Best Of

The really short answer is: there needs to be enough geometry in the larger curve to support the smaller details cut into it. How much more geometry is required really depends on the tools and order of operations used to create the model. 

It's generally considered best practice to adjust the number of segments in both the underlying curved surface and the intersecting shape until the edge segments in both roughly line up with each other. That way the edges that make up the curve have consistent spacing and can also be used as part of the support loops around the intersecting shape.

Over the last few pages there's a couple of brief discussions about how to cut out details on curved surfaces. Even though the shapes are slightly different the basic principles discussed there can also be applied here.

https://polycount.com/discussion/comment/2790602/#Comment_2790602

Even further back in the thread there's a longer discussion about how to approach modeling this exact shape. So definitely check out the different solutions proposed there. A couple of them use very lightweight meshes and still produce good results.

There's also a more in-depth write-up here that covers breaking the shapes down into radially tileable segments.

So lots of different ways to approach the modeling part. The basic shapes and topology routing can be done on a flat strip then bent into a curve.

What most of these examples have in common is the segment spacing on the curves is kept fairly consistent. Which helps prevent shading artifacts caused by unwanted surface deformation when subdivision smoothing pulls unsupported areas out of shape.