I'll dig around and see if I can find some references in my books and will get back here either way.
In the interim, see the attched graphic. It's from US Army Field Manual 21-18, Foot Marches (LINK) It's a rough guide.
Anecdotally, a good Infantry Unit decently trained (all are not...) and in good physical condition (same remark applies...) can reliably do a little over 5 MPH/8Km cross country for about 3-6 hours, terrain dependent, they can average around 4 MPH/6-7 Km for about 6 to 10 hours, terrain dependent. The 3.2 figure below is for day in-day out or continuous foot movement. Note also that a good unit can beat the Night figure given depending on ambient light and their equipment. All those figure assume no enemy contact and minimal security concerns.
As I'm sure you know, years ago, those figures were often exceeded mostly due to more experience walking, they walked almost everywhere as do few today. Also consider that the North American Indians were not the only ones to use the alternating pace of run a while, walk a while -- that method can eat up a lot of miles and a good unit using the technique today can easily do 6 or 7 miles an hour in rolling terrain. Back in the day, units and individuals with a long trip used that technique and knocked out 30-40 miles a day, equaling Cavalry in many cases.
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