In a previous post we discussed the problem. An apparent 190Hz hum coming from a brand new water heater.

In that post, I said I would replace the hard copper mount to flexible couplings. I did that.

And this was the result

We still have a vibration to handle between the tank and the floor.

So now we get into the dark art of vibration dampening.

If we peruse McMaster-Carr's catalog, we see there are a plethora of options. To select the right one, we're going to have to use...

MATH. (insert Futurama reference)

Because I'm an American, this will be in imperial measurements. Adjust your constants per your unit system, country of origin, and time zone.

To start, we need to know the weight.

The datasheet says an empty unit weighs 244 pounds and holds 72 gallons. Water weighs 8.8 pounds per gallon. Some quick math

\[ 244+72*8.8=877.6 \]

Call it 900 pounds to make up for the weight of the piping and inevitable dust build up.

Rheem sells a vibration isolation kit (for $150?!) and it includes 4 mounts. I assume they are COTS parts. And therefore, not worth the price.

So we'll find 4 appropriate mounts, and distribute 225 pounds onto each of them.

Our disturbing frequency is 190Hz \( f_d \).

To get our natural frequency, we divide by 2.45 in order to get 80% isolation (insert reason why). \[ f_n = f_d/2.45 = 190/2.45=77Hz \] We need this to get our static deflection.

Static deflection \[ ds = g/f_n^2 = 9.8/77^2= .00165 inches \]

From there, we can get our spring rate (K)

\[ K = mountLoad / ds = 225 / .00165 = 136,363 lbs/inch \]

As long as our mount is rated for more than 225 pounds, and has a spring rate less than 136,363 lbs/inch, we should be able to stop some of the 190Hz vibration from transmitting into the concrete floor.

But how much of the vibration would be stopped?

Lets compare two options: 64865K87 and 5940K57 (both McMaster-Carr items).

64865K87 says its deflection @ capacity is .18" @ 250 pounds. So its spring rate is K = 250/.18 = 1388.9 lbs/inch. Meets both requirements.

To get our actual deflection, we can reverse that a bit using our known weight. Deflection = 225/1388.9 = .162". A quick sanity check that its deflection is smaller than the uncompressed dimension of the mount and we know it won't be obliterated.

But how much noise will it stop? For that, need to recompute the natural frequency \[ f_n = \sqrt{\frac{9.8}{d}} = \sqrt{\frac{9.8}{.162}} = 7.778Hz \]

Then we can calculate our Transmissability: \[ T = \frac{1}{( (\frac{f_d}{f_n})^2-1 )} = \frac{1}{ (\frac{190}{7.778})^2-1 } = .00167 \]

And our percent blocked:

\[ 100*(1-T) = 100*(1-.00167) = 99.832% \]

So it should stop 99.832% of the noise generated by the Water Heater - Floor interface.

Repeat for 5940K57 (a 1ft^{2} sheet of neoprene rubber)

Weight capacity 1500 pounds, deflection @ weight of .04", we can use the same procedure as above to get 98.94% isolation.

I went with the little feet (64865K87) because they have a lower durometer (how squishy the rubber is), and therefore wiggle a bit more as water flows around (another noise source).

The result:

Peace in the kingdom? For now.

There is still improvement to be done. The foam isolation between the condenser coil and the lid is... insufficient, and the fan itself is hard mounted to metal.

Until I can address those two, I will be adding some automation to put it into electric only or vacation mode whenever the TV is on, just to get rid of the last of the fan noise.