11:20 a.m. on August 30, 2006 (EDT)
Re: Estimating time of hike.
Yeah, Steve, I knew what you wanted in your question. But there is a huge problem with the "magic formula" you wanted, or rather, a bunch of problems. These are hinted at in some of the other responses.
As Dave (our leader) said, the canonical rule published everywhere is 2 miles per hour. However, Dave, the canonical altitude adjustment is 1 hour per thousand feet, not a half hour. But, getting back to Steve's question, there are at least a half dozen variations on this magic formula that give you a range of a factor of 2 or more in the time. Some variations account for pack load, some for trail condition.
Here are several things wrong with using such a formula, most already hinted at or explicitly stated:
1. Everyone is different. Some hike faster, others slower. Personal condition (training, today's state of health) varies from day to day. Got a kid or dog with you? Like to smell the flowers or hug a tree or take lots of photos? It all makes a difference.
2. How long do you feel like hiking before making camp? Some people prefer to hike no more than 3 or 4 hours, others will do 10 hours a day, day after day.
3. What is your hiking style? Do you hike continuously for 4 hours before taking a snack/lunch break, or do you take a break every hour or at the top of every steep climb? How long are your breaks - 5 min to catch your breath, 15 min with pack off, mid-day nap?
3. How long does it take you to set up camp? Some people take 5 minutes (especially here in the West, where we often just roll the sleeping bag out on the ground), some take an hour (some tents take a long time to set up, some people search for the exactly perfect bedsite and orientation, some people like a "kitchen").
4. Depends on the load, terrain (good trail, rough trail, crosscountry), weather (hot, humid, raining, snowing, very cold, snow on the trail, etc), and a bunch of other factors.
5. Depends on how complex the route-finding is. Clearly, a good trail for which there is only one choice, or one with which you are familiar, or one which has excellent signage is faster than an obscure trail that you are on for the first time that has lots of branches to spot. I think of one hike I made up the Right Fork that involved a stream crossing at a fork in the trail that was obscure. The "obvious" trail continued up the same side of the stream I was on for a couple miles before making a sharp turn, while the crossing is hard to see, even now that I have done the hike several times. Same with the trail up the Great Gulf - a couple of obscure stream crossings. And same with a backpack we did in the Smokies. The retracing and searching in each case added 30-60 minutes.
Until you know your own style and develop some sense of your own strengths and weaknesses, you can only do a very rough estimate. As several others have already said here, do a bunch of short overnights that are well within what you think are your limits. Keep a journal with the distance, climb, trail condition, and your condition (healthy, sick, tired, very fresh) and pack weight (heavy, light - not the exact pounds).
If you get the idea that I think rigid magic formulas are nonsense, you have the right idea! Hey, and I am a scientist by training who quantifies everything!