A spring-loaded camming device uses opposed rotating cam lobes biased outward into a rock fissure. Logarithmic-spiral geometry can maintain a constant cam angle over a working surface, but real climbing protection depends on the complete certified device, placement and rock. This calculator performs selected angle-and-coefficient arithmetic only and must not be used to judge whether a placement will hold.
Spring-Loaded Camming Device · Ideal Friction Ledger
Explore an ideal selected cam-angle tangent and coefficient comparison; never use it to assess a climbing placement.
Equation Used
- theta is a selected ideal cam angle.
- mu-selected is a dimensionless comparison input, not a measured or recommended rock coefficient.
- The tangent relationship is evaluated algebraically without a force or structural model.
- The ratio is not a factor of safety.
- Rock, contamination, flare, placement, multiple lobes, walking, dynamic load, damage, rating and standards are excluded.
- The calculator must not be used for climbing decisions.
Former holds, slips, friction-factor and slip-risk language is removed because the two-input idealization cannot assess climbing protection.
Ideal friction-comparison ledger
The selected angle is converted to radians and its tangent is compared with a selected dimensionless coefficient. The ledger reports their ratio and any arithmetic shortfall relative to tan(theta). It does not identify a surface, measure friction or model a fall.
What the calculator determines
Use it only to explore the ideal relationship between a selected angle and coefficient. For climbing, follow the manufacturer's instructions, inspect the device and obtain qualified instruction; this educational comparison is not a placement or safety test.
Exact selected relationships
mu-angle=tan(theta); selected ratio=mu-selected/mu-angle; selected shortfall=max(0,(mu-angle-mu-selected)/mu-angle)×100%.
Selected-input example
At theta=13.75° and a selected coefficient of 0.40, the angle tangent is approximately 0.245 and the selected ratio is approximately 1.63. Those numbers do not establish holding strength or a safety margin.
Not a climbing-safety model
The arithmetic excludes rock condition and breakage, surface contamination, lobe shape and finish, placement range, crack flare, all four contact points, walking, stem direction, dynamic loading, device damage, standards and rated strength.
Questions
Does a ratio above one mean a cam will hold?
No. It is only a comparison of two selected numbers in an idealized relationship.
Is the entered coefficient a measured rock value?
No. It is user-selected and not validated for any surface.
Can this replace manufacturer instructions or training?
No.
References & Further Reading
- Wikipedia contributors. Spring-loaded camming device. Wikipedia
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