Tangent Line on a Curve: Understanding the Forward Tangent

In the field of surveying and civil engineering, especially when designing roads, railways, or pipelines, curves are an essential part of the alignment. A tangent line is a straight line that touches a curve at only one point, called the point of tangency. These tangent lines are crucial for connecting straight sections of an alignment to the curves.

Forward Tangent and Back Tangent Definition

When dealing with a simple circular curve, there are two primary tangent lines associated with it:

• Back tangent: This is the straight section of the alignment that leads into the beginning of the curve. It is tangent to the curve at the point of commencement of the curve, often denoted as PC (Point of Curvature) or T1.
• Forward tangent: This is the straight section of the alignment that leaves the end of the curve. It is tangent to the curve at the point of tangency, often denoted as PT (Point of Tangency) or T2.

The question specifically asks about "the tangent line drawn on a curve at its end." Based on the definitions above, this description perfectly matches the forward tangent.

Analyzing Other Options

Let's briefly look at why the other options are not correct in this context:

• Long chord: A long chord is a straight line connecting the beginning (PC) and end (PT) points of a curve. It passes through the interior of the curve and is not a tangent line.
• Tangent distance: Tangent distance (T) is a specific length, which is the distance along the back tangent or the forward tangent from the point of intersection (PI) to the respective tangent point (PC or PT). It is a measurement, not a line itself. The formula for tangent distance is given by:

  \( T = R \tan\left(\frac{\Delta}{2}\right) \)

  where \( R \) is the radius of the curve and \( \Delta \) is the deflection angle of the curve.

Summary of Tangent Types

Therefore, the tangent line drawn on a curve at its end is known as the Forward tangent.