What is the effect of using a knot with a small internal radius in 1/2 inch kernmantle rope?

Using a knot with a small internal radius can significantly weaken a 1/2 inch kernmantle rope due to the increased stress concentration at the point where the rope bends. Kernmantle ropes are specifically designed with a strong core (the "kern") and a protective sheath (the "mantle"), but when the rope is subjected to a sharp bend, the protective sheath can abrade or damage the core. This damage can lead to a decrease in the rope's overall strength and performance.

Moreover, the tension in the rope at the knot can put a load on the fibers that exceeds their design capacity, especially when the knot must take a path that coils tightly around itself. This is exacerbated in rescue operations, where the integrity of the rope is critical for safety. Therefore, using a knot with a larger internal radius is generally recommended to maintain the rope's strength and reliability.