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Calculation of the difficulty of a climb on climbbybike.com
There are several ways in which to classify the difficulty of mountains. Climbbybike has developed its own formula, in an effort to reflect the most important aspects
in a well-weighted manner, the climbbybike difficulty index.
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CLIMBBYBIKE-INDEX
(H/D*100)*4 + H²/D + D/1000 + (T-1000)/100
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Whereby:
H = difference in height; D = distance in meters; T = top of mountain in meters
The last part of the formula does only apply to mountains above 1000 meters.
Of course, we are aware this formula does not take all aspects into account, like
the distinction between steep passages and moderate passages,
the weather circumstances, condition of the road etc. . Yet, we believe that the use of only the main
variables (height, height difference and distance, all other variables are derived thereof) cater for the
best formula and index to compare climbs with eachother.
Other variables like the distinction between
steep and moderate passages are factors which are dependent on the individual cyclist. E.g. a 20 km mountain with an
average % of 5% can be easy to climb for a tall person of 80 kg+ if there are no passages of 10% plus, while a 65kg cyclist
might have no problem at all with the steep passages.
The height of the climb on the other hand is also weighed into the formula, as
oxygen is available in lesser amounts in the higher zones. Therefor, this aspect is only taken into account starting from 1000 meter above sea-level.
To conclude: for the reasons above, the climbbybike difficulty index can only be considered a measure of
comparison and the individual profile of each climb should be consulted to get a good idea of the individual difficulty of a climb. All these profiles are
available on climbbybike.com. Additional information on road conditions, typical weather conditions etc can be found on the climb pages as well, with the general information
or in the stories and comments of the climbers.
The new formula is active on climbbybike since November 3, 2007.
Other formulas to calculate the difficulty of climbs are:
FIETS-index = [H^2 / D*10] + (T - 1000):1000
Whereby:
H = difference in height; D = distance in meters; T = top of mountain in meters
The climb difficulty rating drawn up by Gabriele Codifava, which also gives prominence to steep gradients.
D - Difficulty rating: outcome of the Formula
d - total difference in altitude (meters)
di - difference in altitude between two points (meters) referring to the i-th interval of the climb
P - avg. gradient expressed as Percentage (%)
pi - gradient of the i-th interval of the climb (%)
L - entire Length of the climb (Km)
li - length of the i-th interval of the climb (Km)
Whereby the principles followed working out the Formula (proceeding from the old well-known elaboration: D=(P*P*L)/10 + 4*P) are four:
- to give as much prominence as possible to steep
gradients; thus avoid to calculate only average gradients
over the entire climb, which would attenuate the importance
of the sharpest intervals. Each interval (defined mainly
by homogeneous gradient) will be taken into consideration
separetely, and the results will be added as the final step
of the operation;
- equal slopes (i.e.: eventually the same climb), even if
considered as parts of different courses, should provide
self-consistent results. E.g.: check the database for
these italian climbs: Prada Alta and Punta Veleno. Punta
Veleno should include the entire difficulty of Prada Alta,
adding eventually some more difficulty points being the
same climb with ADDITIONAL tracts - although easier, anyway
rising;
- the subdivision into intervals should be the least
arbitrary;
- in a theoretically homogeneous climb - in which
the average gradient is equal to the partial gradient for
every interval - the old and the new formulas should
provide the same outcomes.
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The Scanuppia Malga Palazzo in Italy. Most difficult climb in all formulas.
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The Pico de Ariero on the island of Madeira (Portugal), one of the hardest.
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The profile of the Mount Washington in the United States (New Hampshire). The hardest in the States, together with Mount Haleakala on Hawaii.
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