HOW CAN I CREATE TILTED CURVES THAT MAINTAIN EQUAL SPACING ALL OVER A DOUBLE CURVED SURFACE?

Haha, long title.. 

Hi! 

I have to create a set of panels over some doubly curved surfaces similar to the attached one.. But my problem is that the contour component creates rows of lines that differ in width depending on the base surface geometry. 

If you bake the contours and measure the space between the rows you can see that it's not consistent.. 

If anybody out there knows a way of creating curves like these on a surface like mine, you're MORE than welcome to share! 

Good karma is promised to those who's got suggestions:)

XOXO/sophia