Make your own arch designs.

Question

Homi · Accepted Answer

Understand the Question

Arches are strong curved structures constructed using geometry and circular arcs.
We can design three classic types of arches:
- Semicircular Arch: A half-circle where the radius is half the span.
- Pointed (Gothic) Arch: Two intersecting circular arcs where each arc's radius equals the full span.
- Segmental Arch: A flatter arch forming a circular segment with its center located below the base line.

Step 1 · Design a Semicircular Arch

A semicircular arch is shaped like half a circle. Diagram 1

Let the span be $8\text{ units}$ . The radius is half the span:

\begin{aligned} \text{Radius} &= \dfrac{\text{Span}}{2} \\[0.6em] &= \dfrac{8}{2} \\[0.6em] &= 4\text{ units} \end{aligned}

The center is at the midpoint of the span.

Step 2 · Design a Pointed (Gothic) Arch

A pointed arch consists of two curved sides meeting at a point at the top. Diagram 2

Let the span be $8\text{ units}$ . The radius of each arc is equal to the span:

\begin{aligned} \text{Radius} &= \text{Span} \\ &= 8\text{ units} \end{aligned}

The centers of the two arcs are located at the opposite ends of the span.

Step 3 · Design a Segmental Arch

A segmental arch is a flatter arch that forms part of a circle. Diagram 3

Let the radius be $5\text{ units}$ and the center be $3\text{ units}$ below the midpoint of the span.

Let half the span be $x$ . By Pythagoras theorem:

\begin{aligned} x^2 + 3^2 &= 5^2 \\ x^2 + 9 &= 25 \\ x^2 &= 25 - 9 \\ x^2 &= 16 \\ x &= \sqrt{16} \\ x &= 4\text{ units} \end{aligned}

\begin{aligned} \text{Total Span} &= 2 \times x \\ &= 2 \times 4 \\ &= 8\text{ units} \end{aligned}

Answer

Three basic arch designs:

Semicircular Arch: Half of a circle with $\text{Radius} = 4\text{ units}$ for a span of $8\text{ units}$ .
Pointed Arch: Two intersecting arcs of $\text{Radius} = 8\text{ units}$ .
Segmental Arch: A flatter circular arc with $\text{Radius} = 5\text{ units}$ and $\text{Span} = 8\text{ units}$ .

Common Mistakes

Radius vs. Span Confusion: For a semicircular arch, $\text{Radius} = \dfrac{\text{Span}}{2}$ , whereas for a pointed Gothic arch, $\text{Radius} = \text{Span}$ .
Center Placement for Segmental Arch: Placing the center on the span line instead of below it produces a semicircle instead of a flatter segmental arch.

Question 18