# Compute_Mf: Compute Moment of force In aRchi: Quantitative Structural Model ('QSM') Treatment for Tree Architecture

## 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

 ```1 2 3 4``` ```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*FALSE 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, FALSE is the weight of the subtree: FALSE=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

 ```1 2 3 4 5 6 7 8 9``` ```# 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 April 16, 2021, 5:08 p.m.