Infodoc : Sciences, Techniques et Culture

The scaling of three anchorage systems, the fibrous systems of climbing plants and the tap and plate systems found in self-supporting plants, has been investigated. Optimal shapes for both fibrous and tap-root systems are identified; shapes which provide maximum anchorage for a minimum construction cost. To ensure a constant factor of safety against anchorage failure the linear dimensions of each of these anchorage systems must scale with stem radius.
Optimal shapes for plate systems cannot readily be determined; however, their efficiency will rise with plant size because the anchorage provided by the weight of the root-soil plate increases faster than stem strength. As plants get larger, therefore, plate systems become relatively cheaper to construct. This may be one reason why tree [...]

The scaling of three anchorage systems, the fibrous systems of climbing plants and the tap and plate systems found in self-supporting plants, has been investigated. Optimal shapes for both fibrous and tap-root systems are identified; shapes which provide maximum anchorage for a minimum construction cost. To ensure a constant factor of safety against anchorage failure the linear dimensions of each of these anchorage systems must scale with stem radius.
Optimal shapes for plate systems cannot readily be determined; however, their efficiency will rise with plant size because the anchorage provided by the weight of the root-soil plate increases faster than stem strength. As plants get larger, therefore, plate systems become relatively cheaper to construct. This may be one reason why tree saplings have tap-root systems but develop plate systems as they grow.
The investment plants must make to anchorage systems will depend on the manner in which the shoot system scales. With isometric scaling of the stem the relative investment in anchorage will remain constant. With the additive scaling possible in climbing plants, large plants having relatively thinner stems than small ones, anchorage investment will fall. If elastic similarity is maintained, larger plants having relatively thicker stems, the relative investment in anchorage must rise.