● Springing line: a horizontal reference or datum line

at the base of an arched shape (from which the

shape springs).

● Span: the overall width of an arched shape across

the springing line.

● Centre line: a vertical setting out line equal to half

the span.

● Rise: a measurement on the centre line between the

springing line and the highest point of the arched

joinery- shape.

●Intrados: the underside of the arched joinery- shape.

● Extrados: the topside of the arched joinery- shape.

● Crown: the highest point on the extrados.

● Centre or centre point: the pivoting or compass point

of the radius.

● Radius: the geometrical distance of the centre point

from the concaved shape.

BASIC SETTING OUT

TECHNIQUES

Before proceeding, a few setting out techniques in

geometry must be understood.

Bisecting a line

Figure 8.2(a): This means dividing a line, or distance

between two points, equally into two parts by another

line intersecting it at right- angles. Figure 8.2(a) illus-

trates the method used. Line AB has been bisected.

Using A as centre set a compass to any distance greater

than half AB. Strike arcs AC^1 and AD^1. Now using B

as centre and the same compass setting, strike arcs BC^2

and BD^2. The arcs shown as broken lines are only used

to clarify the method of bisection and need not nor-

mally be shown. Now draw a line through the inter-

secting arcs C^1 C^2 to D^1 D^2. This will cut AB at E into

two equal parts. Angles C^1 EA, BEC^2 , AED^1 and D^2

EB will also be 90° angles; this also being, therefore, a

useful practical way to create large right- angles.

8

Geometry for curved joinery

INTRODUCTION

Joinery is mostly straightforward when comprised
of rectangular shapes (windows, doors, etc) or rhom-
boidal shapes (basic stairs and balustrades, etc) and
a general knowledge of plain geometry is usually
sufficient. However, maintenance- and refurbishment-
work of traditionally- built period properties, public
buildings and churches, etc, can involve replacing
joinery items with curved components – such as a
door- and doorframe- head with a Gothic- or Tudor-
arch shape, etc – (covered in Chapter 6) – and this
demands a greater knowledge of setting out geometri-
cal shapes.

BASIC ARCH- GEOMETRY

DEFINITIONS

Figure 8.1: This shows the basic definitions (explained
below) related to the setting out of a segmental-
headed doorframe.

Radius Centre

point

Span

= Centre line

Springing line

Rise

Figure 8.1 Basic arch- geometry definitions.