One bird, one turbine example

library(collision)

# for Band Comparison
library(stochLAB)

library(knitr)

The set up

One of the key differences in this package and previous Band-based models is the geometric calculation for the core probability of a collision, given a bird is passing through the turbine zone.

The turbine is split into it’s static and dynamic components as described in Smales et al. (2013). The static component includes:

the turbine tower, defined by the hub height (hh), and three diameters of the tower: the base diameter (d_base), the top diameter (d_top) and the diameter at the minimum rotor swept height (d_rotormin)
the generator nacelle, defined by it’s maximum width (max_width_nacelle), length (max_nac_l) and height (max_nac_h)
the hemi-spherical hub with the diameter defined by the width of the nacelle (max_width_nacelle)
the rotor blades, defined by the blade length (blade_length), the chord of the blade at the widest point (max_chord) and at at its tip (thinnest point; min_chord), the thickness of the blade at it’s widest and thinnest point (blade_thickness_wide and blade_thickness_narrow), and the blade tilt (tilt_deg)

While the dynamic component is “the area swept by the leading edges of rotor blades during the time that a bird would take to pass through the rotor-swept zone” (Smales et al. 2013) which is defined by the turbine hub and rotor parameters as well as the length and speed of the bird (bird_length and bird_speed).

A worked example - deterministic

To calculate the probability of collision (of one bird with one turbine) will consider a bird with no avoidance behaviour, and compare the collision approach to the basic Band approach, where flights at rotor swept height are assumed to be uniformly distributed.

We’ve coded an internal function collision:::p_collision_band for testing purposes (note the three colons - this function is just for testing) but for the purposes of this vignette we will also use the stochLAB::get_avg_prob_collision() package.

Step one is to set up a turbine - here’s an example based basically on a Vestas 90, set up using the define_turbine function:


str(v90_single) 
#> List of 17
#>  $ model_id              : chr "Vesta V90"
#>  $ blade_length          : num 44
#>  $ blade_thickness_narrow: num 0.07
#>  $ blade_thickness_wide  : num 2.6
#>  $ d_base                : num 4.15
#>  $ d_rotormin            : num 3.55
#>  $ d_top                 : num 2.55
#>  $ hh                    : num 65
#>  $ max_chord             : num 3.51
#>  $ min_chord             : num 0.39
#>  $ max_nac_h             : num 4.05
#>  $ max_nac_l             : num 13.2
#>  $ max_width_nacelle     : num 3.6
#>  $ rotor_diam            : num 91.6
#>  $ rpm                   : num 16.1
#>  $ tilt_deg              : num 6
#>  $ prop_operational      : num 0.98
#>  - attr(*, "class")= chr "turbineInput"

Now we need a bird (see define_bird)


str(wte)
#> List of 7
#>  $ species          : chr "Wedge-tailed Eagle"
#>  $ bird_length      : num 0.945
#>  $ bird_speed       : num 17
#>  $ prop_day         : num 0.5
#>  $ prop_year        : num 1
#>  $ avoidance_dynamic: num 0.9
#>  $ avoidance_static : num 1
#>  - attr(*, "class")= chr "birdInput"

One bird one turbine

Our approach considers both the static ( $P(C)_{s}$ ) and dynamic components ( $P(C)_{dyn}$ )

Without avoidance, and isolated from the overall collision rate calculation, the total probability of collision, given interaction is the

$P(C|I) = P(C|I)_{static} + P(C|I)_{dynamic}$

because the two options are mutually exclusive.

Let’s calculate the collision probability for a Wedge-tailed Eagle and the V90.


p_coll_static <- prob_collision_static(
  d_base = v90_single$d_base,
  d_rotormin = v90_single$d_rotormin,
  d_top = v90_single$d_top,
  hh = v90_single$hh,
  blade_length = v90_single$blade_length,
  max_nac_h = v90_single$max_nac_h,
  max_nac_l = v90_single$max_nac_l,
  max_width_nacelle = v90_single$max_width_nacelle,
  rotor_diam = v90_single$rotor_diam,
  tilt_deg = v90_single$tilt_deg,
  max_chord = v90_single$max_chord,
  min_chord = v90_single$min_chord,
  blade_thickness_wide = v90_single$blade_thickness_wide,
  blade_thickness_narrow = v90_single$blade_thickness_narrow,
  prop_at_height = 0.75,
  prop_below_height = 0.2
)

p_coll_dyn <- prob_collision_dynamic(
  rpm = v90_single$rpm, #s_rot,
  blade_length = v90_single$blade_length,
  max_width_nacelle = v90_single$max_width_nacelle,
  rotor_diam = v90_single$rotor_diam,
  blade_thickness_wide = v90_single$blade_thickness_wide,
  blade_thickness_narrow = v90_single$blade_thickness_narrow,
  hh = v90_single$hh,
  bird_length = wte$bird_length,
  bird_speed = wte$bird_speed,
  prop_at_height = 0.75,
  prop_below_height = 0.2
)

p_coll_dyn + p_coll_static
#> [1] 0.07960969

Hang on - what’s that `edr`?

Note we set our effective detection radius (edr) to half the rotor diameter. Normally this parameter is calculated via distance sampling (Buckland et al. 2001). As the effective detection increases, this probability of collision given interaction also decreases.

But don’t stress!

As the effective detection radius increases, this also influences the flight density calculation. We will come back to this in a different vignette. For now, we want to compare with Band (as far as possible) so let’s use a default that’s the flux window associated with the turbine itself.

Back to Business - whats’ Band say?


stochLAB::get_avg_prob_collision(
  flight_speed = wte$bird_speed, #m/s
  body_lt = wte$bird_length,
  wing_span = 2.12,
  prop_upwind = 0.5,
  flap_glide = 1,
  rotor_speed = v90_single$rpm  ,
  rotor_radius = v90_single$rotor_diam / 2.0,
  blade_width = v90_single$blade_thickness_wide,
  blade_pitch =  30 * pi / 180, #In radian
  n_blades = 3,
  chord_prof = chord_prof_5MW
)
#> [1] 0.09436917


# using the 2007 smaller profile from the spreadsheet
collision:::p_collision_band(
  max_chord = v90_single$blade_thickness_wide,
  pitch_deg = 30, 
  rotor_diam = v90_single$rotor_diam,
  rpm = v90_single$rpm,
  bird_length = wte$bird_length,
  bird_wing_span = 2.12,
  bird_flapping = 0,
  bird_speed = wte$bird_speed
)
#> [1] 0.09426788

References

Buckland, S., D. Anderson, K. Burnham, Jeffrey Laake, David Borchers, and Len Thomas. 2001. Introduction to Distance Sampling: Estimating Abundance of Biological Populations. Vol. xv. Oxford University Press. https://doi.org/10.1093/oso/9780198506492.001.0001.