Thanks 'struktor',

The contact angles in my real-world image of a #206 Munter hitch were (obviously) approximations.

I wasn't really intending to say 179.134 degrees, or 189.3256 degrees (or whatever) etc.

The 180 degree U turns in my photo image are just approximations.

Be that as it may, is it within your scope of math knowledge to be able to directly apply the capstan equations directly to the Munter hitch photo image?

Or is this outside of your scope of knowledge? (its a genuine question - not an insult!).

I will have my new load cell late October, and could verify your calculations.

The coefficient of friction for rope-on-rope, and rope on metal is something you would have to work out?

Note also that under load, modern synthetic rope flatten a little bit and so there is more surface area contact (particularly at the rope on metal carabiner interface).

I suppose that if you knew the tension force at the load cell, you could work backwards and derive the coefficient of friction?

There will be static friction to initially overcome and then once the rope is moving, it is now kinetic friction?

I can easily measure the load while the system is in equilibrium.

Not sure how I would measure load at the brake end of the rope while it is moving? Maybe attach the load cell to the free end of the rope, hold it in my hand and then allow the rope to flow through the Munter hitch (and observe the LCD screen display)?

Summary:What do you think 'struktor' - can you apply the math direct to the real world image of the Munter hitch and try to predict the force on the brake hand end of the rope?

Make your math predictions with calculations

*directly applied to the Munter hitch image* (rather than abstractly on computer generated imagery).

Then I could check your predictions once I have my load cell...

Assumptions:[ ] Rope would be EN892 Beal 'Joker' 9.1mm diameter Link:

https://sport.beal-planet.com/en/mountain-line/1418-5132-joker-91mm-gd.html#/14-color-blue/58-length-50m [ ] Carabiner has radius of 5.0mm

[ ] Contact angle (rope-on-rope): Approx 180 degrees / Pi radians)

[ ] Contact angle (rope-on-carabiner 'first' point): Approx 180 degrees / Pi/2 radians) - feel free to be more precise!

[ ] Contact angle (rope-on-carabiner 'second' point): Approx 90 degrees (variable)

[ ] Mass held by Munter hitch belay = 100kg

Challenge accepted?