aRchi (version 2.1.3)

Compute_Mf: 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 aRchi
Compute_Mf(aRchi, WoodDensity = NULL)

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.

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

Examples

# \donttest{
# 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)
# }