Difficulty rating for daily mileage planning

[LittleRock]

Probably similar to most section hikers or mid-range distance backpackers who are out on the trail for 5-10 days at a time, I've had hikes where I've ended up a day ahead or behind my originally planned schedule. Ending up a day ahead isn't usually a problem since you can just go home early or "hang out" for a day. But ending up a day behind can be a BIG problem, especially if you're taking time off work. Sometimes I've been able to build an "extra" day into my schedule, sometimes I haven't. So far I haven't missed any extra work days because of it, but once I had to really push myself at the end to make up for lost mileage.

Most commonly, my reason for ending up a day ahead or behind has been mis-judging the trail difficulty. Unless you've hiked the trail before, it can be quite difficult to judge how easy or difficult it will be to make your planned mileage for a given day. Being a statistician by trade (and a geek by nature), I've tried to come up with a number quantifying a difficulty score for a planned day of hiking. My formula is:

DIFFICULTY_RATING = DIST_MI * (5 + AVG_GRADE) + NET_ELEV_FT/100

Where DIST_MI is the miles hiked in a day,
AVG_GRADE is the average % trail grade = (ELEV_GAIN_FT + ELEV_LOSS_FT)/(5280*DIST_MI)
and NET_ELEV_FT is the net elevation change for the day (end elevation minus start elevation)

This doesn't account for other factors such as difficult terrain or weather conditions, but it's a pretty good proxy that can be easily calculated from data found in trail guide books. I applied it to all of the AT sections I've hiked, and for the most part, the days I found difficult had high scores, and the days I found easy had low scores. For planning purposes, it's pretty nice because you can easily compare your planned trip to hikes you've done in the past.

Of course, the difficulty score by itself doesn't mean anything - it needs to be judged based on your individual hiking ability and preferences. A score of 200 might be a difficult day for a section hiker on Day 1, but it could also be an easy day for a thru-hiker who's been on the trail for 2 months. For me personally, I try to plan my hikes so that I start out with a few days between 100 and 150 then build up into the low 200's by the end of my trip.

[tdoczi]

ive never fallen a full day behind a plan why not? you need to stick to the plan everyday and not stop early figuring youll make up for it tomorrow. if right out of the gate on day 1 youre so far behind at the end of the day that doign a little extra hiking, maybe past dark if need be, wont get you on schedule then youre planning is way off. i suppose a formula could help with that but i dont know that id universally trust it.

i dont know, ive just never been miles and miles short on any day of any hike ive ever taken. i cant quite really fathom how it could happen, honestly.

[tdoczi]

well, aside from injury, of course. or severely bad weather, etc, but thats not what youre talking about.

[Odd Man Out]

I can see this as useful. I took a 6 day, 70 mile section hike last summer, figuring 12 miles per day would be reasonable. However, it became apparent after 3 days that was not going to be possible as I did not adequately take into account elevation gain/loss into my plans. This summer I'm planning on a 4 day, 40 mile hike (slightly less mpd) but the terrain will be quite flat so I'm feeling more confident. After my experience from last summer, I looked into the elevation gain/loss data for various parts of the section. The best data I could find was the analysis by Map Man, who actually counted lines on a topo map for the whole length of the AT. Here are his data:

http://www.whiteblaze.net/forum/content.php/49

I had previously imported these into a spread sheet. It was easy enough to put the formula above in a version of this spreadsheet to calculate a difficulty factor for each section of the trail.

https://www.dropbox.com/s/b5caj6c8hu9ytr9/difficultyrating.xlsx?dl=0

To use the spreadsheet, indicate where you want to start and stop in column k). It doesn't have to be an x. Anything except a blank cell will work. In columns L and M, next to the stopping point you will see the cumulative miles and cumulative difficulty factor for the proposed section. I don't have time to check the details. Perhaps you can see if the formulas are correct. Also, I'm not sure if calculating a difficulty score for each section and adding them up will give the same result as adding up the data for the section and then calculating the score. Will have to work on that later.

[theoilman]

As an "old man" doing a couple of week long sections a year, also slow (trail name 'inchworm'), I've come up with my simple calculation. No complicated equations, no complicated spreadsheets.
10 miles per day typical max, but with the limit of 2000 feet of total elevation gain. If I get the total gain, whatever the miles, it is a day!
On easier terrain I have done 13 miles per day for 3 days (with 1300 feet elevation gain per day average).
The downhills don't seem to bother me badly, but the ups really do.

[QiWiz]

I find that trail condition (degree of rocks, roots, off-trail, boulder fields, etc), elevation changes, and trail altitude are important in planning distances to try and cover in a day. Also weight carried (eg. how many days of food in the pack). In the end, however, you just have to keep walking till you get there. Leaving earlier helps you arrive earlier at your intended destination.
Hike on!

[Another Kevin]

You seem to be trying to reinvent Naismith's Rule (https://en.wikipedia.org/wiki/Naismith%27s_rule).

Naismith was a speed demon. I'm not. :)

For a first approximation, I figure that travel time will be 30 minutes to the mile, add 40 minutes for every 1000 feet of elevation gained or lost. I then try to guess fudge factors if there are things like fords or scrambles.

I double the estimated time for bushwhacks or if I expect my party to be breaking trail on snowshoes.

I try to hold the time to 6 hours (or at most 8) of actual time in motion, because I never get to take a trip long enough to really get my "trail legs." The rest of the time in my hiking day tends to fill up with vices like photography. I therefore wind up planning 8-12 mile days. (which is a good figure to plan "coming out of the gate" in any case).

Once in a while I surprise myself. On my last trip, I planned 3.5 days, with daily mileages of about 6, 10, 11, 10. (The first day was the short day.) I wound up making 10.2, 12.4, 14.4 and coming home a day early.

I couldn't hold myself to the limit theoilman/Inchworm sets. I had one weekend last summer where Sunday morning started with a 3100 foot elevation gain in about 3.5 miles (and then the next 0.8 had about 400 feet lost and regained, and the day went on from there....) No good places to camp until having done 3500 ft up and about 1200 ft down, and that still would put me 800 ft above the nearest water source. Sometimes life has its ups and downs.

I've only run a day late once in the last five or six years. That was on a bushwhack where I simply ran into a lot of pesky bad luck with routefinding. Kept running into dense spruce, big fields of blowdown, and ledges too steep to scramble. Eventually, running out of daylight, I told my daughter, "The ledge we're standing on is the biggest flat spot I've seen in the last 45 minutes. We're camping here." I don't think I've ever been delayed that badly on trail, but on a bushwhack, particularly on a route you haven't done before, life is less certain.

[MuddyWaters]

Heavily laden scouts use 2 mph + 1 hr per 1000 ft

[tdoczi]

i think i just break it down into 3 categories- terrain i can do 18-22 miles a day on, terrain i can do 14-18 on and terrain i can do 10-14 on. its not hard to tell them apart and the easiest is usually not next to the hardest. and within the approx range, an error is not insurmountable. in other words if i plan on 20 mpd in an 18-22 section and can only get 18 miles done before i might ideally want to stop, grinding out 2 more miles is no biggie. actually in tougher terrain if i plan on 13 and am ready to quit after 11, thats where theres potential to not finish a day i had planned, if ever. over half the trail done in section hikes and ive not once had a day where i had to stop 5 miles short because i just couldnt do something i thought i could. as ive said, i really cant even fathom something like that, injury or weather aside.

[George]

I have often let the mind wrap around a similar concept to fill mindless hours of walking - my term is " units of effort " measured between landmarks, could be shown in a separate column in trail guides

this could best be compiled by careful record keeping by hikers of various fitness levels, with qualifiers for % increase due to seasonal or weather variations (such as mud or black fly season)

an individual would quickly be able to determine a rough average of time taken to personally accomplish a unit of effort

[LittleRock]

Two examples of when I've gotten off schedule:

On a 7 day trip I had planned 15 mi/day, pulled a ligament in my knee on day 4 and had to slow down and stretch the last 3 days out into 4. Thankfully, that was one of the trips where I had built in an extra day, but the injury most likely wouldn't have happened if I had started out slower.

On another trip, I had planned a 16 mi day ending at Roan High Knob, but started out slow and made it only 9 miles to Clyde Smith shelter by 2 pm. Rain was coming and decided it would be unwise to try to push another 7 miles and over 2000' up to Roan High Knob. The next day I made it to Roan High Knob by lunchtime and went down to Carver's Gap, but there were 50+ mph winds and lightning so decided to backtrack to the shelter instead of trying to cross the balds in those conditions. In the end, I made up the miles by pushing 40 miles from Roan High Knob to Dennis Cove in 2 days - basically hiking from dawn to dusk. But it was exhausting, and in the end I realized my mistake was planning the 16 mi day with the big climb up Roan at the end.

So yes, injury and weather played a role, but so did planning longer days than I should have. If I had used the difficulty ratings, I would have seen that my first hike started out with 4 days straight of difficulty rating of 200 or greater (which is clearly too much for me starting out), or that the 16 mi day up Roan had a score of 283 (max for me is about 250 even with trail legs).

Odd Man Out, thanks for sharing this. I modified your spreadsheet a little bit (partially my fault, the AVG_GRADE should have been multiplied by 100 in the formula). The numbers from Map Man's data are very close to what I came up with on my own.

https://www.dropbox.com/s/ps3rkw316usa28h/difficultyrating.xlsx?oref=e&n=449565794

Never heard of Naismith's rule before. The problem is it assumes a constant walking speed, and I don't walk at a constant speed. I always start out fast in the morning, then get slower and slower as the day wears on. On a good day, I can get 8 miles in before noon, then it usually takes me the rest of the day to hike another 8 miles.

[Another Kevin]

ive not once had a day where i had to stop 5 miles short because i just couldnt do something i thought i could. as ive said, i really cant even fathom something like that, injury or weather aside.

On trail, I think I agree with you. As I said, I've had that happen on bushwhacks. Sometimes you just hit stuff that takes an hour to go a quarter mile. The time I was a day late, I was only two miles short, but routefinding was quite difficult. The place was full of stuff like this. (These pictures are from a different trip, but the same sort of terrain.)
https://farm6.staticflickr.com/5583/14735257191_4918e7667c_n.jpg (https://flic.kr/p/os73At)https://farm3.staticflickr.com/2921/14738136242_c13acef629_n.jpg (https://flic.kr/p/osmNrh)https://farm3.staticflickr.com/2930/14738421885_a2bd6a813d_n.jpg (https://flic.kr/p/osogma)https://farm4.staticflickr.com/3876/14551787189_d7b48ded46_n.jpg (https://flic.kr/p/oaTHmz)

[saltysack]

Only time I've come close was a major slowdown do to ice and injury...going over roan mtn in February without spikes...solid ice up and down...twisted ankle....took 14 or so hours to go 15-16 miles... Rested ankle took several vit I and kept going to keep on schedule. With that said I'm skittle concerned with my 14 day schedule for jmt thru....will be longest hike for me....


Sent from my iPhone using Tapatalk

[nsherry61]

Littlerock, I really enjoy math/thought experiments like these. Thanks for the thread
Having played with these ideas in the past, although not seriously, I have a couple of questions:
- Why not have the difficulty rating be converted to an intuitively meaningful number like expected hours on the trail or "flat terrain distance equivalence" since that is essentially what you are working toward with distance * (elevation change correction factor).
- I suspect a non-linear elevation gain correction factor might be significant, at least if things get very steep on the routes being budgeted.
- Most hiking "budget" calculations ignore negative grades or use negative grades as an advantage instead of disadvantage as in yours. I suspect slight negative grades would be an advantage whereas steep negative grades would be a disadvantage. Again a non-linear attribute?

On one other point raised in the thread:
I really like the idea of guide books publishing a effort rating for various sections of trail between common identifiable land marks. What an awesome planning tool that would be for someone new to the area.
It could be essentially distance equivalence correction factor based on known grade and a subjective tread factor.

[tdoczi]

On trail, I think I agree with you. As I said, I've had that happen on bushwhacks. Sometimes you just hit stuff that takes an hour to go a quarter mile. The time I was a day late, I was only two miles short, but routefinding was quite difficult. The place was full of stuff like this. (These pictures are from a different trip, but the same sort of terrain.)



aside from accidentally after loosing the trail i have basically no experience with bushwhacking. i can certainly see how that would be harder to time and was definitely referring only to on trail hiking.

[tdoczi]

Two examples of when I've gotten off schedule:

On a 7 day trip I had planned 15 mi/day, pulled a ligament in my knee on day 4 and had to slow down and stretch the last 3 days out into 4. Thankfully, that was one of the trips where I had built in an extra day, but the injury most likely wouldn't have happened if I had started out slower.

On another trip, I had planned a 16 mi day ending at Roan High Knob, but started out slow and made it only 9 miles to Clyde Smith shelter by 2 pm. Rain was coming and decided it would be unwise to try to push another 7 miles and over 2000' up to Roan High Knob. The next day I made it to Roan High Knob by lunchtime and went down to Carver's Gap, but there were 50+ mph winds and lightning so decided to backtrack to the shelter instead of trying to cross the balds in those conditions. In the end, I made up the miles by pushing 40 miles from Roan High Knob to Dennis Cove in 2 days - basically hiking from dawn to dusk. But it was exhausting, and in the end I realized my mistake was planning the 16 mi day with the big climb up Roan at the end.

So yes, injury and weather played a role, but so did planning longer days than I should have. If I had used the difficulty ratings, I would have seen that my first hike started out with 4 days straight of difficulty rating of 200 or greater (which is clearly too much for me starting out), or that the 16 mi day up Roan had a score of 283 (max for me is about 250 even with trail legs).

Odd Man Out, thanks for sharing this. I modified your spreadsheet a little bit (partially my fault, the AVG_GRADE should have been multiplied by 100 in the formula). The numbers from Map Man's data are very close to what I came up with on my own.

https://www.dropbox.com/s/ps3rkw316usa28h/difficultyrating.xlsx?oref=e&n=449565794

Never heard of Naismith's rule before. The problem is it assumes a constant walking speed, and I don't walk at a constant speed. I always start out fast in the morning, then get slower and slower as the day wears on. On a good day, I can get 8 miles in before noon, then it usually takes me the rest of the day to hike another 8 miles.

ive never subscribed to the doing too much causes injury theory. i know i am basically alone on this. i think you would have just hurt your knee the next day if you were doing less MPD, but i could be wrong.

weather is weather, and no spreadsheet will fix that.

all that said, do you not think if you didnt encounter injury and weather you wouldnt have been able to stick to your plans? sounds to me like you know youre limits but are now kind fo second guessing yourself.

that or you just like making math puzzles.

my completely unscientific contribution is to wonder about the net elevation part of it. once could theoretically hike all day up and down the biggest mtns on the trail and end up finishing at the same elevation one started and your formula doesnt account for this. it seems to assume that a day's hike always has a generally upward or downward trend in elevation and that is hardly the case at all.

[Odd Man Out]

...

For a first approximation, I figure that travel time will be 30 minutes to the mile, add 40 minutes for every 1000 feet of elevation gained or lost. I then try to guess fudge factors if there are things like fords or scrambles.

I double the estimated time for bushwhacks or if I expect my party to be breaking trail on snowshoes.

I try to hold the time to 6 hours (or at most 8) of actual time in motion, because I never get to take a trip long enough to really get my "trail legs." The rest of the time in my hiking day tends to fill up with vices like photography. I therefore wind up planning 8-12 mile days. (which is a good figure to plan "coming out of the gate" in any case).

...

Here is a spreadsheet with AK's formula. I made it customizable, starting with AK's recommendations.

In the upper-left corner you can set your hours want to hike per day (8 hrs)
then you enter the base hiking rate (30 minutes per mile)
Then you enter the extra minutes for each 1000 ft of elevation gain/loss
Then you can enter a scale factor (double the time if conditions are bad, eg.)

https://www.dropbox.com/s/5hvqj72fmhg4ind/difficultyrating2.xlsx?dl=0

[Sly]

PCT Planner (http://www.pctplanner.com/) is unique whereas in a simple interface you can adjust for average speed, hours hiked per day, add time for every 1000' of elevation, along with section between resupply points or the entire trail. I'm surprised no one has come up with an AT version.

[hikernutcasey]

I think it all comes down to planning. My buddy and I study the heck out of our guidebooks and maps when deciding on mileage. We look at things like where the water sources are, where camp spots are, terrain and major climbs/descents. We have done almost half the trail and have never not finished a section hike on the day we originally planned. We occasionally get a little off of our original schedule but if that happens we improvise on the fly and plan on making up the difference by the end of the trip.

I once suffered a stress fracture on day 2 of a 5 day hike between Hot Springs and Erwin. When I woke up on day three at Jerry Cabin shelter I could barely walk. I had 8 miles to the nearest road crossing. I figured I would gut it out until I made it there and see how I felt. By the time I made it there it had basically went numb so I kept walking. Maybe it wasn't the smartest thing but I finished the trip on time. My point is on week long trips or less it is highly unlikely you will get so far behind you can't make it on time. If you are injured so bad you can't make it on time you probably need to get off the trail anyway.

We are leaving to do the Whites in 2 weeks and have researched and planned extensively and have come up with a schedule with a much lower amount of daily miles than we usually do. In this day and time with the amount of information from guides and sites like these there really isn't any reason you can't plan a trip and know pretty much where you are going to be each day before you start.

[LittleRock]

that or you just like making math puzzles.

Yes. Maybe next I should come up with an AT Sudoku puzzle. :-)


my completely unscientific contribution is to wonder about the net elevation part of it. once could theoretically hike all day up and down the biggest mtns on the trail and end up finishing at the same elevation one started and your formula doesnt account for this. it seems to assume that a day's hike always has a generally upward or downward trend in elevation and that is hardly the case at all.

After running the numbers and comparing it with personal experience, I decided to add that factor to emphasize that the hardest days were ones either with significantly more ups than downs, or with a big climb at the end. Other folks may not agree - in that case it's easy enough to drop the term from the formula.


Here is a spreadsheet with AK's formula. I made it customizable, starting with AK's recommendations.

In the upper-left corner you can set your hours want to hike per day (8 hrs)
then you enter the base hiking rate (30 minutes per mile)
Then you enter the extra minutes for each 1000 ft of elevation gain/loss
Then you can enter a scale factor (double the time if conditions are bad, eg.)

https://www.dropbox.com/s/5hvqj72fmhg4ind/difficultyrating2.xlsx?dl=0

That's another way to look at it. Might work for some folks, but I don't like planning my days based on number of hours hiked. Some days I get worn out after 6 hours, others I'm good for up to 12. I also have a non-linear speed (i.e. starting out at 3 mph and slowing to 2 mph by mid afternoon).


Littlerock, I really enjoy math/thought experiments like these. Thanks for the thread
Having played with these ideas in the past, although not seriously, I have a couple of questions:
- Why not have the difficulty rating be converted to an intuitively meaningful number like expected hours on the trail or "flat terrain distance equivalence" since that is essentially what you are working toward with distance * (elevation change correction factor).
- I suspect a non-linear elevation gain correction factor might be significant, at least if things get very steep on the routes being budgeted.
- Most hiking "budget" calculations ignore negative grades or use negative grades as an advantage instead of disadvantage as in yours. I suspect slight negative grades would be an advantage whereas steep negative grades would be a disadvantage. Again a non-linear attribute?

On one other point raised in the thread:
I really like the idea of guide books publishing a effort rating for various sections of trail between common identifiable land marks. What an awesome planning tool that would be for someone new to the area.
It could be essentially distance equivalence correction factor based on known grade and a subjective tread factor.

The elevation correction factor is simple enough - you can just set AVG_GRADE and NET_ELEV_FT to zero and divide. The current formula gives a score of 100 to a 20 mile hike on completely flat ground.

The formula could definitely be tweaked with non-linear elevation factors (maybe using Naismith's rule). I haven't done this, but I suspect other's could play with Odd Man Out's spreadsheet and come up with something.

I agree that it would be nice to see some type of difficulty rating in guide books - but the reason they probably don't is because as you say, it would be entirely subjective.


We are leaving to do the Whites in 2 weeks and have researched and planned extensively and have come up with a schedule with a much lower amount of daily miles than we usually do. In this day and time with the amount of information from guides and sites like these there really isn't any reason you can't plan a trip and know pretty much where you are going to be each day before you start.

Sounds like we're on the same 20-year plan (you're just about 5 years ahead of me). Hope you have a great time in the Whites!

I just do this stuff while bored at my desk job and wishing I were on the trail - thought some folks might find this useful. If not, HYOH!

[saltysack]

Not to hijack the thread....how did your daily miles vary from southern AT verses the Sierras....mainly JMT????


Sent from my iPhone using Tapatalk

[tdoczi]

Yes. Maybe next I should come up with an AT Sudoku puzzle. :-)



After running the numbers and comparing it with personal experience, I decided to add that factor to emphasize that the hardest days were ones either with significantly more ups than downs, or with a big climb at the end. Other folks may not agree - in that case it's easy enough to drop the term from the formula.



i agree a big hike at the end is tough, but i dont think your formula acurately accounts for this in many situations.

for instance, i recently did a trip were i spent the night at horn's pond in maine. going sobo, the next day starts with a big drop, followed by a big gain, followed by a big drop. i ended my day there, BUT had i decided to do a few more miles, next up would have been a BIG climb that would have put me back to the elevation i started at. your formula would actually negate this and would possibly say my day was harder because i stopped at the bottom (giving me a net elevation change for the day) than if i had climbed the last couple miles back up to my starting elevation.

[colorado_rob]

Not to hijack the thread....how did your daily miles vary from southern AT verses the Sierras....mainly JMT????


Sent from my iPhone using TapatalkJust FWIW, having done both, the MPD efforts were pretty similar along the southern AT and the JMT. The JMT goes over a lot of high passes, one or two per day depending on your MPD, but the grade is easier, in general, than a lot of the AT. This assumes you are altitude acclimated, of course. Your first couple of days, especially coming from Florida, will be tougher. But the southern AT is certainly pretty trail-friendly as well, not many big climbs, just a lot of little ones. Really, pretty much a wash, maybe 1-2 MPD difference, but I couldn't say which way, it's that close IMHO.

I really like this math-applied-to-MPD stuff, and I use it myself. I maintain a spreadsheet with all the AT points along the way (about 1500 points of interest), that includes a MPD column that varies along the trail. I have it on my phone and when on the trail, I update it with my actual position every couple days or so and it refreshes where I'll be and when so I can tell my wife or other friends where to meet me, because their "when" is a fixed given time. Very useful tool.

[saltysack]

Just FWIW, having done both, the MPD efforts were pretty similar along the southern AT and the JMT. The JMT goes over a lot of high passes, one or two per day depending on your MPD, but the grade is easier, in general, than a lot of the AT. This assumes you are altitude acclimated, of course. Your first couple of days, especially coming from Florida, will be tougher. But the southern AT is certainly pretty trail-friendly as well, not many big climbs, just a lot of little ones. Really, pretty much a wash, maybe 1-2 MPD difference, but I couldn't say which way, it's that close IMHO.

I really like this math-applied-to-MPD stuff, and I use it myself. I maintain a spreadsheet with all the AT points along the way (about 1500 points of interest), that includes a MPD column that varies along the trail. I have it on my phone and when on the trail, I update it with my actual position every couple days or so and it refreshes where I'll be and when so I can tell my wife or other friends where to meet me, because their "when" is a fixed given time. Very useful tool.

Thx again CR
U confirmed what I've heard from a few others...trying to get mentally prepared...physically I'm ready except for altitude....JMT will be my longest hike as I'm a lowly weekend warrior....


Sent from my iPhone using Tapatalk

[tdoczi]

i agree a big hike at the end is tough, but i dont think your formula acurately accounts for this in many situations.

for instance, i recently did a trip were i spent the night at horn's pond in maine. going sobo, the next day starts with a big drop, followed by a big gain, followed by a big drop. i ended my day there, BUT had i decided to do a few more miles, next up would have been a BIG climb that would have put me back to the elevation i started at. your formula would actually negate this and would possibly say my day was harder because i stopped at the bottom (giving me a net elevation change for the day) than if i had climbed the last couple miles back up to my starting elevation.


boring day at work so i made a very rough example- lets say i hike 13 miles, 2000 feet up, 3000 feet down, ending my hike 1000 feet higher than i started. formula gives a difficulty rating of 75.6.

if i then continue 1 more mile that gains 1000 feet i then have 14 miles, 3000 feet up, 3000 feet down, net elevation of zero for a difficulty of 71.14

that makes no sense. the second hike is clearly the harder of the two, as it contains the first hike plus one more mile. this concept of "net elevation" , as implemented, wrecks the formula.

[tdoczi]

boring day at work so i made a very rough example- lets say i hike 13 miles, 2000 feet up, 3000 feet down, ending my hike 1000 feet higher than i started. formula gives a difficulty rating of 75.6.

if i then continue 1 more mile that gains 1000 feet i then have 14 miles, 3000 feet up, 3000 feet down, net elevation of zero for a difficulty of 71.14

that makes no sense. the second hike is clearly the harder of the two, as it contains the first hike plus one more mile. this concept of "net elevation" , as implemented, wrecks the formula.

should reading "ending my hike 1000 feet lower than i started"

[LittleRock]

i agree a big hike at the end is tough, but i dont think your formula acurately accounts for this in many situations.

for instance, i recently did a trip were i spent the night at horn's pond in maine. going sobo, the next day starts with a big drop, followed by a big gain, followed by a big drop. i ended my day there, BUT had i decided to do a few more miles, next up would have been a BIG climb that would have put me back to the elevation i started at. your formula would actually negate this and would possibly say my day was harder because i stopped at the bottom (giving me a net elevation change for the day) than if i had climbed the last couple miles back up to my starting elevation.

In that situation, stopping at the bottom would give you a negative net elevation, which would subtract from your daily score. If there are a lot of ups and downs, the average grade will probably be high and the net elevation will be small by comparison. Based on personal experience, many of the easiest days were coming into town which involved a drop in elevation at the end of the day. The prospect of sleeping in a bed and eating non-trail food also helps. :-)

[LittleRock]

boring day at work so i made a very rough example- lets say i hike 13 miles, 2000 feet up, 3000 feet down, ending my hike 1000 feet higher than i started. formula gives a difficulty rating of 75.6.

if i then continue 1 more mile that gains 1000 feet i then have 14 miles, 3000 feet up, 3000 feet down, net elevation of zero for a difficulty of 71.14

that makes no sense. the second hike is clearly the harder of the two, as it contains the first hike plus one more mile. this concept of "net elevation" , as implemented, wrecks the formula.

I got 150 for the first example and 184 for the second. Remember the average grade is in unit % (forgot to multiply AVG_GRADE by 100 in the formula in the original post).

First example: 13*(5+100*(2000+3000)/(13*5280) + (-1000/100) = 150 (rounded to nearest whole number)

Second example 14*(5+100*(3000+3000)/(14*5280) + 0 = 184

[tdoczi]

In that situation, stopping at the bottom would give you a negative net elevation, which would subtract from your daily score. If there are a lot of ups and downs, the average grade will probably be high and the net elevation will be small by comparison. Based on personal experience, many of the easiest days were coming into town which involved a drop in elevation at the end of the day. The prospect of sleeping in a bed and eating non-trail food also helps. :-)

im no mathematician and could be wrong, but wouldn't the correct term then be "net elevation gain" which could at times be negative?

now though i also have to wonder if your formula might not make a steep downhill hike seem easier than it is. going down say mahoosuc arm comes to mind. i'll let you do the math if you want, but how does a 1 mile hike thats all downhill for 1500 vertical feet compare to a 5 mile hike that slowly and steadily gains 1500 feet?? that one mile is way harder. (and no im not claiming those are the particulars of mahoosuc arm, just making up hypothetical examples of something LIKE it to test the formula.)

[Malto]

I have not found these estimations of hiking difficulty to be at all accurate especially as I have increased my hiking fitness over the years. I suspect you will find that as fitness increases the impact from elevation gain/loss is less important and the average speed will be more consistent between incline, decline and flat.

[tdoczi]

I have not found these estimations of hiking difficulty to be at all accurate especially as I have increased my hiking fitness over the years. I suspect you will find that as fitness increases the impact from elevation gain/loss is less important and the average speed will be more consistent between incline, decline and flat.

just based on observations of a lot of thrus and other very experienced and conditioned hikers id mostly agree.

me though? while i improve (and backslide) i've always gone much slower in western ME than in SNP. like nearly half speed.

[Another Kevin]

i agree a big hike at the end is tough, but i dont think your formula acurately accounts for this in many situations.

for instance, i recently did a trip were i spent the night at horn's pond in maine. going sobo, the next day starts with a big drop, followed by a big gain, followed by a big drop. i ended my day there, BUT had i decided to do a few more miles, next up would have been a BIG climb that would have put me back to the elevation i started at. your formula would actually negate this and would possibly say my day was harder because i stopped at the bottom (giving me a net elevation change for the day) than if i had climbed the last couple miles back up to my starting elevation.

The formula I proposed referred to GROSS elevation change. I'd count the big drop, the big gain, the big drop as three elevation changes.

I agree that a gentle downgrade might be easier than a flat trail. Where I go, I seldom encounter either. :)

[Odd Man Out]

...now though i also have to wonder if your formula might not make a steep downhill hike seem easier than it is. going down say mahoosuc arm comes to mind. i'll let you do the math if you want, but how does a 1 mile hike thats all downhill for 1500 vertical feet compare to a 5 mile hike that slowly and steadily gains 1500 feet?? that one mile is way harder. (and no im not claiming those are the particulars of mahoosuc arm, just making up hypothetical examples of something LIKE it to test the formula.)

I noticed that in that Naismith's Rule linke posted by AK, they treat steep downhills with a penalty (more time) but gentle downhills as a benefit (less time). This makes sense, but would be harder to program in a spreadsheet. You can calculate the average grade for a section (up and down separately) but you don't know if it is gradual or comes all at once.

[colorado_rob]

I noticed that in that Naismith's Rule linke posted by AK, they treat steep downhills with a penalty (more time) but gentle downhills as a benefit (less time). This makes sense, but would be harder to program in a spreadsheet. You can calculate the average grade for a section (up and down separately) but you don't know if it is gradual or comes all at once.Yeah, agree, definitely gradual downhills are the fastest, but steep downhills probably as slow as steep uphills.

One would have to make a table such as below (my numbers just notional), with the Slope rating like: +5 = steep uphill, 0 = level, -5 = steep downhill, and everything in between....

Slope
Rating ........ Speed
(+5 to -5) .... MPH

5 ............... 1.0
4 ............... 1.25
3 ............... 1.5
2 ............... 2.0
1 ............... 2.5
0 ............... 3.0
-1 ............... 3.5
-2 ............... 2.5
-3 ............... 2.0
-4 ............... 1.5
-5 ............... 1.0

Then, using a discretized trail profile of slope rating at many points along the trail (one could make such a thing easily, though time consuming), one could integrate over any particular section and come up with an elapsed time for that distance (or distance given a particular time).

Then an adjustment could be made for things like trail conditions, rest stops (I generally take none except to pee or fill water, enjoy a view, take a picture, whatever; I even eat while walking generally) or whatever.

[LittleRock]

I have not found these estimations of hiking difficulty to be at all accurate especially as I have increased my hiking fitness over the years. I suspect you will find that as fitness increases the impact from elevation gain/loss is less important and the average speed will be more consistent between incline, decline and flat.

True - but I'd argue that they can be helpful for people (like myself) who live in the Flat Lands and only make it out to hike in the mountains once or twice a year.


I noticed that in that Naismith's Rule linke posted by AK, they treat steep downhills with a penalty (more time) but gentle downhills as a benefit (less time). This makes sense, but would be harder to program in a spreadsheet. You can calculate the average grade for a section (up and down separately) but you don't know if it is gradual or comes all at once.

Yes, you could do it that way, but you would need accurate information on trail elevation/grade at evenly spaced intervals. At least every 1/4 mile, maybe even every 0.1 mile. This information exists for popular trails like the AT, but I doubt it exists for most other trails. And unless the terrain is very steep and rugged, I doubt the results will be that much different than using just the average grade between waypoints.

[Another Kevin]

I have not found these estimations of hiking difficulty to be at all accurate especially as I have increased my hiking fitness over the years. I suspect you will find that as fitness increases the impact from elevation gain/loss is less important and the average speed will be more consistent between incline, decline and flat.

In that case, for your personal formula, use a smaller correction for elevation change. My 40-minute figure, and my penchant for short days, reflect the fact that, as a clueless weekender, I never manage to get out for long enough or often enough to actually get into hiking condition and find my "trail legs." Most hikers would use a smaller number, I suspect, but I know that I'm slow. On the other hand, if I'm going with someone that hasn't backpacked at all before, I'll bump the number to 60 minutes, because I really don't know how they'll handle the hills.

But you surely won't get good results eliminating the correction entirely, unless you're seriously arguing that you'd make the same miles in the Wildcats as you would in Maryland.

In any case, I'm comfortable with being a couple of hours off either way in a day's hiking. The formula is more to get the idea, "is this section a day, or a half-day, or an overnight, or what?" not to make the trains run on time. I'll typically do something back-of-the-envelope like the following, which is an actual example of my thought process from one day of a section hike on the NY Long Path that I did last year.

Day 1:
The Sundown campsite is about 1200 feet.
The summit of Peekamoose is 3846, so that's a 2600 foot gain, and the book says it's 4.35 miles. Call that 2:10 for the mileage and add 1:40 for the elevation, so 3:50 to climb Peekamoose. Either the summit of Peekamoose or the overlook before it at the 3500 foot level might make a nice lunch stop.
Then the ridge over to Table Mountain is 0.85 miles, with about 400 feet of elevation lost and regained (800 feet elevation change). 25 minutes for the mileage and 35 for the elevation is about another hour, so I should hit the Table Mountain summit about 4:50 into the trip.
Boulton shelter is another 0.4 and down about 400 feet, that's another half hour. That'll be 5:20, so I most likely won't be ready to stop for the night when I hit Boulton. I might want to tank up at the spring there.
Coming down the north side of Table Mountain, the descent is interrupted by a couple little knolls, but none of them is much more than 100 feet of elevation regained, so I'll guesstimate 350 feet in addition to the 1650 foot descent. That's 1.95 miles and 2000 feet of elevation change. Round it up to 2 miles, so that's 1 hour for the mileage and 1:20 for elevation, 2:20. That puts me 7:10 into the trip. And the trail guide warns that there are some hands-to-the-rock scrambles on the descent, so allow a cushion of time. Yeah, I'll be ready to stop at the Neversink River campsites. Or if I'm feeling strong, I'll go another 2.2 miles of mostly-level walk to the Curtis-Ormsbee campsite. So this will either be a 7.2 or 9.4 mile day, which feels short, but starting the day off with a 2600 foot climb is pretty brutal.

Day 2:
From Neversink River elevation to the summit of Slide Mountain is just about 2000 feet of elevation gained steadily over 4.5 miles. 2:15 for mileage, 1:20 for elevation for 3:35 total.
Slide Mountain down to the Garden Path is another 0.95 with a loss of 800 feet. Half an hour for mileage, half an hour for elevation The guidebook warns of ladders and Class 3-4 scrambles, so add 20 minutes for difficult terrain. 1:20 for a total of 4:55 so far. No need to stop on the Garden Path campsites, most likely.
From the col to the summit of Cornell Mountain is 1.2 miles and regains about 500 feet. 40 minutes for mileage, 20 for elevation, call it an hour. 5:55.
Cornell Mountain has a 300 foot drop onto Bruin's Causeway with a difficult scramble at the Cornell Crack. Then Wittenberg is another 250 feet up, 0.8 miles. 25 minutes for mileage, 20 minutes for elevation, 15 minutes for rock climbing, call it another hour. 6:55.
Down off Wittenberg to the Terrace Mountain junction is another 1.2, with 1000 feet elevation loss. 1:10 for mileage 0.40 for elevation 8:45.
Then another half mile of level walking gets me to the Cross Mountain campsite, so 9 hours of hiking for the day. The end of the day looks like three solid hours of hiking above the 3500 foot level, where it's not lawful to camp. And with all the rock scrambling, it looks as if 10.6 miles is a strenuous day. It's a bit better if I can cut 2.2 off it by making Curtiss-Ormsbee the night before. That makes the two days 9.4 and 8.4, a little bit better balanced, and puts the hard scrambles on the shorter day.

One point here is that because I'm in "clueless weekender" shape, I have to adjust planned mileages for the strenuous trail. The first day, the planned stop is just 7.2 miles, but it's tough hiking, at least by my standards. The second day is really pushing it for me, despite being "just" 10.6 miles, given the amount of scrambling. The fact that each day has over a mile of elevation change makes for short mileage. The 10.6 is probably more work than 15 miles on level trail would be.

For what it's worth, on the actual trip I stealth-camped (lawfully!) both nights rather than using the indicated shelters and campsites, but made close to the planned mileages.

[Violent Green]

Interesting. I don't use too complex of a formula really, I just know from experience that I will average very close to 2.5MPH up to about 30 miles per day whether it be on the AT, JMT, Colorado Trail, etc. Then just do basic math to determine how many days needed to cover whatever distance I'm shooting for. If for some reason I get behind the pace is increased or the amount of time hiked increases.

Ryan