The window availability() needs, for an observer looking through a side
window of an aircraft: a field of view running forward and aft, rather than a
circular patch.
Arguments
- trackline
Time in view at the trackline, in seconds — \(\alpha\).
- speed
Ground speed, in metres per second.
- angle
Viewing half-angle forward and aft, in degrees from perpendicular. Give this or
slope, not both.- slope
Seconds of view gained per metre of perpendicular distance, \(\tan\theta / v\), if it was calibrated directly. Give this or
angle.- distance
Perpendicular distance, in metres.
Why this grows with distance
The field of view is an angular wedge. An animal further off the trackline
sits inside that wedge for longer, because the wedge is wider out there.
This is the opposite of view_window()'s circular geometry, and it is the
case that applies to a line-transect aerial survey.
Following Ganley et al. (2019), for a time in view \(\alpha\) at the trackline, a viewing half-angle \(\theta\) forward and aft, and ground speed \(v\):
$$t(x) = \alpha + \frac{x \tan\theta}{v}$$
Calibrating it, rather than deriving it
Ganley et al. (2019) obtained \(\alpha\) and \(\theta\) by flying transects past a navigation buoy and timing it through the field of view, which is worth far more than a derivation from window dimensions. For the Cessna Skymaster over Cape Cod Bay, at 185 km/h and 228 or 304 m altitude, they found time in view at the effective trackline to be 51.22 s, and a slope of about 0.03 s per metre of perpendicular distance. Altitude made no detectable difference across the two they flew.
Their trackline is at 100 m rather than 0 m, because the aircraft's flat
windows leave a blind spot directly beneath it — the same blind spot that
sweep_models(left = ) and the gamma key handle at the fitting end. Their
surveys were left-truncated at 100 m for exactly that reason.
References
Ganley, L.C., Brault, S. and Mayo, C.A. (2019) What we see is not what there is: estimating North Atlantic right whale Eubalaena glacialis local abundance. Endangered Species Research 38:101-113. doi:10.3354/esr00938
Examples
# Ganley et al.'s Skymaster, calibrated directly: 51.22 s at the trackline,
# gaining about 0.03 s per metre out
view_window_aerial(trackline = 51.22, speed = 51.4, slope = 0.03,
distance = c(0, 1000, 3000))
#> [1] 51.22 81.22 141.22
# The same thing from a viewing half-angle
view_window_aerial(trackline = 51.22, speed = 51.4, angle = 57,
distance = c(0, 1000, 3000))
#> [1] 51.22000 81.17846 141.09539