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:
\[ h = \frac{0.95977 \cdot f \cdot a^2 \cdot \sqrt{\rho}}{\sqrt{EL + \left(\frac{a}{b}\right)^4 \cdot EC + \left(\frac{a}{b}\right)^2 \cdot (0.02857 \cdot EL + 1.12 \cdot GLC)}} \]
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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