Breast lines lose how much efficiency if the angle is greater than 45 degrees?

Breast lines lose how much efficiency if the angle is greater than 45 degrees?

• A. 10%
• B. 30%
• C. 20%
• D. 50%

Answer: (B)

Breast lines act as restraints by pulling the ship toward the quay, but only the part of the line’s tension that aligns with the direction you want to resist matters. If the line makes an angle theta with that direction, the effective restraining force is proportional to T cos theta. When the angle is greater than 45 degrees, cos theta is less than cos 45 degrees, so a smaller portion of the line’s tension contributes to holding the ship. A useful rule of thumb is that at 45 degrees about 30% of the line’s potential effectiveness is lost (1 − cos 45° ≈ 0.293, roughly 30%), and this loss grows as the angle increases further. So, the approximate efficiency loss for angles beyond 45 degrees is about 30%.

Breast lines act as restraints by pulling the ship toward the quay, but only the part of the line’s tension that aligns with the direction you want to resist matters. If the line makes an angle theta with that direction, the effective restraining force is proportional to T cos theta.

When the angle is greater than 45 degrees, cos theta is less than cos 45 degrees, so a smaller portion of the line’s tension contributes to holding the ship. A useful rule of thumb is that at 45 degrees about 30% of the line’s potential effectiveness is lost (1 − cos 45° ≈ 0.293, roughly 30%), and this loss grows as the angle increases further. So, the approximate efficiency loss for angles beyond 45 degrees is about 30%.