What % grade?

It's rise over run, using consistent units for both (eg, feet gained /
feet ridden horizontally, or meters / meters).

If you climbed 500 meters in 10km, grade would be 500 / 10000 = 5%.

If you climbed 3000 ft in 10miles, grade would be 3000 / (10*5280) =
5.68%

Eagle Jackson wrote:
> It's rise over run, using consistent units for both (eg, feet gained /
> feet ridden horizontally, or meters / meters).
>
> If you climbed 500 meters in 10km, grade would be 500 / 10000 = 5%.
>
> If you climbed 3000 ft in 10miles, grade would be 3000 / (10*5280) =
> 5.68%
>

Thanks... I knew it was something pretty straightforward, but it was
just kinda "stuck" in there. <G>

Thanks..

On Mon, 11 Jul 2005 00:14:54 -0400, Dave R
<[email protected]> wrote:

>Okay, here's one I'm ashamed to ask, but I will anyway...
>
>x mile climb, 6% grade. How is that % grade determined? I was told
>once it is rise over run, but is what is the exact calculation? Like
>4000 feet climb over 10 miles, is like a 4% grade? Or is it in meters
>and km? And what is the calculation?
>
>For some reason, I'm just having a brain fart and can't seem to "get it".
>
>Thanks for indulging me...

Dear Dave,

If you climb 4,000 feet in 10 miles, that's 4,000 feet in
52,800 feet, about a 7.6% grade. You just need to convert
the miles to feet: 4,000 / (10 x 5280) = 0.07575....

Technically, there's a difference between an idealized level
run of 52,800 feet to a point 4,000 feet below where you
arrive and a real-world 10-mile distance from sea-level to
4,000 feet, but the difference is too small at bicycling
grades to be worth worrying about.

angle is 4.345 degrees

diagonal road distance
52,951 .
.____'___________. 4000 vertical
<----52,800------>


angle is 4.332 degrees

diagonal road distance
52,800 .
.____'__________. 4000 vertical
<-----52,648---->

Carl Fogel

> How is that % grade determined?

see http://draco.acs.uci.edu/rbfaq/FAQ/9.3.html


Tom Ace

[email protected] wrote:
> On Mon, 11 Jul 2005 00:14:54 -0400, Dave R
> <[email protected]> wrote:
>
>
>>Okay, here's one I'm ashamed to ask, but I will anyway...
>>
>>x mile climb, 6% grade. How is that % grade determined? I was told
>>once it is rise over run, but is what is the exact calculation? Like
>>4000 feet climb over 10 miles, is like a 4% grade? Or is it in meters
>>and km? And what is the calculation?
>>
>>For some reason, I'm just having a brain fart and can't seem to "get it".
>>
>>Thanks for indulging me...
>
>
> Dear Dave,
>
> If you climb 4,000 feet in 10 miles, that's 4,000 feet in
> 52,800 feet, about a 7.6% grade. You just need to convert
> the miles to feet: 4,000 / (10 x 5280) = 0.07575....
>
> Technically, there's a difference between an idealized level
> run of 52,800 feet to a point 4,000 feet below where you
> arrive and a real-world 10-mile distance from sea-level to
> 4,000 feet, but the difference is too small at bicycling
> grades to be worth worrying about.
>
> angle is 4.345 degrees
>
> diagonal road distance
> 52,951 .
> .____'___________. 4000 vertical
> <----52,800------>
>
>
> angle is 4.332 degrees
>
> diagonal road distance
> 52,800 .
> .____'__________. 4000 vertical
> <-----52,648---->
>
> Carl Fogel

Excellent point. Had not even thought about the extra distance
traversed on the angular road.

I guess one of the things that always got me was when you have a 10 mile
climb at a 3% grade or a 6 mile and 7% and the announcers state that,
and why one of ordinary mathematical knowledge would not just rather
hear 10 mile climb at an average of 30 degree incline. When they say 10
miles at 3%, you have to figure it backwards (okay easier for that
example), but when they say 13.6km climb at 3.6%, only those who are
regular climbers or who follow racing often will appreciate that
description. It also does not give a layperson an appreciate of the
angle of the incline unless they go back and do the math.

I thought it would be easier to state it in terms more laypeople could
appreciate like 13.6 km climb at an average of 33 degrees incline...

Thanks for the descriptions...

to convert from %grade to degrees just take the arctan of the grade.
The thing is that in degrees the angles never seem very steep. a 20%
grade is only about 11 degrees. The steepest hill in Pittsburgh is
only a few blocks from where I grew up and is 37% or 20 degrees
http://wpwbikeclub.org/pgh_hills.html
I literally cannot ride up it. I've never tried on the MTB, but on the
road bike I can't keep the front wheel on the ground. The sidewalk has
steps.

Some of the others lower on the list are part of some of my normal
rides, and even the relatively sedate Dagmar at 20% is remarkably
brutal.

-Tim

You said: "The thing is that in degrees the angles never seem very
steep. "

Actually, IMHO, the degree is more meaningful to a layperson to whom
the % grade does not give the real appreciation of the steepness of the
climb. Most people, when watching on TV, can't really get the idea of
how steep a climb is unless they get a level view from the side, which
you usually don't get on TV. When you tell someone they've got a 30
degree climb, they can hold out their hand/arm at a 45 degree angle to
the ground, drop it back a bit and say "wow, that is steep, and they're
doing this for X miles?" Now granted, us riders know when we hear a
2.8% climb for 20 miles it is really hard, and (opinions vary)
harder/easier than a 9% climb for 1 mile, this does not mean much to
the layperson. After all, the layperson will say, "how steep is a
degree?" to which we end up giving them rise/run, arctan etc
discussions, when all they wanted to know was how steep it is compared
to the hill at home....

<[email protected]> wrote: (clip) When you tell someone
they've got a 30 degree climb, they can hold out their hand/arm at a 45
degree angle to the ground, drop it back a bit and say "wow, that is
steep,(clip)
^^^^^^^^^^^^^^^^
You are making the very point you are arguing against. To talk about a 30
degree climb, as though it is realistic, shows how misleading these numbers
are. When I rode off-road motorcycles I used to measure some of the slopes
we climbed. To go up a 30 degree incline, you needed good power, good
traction and good riding technique. It was usually accomplished for limited
distances by getting a good running start. If you tried to climb a slope
like this on a mountain bike, your front end would lift, so you would lean
forward--then your rear wheel would slip. And your pedalling torque would
not be adequate, and you would lose momentum and stop.

Regarding the difference between the projected horizontal distance and the
actual measured distance: For gradients that are realistic for bicycles,
the difference is small enough to be ignored.

Isn't it just easier to ride on a level surface?
Or get a ride up to the top and then get back on your bike?


Leo Lichtman wrote:
> <[email protected]> wrote: (clip) When you tell someone
> they've got a 30 degree climb, they can hold out their hand/arm at a 45
> degree angle to the ground, drop it back a bit and say "wow, that is
> steep,(clip)
> ^^^^^^^^^^^^^^^^
> You are making the very point you are arguing against. To talk about a 30
> degree climb, as though it is realistic, shows how misleading these numbers
> are. When I rode off-road motorcycles I used to measure some of the slopes
> we climbed. To go up a 30 degree incline, you needed good power, good
> traction and good riding technique. It was usually accomplished for limited
> distances by getting a good running start. If you tried to climb a slope
> like this on a mountain bike, your front end would lift, so you would lean
> forward--then your rear wheel would slip. And your pedalling torque would
> not be adequate, and you would lose momentum and stop.
>
> Regarding the difference between the projected horizontal distance and the
> actual measured distance: For gradients that are realistic for bicycles,
> the difference is small enough to be ignored.
>
>

[email protected] wrote:

> You said: "The thing is that in degrees the angles never seem very
> steep. "
>
> Actually, IMHO, the degree is more meaningful to a layperson to whom
> the % grade does not give the real appreciation of the steepness of the
> climb. [...] When you tell someone they've got a 30
> degree climb, [...]

No road race goes up a 30 degree climb. Period. 6 degrees is (for a
road race) fairly steep - 10.5%. 10 degrees is 17.6%, very steep for
road cycling.

The layman has serious difficulty envisioning a 6 degree angle, or even
10 degrees, as a steep climb.

BTW, two crude methods for quick estimation:

1) To estimate percentage grade,

Figure rise (in feet) per 2 miles, move decimal two places.

Example: 3000 feet in 10 miles is 300 feet/mile or 600 feet per two
miles -> 6% (approx; 5.68% is closer)

2) To estimate grade angle (in degrees) from decimal grade, for SMALL
grades,

angle = arctan(grade) ~= grade*180/Pi ~= grade* 57.3
Expressing the grade as a percentage rather than decimal (10% instead of
0.10), we get the quick-and-dirty rule:

percent/2 ~= degree grade (for SMALL angles)

Example: 10% grade ~= 5 degree climb (actually closer to 5.7 degrees)

Regards,

Mark

So I live in South Florida (yes, home of the hurricanes). Big bridges
over big expanses of water that expect to, at times, have cruise ships
pass underneath. We have several I can name, where I can assure you,
these rises are at least 20-30 degree angles from level. I know that
these bridges, sure, are 1/4 mile, 1/3 mile, and I have been on some
really steep roads in Vermont, and in Austin too (just ask Lance about
RR 1431.)

I'm sure that many of the mountains in France are not 10 mile climbs at
these angles, there have to be spots of pretty steep stuff, and it is
very useful to relate to laypeople here that "that climb was about as
steep as (pick the right bridge) for 10 miles..."

That's really all I'm getting at. They see the tour on TV, and wonder
"how steep is the climb" and you can say "it's like this road" and they
say, "that's all?" and you say "yeah, for 13.8 miles!" or they say
"it's only a 2 mile climb!" and you can say "yeah, like xxyy bridge..."
to give them perspective...

[email protected] wrote:

> So I live in South Florida (yes, home of the hurricanes). Big bridges
> over big expanses of water that expect to, at times, have cruise ships
> pass underneath. We have several I can name, where I can assure you,
> these rises are at least 20-30 degree angles from level.

I think you'd be surprised if you actually went and measured one. 30
degrees is a 50% grade, beyond the normal limits for motor vehicles.

Here is a list of some of the steepest paved roads in the United States:

1. Honokaa-Waipio Road (near Waipio, HI, maximum grade 45%)*
2. Canton Avenue (between Coast and Hampshire, Pittsburgh, PA, 37%)
3. 28th Street (between Gaffey and Peck, Los Angeles, CA, 33.3%)
4. Eldred Street (west of Avenue 48, Los Angeles, CA, 33%)
5. Baxter Street (between Alvarado and Allesandro, Los Angeles, CA, 32%)
5. Fargo Street (between Alvarado and Allesandro, Los Angeles, CA, 32%)
5. Maria Avenue (north of Chestnut, Spring Valley (near San Diego), CA,
32%)
8. Dornbush Street (between Bricelyn and Vidette, Pittsburgh, PA, 31.98%)

* Four-wheel-drive only.


--
Benjamin Lewis

All what we got here is American made.
It's a little bit cheesy, but it's nicely displayed. -- FZ

> 1) To estimate percentage grade,
>
> Figure rise (in feet) per 2 miles, move decimal two places.
>
> Example: 3000 feet in 10 miles is 300 feet/mile or 600 feet per two
> miles -> 6% (approx; 5.68% is closer)

Or just adopt the metric system and all would be swell. In metric,
each %grade is equal to 10m elevation gain over a km, so if you go up
48m in a km then it was, for all practical purposes, a 4.8% grade. We
were in the Pyrenees in May, and there the local conseil has, on the
major climbs, posted signs (e.g.,
http://www.cycle-tours.com/images/france-spain2005/photos/May_28/sign_col_du_tourmalet.jpg)
each km listing altitude, distance to summit, altitude at summit, and
grade over the next km. Was really simple mental math to keep track
of what the average grade was for the remainder of the climb. Just one
more argument for jettisoning the arcane system we have and going
metric

- rick

[email protected] wrote:

> So I live in South Florida (yes, home of the hurricanes). Big bridges
> over big expanses of water that expect to, at times, have cruise ships
> pass underneath. We have several I can name, where I can assure you,
> these rises are at least 20-30 degree angles from level.

I think you're overestimating the angle of those bridges. None of the
streets in San Francisco is as steep as 20° and some of those are rather
difficult to walk up. When we were evaluating plans for a bridge
overcrossing the engineers indicated that the grade should be kept at or
under 5% (2.9°) if at all possible.

> That's really all I'm getting at. They see the tour on TV, and wonder
> "how steep is the climb" and you can say "it's like this road" and they
> say, "that's all?" and you say "yeah, for 13.8 miles!" or they say
> "it's only a 2 mile climb!" and you can say "yeah, like xxyy bridge..."
> to give them perspective...

Giving the angle in degrees doesn't do that since most people have no
idea what the angle might be for local roads or bridges; and they'll
frequently overestimate just like you did above. OTOH, the percent
grade is frequently given on roads - usually at the start of the descent
where truckers are warned to "Use Low Gears, 7% Grade". This gives a
good comparison to grade values specified for some of the tour climbs.

> these rises are at least 20-30 degree angles from level

And I can guarantee you that those bridges are nowhere near that degree
of rise. Motor vehicles cannot climb those grades. Having driven
over a lot of that territory, I will guarantee that those bridges are
no more than a 5-6% grade. Me thinks you would be well served to find
out the exact measurements and calculate the % grade - I think you will
be surprised to find that they are really rather tame by climbing
standards.

>I'm sure that many of the mountains in France are not 10 mile climbs at
these angles, there have to be spots of pretty steep stuff

For the most part, the major climbs used in the major European tours
(TdF, Giro, Vuelta) are long and at what I would consider moderate
grades. The signature climb from last year, up Alpe d'Huez, is a 14km
climb at 7.9% average grade but it does have a spot where the grade is
almost 15%. The big climb in the Giro this year was over Passo dello
Stelvio which is a 25km climb (Prato to summit) with 7.3% average grade
and the maximum is just a bit under 10%. There are a lot of climbs in
the US with steeper grades, but it is tough to find long, sustained
climbs like those in Europe - esp. since they tend to mark down climbs
if there are intermediate descents ;-) One thing you have to add in to
your discussion is the effect of elevation. Stelvio tops out a bit
over 9000' elevation, and a lot of folks climbing it are gasping for
air long before the top; Tourmalet, when it is on the TdF tops at a
measly 6938', still enough to give low landers a desire for more
oxygen.

- rick

On 11 Jul 2005 12:12:10 -0700,
[email protected] wrote:

>So I live in South Florida (yes, home of the hurricanes). Big bridges
>over big expanses of water that expect to, at times, have cruise ships
>pass underneath. We have several I can name, where I can assure you,
>these rises are at least 20-30 degree angles from level.

[snip]

Dear Magic,

Here's an angled view of the Sunshine Skyway bridge, which
is probably the kind of bridge that you have in mind:

http://www.vandoren.net/fpm/skyway/skydm077.jpg

Unfortunately, the five pages of other pictures fail to show
the bridge from a true side angle.

The apparent angle on our left is about 8 degrees.

(The bridge angle on the left in the picture is about 9.3
degrees, but about 1.3 degrees of that is picture tilt,
judging by the water at the bridge).

This 8-degree angle is exaggerated considerably by the
camera angle to the bridge.

Driving up such bridges does give an impression of steepness
because there's nothing else visible--the road just aims at
the sky, without the familiar mountainside to one side or
peak dead ahead.

Carl Fogel

Benjamin Lewis wrote:

> I think you'd be surprised if you actually went and measured one. 30
> degrees is a 50% grade, beyond the normal limits for motor vehicles.
>
> Here is a list of some of the steepest paved roads in the United States:
>
> 1. Honokaa-Waipio Road (near Waipio, HI, maximum grade 45%)*
> * Four-wheel-drive only.

By coincidence I happened to walk down (and up) this road a couple
of days ago. It is certainly the steepest paved road I have ever seen.
It doesn't average 45% grade, probably closer to 25% average, over
about a mile long. Most of the other roads on this list are closer
to a block long.

They aren't kidding about the 4WD. When the asphalt gets any rain
(which is often) it is slick - my shoes were slipping at times on
the way down. I did see a local riding a motorcycle up and down it.

> 2. Canton Avenue (between Coast and Hampshire, Pittsburgh, PA, 37%)
> 3. 28th Street (between Gaffey and Peck, Los Angeles, CA, 33.3%)
> 4. Eldred Street (west of Avenue 48, Los Angeles, CA, 33%)
> 5. Baxter Street (between Alvarado and Allesandro, Los Angeles, CA, 32%)
> 5. Fargo Street (between Alvarado and Allesandro, Los Angeles, CA, 32%)
> 5. Maria Avenue (north of Chestnut, Spring Valley (near San Diego), CA,
> 32%)
> 8. Dornbush Street (between Bricelyn and Vidette, Pittsburgh, PA, 31.98%)

On Mon, 11 Jul 2005 15:16:45 -0600, [email protected]
wrote:

>On 11 Jul 2005 12:12:10 -0700,
>[email protected] wrote:
>
>>So I live in South Florida (yes, home of the hurricanes). Big bridges
>>over big expanses of water that expect to, at times, have cruise ships
>>pass underneath. We have several I can name, where I can assure you,
>>these rises are at least 20-30 degree angles from level.
>
>[snip]
>
>Dear Magic,
>
>Here's an angled view of the Sunshine Skyway bridge, which
>is probably the kind of bridge that you have in mind:
>
>http://www.vandoren.net/fpm/skyway/skydm077.jpg
>
>Unfortunately, the five pages of other pictures fail to show
>the bridge from a true side angle.
>
>The apparent angle on our left is about 8 degrees.
>
>(The bridge angle on the left in the picture is about 9.3
>degrees, but about 1.3 degrees of that is picture tilt,
>judging by the water at the bridge).
>
>This 8-degree angle is exaggerated considerably by the
>camera angle to the bridge.
>
>Driving up such bridges does give an impression of steepness
>because there's nothing else visible--the road just aims at
>the sky, without the familiar mountainside to one side or
>peak dead ahead.
>
>Carl Fogel

Aha! Here's a much larger picture of the Sunshine Skyway
from a better angle:

http://community.webshots.com/photo/304964242/304966519UOTZvm#

The water seems to be dead level in the picture.

The left side of the bridge has an apparent angle of about 3
degrees, while the right side has an apparent angle of about
5.3 degrees.

The bridge span lengths indicate that it's symmetrical:

span lengths of main bridge
42.70 m - 73.20 m - 73.20 m - 73.20 m - 164.60 m -
365.80 m -
164.60 m - 73.20 m - 73.20 m - 73.20 m - 42.70 m

http://en.structurae.de/structures/data/index.cfm?ID=s0000263

Comparing the gaps in the pylons indicates that the camera
angle is still short of 90 degrees, but it's reasonable to
predict symmetrical bridge approaches would be around 3.5 to
4.5 degrees, or 6 to 8% grade.

Carl Fogel

Leo Lichtman wrote:
> are. When I rode off-road motorcycles I used to measure some of the slopes
> we climbed. To go up a 30 degree incline, you needed good power, good
> traction and good riding technique. It was usually accomplished for limited
> distances by getting a good running start.

My 64 Hodaka 90 owner's manual said "Maximium climbing angle: 30
degrees"