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TwoSpirits
07-31-2017, 10:22
Okay, so I'm somewhat embarrassed to have to ask this, but junior high geometry WAS 40 years ago....

On Guthook's AT app, I'm really finding their route building tool very useful. For any A to B point, it will tell you the distance in miles, the total ascent and descent in feet, and then something called "Total Grade", expressed in feet/mile. For example, a route that covers 11.8 miles, the total grade is shown to be "416.3'/mile".

I know a mile is 5280'. I know that slopes can be measured in % as well as degrees...which is how I can best understand the difficulty of a climb (i.e., a climb of 45° is going to be harder than a climb of 30°).

Can someone help me put this expression for "Total Grade" into a context my pathetic brain can comprehend?

(Oddly enough, it seems I ALWAYS paid attention in that class that covered USELESS, POINTLESS TRIVIA. And the one about Movie Quotes.)

Thanks.

SawnieRobertson
07-31-2017, 11:04
Thanks for this information about climbs. I doubt that was ever mentioned in my geometry class. One reason might have been that I grew up in such flat terrain that, when I went on to college at Austin, I thought the hills were mountains. Learned when I referred to them as mountains in front of friends from the Hill Country.

Venchka
07-31-2017, 11:04
Not sure why Total isn't Average.
Distance X Total Grade = Total Elevation Gain.
I think.
Wayne


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Deadeye
07-31-2017, 11:24
If you want to skip the math, 1,000 feet of elevation change per mile is PDS (pretty darn steep). That's the line, for me at least, where hiking turns into a sweaty, heavy breathing climbing exercise, or a hairy descent, with some hand work to pull yourself up, and some butt-slides on the way down.

HooKooDooKu
07-31-2017, 11:24
Grades are usually expressed as a percentage, which would be the climb in feet divided by 5280'.
So a 416.3'/mile would be a 7.88% grade.

As a point of comparison, a 45º slope would be a grade of 100% and a 30º would be a grade of 50%.
I think the reason grades usually are not expressed in degrees is because when you start getting down to reasonable grades, the numbers get to be pretty darn small.
As another example, a 25% grade is considered pretty darn steep. But that's only 14.5º.
You 7.88% grade would be a 4.5º.

BTW, the math is to take the grade and do an Inverse Sine function against it (where 7.88% = 0.0788).
Inv Sin( 0.0788 ) = 4.5º

TwoSpirits
07-31-2017, 11:34
Thank you for these answers!

Venchka
07-31-2017, 12:02
Out west, in the enlightened trail culture, switchbacks are used to moderate grade.
Wayne


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LittleRock
07-31-2017, 12:17
BTW, the math is to take the grade and do an Inverse Sine function against it (where 7.88% = 0.0788).
Inv Sin( 0.0788 ) = 4.5º
This is incorrect.

The correct functions are the tangent function for converting from degrees to grade, and the arctangent function for converting from grade to degrees.

Most calculators and computer programs also have a default unit of radians, so you'll need to perform the proper conversion of 1 radian = 180/pi ~ 57.3 degrees, or 1 degree = pi/180 ~ 0.175 radians.

So if G is your grade in percent, and D is the slope in degrees, then:
G = 100*tan(D*0.175), and
D = 57.3*arctan(G/100)

Slo-go'en
07-31-2017, 12:24
Out west, in the enlightened trail culture, switchbacks are used to moderate grade.
Wayne
In the East, we want to get to the top of the mountain with the shortest path as possible, without all that extra back and forth.

I did a 1700 foot climb in 1.3 miles to an outlook the other day. That's a 25% grade. It really didn't seem that steep, but it was a steady and relentless slope.

HooKooDooKu
07-31-2017, 14:35
This is incorrect.
The correct functions are the tangent function for converting from degrees to grade, and the arctangent function for converting from grade to degrees.
Most calculators and computer programs also have a default unit of radians, so you'll need to perform the proper conversion of 1 radian = 180/pi ~ 57.3 degrees, or 1 degree = pi/180 ~ 0.175 radians.
So if G is your grade in percent, and D is the slope in degrees, then:
G = 100*tan(D*0.175), and
D = 57.3*arctan(G/100)

Technically correct.

True slope is a measurement of 'Rise' / 'Run', where 'Rise' is the elevation change, and 'Run' is the horizontal displacement.

But often we don't have a measurement for 'Run' in these situations. What we usually have is the rise and distance traveled, where distance traveled is call 'Slope Length'. Since that measurement is technically the length of the hypotenuse, you have to use Pythagoras's theorem to calculate the 'Run'.

If you calculate the Slope from the true 'Rise' and 'Run', then yes, you should use the Inverse Tangent function to calculate angle.

But if you use the 'Slope Length' to calculate the Slope (something things like railroads do because there is a negligible difference for the low grades most railroads use), then the correct calculation for the angle is Inverse Sine.


It boils down to Tangent and Sine are nearly the same at low angles, and therefore it doesn't mater which way to do it. Here's a practical example:
You drive a mountain road for a distance of 10 miles (based on the odometer) and a Topo map shows the elevation gain was 4,000'

TRUE SLOPE:
Rise = 4,000'
Slope Length = 52,800'
Run = SqrRt( 52,800 * 52,800 - 4,000 * 4,000 ) = 52,648.3
Slope = 4,000' / 52,648.3' = 0.0759759 = 7.59759% ... which rounds to about 7.60%
Arc Tan( Slope ) = 4.34475º

Estimated Slope
Slope = 4,000' / 52,800' = 0.0757576 = 7.57576% ... which rounds to about 7.58%
Arc Sin( Slope ) = 4.34475º

tdoczi
07-31-2017, 14:46
In the East, we want to get to the top of the mountain with the shortest path as possible, without all that extra back and forth. .

sadly thats only in the NORTH east.

my limited experience out west combined with my second hand impressions is that their motif is often more "why go all the way to the top of the mountain when we can just get most of the way up and then sort of shimmy around it?"

i suppose that might be enlightened? i dont know.

Another Kevin
07-31-2017, 14:56
In the East, we want to get to the top of the mountain with the shortest path as possible, without all that extra back and forth.

I did a 1700 foot climb in 1.3 miles to an outlook the other day. That's a 25% grade. It really didn't seem that steep, but it was a steady and relentless slope.

I think that's because we suffer from altitude envy. Our high peaks are the 4000-ers, not the 14000-ers. So we overcompensate by having our trails charge straight up the fall line.

Yeah, it's more fun that way.

(Or it was until I had a year and a half of hardly being able to hike. Now I'm sucking wind on a 1900-foot elevation gain on three miles of abandoned jeep trail, no scrambling. Working on it, but it's painfully slow getting back.)

blw2
07-31-2017, 16:37
getting back to the question
"Total Grade", expressed in feet/mile. For example, a route that covers 11.8 miles, the total grade is shown to be "416.3'/mile".
Correct me if I'm wrong....but i think that over your total 11.8 mile route
they look at all the little climbs
maybe a 50 ft climb, then later a 200 ft climb, then a 25 ft climb... then later a 412 ft climb.... etc....
so adding up all those little climbs over the entire route, you get 4,912.34 feet of total climb
then divide that by the 11.8 miles traveled to get an average 416.3 ft of climb per mile

Venchka
07-31-2017, 17:02
Way too much information Peeps.
El Capitan is roughly 3,000' high. The grade is approximately 100%. You don't need a slide rule (still have yours?) to know that El Capitan is essentially vertical or occasionally overhanging. The new record is slightly less than 4 hours. "Without a net"
K.I.S.S.
Wayne



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lonehiker
07-31-2017, 17:20
sadly thats only in the NORTH east.

my limited experience out west combined with my second hand impressions is that their motif is often more "why go all the way to the top of the mountain when we can just get most of the way up and then sort of shimmy around it?"

i suppose that might be enlightened? i dont know.

It is more a function of horse travel.

Venchka
07-31-2017, 17:29
Let common sense prevail. The following is a description of a portion of Segment 7 of the Colorado Trail. No math required.
"Segment 7 (2014): I met Devin, with whom I was also destined to spend a lot of time hiking with, coming out of Breckenridge and we climbed 3600 feet in six miles to the top of the Tenmile Range on our way to Copper Mountain." RawahRanger.
Wayne


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rocketsocks
07-31-2017, 20:11
___ F ___
G X L

Grade devided by Fall equals Length
Grade times Length equals Fall
Fall devided by Length equals Grade

Good
F***ing
Luck

is the way I set up the problem, my teacher had a bit of a sense of humor

TwoSpirits
07-31-2017, 20:28
So at the end of the day, I'm getting that the "Total Grade" as stated in my particular route is essentially meaningless to me?

MtDoraDave
07-31-2017, 21:08
Sounds like it. The average listed like that doesn't really tell you how steep or long the individual climbs will be.
As was said earlier, 1000' climb in one mile (Jacob's ladder) is going to be one that gets your attention. It's steep AND long enough to be challenging for most.

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Venchka
08-01-2017, 07:27
I find that the profile view and elevations on the left scale tells me what's coming better than the numbers across the top banner.
Wayne

rocketsocks
08-01-2017, 08:09
So at the end of the day, I'm getting that the "Total Grade" as stated in my particular route is essentially meaningless to me?not necessarily, only if it matters to you. You'd likely hike it anyway...so.

TwoSpirits
08-01-2017, 08:31
True. Until I see a section that indicates that climb/descent is in the 1000'/mile category...then I'll just cry.

And probably hike it anyway.

atraildreamer
08-01-2017, 09:29
Any more questions?

39998

English Stu
08-01-2017, 09:55
I see by the answers why on the other side of the pond we do gradients 1:3 etc
1 in 1 represents traveling the length of a hypotenuse created by vertical and horizontal distances of 1 unit of measure. Thus, 1(vertical) in 1(horizontal) is a 45% incline, and flippin' hard work on a push bike!

I do hope I am right.

rocketsocks
08-01-2017, 09:59
True. Until I see a section that indicates that climb/descent is in the 1000'/mile category...then I'll just cry.

And probably hike it anyway....and that's basically what I'd use it for as well. To determine/remind me that which is no longer fun for me, and to look else where.

gpburdelljr
08-01-2017, 13:09
It doesn't really matter if you express a grade as 416.3 feet per mile, 7.88%, or 4.63° until you have hiked it and decided it was easy, moderate, or strenuous. The app gives grade as feet per mile, and after awhile you will have a feel for how difficult a given amount of feet rise per mile is for you, with no need to do any math. Why make things complicated?

George
08-01-2017, 17:30
i think that over your total 11.8 mile route
they look at all the little climbs
maybe a 50 ft climb, then later a 200 ft climb, then a 25 ft climb... then later a 412 ft climb.... etc....
so adding up all those little climbs over the entire route, you get 4,912.34 feet of total climb
then divide that by the 11.8 miles traveled to get an average 416.3 ft of climb per mile

So at the end of the day, I'm getting that the "Total Grade" as stated in my particular route is essentially meaningless to me?

it is not meaningless - but it is also not extremely useful

ie: for most hikers, a series of short ups and downs of moderate incline is less fatiguing than a long steep grade up then down, followed by flat (but both could show the same "total grade" )


I once set up in my mind, while walking, a comprehensive system of rating trail sections in "units of effort" including adjustments for temp/ season etc -- a person could quickly determine how many units of effort they preferred each day and planning would be a bit simpler

something I may work on in retirement