# Grade = Steepness of hill



## Mellow Yellow (Sep 5, 2003)

Got this in an eMail today. Thought it was interesting:

Grade = steepness of hill*

Most of us find that climbing up a 200-foot hill which is steep takes more out of us than a 200-foot hill which is gentle.* A simple and very useful measure of steepness is "grade":

grade = vertical climb / horizontal distance

where both vertical climb and horizontal distance are both converted to the same measurement units.* So if a hill goes up 264 feet in 2 miles, then we can first convert 2 miles to 10560 feet -- so the grade is then 0.025 = 264 feet / 10560 feet, which is 2.5%.**

What does this "grade" number mean?**
0% grade is exactly flat (and a negative grade, less then zero, is downhill).**
2% grade does not seem very steep, but it's enough to substantially reduce forward speed, and for most riders it will absorb more than half their power output.**
6% grade is enough to cut speed to well under half, and absorb more than 80% of a rider's power output (leaving less than 20% to fight air resistance and rolling friction).**
10% grade, and anyone who is not a fit and frequent rider is off their bike walking -- and anyone who is not a racer is reaching for all the extra power they've got.*


----------



## glenzx (Dec 19, 2003)

*cool*

Great explanation! That's a good description of why few mtbike trails sustain anything 6% or greater. 10% is brutal indeed.



Mellow Yellow said:


> Got this in an eMail today. Thought it was interesting:
> 
> Grade = steepness of hill*
> 
> ...


----------



## Stick (Jan 12, 2004)

Aw, c'mon, M.Y., that's like junior high geometry!


You want grade? You can't handle the grade!!!!

check out mile 52.4


----------



## george_da_trog (Jul 1, 2003)

Mellow Yellow said:


> Got this in an eMail today. Thought it was interesting:
> 
> Grade = steepness of hill*


What's really fun is when you convert %grade to degrees. So a 10% grade, which hurts, is actually 4.5 degrees. How many times have you heard someone talking about a 45 degree slope they just climbed... 45 degrees = 100% grade.

george


----------



## george_da_trog (Jul 1, 2003)

Stick said:


> Aw, c'mon, M.Y., that's like junior high geometry!
> 
> 
> You want grade? You can't handle the grade!!!!
> ...


Hell, it's only .3 miles long.. We've got a little local section that floats between 14% and up to 18% for a good mile. Then there is the county line climb which averages 12% for 2 miles.

george


----------



## Noelg (Jan 21, 2004)

*Close, but no cigar Mellow Yellow!!!!!!*



> grade = vertical climb / horizontal distance....So if a hill goes up 264 feet in 2 miles, then we can first convert 2 miles to 10560 feet -- so the grade is then 0.025 = 264 feet / 10560 feet, which is 2.5%.**


ohhhh so close....(your formula is right but not the measurements)



> In common practice, people often refer to percent grade as the rise divided by the distance you would travel *going up the hill*, rather than the *horizontal distance*. If you have an odometer and an altimeter, this is pretty easy to calculate. You check the altitude at the starting point and reset the odometer trip meter. You climb a certain distance and divide the change in altitude by the miles you've traveled. *This is not technically the grade*, but for normal roads that aren't very steep, it ends up being pretty close because the horizontal distance and the length of the actual road are nearly the same.


you learn something new everyday  
The EXACT grade


----------



## Stick (Jan 12, 2004)

george_da_trog said:


> Hell, it's only .3 miles long.. We've got a little local section that floats between 14% and up to 18% for a good mile. Then there is the county line climb which averages 12% for 2 miles.
> 
> george


Actually, it's almost 2 miles long. (52.4 to 54.3, the Hawk Mountain sign at 52.7 is not at the top.) Never said it was the biggest or toughest climb in the world, just one of the steeper ones around here.


----------



## papajohn (Feb 1, 2004)

*George, I don't think you are right about the degrees thing...*



george_da_trog said:


> What's really fun is when you convert %grade to degrees. So a 10% grade, which hurts, is actually 4.5 degrees. How many times have you heard someone talking about a 45 degree slope they just climbed... 45 degrees = 100% grade.
> 
> george


I may eat my words, but a flat road has zero degrees of incline, and a road that went straight up to the sky would have a 90 degree incline. So a 45 degree climb is a 50% grade (50% of the possible maximum of 90 degrees).

And as far as Noelg's explanation above, grade has to do with whether the surface has been smoothed out mechanically, as in "has that road been graded recently?"

John W.


----------



## Noelg (Jan 21, 2004)

*PJ - I hope you're hungry *

Check out the link on my last post.

You are talking about the ANGLE and that is actually the arc tangent of the rise/run.

Now we're getting into trigonometry and that's why they invented GRADE to begin with - to avoid that.


----------



## TTU-XC (Jan 13, 2004)

45* is 100% because the rise is equal to the run (or 100% of the run)


----------



## lidarman (Jan 12, 2004)

*Spring Fling teaser*



george_da_trog said:


> ...How many times have you heard someone talking about a 45 degree slope they just climbed... 45 degrees = 100% grade.
> 
> george


 No kidding! I know very few ppl who can even ride down 100% grade and no one who can ride up it. For those who have been to moab, every single part of the main slickrock trail is less than 100% (45 degrees) and most are less that 30 deg. Gotta go to other sections to approach 100%..John, the way grade is defined you can have over 100% grade...all the way to infinite percent grade (pure vertical).


----------



## papajohn (Feb 1, 2004)

*I'm going out for some salt/pepper and salsa...*

I'll get back to you on this one. Noel, the grade comment was definitely tongue in cheek!

John W.


----------



## Noelg (Jan 21, 2004)

*we're still not exactly right*



george_da_trog said:


> What's really fun is when you convert %grade to degrees. So a 10% grade, which hurts, is actually 4.5 degrees. How many times have you heard someone talking about a 45 degree slope they just climbed... 45 degrees = 100% grade.
> 
> george


a 10% grade is actually an angle of 5.71 degrees:



> To calculate the angle of ascent when you know the percent grade, you simply take the arc tangent of the grade (the inverse of the tangent). So, if you have a 10% grade, you look up the arc tangent of 0.1 and find that the angle is 5.71 degrees.


GRADE


----------



## glenzx (Dec 19, 2003)

Stick said:


> Aw, c'mon, M.Y., that's like junior high geometry!
> 
> 
> You want grade? You can't handle the grade!!!!
> ...


Is that on the road? If so, still pretty steep, but I'll take that over a 10% trail!!!!!


----------



## george_da_trog (Jul 1, 2003)

Stick said:


> Actually, it's almost 2 miles long. (52.4 to 54.3, the Hawk Mountain sign at 52.7 is not at the top.) Never said it was the biggest or toughest climb in the world, just one of the steeper ones around here.


I looked at it wrong... I still don't want to climb it.

george


----------



## Fast Eddy (Dec 30, 2003)

*ShortCut in Henry Coe SP*

(Hobbs Rd, from Middle Fork of Coyote Creek up to Blue Ridge) climbs 1300' in 1.3 miles, so it _averages_ 20%. Bear Mountain Road has a section that climbs over 1000' in under a mile, so it's about the same. I will never be able to ride up either. I heard that Fourarm Crank has climbed Bear Mtn Rd.








*Actual elevation is 900' less than this graph shows*​


----------



## radair (Dec 19, 2002)

The Mt Washington, NH Auto Road is 7.6 miles long, has an average grade of 12% with extended sections of 18% and the last 50 yards is 22%!

Tyler Hamilton _shattered _the record with a stunning climb of 51 minutes, 56 seconds on Saturday, Aug. 23, 1997. Tom Danielson of Durango, Colorado and East Lyme, Conn holds the current record at 49:24, set in 2002.

Genevieve Jeanson of Lachine, Quebec holds the women's record of 54:02, also set in 2002.

The preceding was a copy & paste from Google. Riding down the Auto Road (prohibited) is a blast, if you get permission from the right people.


----------



## pacman (Jan 16, 2004)

*For practice climb this*

Towsley Canyon loop near Magic Mountain. Burned over by last year's fires the views are stark and unobstructed. The loop is 5.24 miles with an average grade of 14%. At least one section is 29%. Look carefully in the photos for a rider on a Pink SS! (insert evil laughter here).


----------



## papajohn (Feb 1, 2004)

*It's better to learn something new than be right!*



Noelg said:


> you learn something new everyday
> 
> Having gotten such a RISE out of Noel, I hated to RUN, but the lure of 50-Year Trail took me on a TANGENT down a steep mountain GRADE that couldn't be resisted. When I got home I decided to come at this issue from another ANGLE, and I went to the website Noel had linked us to. I nearly ARCED  when I realized how wrong I had been about this whole matter.
> 
> ...


----------



## Brown_Teeth (Jan 15, 2004)

Ouch that is one sick graph if you're over 40 employed and married


----------



## george_da_trog (Jul 1, 2003)

Noelg said:


> a 10% grade is actually an angle of 5.71 degrees:


I'm thinking it's linear when obviously the arctan functon is anything but a straight line.

george


----------



## endo verendo (Jan 13, 2004)

pacman said:


> Towsley Canyon loop near Magic Mountain. Burned over by last year's fires the views are stark and unobstructed. The loop is 5.24 miles with an average grade of 14%. At least one section is 29%. Look carefully in the photos for a rider on a Pink SS! (insert evil laughter here).


Cool! Which part is 29%? I rode it both directions a few weeks ago and everything is surprisingly cleanable, especially that heinous climb past the bubbly tar pit if you're doing the loop clockwise.

I did a road ride in San Diego recently up the back side of Mt. Soledad. My bike puter showed a few 18% grades. Very slow and out of the saddle at those points.


----------



## Yeti_Rider (Dec 26, 2003)

*Via Capri?*



endo verendo said:


> Cool! Which part is 29%? I rode it both directions a few weeks ago and everything is surprisingly cleanable, especially that heinous climb past the bubbly tar pit if you're doing the loop clockwise.
> 
> I did a road ride in San Diego recently up the back side of Mt. Soledad. My bike puter showed a few 18% grades. Very slow and out of the saddle at those points.


that's a heinous climb. I only go down it into La Jolla!

Palomar Mountain is allegedly one of the longest, steepest road climbs in the country. I can't remember the specific ranking of it but it's up there. There are roads that are longer and roads that have steeper sections but this one is apparently consistently steep longer than any other. Again, fun to go down but a major biatch to go up!

A few pros used to come out here and train on it in the off season. Floyd Landis used to ride it all the time when he lived in San Diego and the real crazies go out nad have an uphill time trial just for fun.

YR


----------



## STinGa (Jan 14, 2004)

*Ouch, I just pulled something in my brain*


----------



## pacman (Jan 16, 2004)

*the steepest*



endo verendo said:


> Cool! Which part is 29%? I rode it both directions a few weeks ago and everything is surprisingly cleanable, especially that heinous climb past the bubbly tar pit if you're doing the loop clockwise.


 right before the peak when doing the loop CCW. There are many steep parts as your smoking brakes will tell you on he way down. CCW -> you get that cool canyon run.


----------



## Yeti_Rider (Dec 26, 2003)

*That brings back*

some really bad memories of multiple Calculus course I had to take many years ago.............

YR


----------



## Dijridoo (Jan 14, 2004)

*Fun math*

No offense to the girls (well, not much anyway).


----------

