Steepness of traditional routes

Steepness of traditional routes

Joined: January 26th, 2004, 5:02 pm

June 10th, 2005, 4:22 pm #1

I used my spreadsheet of highpoints, as documented in http://americasroof.com/usa.shtml to determine which HPs have the steepest traditional routes. Here is the list, from steepest to least steep. It used the rise over run formula from algebra:

vertical climb / (RT mileage * 5280)

I had suspected that Idaho was steepest, but I was surprised at how far down the list Wyoming placed. This of course includes the approach hikes, which Granite, Gannett and Kings all have. It is also interesting how 'easy' HPs such as Mt Mitchell & Brasstown Bald rated so high.


Idaho 0.155
Oregon 0.125
Nevada 0.113
Hawaii 0.109
Washington 0.108
Colorado 0.105
Alaska 0.101
New Mexico 0.099
North Carolina 0.095
Maine 0.076
Georgia 0.076
Arizona 0.074
Texas 0.067
Montana 0.066
Maryland 0.065
Tennessee 0.063
Wisconsin 0.062
California 0.060
South Dakota 0.049
Arkansas 0.043
New York 0.041
Wyoming 0.041
New Hampshire 0.038
North Dakota 0.038
Massachusetts 0.038
New Jersey 0.038
Indiana 0.038
Vermont 0.037
Illinois 0.036
Utah 0.035
Virginia 0.033
South Carolina 0.028
Michigan 0.028
Connecticut 0.024
Iowa 0.019
Oklahoma 0.017
Minnesota 0.016
Louisiana 0.016
Missouri 0.014
West Virginia 0.009
Rhode Island 0.008
Kentucky 0.000
Florida 0.000
Quote
Like
Share

Joined: January 20th, 2004, 9:11 pm

June 10th, 2005, 5:28 pm #2

According to your formula, you calculated the ratio of altitude gain to the ROUND TRIP [RT] distance. Usually a slope (i.e., steepness) is measured in terms of altitude increase against horizontal distance traversed. If you used RT distance, then the slope ratios would appear to be one-half of what they really are. The only time when a round-trip distance MIGHT come into consideration is when there is significant descent and subsequent climbout during the approach (traversing a valley, for example).

In addition, it seems to me that the true measure of steepness for climbing purposes is the total elevation gained during a climb, divided by the actual horizontal distance between the starting point and the summit. Trail distance is usually MUCH longer than horizontal displacement distance (switchbacks, stream following, etc.), especially on higher peaks, which would reduce the steepness ratio significantly. Using trail distance (one-way) would give you the average slope ratio per trail mile, but not the actual steepness ratio from a topographical perspective.

Others may have different ideas on how this should be calculated. Any thoughts? JES
Quote
Like
Share

Joined: January 20th, 2004, 6:42 pm

June 10th, 2005, 5:36 pm #3

I used my spreadsheet of highpoints, as documented in http://americasroof.com/usa.shtml to determine which HPs have the steepest traditional routes. Here is the list, from steepest to least steep. It used the rise over run formula from algebra:

vertical climb / (RT mileage * 5280)

I had suspected that Idaho was steepest, but I was surprised at how far down the list Wyoming placed. This of course includes the approach hikes, which Granite, Gannett and Kings all have. It is also interesting how 'easy' HPs such as Mt Mitchell & Brasstown Bald rated so high.


Idaho 0.155
Oregon 0.125
Nevada 0.113
Hawaii 0.109
Washington 0.108
Colorado 0.105
Alaska 0.101
New Mexico 0.099
North Carolina 0.095
Maine 0.076
Georgia 0.076
Arizona 0.074
Texas 0.067
Montana 0.066
Maryland 0.065
Tennessee 0.063
Wisconsin 0.062
California 0.060
South Dakota 0.049
Arkansas 0.043
New York 0.041
Wyoming 0.041
New Hampshire 0.038
North Dakota 0.038
Massachusetts 0.038
New Jersey 0.038
Indiana 0.038
Vermont 0.037
Illinois 0.036
Utah 0.035
Virginia 0.033
South Carolina 0.028
Michigan 0.028
Connecticut 0.024
Iowa 0.019
Oklahoma 0.017
Minnesota 0.016
Louisiana 0.016
Missouri 0.014
West Virginia 0.009
Rhode Island 0.008
Kentucky 0.000
Florida 0.000
I question the usefulness of a metric that rates New Jersey's High Point higher than Utah's Kings Peak.

I also question the horizontal distance used for Alaska's Mount McKinley and the elevation gain used for Wyoming's Gannett Peak. Does the horizontal distance for Mount McKinley include the double carries (as Roger has listed on the America's Roof Website)? Does the elevation gain for Gannett Peak incorporate the numerous ups and downs on the route from Pinedale via Upper Titcomb Lake?
Quote
Like
Share

Joined: January 26th, 2004, 5:02 pm

June 10th, 2005, 8:13 pm #4

According to your formula, you calculated the ratio of altitude gain to the ROUND TRIP [RT] distance. Usually a slope (i.e., steepness) is measured in terms of altitude increase against horizontal distance traversed. If you used RT distance, then the slope ratios would appear to be one-half of what they really are. The only time when a round-trip distance MIGHT come into consideration is when there is significant descent and subsequent climbout during the approach (traversing a valley, for example).

In addition, it seems to me that the true measure of steepness for climbing purposes is the total elevation gained during a climb, divided by the actual horizontal distance between the starting point and the summit. Trail distance is usually MUCH longer than horizontal displacement distance (switchbacks, stream following, etc.), especially on higher peaks, which would reduce the steepness ratio significantly. Using trail distance (one-way) would give you the average slope ratio per trail mile, but not the actual steepness ratio from a topographical perspective.

Others may have different ideas on how this should be calculated. Any thoughts? JES
Yes, I goofed and the numbers are too large by a factor of 2.

As for the difference between trail miles and 'as the crow flies' issue, I see your point. However the starting elevation and distances are from a trailhead that might be partly up the mountain or many miles from it. I don't think that any number calculated from the straight-line distance from the trailhead to the summit would be overly useful. But the steepness of the hike itself CAN be calculated and to some extent IS useful.

Quote
Like
Share

Joined: January 26th, 2004, 5:02 pm

June 10th, 2005, 8:34 pm #5

I question the usefulness of a metric that rates New Jersey's High Point higher than Utah's Kings Peak.

I also question the horizontal distance used for Alaska's Mount McKinley and the elevation gain used for Wyoming's Gannett Peak. Does the horizontal distance for Mount McKinley include the double carries (as Roger has listed on the America's Roof Website)? Does the elevation gain for Gannett Peak incorporate the numerous ups and downs on the route from Pinedale via Upper Titcomb Lake?
It does not rate NJ HIGHER than UT, it rates NJ STEEPER than UT. And if you recall the steep walk from the parking lot to the tower, you will remember that it is indeed steep, whereas the average steepness of the traditional route up Kings is less. The other near-drive-up that I've done and that is high on the list is NC. I do recall that the walk from the parking lot was steep, but very short.

Yes, the elevation change does account for the various ups and downs that are required up Gannett and it does account for the multiple carries up Denali. Those numbers are reflected (once) in the chart and so they are reflected in my calculations. I say once, because if you have a theoretical 300 ft descent and 300ft climb on the way to a HP that is level with the parking lot, the elevation listed in the chart would be 300 ft. And that hill has some amount of steepness and such a 'climb' would have some distance. If only we could drive to the summit of Mt Frizzle, we could have a negative slope.

So is it useful? I don't know. Maybe not, but I certainly find it interesting and thought others might like to see it. It may be useful in comparing somewhat similar climbs, such as ID vs NV or NM vs AZ or even (if you cared) NJ vs NC. But I don't think it has any meaning or relevance in terms of comparing disparate summits such as TX vs NC.

Again, the numbers are too high by a factor of 2, since I mistakenly used round trip numbers.

Jack

Quote
Like
Share

Joined: January 21st, 2004, 3:15 pm

June 10th, 2005, 8:38 pm #6

Very interesting table!

Does this steepness grading provide for variations? While NJ is steeper from start to stop, there are long stretches of UT that are much steeper than NJ. There are long flat stretches in UT too. Perhaps we need a deviation calculation to recognize variation.
Quote
Like
Share

Joined: August 2nd, 2001, 8:13 pm

June 10th, 2005, 8:39 pm #7

I used my spreadsheet of highpoints, as documented in http://americasroof.com/usa.shtml to determine which HPs have the steepest traditional routes. Here is the list, from steepest to least steep. It used the rise over run formula from algebra:

vertical climb / (RT mileage * 5280)

I had suspected that Idaho was steepest, but I was surprised at how far down the list Wyoming placed. This of course includes the approach hikes, which Granite, Gannett and Kings all have. It is also interesting how 'easy' HPs such as Mt Mitchell & Brasstown Bald rated so high.


Idaho 0.155
Oregon 0.125
Nevada 0.113
Hawaii 0.109
Washington 0.108
Colorado 0.105
Alaska 0.101
New Mexico 0.099
North Carolina 0.095
Maine 0.076
Georgia 0.076
Arizona 0.074
Texas 0.067
Montana 0.066
Maryland 0.065
Tennessee 0.063
Wisconsin 0.062
California 0.060
South Dakota 0.049
Arkansas 0.043
New York 0.041
Wyoming 0.041
New Hampshire 0.038
North Dakota 0.038
Massachusetts 0.038
New Jersey 0.038
Indiana 0.038
Vermont 0.037
Illinois 0.036
Utah 0.035
Virginia 0.033
South Carolina 0.028
Michigan 0.028
Connecticut 0.024
Iowa 0.019
Oklahoma 0.017
Minnesota 0.016
Louisiana 0.016
Missouri 0.014
West Virginia 0.009
Rhode Island 0.008
Kentucky 0.000
Florida 0.000
First, using the round-trip distance made the estimates 2x too low, not high.

That said, a more useful measure might be the "instantaneous" (peak?) steepness, not average. Things like Gannett and Kings that have 15-25 mile approaches, will be quite underestimated in comparison to Hood and Rainier where you drive to the base of the peak and start climbing immediately.

Not that it's a trivial thing to figure, but how about the "steepest mile" of the approach and climb? That would change the ranking quite a bit, although Borah (ID) will still come in darned high!!

Now, I will grant that falling back on the good old Yosemite Decimal System also represents the instantaneous steepness/difficulty, so this may become another of the classic highpointers' debates that goes on and on and on...

The YDS, by the way, goes something like:

Class 1: Hands in pockets, on-trail hiking or walking through a meadow.
Class 2: Boulder hopping, off-trail hiking, use of hands (occasionally) for balance but NOT for upward motion. Also, snow less than 45 degrees.
Class 3: Climbing with hands and feet, steep but not vertical, most climbers do not use a belay. Also, snow greater than 45 degrees.
Class 4: Near-vertical rock but ample holds. Most climbers do use a belay.
Class 5: Vertical rock, varying levels of missing/difficult holds. Subclasses 5.0 to 5.14 vary from easy to basically plate glass to the uninitiated.

By whatever standards, I concur that Borah is the steepest son-of-a-gun short of "real" climbing of the 40 I've done. (Including Wheeler [NM], Whitney [CA] and Katahdin [ME])
Quote
Like
Share

Joined: January 20th, 2004, 7:34 pm

June 10th, 2005, 10:29 pm #8

I used my spreadsheet of highpoints, as documented in http://americasroof.com/usa.shtml to determine which HPs have the steepest traditional routes. Here is the list, from steepest to least steep. It used the rise over run formula from algebra:

vertical climb / (RT mileage * 5280)

I had suspected that Idaho was steepest, but I was surprised at how far down the list Wyoming placed. This of course includes the approach hikes, which Granite, Gannett and Kings all have. It is also interesting how 'easy' HPs such as Mt Mitchell & Brasstown Bald rated so high.


Idaho 0.155
Oregon 0.125
Nevada 0.113
Hawaii 0.109
Washington 0.108
Colorado 0.105
Alaska 0.101
New Mexico 0.099
North Carolina 0.095
Maine 0.076
Georgia 0.076
Arizona 0.074
Texas 0.067
Montana 0.066
Maryland 0.065
Tennessee 0.063
Wisconsin 0.062
California 0.060
South Dakota 0.049
Arkansas 0.043
New York 0.041
Wyoming 0.041
New Hampshire 0.038
North Dakota 0.038
Massachusetts 0.038
New Jersey 0.038
Indiana 0.038
Vermont 0.037
Illinois 0.036
Utah 0.035
Virginia 0.033
South Carolina 0.028
Michigan 0.028
Connecticut 0.024
Iowa 0.019
Oklahoma 0.017
Minnesota 0.016
Louisiana 0.016
Missouri 0.014
West Virginia 0.009
Rhode Island 0.008
Kentucky 0.000
Florida 0.000
There is the story of the person who drowned while crossing a stream of average depth of a few inches

I believe that this is one area where averages are of minimal or zero utility. I suspect that the only really useful measures here are those based on human judgement.

Average steepness, as many have pointed out, may be totally dominated by a long gentle approach, completely masking a brutally steep climb.

Peak instantaneous steepness suffers from the opposite defect, a trail that is by and large gentle may have a short steep section, but is still, all things considered, a gentle trail.

Total elevation gain measures a different concept, totally unrelated to steepness.

YDS does not distinguish between a brutally steep by hikeable trail and a totally flat one; both are Class 1.

But get a group of experienced hikers together, produce some beer, and ask them what are the steepest trails in their region. You will get a surprising degree of agreement.

Can an algorithm mimic their thought process? Probably, but I for one have not yet been able to figure it out

I have discussed the issue of the "difficulty" of a trip in the difficulty FAQ on my web site.
Quote
Like
Share

Joined: January 23rd, 2004, 4:14 pm

June 10th, 2005, 11:21 pm #9

I used my spreadsheet of highpoints, as documented in http://americasroof.com/usa.shtml to determine which HPs have the steepest traditional routes. Here is the list, from steepest to least steep. It used the rise over run formula from algebra:

vertical climb / (RT mileage * 5280)

I had suspected that Idaho was steepest, but I was surprised at how far down the list Wyoming placed. This of course includes the approach hikes, which Granite, Gannett and Kings all have. It is also interesting how 'easy' HPs such as Mt Mitchell & Brasstown Bald rated so high.


Idaho 0.155
Oregon 0.125
Nevada 0.113
Hawaii 0.109
Washington 0.108
Colorado 0.105
Alaska 0.101
New Mexico 0.099
North Carolina 0.095
Maine 0.076
Georgia 0.076
Arizona 0.074
Texas 0.067
Montana 0.066
Maryland 0.065
Tennessee 0.063
Wisconsin 0.062
California 0.060
South Dakota 0.049
Arkansas 0.043
New York 0.041
Wyoming 0.041
New Hampshire 0.038
North Dakota 0.038
Massachusetts 0.038
New Jersey 0.038
Indiana 0.038
Vermont 0.037
Illinois 0.036
Utah 0.035
Virginia 0.033
South Carolina 0.028
Michigan 0.028
Connecticut 0.024
Iowa 0.019
Oklahoma 0.017
Minnesota 0.016
Louisiana 0.016
Missouri 0.014
West Virginia 0.009
Rhode Island 0.008
Kentucky 0.000
Florida 0.000
These numbers seem to suggest that peaks like Gannett and Kings with long approaches are nice gradual strolls to the summit. Using Wyoming for example, taking away the approach to Titcomb Basin, you're left with 4 miles and about 4,600 feet from Upper Titcomb Lake to the summit of Gannett. Numbers are from National Geographic Topo!

4600 / (4 * 5280) = .218

We climbed a shorter/steeper route than the standard Gooseneck route, so using numbers from Topo! our ascent route was:

4600 / (3.5 * 5280) = .249

Keep in mind you still have to climb Bonney Pass on your return trip, so depending on how far you drop down the Gooseneck Glacier, you're looking at between 1,500 to 2,000 feet of climbing on your return to camp.

2,000 / (4 * 5,280) = .095

Using the northern approach for Gannett, assuming a high camp in Floyd Wilson Meadow at 10,000 feet, you're looking at:

3,800 / (3.5 * 5,280) = .206

Paints a much different picture and gives a better picture of the actual climbing.

Same applies for Utah, anybody have National Geographic Topo! for Utah and care to do the calculations from a high camp around Dollar Lake? The route from Anderson Pass to the summit Kings gains alot of elevation in a very short distance.

I agree that Borah is indeed steep, but it is still just a dayhike. It would be nice to have a metric to measure the overall effort of a peak. I guess calories burned would be pretty accurate and reflective of the overall effort. I should have wore my heart rate monitor on all these high points, would be interesting to compare the peaks in those terms.
Quote
Like
Share

Joined: January 26th, 2004, 5:02 pm

June 13th, 2005, 8:00 pm #10

I agree that calories burned might be a useful measure of difficulty. But from a practical matter, how would one go about measuring that? And wouldn't it vary from person to person and not by the same amount on each summit?

Even a heart-rate monitor would only tell you max and maybe avg heart rate. What would that say? It would totally depend on the speed of your ascent, fitness, cardiac health, etc.

As for steepness of the actual mountain, if someone would choose to identify the elevation and distance to the 'begining of the climb', such as Dollar Lake, then I would be glad to add them to my spreadsheet and recalculate. Maybe a more accurate measurement of Denali could be made, to take into account only a single pass of the route. I suppose that the candidates for reanalysis are, AK, CA, WY, MT, UT, and possibly TX, NM, SD, ME.

Yes, this would still only account for an average (mean) slope, which COULD be misleading if a long trail had a short steep section.

It was calculated for training purposes. I want to train on trails at least as steep as the mean slope of the summit I intend to climb (NV).

Quote
Like
Share