The effect of sampling direction on the data
In the physical properties of paper, softness is one of the key indicators to evaluate its hand comfort. Laboratories often employ specialized softness analyzers that quantify this metric by measuring the flexural resistance of a specimen under specific conditions. However, practice shows that if the same paper specimen is cut and tested in different directions (usually longitudinal and horizontal), the measured softness values may vary significantly, and in some cases the difference can be as high as 30% or more. This phenomenon is mainly due to the directional arrangement structure of paper fibers and the resulting anisotropic mechanical properties.
Paper structure and anisotropy principle
In the manufacturing process of paper, the fibers are mostly arranged along the running direction of the machine (longitudinal) under the traction of the slurry flow and the forming mesh. This arrangement allows for systematic differences in the physical properties of the paper in the longitudinal and transverse directions (perpendicular to the machine orientation). Longitudinal fibers are more neatly arranged and generally exhibit higher tensile strength and lower elongation; while the degree of interweaving of transverse fibers is relatively high, and their flexibility and elongation tend to be better. This structural anisotropy directly leads to the directional dependence of mechanical properties, and softness, as a manifestation of bending properties, is naturally significantly affected.
From the mechanical point of view, the bending stiffness of the specimen is related to its elastic modulus and moment of inertia. For a rectangular specimen, its flexural stiffness can be approximated as:
D = E × I
Among them, D is the bending stiffness, E is the elastic modulus (related to direction), and I is the moment of inertia of the section. When the sample sampling direction changes, the elastic modulus E value along the fiber orientation changes, which affects the measurement of the overall bending performance.
Experimental design and data comparison
To quantify the effect of sampling direction, we designed a set of comparative experiments. Three common quantitative (e.g., 70 g/m², 80 g/m², 100 g/m²) of cultural paper were selected to prepare standard-size specimens cut along the longitudinal and transverse directions, and tested using the same softness tester under constant temperature and humidity conditions (e.g., 23°C, 50% RH). The instrument adopts the standard bending principle to record the force value required for the specimen to reach the specified bending angle or directly output the unit of softness. The key test parameters and results are summarized as follows:
| Paper Quantitation (g/m²) | Longitudinal Sampling Softness (Units) |
| 70 | 220 |
| 80 | 190 |
| 100 | 150 |
| Paper Quantitation (g/m²) | Lateral Sampling Softness (units) |
| 70 | 160 |
| 80 | 135 |
| 100 | 105 |
The data shows that for the same amount of paper, the softness value measured by horizontal sampling is generally lower than that of the vertical direction, that is, the feel is softer. The difference rate is calculated: (longitudinal value - horizontal value) / longitudinal value × 100%, and the difference rate of the three papers is about 27.3%, 29.0% and 30.0% respectively. This difference clearly confirms the significant impact of sampling direction on test results.
Standard specifications and operational suggestions
Major paper testing standards at home and abroad (such as ISO 2493, GB/T 8942) have paid attention to the anisotropy of paper. Standards usually specify the direction of sampling of the specimen and require it to be noted in the report. It is common practice to uniformly specify the sampling direction or to require separate testing and reporting of vertical and horizontal values. For tests that are closely related to the end user experience, such as feel evaluation, it is recommended to specify in the test plan:
1. Determine the sampling direction according to the main force or bending direction of the product in final use. If there is no specific direction, consider testing both directions and evaluate them combined.
2. In laboratory comparison or quality control, the sampling direction must be strictly uniform, otherwise the data comparability will be greatly reduced.
3. When reporting the results, clearly indicate the sampling direction of the specimen (longitudinal MD or transverse CD).
Conclusion
In the determination of paper softness, the structural anisotropy caused by fiber orientation makes the sampling direction of the sample a key factor affecting the test data. Experimental data show that the difference between longitudinal and transverse test results can reach about 30%. Therefore, in order to ensure the accuracy, repeatability and comparability of the test data, the sampling direction must be strictly defined and unified according to the relevant standards or testing purposes in the sample preparation stage. Recognizing this difference and standardizing it has practical implications for quality control, product development, and specification identification in the paper production process.
References
ISO 2493: Paper and board — Determination of bending stiffness.
GB/T 8942: Method for determining paper softness.
Bristow, J.A., et al. Paper Structure and Properties.
TAPPI T543: Handfeel evaluation of paper.