Calculating miles for long hikes (high nerd content warning)

[HappyHour]

So there's a foot of snow on the ground, the temps have been in the single digits (both positive and negative).  I should get out and go for a ski, but the NWS says winds of 30+ MPH in the high country.

Clearly, the proper thing to do today is start planning a long-distance hike.

For section-hiking the PCT, I have relied on Craigs PCT Planner to help me estimate how many miles I'll hike per day and thus how many days it will take to get from one resupply point to another.  It does this by having you put in an average pace, hours hiked per day, and an elevation gain factor.  It works pretty well, and I highly recommend you use it (and donate) if you are hiking the PCT.

But I am thinking of the AZT this spring and there is no ready-made app that I know of for it.  But I do a lot of quantitative analysis in my line of work, and wondered if I could come up with my own predictive formula. I hiked the PCT from Walker Pass to Lake Tahoe last summer. Thanks to Halfmile's PCT maps and app I could estimate the miles hiked and the elevation gained and lost pretty accurately.  I put these into a data table in JMP, and then added in other factors that I thought might affect my daily mileage: days on the trail, days of food carried, ± bear canister.  I put these together into a model that also looked for interactions between factors and non-linearities within them, and then ran multivariate regressions to determine which were the most influential and fit the data best.

The model did a pretty good job:

About 77% of the day-to-day variance in miles hiked is accounted for, and the average error between predicted and actual miles hiked is 1.5 miles.

What surprised me was the factor that turned out to be far and away the most influential: how many days I had been hiking.  In fact, if I just plot miles per day vs days on the trail I get a pretty good correlation:

This wasn't totally unexpected.  I knew I was hiking longer distances as I got in better shape. But I was surprised at just how little influence other factors like weight carried or elevation gain or loss had on mileage.  Here's the plot for elevation gain vs miles hiked:

It has a negative correlation, just as you'd expect, but the effect is fairly small and in fact is of weak significance (P = 0.11 vs P < 0.0001 for trail days).  A Pareto plot illustrates the relative influence of the factors (all other factors were insignificant and were left out of the model):

That central term accounts for the non-linearity of the EG effects, meaning that going from 400 ft/mile to 500 ft/mile slowed me down more than going from 100 ft/mile to 200 ft/mile.  I don't think I have to convince anyone in this forum that this makes sense.

There is an obvious problem with this model - it predicts that if I were on the trail for 50 days I would be hiking some 35 miles/day, which is not likely.  My mileage would surely flatten out at some point in the hike, if for no other reason than that I like to swim, fish and take naps when the conditions are opportune.

The prediction expression ends up being miles/day = 18.4 + 0.31*Day - 0.014*EG/mi + (EG/mi-193*((EG/mi-193)*-0.00014).  It's fairly easy to plug this into a spreadsheet and limit the intercept + Day factors to ≤ 25 miles a day and then use the rest of the equation to adjust for elevation gain.

Of course this just applies to me.  Your mileage, as they say, may vary.  But I wonder if anyone else has seen a similar pattern on their long hikes.

[Aaron Zagrodnick]

Interesting research and thanks for sharing...enjoyed checking this out - plugged in the numbers from a few past hikes and seems to work out pretty well! It seems these short days always have me personally looking at maps a bit more often (with a little math perhaps), great to get plans in place or assemble the possibilities.

I have also noticed a ramp up and level out on longer trips, but actually find my longest mileage days are on shorter overnight or weekend style trips where I'm trying to fit a lot into a short amount of time. For my longer trips though I like to slow it down to more of a moderate level especially if there's good fishing and photographic opportunities, or to leave time for that possible 2nd cup of coffee in the morning. I do have the luxury in those situations of not racing against the seasons, allotted PTO, etc., however and always try to allocate a bit of a buffer in regards to time and distance.

Overall, I think for me I defintiely like to take in the sunrise with a cup of coffee and the sunset with my camp already setup and dinner on the way, with the hiking in between and the miles falling where they may. As a result I generally plan on 15 mpd or so for average mountain trails. On trips where things like fishing and photo opportunities are on the light side I've found my mileage to definitely trend higher however. All bets are off on unexplored off trail routes (who knows), or on that last day of a trip with the promise and motivation of a good meal (what time do they close again?) and a known rest the next day - many of my longer hiking days - and nights! 

[Dogwood]

Not another Statistical Mathematics  major? Knows one to suspect one.  

After so many trail miles and hikes I've developed a keen sense of backpacking and hiking variables that impact my pace and time between resupply pts. Based on my own and a great many other experienced LD hiker's approaches I can safely average 2.25-2.5 miles per hr in general. Even after so well knowing these variables and myself I still think it best to factor in room for unexpected circumstances. One of the key traits to have for any LD hiker is adaptability.  

[Surfcam]

I appreciate your calculations and research but I feel like it's too complicated with something that has too many variables. I would look at the data for your past hikes to estimate. I know that generally my walking speed is around 3 mph but when I factor in stops for breaks, calls of nature, pictures, ... that my average can vary between 1.75 mph-2.5 mph. Overall, I will use 2 mph to get an estimate and also figuring that the longer I hike, my average speed will drop. That being said, I "fill the time allotted" so to speak in one of two ways.

1. hours per day. If I want to hike 10 hours per day, that's what I hike.

2. Miles per day goal. I will hike until I reach the daily goal usually because of time constraints. When I thru hiked the JMT last July I had 13 days until I had to be home. About half the days we hiked until an hour after it got dark. One time we got a late start and hiked until 11 pm to make a 25 mile day.

[HappyHour]

Fair enough. There are plenty of ways to roughly estimate miles per day that work just fine. And there is such a thing as overplanning a hike. This analytical exercise was definitely done more for amusement than to develop a practical tool.

[Dogwood]

Since we're referring to multi day hikes what I tend to lend greater wt to than MPD avg during the hike's prep phase is the miles between  resupply or amount of miles for the hike.  I then look at things like elevation profiles, maps, grades, trail/route conditions, typical weather patterns for the hike's time frame, anticipated fitness/mental backpacking condition at the the start, total max wt hauled, etc. I may have in the back of my mind the  MPD avg I need for that resupply segment or the hike but almost always  know I can ramp it up or slow it down as needed to arrive where and when as needed. Rarely do I go pedal to the metal non stop FKT style. I work on not getting too far behind that daily MPD avg. For me, backpacking is about being in the flow letting it happen not always forcing something according to an anal agenda.  Even the most well laid out hiking plans can change on a dime with basically an infinite possible unknown variables that can enter the picture. At these times, in the real world, I like to know that I can cheerfully adapt.