Guitar Plate Thickness Calculator
This calculator and equations below are based on Gore & Gilet's "Design" book and have been validated with the data in the example tables. Please see sections 4.5.2 and 4.5.3 for details.
Important - I've had a couple of folks report that this returned numbers that were too thin - if this occurs. Please exercise caution and judgment while I'm looking into this and send me the numbers being used so that I can take a look.
Target Plate Thickness
How the Calculation Works
Step 1: Calculate Density (ρ): The density of the panel is calculated using the mass and dimensions (height, length, width) of the panel:
\[ \rho = \frac{m}{h \cdot l \cdot w} \]
Step 2: Calculate Young's Moduli (EL, EC): These values represent the stiffness of the material along and across the grain. They are calculated using the density, frequency, and dimensions:
\[ E = 0.94146 \cdot \frac{\rho \cdot l^4 \cdot f^2}{h^2} \]
Step 3: Calculate Shear Modulus (GLC): This represents the rigidity of the material under twisting forces, calculated as:
\[ G = 1.21585 \cdot \frac{\rho \cdot l^2 \cdot w^2 \cdot f^2}{h^2} \]
Step 4: Calculate Target Thickness (h): Using the target frequency, length, and width of the box, the thickness is derived from:
\[ h = \frac{0.95977 \cdot f \cdot a^2 \cdot \sqrt{\rho}}{\sqrt{EL + \left(\frac{a}{b}\right)^4 \cdot EC + \left(\frac{a}{b}\right)^2 \cdot (0.02857 \cdot EL + 1.12 \cdot GLC)}} \]
Ted – both this calculator and Giulano’s book are base their calculations off of the formulas in Trevor Gore’s book. So I’m glad they are showing the same results.
The calculator is correct.
Hi, thank you for developing this calculator and making it available. Just an observation: I have been reading Guiliano Nicoletti’s book “Mastering the sound of the Acoustic Guitar.” I used the process he presents in Appendix D to determine the three frequencies and then his spreadsheet to calculate the target thickness of two tops and two backs. Presumably Nicoletti’s spreadsheet and your calculator use the same formulas, since after entering the frequencies into your calculator, it produced the same target thickness. :-) Thanks again.
I’ve had a few folks ask about what resonances and thicknesses are typical here, what I’ve observed is that its pretty important to get the diagonal / transverse resonance correct and it should be in 40-60 Hz but not much higher than that… So if your final thickness comes in low like 1.5 or 1.6mm please go back and check the measured resonances.
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