Plotting the curve of a peregrine falcon’s stoop

α = π/4;  (* line of sight angle *)

r[θ_] := E^(-Cot[α]*θ);    (* assuming r[0] = 1 *)

PolarPlot[
r[θ],{θ,0,8π},
PlotStyle->{Red,Thick},
PlotRange->All,
Ticks->None,
ImageSize->Large
]