# Rotation, gravitropism and mechanical exposure Canonical HTML: https://flavorotor.com/research/rotation-gravity Machine-readable index: https://flavorotor.com/research/data/chapters/index.json Horizontal-axis rotation expressed as an angle-time history, its relation to plant gravity sensing, measured mechanical acceleration, root-zone coupling and controlled biological comparisons. ## Rotation in the plant frame The FlavoRotor drum turns around a horizontal axis. Gravity remains vertical and close to 9.81 m·s⁻², while each plant module changes orientation relative to that vector. Rotation therefore produces a periodic directional stimulus, not reduced gravity. The encoder record links angle, angular speed and direction to every image and sensor sample. [I01] [I02] [R22] [R32] FlavoRotor horizontal-axis drum geometry; gravitropic sensing and signalling are described by Nakamura, Nishimura, and Morita (2019). [I01] [I02] [R63] ROT-1 ω = 2 π n 60 \omega=\frac{2\pi n}{60} ω = 60 2 π n ​ Angular velocity ω in r a d   s − 1 \mathrm{rad\,s^{-1}} rad s − 1 from drum speed n in rev·min⁻¹. **Explanation**Revolutions per minute are converted into angular speed in radians per second. ROT-3 θ ( t ) = θ 0 + ω t \theta(t)=\theta_0+\omega t θ ( t ) = θ 0 ​ + ω t The plant-module angle follows the encoder angle θ₀ and measured angular velocity. **Explanation**A basket's angle equals its starting angle plus angular speed multiplied by elapsed time. ROT-4 T = 2 π ω = 60 n T=\frac{2\pi}{\omega}=\frac{60}{n} T = ω 2 π ​ = n 60 ​ One complete orientation cycle lasts 120 s at 0.5 rpm and 30 s at 2 rpm. **Explanation**One complete rotation takes 60 divided by the drum speed in revolutions per minute. ## How a plant detects reorientation Gravity-sensing cells contain dense, starch-rich amyloplasts. After reorientation, the amyloplasts move towards the new lower side of the cell. That physical change alters gravity signalling and directional auxin transport. Unequal growth on opposite sides of the organ produces curvature: primary roots usually bend with gravity, while shoots usually bend against it. [R63] | Stage | Root | Shoot | Measurement | Gravity sensing | columella cells in the root cap | endodermal cells | module angle and time after reorientation | Signal | asymmetric auxin transport towards the lower flank | directional auxin redistribution | organ angle and curvature over time | Growth response | positive gravitropic bending | negative gravitropic bending | root-tip angle, shoot angle and elongation rate The biological input depends on both orientation and exposure time. A slow cycle permits a longer dwell at each angle; a faster cycle changes direction more often. Drum speed is therefore reported together with acceleration ramps, stop duration and the complete angle-time series. ## Mechanical acceleration ROT-2 a c = ω 2 r a_c=\omega^2r a c ​ = ω 2 r Centripetal acceleration at radial distance r. **Explanation**Centripetal acceleration increases with radius and with the square of angular speed. ROT-5 a e f f ( t ) = g + a c ( t ) + a v i b r a t i o n ( t ) \mathbf{a}_{\mathrm{eff}}(t)=\mathbf{g}+\mathbf{a}_{c}(t)+\mathbf{a}_{\mathrm{vibration}}(t) a eff ​ ( t ) = g + a c ​ ( t ) + a vibration ​ ( t ) The measured acceleration at a plant module combines gravity, rotation and vibration as vectors. **Explanation**The plant experiences Earth's gravity together with the acceleration caused by rotation and any measured vibration. | Speed | Cycle period | Radius | Centripetal acceleration | Fraction of g | 0.5 rpm | 120 s | 0.15 m | 0.000411 m·s⁻² | 0.0000419 | 2.0 rpm | 30 s | 0.15 m | 0.00658 m·s⁻² | 0.000671 At these example settings, centripetal acceleration is less than 0.07% of g. The dominant physical input is the changing direction of the gravity vector in plant coordinates. Vibration, airflow, liquid movement and start-stop transients are measured separately because they can also change plant growth. [R21] ## Rotation and root-zone exposure Drum angle also determines when each root module enters and leaves the nutrient solution. For every position, the run record stores immersion depth, immersed duration, drainage duration and retained liquid mass. A biological comparison must match average light and root-zone exposure between rotating and control plants; otherwise orientation, illumination and hydroponic contact change together. ## Controlled rotation experiment | Group | Variable isolated | Static plant with matched mean light and root exposure | baseline | Rotating plant | combined periodic orientation treatment | Static plant with matched time-varying light | light distribution | Static plant with matched vibration | mechanical vibration | Rotating plant with slow acceleration ramps | start-stop transient Primary endpoints are chosen before cultivation: root-tip angle or shoot curvature for orientation response, plus one growth or chemistry endpoint. Encoder angle, three-axis acceleration, plant images, light exposure, immersion and air velocity are synchronised by timestamp. The analysis uses the plant or independent cultivation cycle as the experimental unit. [R02] [R21] [R63] ## References - [I01] FlavoRotor project team (2026). FlavoRotor prototype implementation record. *Internal engineering report*. - [I02] FlavoRotor project team (2026). FlavoRotor v2.0 system architecture. *Internal engineering design report*. - [R02] Seeburger, P.; Herdenstam, A.; Kurtser, P.; Arunachalam, A.; Castro-Alves, V. C.; Hyötyläinen, T.; Andreasson, H. (2023). Controlled mechanical stimuli reveal novel associations between basil metabolism and sensory quality. *Food Chemistry*. https://doi.org/10.1016/j.foodchem.2022.134545 - [R21] Chehab, E. Wassim; Eich, Elizabeth; Braam, Janet (2009). Thigmomorphogenesis: a complex plant response to mechano-stimulation. *Journal of Experimental Botany*. https://doi.org/10.1093/jxb/ern315 - [R22] Kiss, John Z.; Wolverton, Chris; Wyatt, Sarah E.; Hasenstein, Karl H.; van Loon, Jack J. W. A. (2019). Comparison of Microgravity Analogs to Spaceflight in Studies of Plant Growth and Development. *Frontiers in Plant Science*. https://doi.org/10.3389/fpls.2019.01577 - [R32] Böhmer, Maik; Schleiff, Enrico (2019). Microgravity research in plants: A range of platforms and options allow research on plants in zero or low gravity that can yield important insights into plant physiology. *EMBO Reports, 20, e48541*. https://doi.org/10.15252/embr.201948541 - [R63] Nakamura, Moritaka; Nishimura, Takeshi; Morita, Miyo Terao (2019). Gravity sensing and signal conversion in plant gravitropism. *Journal of Experimental Botany, 70(14), 3495–3506*. https://doi.org/10.1093/jxb/erz158