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Old 01-13-2021, 10:52 AM
Alan Carruth Alan Carruth is offline
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Join Date: Feb 2011
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jt1 asked:
"Lighter, even though thicker? Numbers, please."

OK.

A more or less normal density for WRC is around 360 kg/m^3, and Red spruce tends to run around 480. If you like you can stick in a decimal point to get specific gravity (.36 and .48) and taking the density of water as about 62.5 lb/ft^3 you get 22.5 #/ft^3 and 30 #/ft^3. Any particular piece could be plus or minus 20% from those numbers, or even more. I use metric measures in my work.

If those two pieces are typical in terms of the way the Young's modulus along the grain (Elong) relates to the density, then the cedar will have an Elong value of about 8600 megaPascals, and the spruce will be around 14,000 mPa. The formula I use to calculate the thickness of the top based on these numbers and a desired stiffness gives a thickness for the cedar top of just over 3 mm; .125". The spruce top comes in at 2.6 mm, just over .102".

Multiply the density of the wood times the thickness for each, and you find that the spruce top weighs 3.06/2.82= 1.088, or about 9% more than the cedar. That's less than the number I got yesterday using a 50% difference in the density as an example, but yesterday's numbers would have been outliers in opposite directions for both woods; the cedar lower and the spruce higher in density than average. Again, when choosing wood for a top to give the desired response, you might well select an outlier; denser to give more 'headroom' and lighter for 'responsiveness'. In this example I used more 'average' values as a production line would. From what I know a 9% change in the weight of the top (without bracing) would be enough to produce a noticeable change in sound all else equal. If you use spruce bracing on both (as would be normal) the actual difference between the tops would be a smaller percentage, but still enough to matter, IMO. At any rate, the cedar top is lighter, even though it is thicker.
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