Calculate the probabilities between one-unit increments of a right triangle distribution.
triangleProb(hubHeight, bladeRadius, lowerBound = 0, upperBound = Inf, ...)List of two data frames: the first has distances in one-unit increments (the outer distance), the probabilities between the distances, and a column indicating size class; the second gives the maximum distance of each size class.
Numeric, turbine hub height.
Numeric, turbine blade radius.
Numeric, default is zero, see Details.
Numeric, default is Inf, see Details.
Currently ignored.
A right triangle is constructed with the 90 degree corner at the
origin in the first quadrant of the cartesian plane. The lowerBound
will move the left edge of the triangle to the right. The upperBound will truncate the
triangle distribution at that value.
The maximum horizontal distance is calculated using
hullMuirMaxDistance. This is typically not a
whole number and the ceiling is used. The maximum
vertical distance is such that the area under the hypotenuse edge of triangle
integrates to one. This is done using the equation for the area of a triangle.
The two points that make up the hypotenuse are used to calculate the slope
and intercept of the line. The area under the line in one-unit increments is
calculated using
$$\int_{x-1}^{x}mZ+b dZ = m(x-.5)+b$$
where m is
the slope, b is the intercept, and x is a distance. Integrating
between x-1 and x gives the probability between the one-unit
increments.
All of this is done for three size classes (bats, small birds (SB), and large birds (LB)) separately. An additional size class (RAPTOR) is included and identical to the large bird result.
The floor function is applied to lowerBound.
It is assumed that hubHeight and bladeRadius have the same units.
Hull, C. L., & Muir, S. (2010). Search areas for monitoring bird and bat carcasses at wind farms using a Monte-Carlo model. Australasian Journal of Environmental Management, 17(2), 77-87.
Huso, M. & Dalthorp,D (2014). Accounting for Unsearched Areas in Estimating Wind Turbine-Caused Fatality. The Journal of Wildlife Management. 78. 10.1002/jwmg.663.
hullMuirMaxDistance
triResult <- triangleProb(hubHeight = 100, bladeRadius = 50, lowerBound = 0)
names(triResult) ## list names
triResult$maxDist ## max distance for each size class
head(triResult$triDistProb)
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