PARTICLE PACKING — MEASUREMENT SHEET
Version: 2026-09-11
Guide: https://yenra.com/particle-packing/

Purpose: compare solid volume and the bulk volume including interparticle gaps.
Use intact particles with estimable volume and a measurable container.
Define pouring/settling and the upper fill surface before collecting results.
Empty and refill independently for each repeat. Record each result.

Question / date / operator:
Particle shape, dimensions, size spread and condition:
Container internal dimensions relative to particle size:
Particle-volume method (count and geometry, or mass/material density):
Density definition and particle porosity assumptions, if applicable:
Pouring rule / settling or tapping rule:
Upper-surface measurement rule:
Measurement instruments / units / uncertainty:
Variables held constant between compared samples:

Packing fraction φ = total particle volume / bulk occupied volume.
For solid nonporous particles, interparticle void fraction = 1 − φ.
Use the same volume units in numerator and denominator.
For N equal spheres of diameter d, total volume = N × π × d³ / 6.

FICTIONAL EXAMPLE (ideal spheres, not measured data)
100 spheres, diameter 1.00 cm: total volume = 52.3598776 cm³.
Bulk volume 80.0 cm³: φ = 0.65449847, about 65.4% occupied.
Void fraction about 34.6%. Extra digits show arithmetic, not precision.
Independent bulk volumes 80.0, 82.0, 81.0 cm³ give fractions
0.6545, 0.6385, 0.6464; mean of the fractions is about 0.6465.

REPEAT RECORD (copy rows as needed)
Fill ID | particle volume (units) | bulk volume (same units) | φ | 1 − φ | notes
1:
2:
3:
Mean of individual fractions:
Variation across repeats and measurement uncertainty:
Setup changes or excluded observations, with reasons:

Compare variation and method before attributing differences to shape.
Changing the tapping/filling rule creates a separate experimental condition.
Volume scales with the cube of sphere diameter: dimension errors matter.
Keep particle shape, size distribution, walls, order and preparation attached
to comparisons with published packing numbers. Preserve raw observations.