How much rope do you need to circle the Earth?

The circumference of the Earth is 40,076 km (24,902 mi). Let’s say we had a rope that long and used it to circle the Earth, like the red line in the picture. For purposes of this puzzle, assume that the Earth is a perfectly smooth sphere, with no hills or mountains, and that the rope floats on the oceans, which have no waves.

Now let’s raise the rope up on poles that are each 1 m (3.3 ft) long, as shown by the yellow lines in the second picture, which is not drawn to scale.

This path will be longer. How much more rope do we need?