\(θ=mL\ [°]\)
This linear relationship between linewidth and fold angle has been confirmed in our previous research.[28] Figure 3c shows that the coefficient of determination R2 values are close to 1 for all numbers of lines, and so the triangle approximation can be considered reasonable. Although even for the same linewidth, θ differs according to n. The value of m decreases as n increases. When the linewidth is low (L = 5 mm), as shown in Figure 3d, the error of the triangle approximation is small because the creases are far from each other. However, as the lines become thicker (L =15 mm), the effect of the approximation increases, and θ decreases. As shown in Figure 3e, the more the number of lines, the closer the folds, and the shorter the straight-line parts. Consequently, if the distance between the lines is small, the change in the gradient of the straight-line parts caused by the linewidth is difficult to observe, and the observed value is smaller than the actual value. Thus, although some errors occur in this case, we can successfully relate the fold angle to the corrugated structure parameters by modeling.
Next, we derived the relationship between L and d and L and w from the fold angle. The diagonal side i/2+L/2 of the right triangle shown in Figure 3a is defined from Equation (1) as follows.
\(\frac{i}{2}+\frac{L}{2}=\frac{105}{n}\)
Therefore, the amplitude d and half-wavelength w are obtained from Equations (4) and (5).