The Tequendama waterfall would not measure what Humboldt claimed
The height measurements of the Tequendama waterfall carried out by geographer Alexander von Humboldt in 1801 do not concur with the current measurements. Therefore Universidad Nacional de Colombia (UNal) researchers reviewed and calculated the real height of the fall.Bogotá D. C., 01 de julio de 2016 — Agencia de Noticias UN-
According to Humboldt’s measurements the height of the Tequendama waterfall was of 210 meters (688.97 ft.).
“The measurement carried out by Humboldt with methods of his time was 210 meters (688.97 ft.) and differ from current sources which say the total is actually 157 meters (515 ft.),” said Plinio Del Carmen Teherán, Professor of the UNal Department of Physics.
To accurately measure the height, the researchers performed calculations based on the data provided by Humboldt, estimating an uncertainty of the height of approximately 25 meters (82 ft.), far from the more current reports between 139 and 157 meters (456 and 515 ft.).
According to UNal Department of Physics Professor Roberto Martínez the purpose is to analyze the calculations established by Humboldt in a document recently published by the Colombian Academy of Exact, Physical and Natural Sciences.
Alexander von Humboldt visited the Tequendama waterfall and wrote in his diary: “…the aspect of the fall is infinitely beautiful. […] I think there is no other waterfall of this height with so much falling water and that evaporates so much.”
The manuscript also describes the methods used to calculate the height. At first he used a barometer to measure the atmospheric pressure and obtained a height of 183 meters (600.3 ft.). However more recent measurements indicate that the measurement carried out by Humboldt was inaccurate and the method is untrustworthy.
He also carried out a measurement with triangles and used the Thales of Miletus theorem.
“Using the triangle method is possible to measure heights but in the case of the Tequendama waterfall it is not accurate due to the staggering cliff. Therefore it is complicated to establish a set of triangles for each step and find the exact measurement,” said Martínez.
Another method used was to use a long rope and the result was 147 meters (482.2 ft.). This method is unclear on how it was implemented and cannot be considered as true as the rope could have elongated or have sectors which were not vertical.
The method Humboldt reported as most trustworthy was letting objects fall and measuring the time it took to reach the bottom of the cascade.
For this the scientists let rocks fall 15 times from the cliff and determined the average time and the uncertainty of the measurement. Despite this the method described by Humboldt was inaccurate as it did not specify if the process used visual or sonorous signals.
Teherán says that due to the ambiguity of the descriptions they recorded different results.
Besides the calculations carried out, the experts decided to visit the waterfall and discuss different models to obtain more precise data. Visiting the location they determined the experimental difficulties of the area and dismissed the least feasible alternatives.
Among the options was to use a GPS and visit the bottom of the cascade but this method could have a mistake of 14 meters (45.9 ft.).
Using modern barometers and lasers which measure the height to the millimeter also poses some challenges as they need to climb down to the base of the waterfall, which may only be performed using cords and with help of experts.
“This is an interesting exercise and moved only by curiosity using Humboldt’s data trying to apply the correction to the model to obtain an indirect height measurement closest to real data,” said Teherán.(Por: Fin/VC/MLA/APBL