Measuring the how steep a slope is.

[RGF1]

I recently had a interesting conversation with another hiker about how steep a slope is. We came to the conclusion that a slope appears steeper than it really is while you are climbing it. . While having this conversation we were at crag camp and tried to figure out how step the head wall of King Ravine is in particular the trail. Not being math geniuses and long forgotten any thing remotely close to trigonometry.
Can some one explain how to measure the angle of a slope in terms a non-mathematically inclined person can understand?
FWIW We thought the average angle of King ravine was about 50 degrees. But that is probably wrong. Although it sure is steep when climbing it in the summer or early fall. .

 

[jfb]

Can some one explain how to measure the angle of a slope in terms a non-mathematically inclined person can understand?

If you're viewing the slope from the side, hold your thumb of one hand horizontal then rotate your index finger to match the angle of the slope. Then look at your compass and estimate the angle between your thumb and finger.

 

[Tom Rankin]

I recently had a interesting conversation with another hiker about how steep a slope is. We came to the conclusion that a slope appears steeper than it really is while you are climbing it. . While having this conversation we were at crag camp and tried to figure out how step the head wall of King Ravine is in particular the trail. Not being math geniuses and long forgotten any thing remotely close to trigonometry.
Can some one explain how to measure the angle of a slope in terms a non-mathematically inclined person can understand?
FWIW We thought the average angle of King ravine was about 50 degrees. But that is probably wrong. Although it sure is steep when climbing it in the summer or early fall. .

You need to know 2 things, often called 'run' and 'rise'. Run is the distance on a map, measured horizontally. Rise is the elevation gain over that run. If the 2 are equal, you have a 45 degree angle. If rise/run is .5, it's 27 degrees. If it's 1/3, it's about 18 degrees. For your 50 degree example, the ratio would be 1.2.

Non-math people can stop here!

To be more precise, The mathematical formula is:

Angle = Inv(tan(rise/run))

Which means, divide the 2 numbers, and find the angle whose tangent is that ratio. Some calculators have an 'inv' button, that you push before you push the 'tan' button.

 

[Puck]

to keep it simple....convert everyting into one unit. lets say you will go one mile as the crow flies with and elevation gain 2000'.Height is 2000divided by distance 5280 =.378 and take tangent ^-1 (it should be the shift- tan botton on your calculator) = 21 degrees.

H/D=Tan theta.

 

[DougPaul]

You need to know 2 things, often called 'run' and 'rise'. Run is the distance on a map, measured horizontally. Rise is the elevation gain over that run.

If you are trying to estimate the angle of a slope that you are standing on, you can use ski/trekking poles to estimate the rise and run.

grade=rise/run (frequently expressed as a percentage)
As Tom noted: angle=arctan(grade)

Some high end compasses (eg Silva Ranger) have an inclinometer needle built in.

If you can estimate vertical (line up with 90 deg) or horizontal (line up with 0 deg), you can just hold a baseplate compass up and read the angle off its scale. If it is not too windy, you can estimate vertical with a weighted string.

There are protracter (angle measuring) cards for snow slope angle estimation for avalanche hazard prediction.

All of these methods require you to be standing on a slope or can see a profile of it. Looking straight on to a slope causes foreshortening which tends to make it look steeper than it really is.

You can also estimate the rise and run from a topo (make sure you convert both distances into the same units (eg feet) before applying the formula). This, of course, gives an average slope over a region whose minimum size depends upon the resolution of the map. Some computer topo map systems will measure the slope for you.

From a digital topo:
Great Gulley Trail: steepest spot 41 deg, average 24 deg.
Steepest area I could find in King Ravine (below and just S of Craig Camp): 50 deg.

Having been in King Ravine, I'm sure there are steeper spots.

Doug

 

[Mark]

Help from Compass

Like DougPaul said, some compasses will allow you to measure a slope. I have a Buck Knives BUCO-4. It contains a small needle inside the compass that hangs straight down. If you sight along the edge of the compass, you can then view the hanging needle in the sighting mirror to read the slope in degrees. For a more accurate measurment, I guess you would want to take your measurement low to the ground.

You can estimate slope too. Your fist held out at arm's length is equal to approximately 10 degrees. Stand facing downslope and hold out your fist lining up the top with the horizon. The bottom of your fist will be a 10 degree descending slope. Count off the number of "fists" down to the actual path to get the approximate slope.

 

[kurcam]

http://www.planetfear.com/article_detail.asp?a_id=360

here is a quick and dirty measurement with ski poles. it is not meant to be used for slope angle accuracy, but is a tool to let skiers know when they are in avy terrain of 30-45+ degrees.

 

[nhski]

The seven gully (aka Great Gully Trail) in King Ravine has a maximum pitch of 50 degrees at the headwall. I measured it with an inclinometer. The gully starts at about 35 degrees and gets progressively steeper to the headwall.

 

[giggy]

Interesting thread - am I correct in saying the mt washington summit cone is about 25-30 degrees on average.

 

[DougPaul]

Interesting thread - am I correct in saying the mt washington summit cone is about 25-30 degrees on average.

Estimates from the digital topo:

The steepest section of the east face (on a line between the summit and a point just south of Lions Head): 32 deg.

Tuckerman RavineTr, between the junction with the Lions Head Tr and the summit has a fairly steady grade of about 20 deg.

Doug

 

[Stan]

It's after five so all math aside, it's amazing how steep slopes look from a distance ... even steeper when you're at the top of one and more so when you're at the bottom of one. Yet, a calculation of the actual angle when the rise and run are taken from a topo is surprisingly small. Don't try the calculation at home, it is after all, after five ... just think about it and estimate the specific heat of ice cubes instead.

 

[giggy]

20 - thats all - wow - though that would have been at least 25 - maybe even 30.

 

[imarchant]

You can estimate slope too. Your fist held out at arm's length is equal to approximately 10 degrees. Stand facing downslope and hold out your fist lining up the top with the horizon. The bottom of your fist will be a 10 degree descending slope. Count off the number of "fists" down to the actual path to get the approximate slope.

This is assuming the horizon is horizontal. This is not a good assumtion in a mountainous area. If you were on top of the highest peak in a region any point on the visible horizon would be at a down slope. The 10 degree fist measurement would be subtracted from the angle from actual horizontal to the visible horizon.

 

[John H Swanson]

Macomb Slide at the steepest point = 42degrees
measured by inclinometer (in compass)

 

[CatskillsYeti]

One of the reasons slopes look steeper, especially when looking straight on, is that the "run" part appears foreshortened, but the "rise" doesn't. And this can be accentuated if you're close to the slope in question.

But, for me, what really counts is how steep it FEELS!

 

[Pete_Hickey]

But, for me, what really counts is how steep it FEELS!

especially when you slip!.

to keep it simple....convert everyting into one unit.

Ahhhhh.... Metric maps and a metric ruler.

 

[Mark]

This is assuming the horizon is horizontal. This is not a good assumtion in a mountainous area. If you were on top of the highest peak in a region any point on the visible horizon would be at a down slope. The 10 degree fist measurement would be subtracted from the angle from actual horizontal to the visible horizon.

True, however for all of the mountains in the Northeast, the down slope to the true horizon is about 0.5 degrees (if I remember my trig correctly) which you would have to add to your initial 10 degree fist measurement.

Like I said, it's only an estimate.

 

[DougPaul]

This is assuming the horizon is horizontal. This is not a good assumtion in a mountainous area. If you were on top of the highest peak in a region any point on the visible horizon would be at a down slope. The 10 degree fist measurement would be subtracted from the angle from actual horizontal to the visible horizon.

Measure from your estimate of horizontal.

Works for angles both up and down.

Doug

 

[CaptainJim]

Are all measurements expressed in Degrees?

I've often heard of slopes expressed in grade percentage. To use PUCK'S example... if a slope rises 2000' in 1 mile (5280') it has a 37% grade. (2000 X 100 divided by 5280)

Capt.Jim

 

[Mark]

Capt,

I think the last time this was discussed (here), the consensus was that slope is expressed in degrees and grade in percentage.