## 3 Experimental Study on the Coefficient of Restitution of Wheat Grains
### Pre-Collision Velocity Measurement  
A high-speed camera measured the pre-collision velocity \((u)\) at 640 \(\times\) 240 px resolution and 8816 fps. The field of view spanned \(\Delta z=80\) mm, overing the region between the exit of the transparent guide and the force-sensor surface.  
The trajectory of the grain's geometric centre was tracked to eliminate the influence of rotation. The velocity obtained with respect to the stationary camera was assumed to be identical to that relative to the stationary force sensor [36].  
Figure 5: Grain impact test stand [7].  
The transit time \(\Delta t\) of the grain over a known distance \(\Delta\phi\) was obtained from the number of frames (\(FR\)) recorded during that travel. Referencing \(FR\) to the camera frame rate (\(FPS\)) gives the impact velocity \(v\):  
\[v=\frac{\Delta\phi}{\Delta t}=\frac{\Delta\phi}{\frac{FR}{FPS}}=\Delta\phi \frac{FPS}{FR} \tag{12}\]  
where \(FPS\) is the camera frame rate, expressed in frames per second.  
The optical method used to measure grain velocity also enabled precise high-speed video analysis [37]. Each drop was analysed with respect to grain orientation at impact. Example frames are shown in Figure 6, illustrating the final flight frame and the impact frame. During the experiment, we discarded grains that exhibited excessive rotation, as this significantly distorts contact-force readings. This procedure ensured that only valid results were retained, thereby improving the accuracy and reliability of the dataset.  
Oblique impacts produced several artefacts, visible for example as multi-peak force curves (Figure 7). Such cases are undesirable because they do not represent the single-impact force trace expected for perpendicular collisions and were therefore excluded from further analysis.  
In order to minimise measurement distortion caused by rotational motion, the following multi-step procedure was adopted:  
* Free-fall through a guide tube: Each grain was dropped through a vertical polycarbonate tube (internal diameter 5 mm). Preliminary tests confirmed that this diameter suppressed lateral movement and matched the geometry of 'Memory' grains.  
Figure 6: Selected grain orientations during flight and collision with the force-sensor surface: (**a**) angular; (**b**) perpendicular; (**c**) parallel [7].  
Figure 7: Example force–time profiles for collisions with angular grain orientations: (**a**) rotating grain, case 1; (**b**) rotating grain, case 2 [7].  
Visual inspection: Every drop was filmed with a high-speed camera (8816 fps). Trajectories were reviewed frame-by-frame, and grains showing visible rotation or instability were discarded.
* Force-signal analysis: Each force-time trace was checked for the characteristic elastic-plastic shape expected for biological impacts [4; 16; 28; 38]. Only curves that met this criterion were kept.
* Reduction of random effects: a large sample (\(n=400\)) was tested, providing statistical stabilisation of the results.
* Method validation by repeatability tests: From each moisture level, 20 grains were re-measured. The resulting \(CoR\) values differed by no more than \(\pm 0.02\), confirming high repeatability. All calibration and uncertainty estimates followed ISO GUM guidelines.  
This protocol yielded reliable data consistent with theoretical grain-to-plate contact models described by [PERSON] (2018) [4], [PERSON] et al. (2010) [39] and [PERSON] and [PERSON] (2017) [24].