I have been looking at long distance travel via mounts versus travelling on foot, so that I can more effectively build and describe the world, as well as manage random encounters and such. I am having trouble figuring out a certain part of the PHB description of mounted travel:
For short spans of time (up to an hour), many animals move much faster than humanoids. A mounted character can ride at a gallop for about an hour, covering twice the usual distance for a fast pace. If fresh mounts are available every 8 to 10 miles, characters can cover larger distances at this pace, but this is very rare except in densely populated areas.
I have already extrapolated the normal travel pace of a creature to be its walking speed divided by 10 rounded up in miles per hour, as this leads to 3 miles/hour for the player characters with exceptions of permanent speed increases as well as with Flying mounts as described in the DMG Page 119:
A creature that serves as a flying mount must rest 1 hour for every 3 hours it flies, and it can't fly for more than 9 hours per day. Thus, characters mounted on griffons (which have a flying speed of 80 feet) can travel at 8 miles per hour, covering 72 miles over 9 hours with two 1-hour-long rests over the course of the day.
So looking at either a Riding Horse or a Warhorse, each of which has a walking speed of 60 ft., I would double the travel pace distances covered by a creature with 30 ft. speed. However, the part mentioning acquiring fresh mounts every 8 to 10 miles confuses me, as a horse could move 16 miles per hour during a gallop. Unless the phrase "twice the usual distance for a fast pace" does not refer to the fast pace of a horse, but of typical medium creatures like many PCs, and it doesn't say one way or the other.
So how does that work, exactly? Does a galloping horse travel at twice its own fast pace, or can it only travel at twice the fast pace of a typical medium humanoid? Furthermore, if the correct answer is the latter, since galloping would be akin to the horse's fast traveling pace, does that mean galloping effectively replaces a fast travel pace by horseback?