I think one of the most important features of being an engineer is realizing one doesn't know everything, so I'm not taking for granted how nice it is to be "debating" a topic like this without either party digging in and getting emotional and refusing to accept that possibility.

Same on the time constraints...I'm supposed to be tying up some loose ends before I miss 4 days of work for a wheeling trip, while also tending to a couple of racks of ribs in the smoker to have my parents, brother and in-laws over for dinner, which I guess is for my birthday but I think is really just an excuse for my wife to entertain. And also getting the LJ loaded up and ready to roll out at 7:30am to meet some buddies for dinner in Pueblo, CO.

The advice for the motorcycle rider makes perfect sense. I don't know if I've been clear up to this point but when I say the heat generated is the same, I'm definitely NOT talking about degrees of temperature; I'm talking about Joules or BTU of energy. The area that those Joules are converted in, how they are conducted through the aluminum of the fairlead, the dyneema (which I suspect is not a great conductor), and convected to the air will certainly result in a different peak temperature.

I like to take an energy approach to thinking of this stuff, because that's my bag, so if we say that motorcycle rider weighs 160 and crashes at 80mph he has about 45kJ of kinetic energy that has to be converted to friction to bring him to a stop. It's completely independent of where or how big of an area he uses for ground contact - to go from 80 to 0 he needs to convert 45kJ of KE to heat, period. Rolling around to alternate his contact points is the best way he has to put that 45kJ into a larger mass of protective gear and reduce the temperature reached at any point.

If humans lacked skeletons and could take any shape at will, I think it would be equally effective to advise the motorcycle rider to assume the shape of a pancake and maximize the surface area in contact with the ground. The rider hasn't changed his weight so total Fn would be unchanged, but the Fn at all points would be reduced to the minimum achievable and the total heat energy generated would be distributed along the maximum possible surface area of the gear instead of localized to his elbows, hips, knees, ankles and shoulderblades and therefore the peak temperatures reached would be far less.

In the brief amount of time I've spent looking at the capstan equation I notice that the holding force is a function of the radians of contact and the wikipedia article says it's independent of the radius of the capstan. Since we're dealing with a quarter turn for both of these fairleads, φ would be pi/2 in both instances and the capstan equation would produce the same result.

To detail my approach, which again, may be omitting things that I haven't thought of since I don't usually do this sort of stuff...

I think we would agree that the force vector on the hypothetical posts is purely a function of rope tension - it's the sum of the vectors applied by the rope in the x and y direction. Where we might be missing one another is whether this vector represents the peak Fn or the area under the Fn curve. I believe it to represent the area under the curve, because that's the sum total of the force applied to the post by the rope, whereas the height of that curve at any point is actually just the contact pressure (force/area, pounds per sq in) at that point. The total pounds of force don't change, only the area it's applied to.

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The next step I take is Ff = µ*Fn. I started to doubt myself yesterday when you questioned my claim and had to do some research to re-learn Amontons-Coulomb second law of friction which states that the force of friction is independent of the area of contact, so there wasn't some mechanism making the coefficient change for each of these situations which would make this step invalid. So if the Fn is unchanged by the radius, the Ff is unchanged as well.

Next I use W = Ff * d (which would be the change in rope length from start to finish of the pull), and then you have the total Joules of energy converted to heat due to the friction between the fairlead and rope over the duration of the pull, or you could integrate the Work equation over the distance of the pull and calculate Watts (J/s) or horsepower or BTU/h of power dissipated over time and compare that to the heat dissipated...basically the fairlead will continue to rise in temperature until it is able to dissipate heat as quickly as it's being converted, and that may mean exceeding the max temperature of the rope.

So here's the big reveal - The rope isn't just having to deal with the heat that is generated in the time that it's rubbing the fairlead. It's also having to deal with a lot of the heat generated in the fairlead by all of the rope that preceded it. By the time you get 60 feet drawn in that fairlead is going to be HOT and the larger radius has potentially doubled or tripled how long the rope is in contact and drawing heat from the aluminum. Now we have a race between how fast the larger mass and surface area of the fairlead can carry heat away from the interface vs how much heat the rope is picking up because of how much longer that contact lasts.

From there are a few additional considerations that will play into the peak temperature reached by the rope/fairlead interface but are difficult to predict:

1. faster line speed (a common marketing differentiator of Warn winches vs cheaper brands, which are less likely to be paired with a Warn fairlead) means the energy is converted more quickly, but that does not change the thermal conductivity of the aluminum so will act as a positive influence on the peak temp of the fairlead, however it also reduces the time the rope has to be in contact with it. I think it would come out in the wash, but can't say one might not dominate the other.

2. coatings such powdercoating will impact the coefficient of friction possibly generating more heat than an anodized or bare fairlead as well as affecting the heat transfer between the fairlead and the rope.

3. the coefficient of friction probably DOES change as both the coating and the rope heat up, creating a positive feedback loop, so once a heat problem reaches a threshold it would accelerate itself to failure.