Horse average speed rate

Jonah Hex

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According Wikipedia: 4 miles (6,4 km) per hour;
According "The West that was" edited by Joe Lansdale: 4 miles (6,4 km) per hour.

Trot
Wiki: 8 miles (13 km) per hour;
TWtw: 8 miles (13 km) per hour.

Gallop (canter)
Wiki: 10 to 17 miles (16-27 km) per hour;
TWtw: 12 miles (19 km) per hour.

Full gallop
Wiki: 25 to 30 miles (40 to 48 km) per hour;
TWtw: 16 miles (25 km) per hour.

"Obviously, the terrain, weather, and condition of the horses significantly affected the rate" (The West that was, pag. 126).
 

Straggler

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But don't forget you can't gallop a horse all day...

Horses can travel upwards of thirty (and some, even forty) miles per hour. They cannot sustain this pace for long, though. A horse can gallop a couple of miles at full steam, but the same horse can canter (or lope) much farther. Trotting (either a fast trot or a jog trot) isn't a bad way to travel, but you don't get very far very fast. Faster trotting is tiring to the rider as well because you are posting (rising up and down out of the saddle on alternate beats). Horses can walk all day, with brief rest periods. The condition of the horse can make a difference in endurance. A conditioned horse can do much more than one who isn't. The same is true for diet. A horse who has had all he needs to eat and drink is more likely to be a reliable mount. A horse that isn't in shape is more susceptible to injury as well. That being said, distances a horse can travel vary depending on the size of the party, mounts, weather, terrain, and condition of the roads. Medieval people traveled with everything they needed following in carts behind them. A train of this sort wouldn't move fast. Mounted knights-- all on well-conditioned destriers or palfreys -- would move fairly fast and cover upwards of 50 or 60 miles per day. However, traveling 20 to 30 miles a day would be considered a good day's journey.
 

Jamesaritchie

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And of course if you gallop your horse for hours, pretty soon you won't have a horse.

The great thing about a horse is that when this happens you still have a bunch of very tasty meat, even if you can't ride it.

You can't say that about a car that dies.