Asymmetrical Information

5.7 degrees

If I recal correctly, grades are measured in Radians. 100 gradians = 90 degrees, so a 10% grade is about 9 degrees of incline.

To measure grade, use the equation:
grade = (vertical climb)/(horizontal distance). For instance, if you are climbing up a 100 ft hill, over a mile of distance, you would use say:
grade = 100 ft/5280 ft = .0189 or 1.9% grade. Keep in mind that it is much easier to have an elevation gain of 100 feet over a mile than, say, over 500 feet.
So, 10% grade is fairly steep, especially to be biking up.

There is a satelite picture and description at http://earthobservatory.nasa.gov/Newsroom/NewImages/images.php3?img_id=16611
the worst climb is 1240 meters over 15.9 kilometers, but within that 7.8% grade ([vertical distance/horizontal distance]X100) there are 9.5% grades according to the article. For anyone familiar with Acadia National Park, the road to the summit of Cadillac Mountain, Maine climbs about 1000' over 3.5 miles, for about a 5% grade to the many tourists who bike up to the summit.

http://www.geocities.com/sidestreetluge/grade.html

I now remember why I hated geometry in JHS.

Trying to keep it simple - it's a ratio of vertical to horizontal distance.

If I recall correctly, the Interstate system requires grades to be less than, hmm, I don't recall exactly which one, but I believe 5% or possible 5 degrees. At any rate, double the grade of the steepest hill you've driven up on an Interstate and you'll get a feel for the harder grades on the Tour de France.

Blair beat me to it. 1 foot rise in 10 feet doesn't sound steep, and 5.7 degrees really doesn't sound steep, but there's something peculiar about human perception of grades. It won't look that shallow - and it does add appreciably to the energy input needed for hiking, and hits a bicyclist much harder. If biker + bike = 180 pounds, it's an extra 18 pounds of force needed to maintain speed, on top of wind resistance and other frictional forces.

A 10% grade is pretty steep to bike. In my grad school days I was a pretty avid biker. When I hit a 10% grade I would end up going at a blistering 3 miles per hour (at that speed I would pass people).

I believe that a 5% grade is the general limit allowed by the various Transportation Engineering organizations in Canada and the U.S. 6 or 7% are doable, but generally only done if absolutely necessary.

You can get higher grades in mountainous areas where things simply cannot be done another way. I have never heard of anything over 11%, though.

10% would be one vertical to ten horizontal, or 5.7 degrees.

A percent grade means the number of vertical feet over 100 horizontal feet. Therefore, a 10% grade means that the road rises 10ft for every 100ft horizontally.

So, for an angle in degrees, angle=arctan(10/100)=5.7 deg

We have some 6% grades on I-70 west of Denver. There are numerous, very large signs warning truckers to check their brakes and stay in low gear, and runaway truck ramps for those whose brakes fail anyway. My own car (Outback H6 Auto) can't even maintain 60mph in 4th gear going uphill.

We have a street near where I live in one of the Denver suburbs that has about a 300-yard straight stretch from the crest of the hill down to a flat runout that's posted as 14%. Visitors' usual reaction as you top the hill and start down is "Oh, sh*t!!"

A 10% grade would be about 500' of gain in a mile. In biking terms I guess that's difficult, although I know I've probably done it, give or take.

Since I gain elevation more frequently by hiking, and I pay attention when doing so, in hiking terms that's not difficult at all. I occasionally do a slow jog over 1.25 miles and 500' of gain. Some of the trails in the San Gabriels of SoCal gain 1000' over a mile or a little more for stretches; one route up to Mt. Baldy gains a little under 1000' a mile for almost four miles.

In fact, the ski access road up to Baldy gains about 1600', and I think it's about 3 miles long. I've biked that before (then gone on to hike to Baldy), and it wasn't that overly difficult.

The routes on Rainier or Shasta gain around 1000' in a mile over 7 or 9 miles, and that's walking through snow or on ice.

In the case of the TDF, I'd imagine the problem is not so much the grade as the constant output hours per day.

It should also be added that I did the ski access road in first or second gear at around 2 or 3 MPH. I'd imagine - just as a wild guess - that Lance and Friends are in a higher gear and at a greater speed.

" If biker + bike = 180 pounds, it's an extra 18 pounds of force needed to maintain speed, on top of wind resistance and other frictional forces."

Markm, dropping knowledge. Very impressive (I'm assuming that math is right), and a great example of what I like about this blog.

Imagine climbing 1' in elevation for every 10' of forward wheel travel.

I'm guessing they're climbing 1' vertical approx every 2 bike lengths.

It is brutal to sustain a climb such as this for any length of time.

The Lonewacko Blog: "Since I gain elevation more frequently by hiking, and I pay attention when doing so, in hiking terms that's not difficult at all."

An 8% grade for hiking is not bad at all. Just to keep a perspective, though, Lance averaged almost exactly 15 MPH while making the climb. 15 MPH is a reasonable speed for a casual rider to maintain on the flat -- and Lance did it up an almost 8% grade. Also, the energy required to maintain velocity is a squared-law thing -- roughly 14 times as much energy needed for 15 MPH as for a 4 MPH jog. Yes, the bicycle provides considerable advantage over a person on foot, but not nearly that much.

In terms of lactic acid tolerance and oxygen utilization, most of the top riders are far enough out in the tail of the human distribution to probably count as being mutants...

Just to put Michael Cain's comment into perspective, Lance's speed of 15 mph is the same as that of a runner doing a four minute mile.

Or his vertical speed is about 2 feet per second, which is like climbing stairs at one floor every five seconds. For hours straight at a time.

To echo others, 10% is ridiculously steep. Driving, a 5% grade feels like 45 degrees (I know it's not).

There's a stretch of trail between Marcy Dam and Avalanche Lake on the way to Algonquin that rises 800' in a half-mile, which works out to a 30% grade. I rest a lot on the way, and I'm doing something easy (compared to bicycle riding).

More tidbits...

When ski jumpers land, the hill is 55% to 70% grade (or 30-35 degrees) roughly the angle of repose for fallen snow.

San Francisco's Lombard street averages 14.3% grade. (you can find 12% to 18% streches of backroads in most states - both the Giro d'Italia and the Vuelta Espana have regular climbs with bits at this grade)

Highway engineers typically limit interstate grades to 7%.

For normal railroads its closer to 2%.

Most mountain communities, you cant have any part of a driveway over 7% without snowmelt - for fire access.

Water will drain off concrete with a .01% grade

Tomorrow's second climb, the Col de la Madeliene averages 8% - for 12.5 miles. L'Alpe D'Huez is only 8.6 miles long. Over the entire stage, the cyclists will climb a total of 16,827 feet. That's 2,400 feet more that the highest mountain in the lower 48...

perhaps a visual reference of the 14.3% grade of Lombard street will help.

lots of good notes...

angle of repose for sand is 32 degrees, or just over 5 times the average slope of alpe d'huez

angle of repose is the angle beyond which you cannot naturally get a surface to go beyond, where gravity pulls things down more than friction holds them up.

angle is very sport dependent, obviously. a hiker or runner can handle a much steeper grade as they are naturally more resistant to gravity than a biker or a kayaker

for example, the grand canyon drops 2200 feet over 277 miles, with rapids making up for about 1100 feet of drop in approx. 27 miles of that length. The river's average drop of 100 ft per mile makes it one of the fastest in the US.. you really don't want to go up the colorado.. not fun at all

for skiers, the kitzbuhel downhill (hardest downhill in skiing) averages 16% grade, but ranges from 2% (flats) to 85%! average speed at kitz tends to 80mph...

for a 15mph speed, you expend 39.7 watts to overcome wind resistance and friction. Going to a 5.7 degree grade, you get to 573.7 watts (with about 20% efficiency, that gets you to 40 calories consumed per minute, or 1600 calories for the 40 minutes it took lance to get up the hill) this is about comparable to biking 21 miles an hour faster (36 versus 15 miles per hour)

in other words, alped d'huez kicks your ass. Lance made it up more than 10 minutes faster than other professional cyclists... and 1-3 minutes faster than his closest competitors in the race so far...

were it not for the incredible crowding at the bottom, lance would have easily set the record for fastest time up the mountain (he missed by one second today)

so all in all, a 10% grade is incredibly hard for a bicyclist, harder than it would be for a runner, though not as hard as it would be for a kayaker. a skier would find it fun, but not all that crazy.

The Iron Horse trail up Snoqualmie Pass in Washington State has a maximum grade of 2.2% and I'm gasping like Aqualung after a 17 mile ride (the downhill return is much more fun). The access trail from the parking area is 10% and I usually wind up pushing the bike up that. Lance Armstrong and the rest of those guys are flippin' machines, my hat is off to them.

Nice photo bains...whoever took it captured a 1988 (or 1989, or 1990) two-door Toyota Corolla. Paint it red and add the factory GT-S sideskirts and you've got my own car, right down (up?) to the sunroof.

You can find the occasional 17-18 percent grade on a few urban streets; there are some that approach that in San Francisco, and one in the Long Beach/Signal Hill area. They're scary to look down when you top the hill and see them descend in front of you. Terminal speed on a skate board down one would double or triple the speed limit. Anyone but a bicycle racer would push up even a 10 percent grade. A 3 percent grade makes bicycling go from a pleasure to sweaty work.

An 8% grade for hiking is not bad at all. Just to keep a perspective, though, Lance averaged almost exactly 15 MPH while making the climb. 15 MPH is a reasonable speed for a casual rider to maintain on the flat -- and Lance did it up an almost 8% grade. Also, the energy required to maintain velocity is a squared-law thing -- roughly 14 times as much energy needed for 15 MPH as for a 4 MPH jog. Yes, the bicycle provides considerable advantage over a person on foot, but not nearly that much.

The trouble with hiking a trail with an 8% grade is not the effort it takes to go up it, the problem is the damage done to knees and hips coming down it. Hiking trails in the west that are a 20% grade for miles at a time are not uncommon. Much steeper than that and you aren't hiking anymore, you're climbing (or sliding down on your butt). Again - the key here is that getting down is the hard part.

If I recall correctly, the Interstate system requires grades to be less than, hmm, I don't recall exactly which one, but I believe 5% or possible 5 degrees

Apparently a guideline rather than an absolute rule, I know there's a 6 mile 6% grade stretch of I-84 in Oregon near Pendleton (and a nice viewpoint, too).

And a quick google search turns up the definitive source on the matter, a truck driver's web page:

A large percentage of the grades in the western states are in the 6% range. A large percentage of the grades in the eastern states are 8, 9, or 10% and sometimes even more. The eastern grades are often shorter but this is not always so. A quick glance through the eastern book will reveal over 50 grades that are between 7 and 10% and from 4 to 7 miles long. There are others that are even more challenging. The road to the top of Whiteface Mountain in New York is 8 to 10% for 8 miles. There would be no need for truckers to use this road but RVs are allowed. Near Cumberland, Maryland there is a hill on I-68 that is posted as 6% for 13 miles. In North Carolina highway 181 crosses the Blue Ridge Parkway and the southbound descent is 11 miles of grade that varies from 6 to 10%. Much of it is 8 to 9%. These grades are just as hazardous as the grades in the western states.

I have read that the same thing is true of hiking trails as well - while the trails in the east are at a lower elevation, they are often steeper (because the people who built them did not understand the concept of a "switchback", or did not have a large enough right-of-way to implement one). The average elevation gain/loss per mile on the Appalachian(sp?) Trail is greater than on its wester cousins - the Continental Divide Trail and the PCT, even though the western trails reach 12-13000 feet elevation, while the AT's highest point is under 7000 feet.

Jane:

"the steepest part of the Tour de france is a 10% grade"

That must the average of a whole climb, there are definitely parts of climbs that are steeper. One part of Alp d'Huez where Lance won yesterday is at least 12-13%.

Besides, both Giro di Italia and Vuelta España have had som really steep climbs, close to 20%, so the Tour isn't extreme for that matter.

Btw, a page about Angliru, the steepest climb in the Vuelta:
http://www.geocities.com/ciclismoenasturias/eng/especiales/angliru00.htm

And one about Monte Zoncolan in the Giro:
http://www.velonews.com/race/int/articles/3950.0.html

I've ridden on paved roads in southern Nevada that were over 11% grade. Even if you're in decent condition, unless you ride hills like this all the time you're going to be brought to a near standstill. I found myself using the width of the road to do multiple switchbacks after a few hundred feet of this.

Following up on Michael Cain's comment -

A physiology professor I had was a fairly dedicated amateur cyclist, and once had the opportunity to do some physiologic testing on Miguel Indurain. His heart was so powerful that he had a resting pulse of 25. His wife wouldn't sleep in the same bed as him because his heart pumped so much blood per beat that it shook the bed - preventing her from getting to sleep. (For the uninitiated, normal pulse is 60-80, depending on age, sex, and activity. He's pumping about 3x as much blood as the average heart with every beat.) Anyway, guys like that still have the same peak heart rate as the rest of us - so he is easily capable of raising cardiac output to 7-8x normal (and it's cardiac output, not your lungs, that determines when you give out).

To echo what people said, most collegiate bike races here in California have a climb of about 7 or 8%; one time trial that UC Santa Cruz holds has two miles of 10% followed by two miles of 7%. Bonny Doon Grade if anyone knows where that is. After the 10%, the 7% feels like it's almost flat. Coming down it was a white-knuckle descent. I'm a lousy climber (from Chicago originally) so it was my idea of hell.

The horrible bit is not having a 10% grade per se; it's having it embedded in a long stage. One must be in really top shape in order to clear out all of the lactic acid and recover quickly after such a climb. This also includes temperature control as anyone who's done even a short climb on a 75-degree day can tell you. But carrying too much water up has its own problems--more mass....

12% at any time is truly brutal.

What's even more amazing is the kind of sprint that these guys can put on at the end of all of this. Today's stage is a wonderful example of that. Even better, no French riders to be seen.

This all goes to show how much work (and lucky biology) this requires.

Biggest grade I've ever seen on a highway was coming in/out of Death Valley, to the west... 9% (CA 190). My poor, abused, overloaded truck was keeping a good steady 30mph... barely.

My view? A 10% grade is 90% too much.

Simple.

Great comments! This is why I love this blog. You all drew some great pictures.

Jane -- I don't know if it's correct blog etiquette to ask this here but I don't know how else to do it. I tried to email an article to you for your comments (if you felt so inclined) but your janegalt@ address returned a message saying something about it being locked?

Is there a way that I can send you the article?

Let me add a more urban observation: the Federal standard for wheelchair ramps is 1-in-12, or an 8.3% grade. I've seen numerous 1-in-10, which would be the 10% grade being discussed here; not sure if that was an old standard or just what many builders did before the regs were written.

If you turn the that number around, you see the real problem with wheelchair ramps: a 1-in-12 ramp will have to be 12 feet long to rise one foot. So the ramp necessary to rise the 4 feet a typical house porch is above ground is... _48 feet long!_

I haven't measured, but stairs are in the neighborhood of 1-in-2 (26.5 degrees), so your porch stairs can be done in 8 feet. Or less: I think basement steps are close to 1-in-1, which would be a 45% angle.

Personally, I'm a big fan of elevators.

10% grade makes most people (i.e., normal humans) on bikes stop and get off and walk their bike, albeit with difficulty (esp if you are wearing biking shoes..)

One thing to consider as well is the eleveation gain they are experiencing along with the tremendous effort expended climbing. The air gets thinner and thinner on the way up..

Rise over Run = Slope

1' of rise over 10' = .10 or 10%

Ten percent with the gearing they're pulling will practically rip your guts out. The speeds at which they climb these passes are unimagineable. Armstrong is a combination of ability and will the likes of which we may not see again in our lifetimes. I feel honored to simply watch him.

Hardest ride I've ever done is the Markleeville Death Ride, which is a decent approximation of a Tour mountain stage, with a max 12% grade. It's a LONG day's work!

Here's an elevation map (with a serious vertical exaggeration):

http://www.deathride.com/elevmapbig.html

"...Because there's really nothing more pathetic than a bunch of journalists sitting around trying to do math."

Journalists trying to do professional news work is just as pathetic. Does the superlative-ridden cliche "really nothing" indicate the writing of a journalism wannabe? Perhaps such language merely illustrates the extent to which journalists adversely affect our society.

  Qua amateur, I've cycled up Mt Evans in Colorado, the highest paved road in North America (14,200+), and it has some pitches at ~ 10%, particularly near the top -- Ugh.

  I'm aware of at least one climb in North America where the average grade is >10%, even reaching 20+% for a short spurt!

From: Mount Washington, New Hampshire

"Automobiles first climbed Mount Washington in the White Mountains of New Hampshire. Begun in 1904 and considered the nation's oldest motorsports event, the Audi-Mt. Washington Hillclimb is nicknamed the "Climb to the Clouds." Then there's the bike race. Only 7.6 miles long, the road climbs over 4,700 feet at an average grade of 12%, with the last 200 yards at 22.5%. It has 72 turns and switchbacks, and the longest straight section is only 3/10 of a mile long. Weather, be it fog or wind or rain, is always a factor for cyclists."

  What those pro cyclists achieve in the TdF is nothing short of super human.

I live on the Big Island of Hawaii. We have two mountains over 13,000' and one mountain over 8,000' on an island about seventy miles across. There are a LOT of steep grades here, especially on the west side. Many roads in older subdivisions have grades of 18%, though the newer developments stick to a standard of 6% for the steepest grade. Trucks have real problems with their brakes when the grade gets over 6%.
When I used to bicycle over on the Kona side most of the roads I used had 6% grades. Over the years I noticed that, regardless of the length of the ride I averaged very close to about a 30'/minute vertical climb limit, i.e. a five mile ride with a vertical gain of 1,500 feet would take me about fifty minutes. That's an average speed of 6 mph. Champion athletes, people who did the Ironman race, averaged 10-15 mph on the same slope. I guess I should have given up smoking.

"I have read that the same thing is true of hiking trails as well - while the trails in the east are at a lower elevation, they are often steeper (because the people who built them did not understand the concept of a "switchback", or did not have a large enough right-of-way to implement one)."

I've hiked about a dozen trails in the eastern U.S. and I don't recall them having switchbacks. They seem to take advantage of natural features more, such as going up streambeds and over rocks and branches. Perhaps it has something to do with snow or a desire to prevent weather erosion or a desire to blend in with the surroundings.

Lonewhacko,

If you've ever tried to bushwack on the Eastern trails, you quickly realize why the trails don't have switchbacks--the trails really do follow streambeds in order to avoid the vegetation. And the streambeds follow the steepest routes. Another consideration is what with all the rain (comparatively) in the East, erosion has to be taken into account. Trails not in dry streambeds tend to become streambeds themselves.

Of course, this is not true of most of the trails along the Blue Ridge Parkway, especially Skyline Drive, because of the nice wide trails put in by the CCC.

Journalists trying to do professional news work is just as pathetic.

They is, is they?

Lots of comments here! Would just add that:

(1) Lance Armstrong's stage 16 time trial the other day was 9.6 miles with 21 uphill turns, which he completed in 39 minutes 30 seconds, a full minute ahead of the second-place finisher.

(2)The expanation that a 10% grade means that you gain 1 unit of altitude for every 10 units of length is the way that road engineers explained it to me.

(3) In Capitol Reef National Park in southern Utah, State Route 24 has signs warning of 15% grades in at least two places. It's not the steepest road I've ever driven, but it's the highest number I've ever seen on signage.

"Because there's really nothing more pathetic than a bunch of journalists sitting around trying to do math." While the many journalists do seem to be arithmetic-challenged, Jane's biographical link in the sidebar says she majored in economics and has an MBA. Don't both of those require considerable math?

Or do new journalists receive an operation to excise the portions of the brain that enable math, science, common sense, and critical thinking? That could explain a lot ... but obviously they missed two or three sections in Jane's case.

I am going to be riding my bike on the natchez trace parkway and the book only says the grade in so many feet average per mile. I was wondering how to figure that in grade. Can you help me?

dara bricker posted:
"I am going to be riding my bike on the natchez trace parkway and the book only says the grade in so many feet average per mile. I was wondering how to figure that in grade. Can you help me?"

% Grade = # ft per mi/52.8

Example:
500 ft rise/mi

500/52.8 = 9.5%

Remember, this is only an *average* grade. Over the whole stretch of trail, there may be grades significantly more than this.

In most cities in the SF Bay Area, the limit for residential streets is 18%, though few approach that steep.

Marin Street in Berkeley (above the traffic circle) averages (including the nearly level patches where it crosses other streets) over 17%, and is steeper in places.

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