Log Geometry

Log stems without rootwads are modeled as simple cylinders with a length and diameter. Rootwads are modeled as fustrums, the height of which is included in the total length of the log. Rootwad length and diameter are defined as a factor of the stem diameter.

Log volume with no rootwad:

log volume

Where l is the length of the log stem and d is the diameter of the log.

Rootwad volume is defined as the volume of a fustrum:

TODO: equation.

Volumes

Wood calculator volumes are approximate. The log stem and rootwad are divided up into small cubes, the volume of each is easy to calculate, we well as whether it is burrid, submerged or dry. The size of each cube is specified on the advanced tab.

Forces

Force calculations are adapated from Rafferty (2016). Differences are largely due to the different integrations used. Rafferty slices the log into discs, whereas this wood calculator uses cubes. A thorough explanation of each force can be found in Rafferty (2016).

Rafferty, M. 2016. Computational Design Tool for Evaluating the Stability of Large Wood Structures. Technical Note TN-103.2. Fort Collins, CO: U.S. Department of Agriculture, Forest Service, National Stream & Aquatic Ecology Center. 27 p.

Vertical Forces

Buoyancy Force

The upward force of the log is calculated as the sum of wood cubes with a centroid that is above the river bed and below the water surface. The buoyant force FB is:

vertical buoyancy

Yw = specific weight of water (2.4 lb/ft^3 at 50F)

VTWSE = the volume of a cube of wood (ft^3)

n = number of cubes of wood below the water surce

Gravity Force

The downward force of the weight of the structure WT is:

gravity

YTd = specific dry weight of tree (lb/ft^3)

VTd = volume of tree above the channel thalweg (ft3)

YTgr = specific green weight of tree (lb/ft^3)

VTgr = volume of tree below channel thalweg (ft^3)

n = number of cubes of wood above the river bed

Lift Force

The lift force FL acting on the underside of the log is:

lift

CLT = lift coefficient ATP = projected area of wood in the plane perpendicular to flow (ft^2) udes = design velocity of flow (ft/s) g = gravitational acceleration constant (32.3 ft/s^2)

Ballast Force

Soil on top of the log is calculated by identifying the cubes of wood on the upper surface of the log that are burried under the river bed. The volume of soil is calculated as the planimetric area of the cube multiple by the depth of the cube below the transect elevation at that cubes position.

ballast

Vsoildry = sum of the volume of soil above the upper surface of all cubes below the river bed and above the water surface.

Ys = dry unit weight of soil (ft^3)

Vsoil,sat = volume of saturated soil below the water surface.

Y’s = effective buoyant saturated unit weight of soil (lb/ft^3)

Vertical Anchor Force

Soil ballast Favsoil is:

soil ballast

Boulder ballast is first defined by the weight of the boulder Wr:

boulder weight

Vrdry = volume of rock above the water surface (ft3) Yrock = specific weight of rock (165 lb/ft3) Vrwet = volume of rock submerged below the water surface (ft3)

Boulders are approximated as a sphere. The submerged portion is found by:

boulder vol wet

And the dry volume of the boulder is:

boulder vol wet

The portion of the boulder exposed to flow will experience lift forces FLr:

boulder lift

CLrock = Lift coefficient for large roughness elements (0.17, D’Aoust and Millar, 2000)

Apr = projected area of the rock in the plane perpendicular to flow. For conservative estimates the entire rock profile is always assumed to be exposed to flow.

The resultant force of each boulder anchor is:

boulder ballast