46 dBA
SPL @ 980 RPM = 25 dBA
50LogX Prediction = delta 19.8 dB
60LogX Prediction = delta 23.8 dB
Actual Result = delta 21 dB

Antec Tricool 120
SPL @ 1930 RPM = 36 dBA
SPL @ 1220 RPM =23 dBA
50LogX Prediction = delta 9.9 dB
60LogX Prediction = delta 11.9 dB
Actual Result = delta 13 dB

These results support Felger Carbon's 60LogX contention. Felger, I apologize for questioning your testing skill.

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