Doug Sears

"Marc R" wrote:

> if the road rises 5 ft for every 100 foot HORIZONTAL change (so grade =
> 5% and slope = 5/100 or .05). But in looking at some Tour de France
> numbers last summer I concluded that that was NOT how the grade of a
> climb there is measured. Can anyone explain their system? Is their
> 'grade' maybe the ratio of the vertical change to the actual change in
> distance of the rider -- i.e., the ratio of the vertical leg of the
> appropropriate right triangle to the HYPOTENUSE? Help! ;)

Using Marc's example of a 5% grade, the hypotenuse (distance traveled by
the cyclist) would be 100.12 feet for every 100 foot horizontal distance.
To look at it another way, if you mistakenly calculate the grade by
dividing the vertical change by the distance traveled, you'd get a grade of
4.99% instead of 5% -- hardly worth worrying about. This is because the
angle involved (2.86 degrees) is small. The sine of A is approximately
equal to A when A is small.

--Doug Sears

David Auker

Hypotenuse is always the longest side of a right triangle...so taking
the hill-slope rather than the vertical ladder is always best. :-)

Curt Dewees wrote:
> It's been too long since high-school algebra for me to remember what a
> hypotenuse is, but Joe C.'s formula is correct.
>
> Remember:gradient is not the same as angle.
>
> For example: A 100% rise (rising 100 feet for every 100 feet in
> distance) would be seen as a 45-degree angle when viewing the profile
> of the hill from the side.
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Long, Steve

http://en.wikipedia.org/wiki/Hypotenuse

-----Original Message-----
From: obra-bounces@list.obra.org [mailto:obra-bounces@list.obra.org] On
Behalf Of Curt Dewees
Sent: Monday, March 12, 2007 9:47 AM
To: LAURA SANTOS
Cc: obra@list.obra.org; Marc R
Subject: Re: [OBRA Chat] Measuring Hill Gradients Mathematically

It's been too long since high-school algebra for me to remember what a
hypotenuse is, but Joe C.'s formula is correct.

Remember:gradient is not the same as angle.

For example: A 100% rise (rising 100 feet for every 100 feet in
distance) would be seen as a 45-degree angle when viewing the profile of
the hill from the side.
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Curt Dewees

It's been too long since high-school algebra for me to remember what a
hypotenuse is, but Joe C.'s formula is correct.

Remember:gradient is not the same as angle.

For example: A 100% rise (rising 100 feet for every 100 feet in
distance) would be seen as a 45-degree angle when viewing the profile
of the hill from the side.

Joe Cipale

The %grade of a hill will always be rise over run (i.e feet of climb/100
foot horizontal). What I think you are referring to (and for that
matter, what the orignal poster was looking for) was how are the cols
rated in Europe. To (poorly) mimic Phill Liggett, it has to do with the
rate of ascent (%grade), the distance (how long the climb is) and the
elevation (the height of the summit).

A more complete definition I am almost certain can be found at the UCI
or the USACylcing website(s).

Joe
--
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LAURA SANTOS

It was my understanding there would be no math.

J
----- Original Message -----
From: Marc R
To: obra@list.obra.org
Sent: Sunday, March 11, 2007 12:07 PM
Subject: [OBRA Chat] Measuring Hill Gradients Mathematically

(The hillclimb subject reminded me of this). When I teach algebra, I often tell my students that slope of a line is like grade of a road: slope is rise over run, and grade of a road is 5%, for example, if the road rises 5 ft for every 100 foot HORIZONTAL change (so grade = 5% and slope = 5/100 or .05). But in looking at some Tour de France numbers last summer I concluded that that was NOT how the grade of a climb there is measured. Can anyone explain their system? Is their 'grade' maybe the ratio of the vertical change to the actual change in distance of the rider -- i.e., the ratio of the vertical leg of the appropropriate right triangle to the HYPOTENUSE? Help! ;)
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Marc R

(The hillclimb subject reminded me of this). When I teach algebra, I often tell my students that slope of a line is like grade of a road: slope is rise over run, and grade of a road is 5%, for example, if the road rises 5 ft for every 100 foot HORIZONTAL change (so grade = 5% and slope = 5/100 or .05). But in looking at some Tour de France numbers last summer I concluded that that was NOT how the grade of a climb there is measured. Can anyone explain their system? Is their 'grade' maybe the ratio of the vertical change to the actual change in distance of the rider -- i.e., the ratio of the vertical leg of the appropropriate right triangle to the HYPOTENUSE? Help! ;)