Question

A set of yarns is produced with the same linear density. If these yarns follow a helical model and their diameter is inversely proportional to twist (turns per unit length), then the yarns have the same:

• A. Packing density
• B. Twist multiplier
• C. Twist angle of surface fibres
• D. Area of cross-section

Hint:

In helical yarns, a constant linear density with an inversely proportional relationship between diameter and twist results in a constant surface twist angle.

Answer 1

The Correct Option is C

In this problem, we are asked to determine the common property of a set of yarns that are produced with the same linear density, where the diameter of the yarn is inversely proportional to the twist. This requires an understanding of yarn geometry and how twist, diameter, and linear density relate to each other in the helical model. Step 1: Understand the relationship between diameter and twist.
In the helical model of yarns, the yarn is made up of fibres that are twisted around a central axis. The twist level refers to the number of turns per unit length, which affects the yarn’s diameter. The problem states that the diameter of the yarn is inversely proportional to the twist. This means that as the twist (number of turns per unit length) increases, the diameter of the yarn decreases. Conversely, if the twist decreases, the diameter of the yarn increases. Step 2: Analyze the implications of linear density.
Linear density refers to the mass per unit length of the yarn. Since all the yarns in the set have the same linear density, the total mass of each yarn per unit length is constant. This means that the yarns must adjust their structure to maintain this constant density, which results in a change in diameter when the twist changes. Specifically, as the twist increases, the yarn becomes finer (smaller diameter) while still maintaining the same linear density. Step 3: Identify the common property of the yarns.
Given that the diameter is inversely proportional to the twist and all yarns have the same linear density, we know that the surface twist angle of the fibres will remain the same across all the yarns. The twist angle is the angle between the yarn axis and the fibres' orientation. Since the twist and the diameter are related in this specific way, the twist angle of the surface fibres remains constant, regardless of the actual twist level or diameter. This is because the relationship between twist and diameter ensures that the surface fibres always orient themselves at the same angle. Step 4: Conclusion.
Therefore, the correct answer is (C), as the twist angle of the surface fibres remains the same in all the yarns due to the constant relationship between twist and diameter, and the constant linear density. The twist angle is determined by the geometry of the yarn, which is controlled by these parameters.