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.