CreateMesh, axis step, for spiral 3d draw

Hello there,

Listen, I'm try to use a 3D function to describe a path of an ant in a surface.

The surface rotate at 2*pi/ sec and the ant walks in line from center to away 1 cm/s. The surface is a circle with 1m radius.

After all parametrizations, i have problem to draw it. (you can see document attached)

This is the function that indicates the position of the ant dependent on time:

Then I CreateMesh and this came:

From 0 to 50, it should draw a spiral with 50 lines, or I'm I wrong? And how can i chose Step size in CreateMesh?

I want like t:=0, 1, 2, 3 .. 100. How can i do that on CreateMesh?

Regards,

L. L.