Boundary Depth Scans

line-force-floor-three-row-scan

Contact length is scanned below, at, and above a force floor. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Line length is scanned against a force floor

Keep gamma fixed at 3 N/m and change only the contact length to 2 m. The checked force is 6 N so this row is below boundary relative to the 12 N floor.

F=γL=3 N/m×2 m=6 NFmin⁡=12 NF=\gamma L=3\ \text{N/m}\times2\ \text{m}=6\ \text{N}\qquad F_{\min}=12\ \text{N}
Line-force boundary rowOnly contact length changes across the three force rows.lengthforcebelow boundary

Line length is scanned against a force floor

Keep gamma fixed at 3 N/m and change only the contact length to 4 m. The checked force is 12 N so this row is on boundary relative to the 12 N floor.

F=γL=3 N/m×4 m=12 NFmin⁡=12 NF=\gamma L=3\ \text{N/m}\times4\ \text{m}=12\ \text{N}\qquad F_{\min}=12\ \text{N}
Line-force boundary rowOnly contact length changes across the three force rows.lengthforceon boundary

Line length is scanned against a force floor

Keep gamma fixed at 3 N/m and change only the contact length to 6 m. The checked force is 18 N so this row is above boundary relative to the 12 N floor.

F=γL=3 N/m×6 m=18 NFmin⁡=12 NF=\gamma L=3\ \text{N/m}\times6\ \text{m}=18\ \text{N}\qquad F_{\min}=12\ \text{N}
Line-force boundary rowOnly contact length changes across the three force rows.lengthforceabove boundary