Measuring an arch is required for any project involving preservation, replication, or structural analysis. Precision is paramount, as small errors can compromise structural integrity or visual accuracy. Understanding the arch’s geometry allows engineers to correctly calculate the forces at play, ensuring long-term stability. The process involves defining the arch’s fundamental parts and applying direct or indirect methods to capture its precise dimensions.
Fundamental Arch Anatomy and Terminology
The geometry of an arch is defined by specific technical terms necessary for measurement. The span is the clear horizontal distance between the arch’s supports, known as abutments or piers. The springing line is the imaginary horizontal line connecting the points where the curve begins to rise from the vertical support.
The rise is the clear vertical distance measured from the springing line up to the highest point on the inner curve, or intrados. The outer, upper curve is called the extrados. The highest point of the extrados is the crown, which often contains the keystone, the final masonry unit placed during construction. The perpendicular distance between the intrados and the extrados is referred to as the arch’s depth.
Direct Measurement Techniques for Simple Arches
Direct measurement is used for accessible arches, such as semi-circular or segmental arches, relying on physical contact with the structure. To determine the span, a steel tape measure is stretched horizontally between the two springing points at the base of the arch opening. For maximum accuracy, a helper or clamp may be needed to ensure the tape remains perfectly level and straight across the opening.
Establishing the springing line requires using a long, straight edge or a builder’s level placed horizontally across the arch supports. The straight edge must align with the exact points where the curve begins its ascent from the vertical sides. Once the line is established, the rise is measured vertically from the center of this line up to the highest point of the intrados, using a plumb bob or digital level to ensure perpendicularity to the springing line.
Indirect Measurement Methods and Advanced Tools
Measuring the radius of a circular arch cannot be done directly if the center point is inaccessible. In these cases, the geometric Chord and Sagitta method is employed to calculate the radius. This technique requires two primary measurements: the arch’s chord length and its sagitta (height).
The relationship between these elements is fixed, allowing the radius (r) to be calculated using the formula: r equals (l squared divided by 2s) plus (s divided by 2), where l is half the chord length and s is the sagitta. This geometric principle allows technicians to determine the original design radius without locating the physical center point. For highly complex or inaccessible arches, advanced non-contact tools are necessary.
Modern surveying uses laser distance measurers (LDMs) or total stations to capture precise measurements from a distance. For complex structures, such as a pointed Gothic arch or an irregular historic arch, 3D laser scanning technology is used. This method rapidly collects millions of data points, called a point cloud, which accurately maps the entire geometry and any existing deformations in three dimensions.
Applications of Arch Measurement
The meticulous measurement of arches is performed for several important practical reasons. Structural engineers rely on these measurements for structural assessment, using the precise geometry to calculate stress distribution and identify any deformation or settlement. The rise-to-span ratio, for example, is a parameter used to quantify the arch’s behavior.
For historical projects, accurate measurement is necessary for preservation and documentation, creating a record of the structure’s current condition. These records inform replication or reconstruction projects, ensuring new materials precisely match the original form and dimensions. Finally, precise dimensions allow for accurate material estimation, calculating the volume of stone or brick required for restoration.