Engineering Calculation Methods and Unit Checks

Start With the Model

A calculator is only valid for the physical and mathematical model it implements. Identify the geometry, coordinate system, constitutive assumptions, load definition, detector convention, or crystal cell before entering numbers.

Keep Units Consistent

Dimensional analysis catches many errors. A line load in force per length multiplied by length must produce force. A sky rate in electrons per second per pixel multiplied by seconds and pixels must produce electrons.

Test Limiting Cases

Useful checks include:

• zero load should produce zero nodal loads,
• equal beam-end intensities should recover the uniform-load result,
• a 90-degree planar cell should have area a × b,
• zero detector dark current should produce zero dark electrons,
• increasing sky brightness numerically in magnitudes should reduce count rate.

Check Conservation or Equilibrium

The Equivalent Nodal Loads Calculator reports a force-equilibrium residual. The two nodal shear components should sum to the integrated line load.

Keep Conventions Visible

The Sky Background Electron Rate Calculator requires an electron-rate zero point, while the Planar Density Calculator requires atom centers in a valid repeating planar cell.

Do Not Hide Uncertainty

Instrument calibrations, finite-element sign conventions, and crystallographic cell choices can change the correct interpretation even when the arithmetic is exact.