The air flow around the wing tip of an airplane is extremely complex.
The original vertical winglets designed in the late 80’s and early 90’s weren’t very good. They saved fuel but they added weight. They barely paid for themselves. I would say these winglets were more for cosmetics and made the planes look more cool.
The newer vertical winglets worked much better and do save fuel.
However, more recently, Boeing has decided that they have a better solution than a vertical wing tip. They use a rake wing wing tip. Take a look at the 787 and 777-9. They believe that these are more fuel efficient.
[https://www.flickr.com/photos/27889738@N07/6714985457](https://www.flickr.com/photos/27889738@N07/6714985457)
[https://d3lcr32v2pp4l1.cloudfront.net/Pictures/780xany/0/9/3/67093_777xv77wcomparison_250019.jpg](https://d3lcr32v2pp4l1.cloudfront.net/Pictures/780xany/0/9/3/67093_777xv77wcomparison_250019.jpg)
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