This question and its counterpart is long overdue; I should have posted it immediately after (Why would merpeople let people ride them?)
So; we have merpeople, both willing and able to carry people. What's The Best (most efficient in terms of energy expenditure) Way To Ride Them?
- Saddle Plausibility-I doubt riding on someone's back will be comfortable for more than a few minutes for both involved unless you have a strategically made (and padded) saddle that will make things more comfortable for both involved. Plus, saddles make it less likely you'll fall off, or be pushed or pulled off by a current. (Mother Ocean wants to claim you for her own, finless one....)
- Riding Style Pros and Cons-Riding on the lower back, close to the center of gravity, seems the best position, but I could be wrong. Riding a mermaid like a horse will add a lot of drag and put a large amount of weight on a relatively small area. Riding a mermaid like a sled will reduce drag, distribute weight, and be really, really awkward. Riding a mermaid on the surface of the water will put much less drag on the rider but is likely rather demanding for the mermaid, as they will have to hold their rider above water. Riding underwater is better for the merson energy-wise, but will put a lot of additional drag on the rider and will entail surfacing.
- Design Considerations-Johnny suggested large frontal horns on the saddle to split waves so you get hit by less water and the mermaid gets more resistance. This would be great for surface riding, but maybe not so much for sled-style riding. Also, keep in mind we are talking mermaids here; they won't wear an ugly saddle, and if it's not sparkly, glittery, or in some way shiny, that might not end well.....