Except the helix curve shown in OP is NOT a loxodrome or rhumb line.

It has equal spacing on the surface between lines, a loxodrome can't have that property since by definition it must cross the meridians at the same angle at all times. That means it always gets denser near the poles.

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Start with the curve:

x = 10 · cos(π·t/2) · sin(0.02·π·t)

y = 10 · sin(π·t/2) · sin(0.02·π·t)

z = 10 · cos(0.02·π·t)

Convert to spherical coordinates (radius R=10):

λ(t) = π/2 · t (longitude)

φ(t) = π/2 - 0.02·π·t (latitude)

Compute derivative d(λ)/d(φ):

d(λ)/dt = π/2

d(φ)/dt = -0.02·π

d(λ)/d(φ) = (π/2)/(-0.02·π) = -25 (constant)

A true rhumb line must satisfy:

d(λ)/d(φ) = tan(α) · sec(φ)

which depends on latitude φ.

Since φ(t) changes, sec(φ) changes, so no fixed α can satisfy this.

Conclusion: the curve is not a rhumb line.

this is how one should look for varying intersection angles:

https://beta.dwitter.net/d/34223

Indeed. It is one of the many well known spherical spirals / seiffert spirals.