The cache is not hidden at the posted coordinates and it is not necessary to visit the place to get the final coordinates.
The name Lehmann might remind you of Lehman Brothers, the investment and private banking institution that collapsed during the real estate market crash, leading to the largest bankruptcy in U.S. history, but this cache isn’t about that.
You might think of the Lehman Formula, a method in investment banking for calculating fees on large financial transactions like mergers or acquisitions. That’s not it either.
If Johann Gottlob Lehmann, the geologist who pioneered stratigraphy, comes to mind, you’d be thinking along the lines of an Earth cache.
Closer still is Johann Georg Lehmann, the surveyor and cartographer who developed a terrain mapping method using hatching to show slopes. Yet, this cache isn’t about him either.
This cache highlights staircase design, reflected in the posted coordinates. A staircase is a series of steps connecting different levels. Each step has two main parts: riser is the vertical front of the step and tread is the horizontal surface you step on. The riser height (R) is the vertical distance between consecutive steps, while the going (G) is the horizontal distance between the front edges of treads.
Staircase design balances functionality, safety, and comfort. Historically, risers ranged from 11.4 to 30.0 cm and goings from 27.9 to 91.4 cm. In 1675, François Blondel introduced a formula linking risers and goings to human gait: 2 × R + G = 71 cm. However, this often resulted in larger treads than commonly used today.
Gunther Lehmann and Bruno Engelmann later refined the formula to better fit natural human movement:
2 × R + G = 63 cm
This formula aligns with an average step length of 63 cm, slightly shorter than walking strides, accounting for the vertical and horizontal effort of stair climbing.
Optimal stair design ensures balance:
- Risers too high or goings too short make stairs tiring and unsafe.
- Low risers and long goings increase physical effort due to more steps.
The ideal balance follows the relationship:
G - R = 12 cm
Despite these advances, research into stair design continues, as modern demands and unique architectural challenges call for further refinement of these principles.
Inspired by the TV series Norwegian Dream Houses (Eventyrlig oppussing)
Source:
John Templer, The Staircase: Studies of Hazards, Falls, and Safer Design, The MIT Press, 1995, ISBN 9780262367806
G. Lehmann, B. Engelmann, Der zweckmäßigste Bau einer Treppe, Arbeitsphysiologie, January 1933, Volume 6, pages 271–282.
How to find the final coordinates
Using the given theory, calculate the ideal stair dimensions for comfortable walking. Find the optimal riser height (R) and going (G) in centimeters. Determine the staircase slope (alpha) as the angle of inclination with the horizontal plane. Round this angle to the nearest whole degree. Enter the values in the format R_G_alpha into the Certitude checker to get the final coordinates and a hint.
Just in case, a local cacher will provide maintenance assistance.