The drawing is of a rope deviated by an angle "a" degrees by a horizontal deviation.

Sorry it's old tech. I'm not up to the fancy stuff.

And I've never attached anything before, so no guarantees.

The caver weighs 1000 Newtons

T represents the tension in the top section of rope which of course is the load on the main belay.

D is the deviation force to the right.

View attachment 16984
*It is immediately obvious that T will be more than 1000 Newtons so long as the angle a is not zero*.

The line A-----A is a line that makes an angle of a/2 degrees with the horizontal.

The analysis is familiar to many on this forum.

T cos a = 1000, so T = 1000/cos a

So for example when a is 20 degrees T will be 1000/0.94= 1064 Newtons

T sin a = D

So D = 1000 sin a/cos a and therefore D = 1000 tan a

For a 20 degree angle D will be 363 Newtons

The frictional force, F, that must be sustained by the krab/rope surface is T – 1000

The normal reaction to the surface, usually given the symbol N, is the component of D along the line A-----A, which is D cos (a/2)

The required coefficient of limiting friction for this to happen is F/N, and if the coefficient is greater the krab will stay in that position. Otherwise it will slide down the rope.

I put together an Excel spreadsheet.

a degrees | a/2 degrees | a radians | a/2 radians | cos a | cos (a/2) | tan a | F Newtons | N Newtons | Required coefficient F/N |

| | | | | | | | | |

| | | | | | | | | |

5.00 | 2.50 | 0.09 | 0.04 | 1.00 | 1.00 | 0.09 | 3.82 | 87.41 | 0.04 |

10.00 | 5.00 | 0.17 | 0.09 | 0.98 | 1.00 | 0.18 | 15.43 | 175.66 | 0.09 |

15.00 | 7.50 | 0.26 | 0.13 | 0.97 | 0.99 | 0.27 | 35.28 | 265.66 | 0.13 |

20.00 | 10.00 | 0.35 | 0.17 | 0.94 | 0.98 | 0.36 | 64.18 | 358.44 | 0.18 |

25.00 | 12.50 | 0.44 | 0.22 | 0.91 | 0.98 | 0.47 | 103.38 | 455.25 | 0.23 |

30.00 | 15.00 | 0.52 | 0.26 | 0.87 | 0.97 | 0.58 | 154.70 | 557.68 | 0.28 |

35.00 | 17.50 | 0.61 | 0.31 | 0.82 | 0.95 | 0.70 | 220.77 | 667.80 | 0.33 |

40.00 | 20.00 | 0.70 | 0.35 | 0.77 | 0.94 | 0.84 | 305.41 | 788.50 | 0.39 |

45.00 | 22.50 | 0.79 | 0.39 | 0.71 | 0.92 | 1.00 | 414.21 | 923.88 | 0.45 |

50.00 | 25.00 | 0.87 | 0.44 | 0.64 | 0.91 | 1.19 | 555.72 | 1080.10 | 0.51 |

The coefficient of friction will be different with different ropes, krabs etc. but I think is unlikely to be less than 0.2 so an angle of 20 degrees is quite possible, with the load on the main belay 6% greater than the weight of the caver.