Compute_Mf: Compute Moment of force

In aRchi: Quantitative Structural Model ('QSM') Treatment for Tree Architecture

Compute Moment of force

Description

Compute the moment of gravity force Mf and the moment of gravity force relative to cylinder radius Mf_r from an object of class aRchi.

Usage

Compute_Mf(aRchi, WoodDensity)

## S4 method for signature 'aRchi'
Compute_Mf(aRchi, WoodDensity = NULL)

Arguments

aRchi	an object of class aRchi with at least the QSM and the paths table.
WoodDensity	a numeric or a data.table. A single wood density value for the whole tree or one value per cylinder in kg/m3. If wood density is given for each cylinder a data.table with two column (i.e cyl_ID and WoodDensity) must be given.

Details

The moment of gravity force (i.e Mf) is calculated at each cylinder position. Mf can be seen as a proxy of the mechanical loading history due to gravity at a given position of a tree. This quantity is defined by the following the equation: Mf=R*F where R is the lever arm, which is the norm of the horizontal vector between the position where Mf is measured (i.e a cylinder) and the position where the force is applied (i.e., the center of mass, G, of the whole structure upstream a cylinder: a subtree).

The mass of the cylinders are needed to calculate the center of mass and are estimated using their volume and the wood density provided in argument WoodDensity. Finally, F is the weight of the subtree: F=g*M with g the standard acceleration due to gravity (9.81 m.s-²).

The moment of gravity force relative (i.e Mf_r) to cylinder radius r is also computed following the formula: Mf_r = Mf/r^3

Value

The aRchi file with the QSM slot having three new columns: the biomass upstream the cylinder sub_tree_biomass, the moment of gravity force Mf and the moment of gravity force relative to cylinder radius Mf_r.

Examples

# Read an aRchi file with a QSM and paths tables.
file=system.file("extdata","Tree_1_aRchi.aRchi",package = "aRchi")
Tree1_aRchi=read_aRchi(file)

# Compute the moment of force for each cylinder
Tree1_aRchi=Compute_Mf(Tree1_aRchi,WoodDensity=550)

# show the QSM data.table with the three new columns sub_tree_biomass, MF and Mf_r)
get_QSM(Tree1_aRchi)

aRchi documentation built on Sept. 3, 2022, 9:06 a.m.