Can A Rising Drone Freeze Sunset?

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How fast would a drone have to rise vertically to keep sunset perpetually in sight? By climbing while earth’s surface (and the drone) rotate away from the sun the drone could, in principle, rise at the same rate the sun drops and “freeze” sunset. My calculation below predicts that a drone rising at 8 ft/s (2.4 m/s) should keep sunset in sight for 2 min 15 s up to an altitude of 1000 ft (305 m). The video test footage shows very close agreement!
(Shot with Lumix G95, Parrot Anafi drone and edited with Filmora9)

In the diagram shown in the video:
R = Radius of rotation on surface of earth = 3959 miles at the equator and decreases as cosine of latitude.
H = Height of drone above the starting point required to keep sunset in sight
x = Angle the earth (and drone) have rotated during the flight

(R+H)cos x = R
Angle of rotation x = zt, where z = 360 deg/24 hr, t = time
Solving for height H = R(1/cosx - 1)
With time dependence H(t) = R(1/cos(zt) - 1)
Vertical speed to keep sunset in sight = d/dt[H(t)] = Rz[tan(zt)/cos(zt)]