Disconerting for the beginner, but often commonplace for experienced climbers to walk up and down slopes approaching this angle. The body out away from the rock results in a greater normal force thus leading to an increased firctional force. Too much weight distributed on the hands and the frictional force isn't nearly as good. The principle of opposition is the same. At an angle of less than this amount the frictional force is larger and the climber is more secure, but at the expense of increased stresses in the leg muscles and hips.
Flexibility is also a factor as well.
Each person has an optimal angle arrived at naturally through experience. Balancing horiz. and vert. Combing these 3 equations yields the fundamental design reqt. Any mathematician will know the answer immediately. The spiral continuously approaches the origin but never arrives, much in common with a fractal.