The physics of cranberry bogs

TL;DR

The paper analyzes cranberry bog harvesting through four linked problems: buoyant rise of submerged cranberries, stable surface flotation, capillary-driven surface aggregation, and loading onto a truck. It combines first-principles fluid-solid models with simple simulations and tabletop experiments, supported by Python resources for classroom use. Key contributions include explicit expressions for terminal velocity $v_T$ and rise time $T_R$ during buoyant rise, a density-ratio–dependent relation for the submerged fraction on the surface, a Morse-type capillary interaction framework for aggregation with confinement, and a geometric plus friction-based perspective on the angle of repose for the granular pile. Together, these results illustrate how soft matter and fluid dynamics govern cranberry harvesting and provide accessible teaching tools that bridge undergraduate curricula with soft matter research, enabling hands-on exploration of buoyancy, capillarity, and granular phenomena.

Abstract

The common New England sight of a cranberry bog presents a rich tapestry of fluid dynamics and soft matter phenomena. Here, we present four connected problems exploring the behavior of cranberries in their stages of harvest: the buoyant rise of a cranberry in a flooded bog, the stable floating configuration of a cranberry on the surface, the aggregation and interaction between many floating cranberries collected with a boom, and the piling of cranberries onto a truck for transportation. We model these phenomena from first principles and develop simple computational simulations of their collective behaviors. Additionally, we describe tabletop experiments to accompany these problems, either as in-class demonstrations or lab activities. Throughout, we draw connections to broader physical principles in soft condensed matter and fluids, allowing the real-world example of the cranberry bog to serve as a bridge between the undergraduate curriculum and topics in soft matter research.

Figures (6)

• Figure 1: Cranberry harvesting is host to multiple processes governed by basic concepts in physics. A cultivator (right) tears cranberries off their vines, allowing them to rise to the surface, where they aggregate in clumps (center). A confining boom is used to collect the cranberries, and the harvested cranberries are loaded onto a truck (left).
• Figure 2: (a) A fresh cranberry is cut in half, showing the air pockets responsible for the buoyant rise. (b) Cranberries rise to the surface via a balance of hydrodynamic forces. (c) The rising cranberry's theoretical vertical position as a function of time. The cranberry rises at a terminal velocity after a short $(\sim 0.1 \text{ - } 0.2$ s) transient given by Eq. \ref{['eq:term']}. (d) The time to reach the surface from a depth $\Delta z=0.5$ m as a function of the size of the cranberry ($R$), with a rise time on the order of a second. The full analytical rise time (solid, Eq. \ref{['eq: timerise']}) and the approximate rise time ($T_R \approx \Delta z/v_T$) assuming that the cranberry is always at terminal velocity (dashed) are shown. (e) In experiment, a frozen cranberry released from confinement rises to the surface (right, with tracked trajectory). The vertical $(z)$ position of the cranberry is tracked over time. It reaches the surface near $t\approx 0.5$ s and then bobs up and down. The cranberry has already reached terminal velocity before tracking begins.
• Figure 3: (a) A trio of cranberries rest on the surface, partially submerged. (b) A cranberry's height above the water is given by the balance between gravity and buoyant forces. (c) The dimensionless height of the spherical cap $h/R$ as a function of the density ratio $\rho_c/\rho_f$ (Eq. \ref{['eq: floating']}). Inset: A zoomed-in part of the plot in the range of density ratios observed for cranberries.
• Figure 4: (a) Two cranberries attract each other due to the curvature of the air-water interface in a bowl of water. (b) Diagram of the Cheerios effect, which drives the attraction between the floating cranberries. (c) The interaction is phenomenologically modeled as a weakly attractive Morse potential between the two cranberries (Eq. \ref{['eq: Morse']}), with a stable equilibrium occurring at $r=2R$. A.U. stands for arbitrary units.
• Figure 5: (a) Comparison between cranberries in circular confinement in experiment (top) and simulation (bottom) at varying densities. (b) A simulated boom with a decreasing radius confines 300 cranberries, halving the radius of the circular confinement.