For unladen biking (not touring) around town and for trips of two or three hours:

- Horizontal - I average about 13 mph on flat horizontal unpaved trails, about 14 mph on pavement.

- Vertical - On a grade of about 10 percent when I am in my lowest gear, I am traveling about 3.7 mph. On this steep a hill, almost all energy is applied to elevation gain, there is very little mechanical or rolling resistance and very little aerodynamic drag. Thus at a 10 percent grade that is climbing at roughly 0.37 mph in the vertical dimension which is equivalant to roughly 2,000 feet per hour. But at the top of the hill I am a bit winded so if I was planning for a long day with a lot of climbing I would assume that I could climb roughly 1,500 feet per hour instead of 2,000 feet per hour.

- Estimate times for horizontal and vertical, then take the sum.

Loaded touring, I would add 15 percent more time than I got with the above. This accounts for going slower with the additional weight, riding a bit slower with a loaded bike because it does not feel as stable, and pacing myself to go a bit slower so I can last all day.

You might want to calculate your own horizontal and vertical averages instead of using mine.