Manual of Purpose-Made Woodworking Joinery

144 Geometry for curved joinery

as that used for the three- centred method described

above under that heading at 8.5(g).

EQUILATERAL GOTHIC ARCHED

SHAPE

Figure 8.6(a): The radius of this arched shape, equal

to the span, is struck from centres A and B to an

apex point C. The extended line AD highlights a

geometric normal to the curve – and a line at right

angles to this, as shown, is known as a tangent. The

normal lines E, F, G, H, I, J, K, L are indicated by

broken lines to give an appreciation of the bricklay-

er’s use of a centre point from which to line- up the

joints of the brick- arch voussoirs. Incidentally, points

A, B and C of this arch- shape, if joined by lines

instead of curved arcs, form an equilateral triangle,

where all three sides are equal in length and contain

three 60° angles.

DEPRESSED GOTHIC ARCHED

SHAPE

Figure 8.6(b): This depressed shape is sometimes

referred to as an obtuse- or drop- Gothic arch. The

centres for striking the shape come within the span,

on the springing line. First, bisect the span AB to give

the centre line through E. With a compass less than

FIVE- CENTRED METHOD

P

C

R

B

L

NM

E

D

I

J

2

K 1

G

H

F

A

1

2

Figure 8.5 (h) Approximate semi- ellipse by five- centred
method.

Figure 8.5(h): Set out the major and minor axes as
described above. Draw lines AF and CF, equal to CE
and AE, respectively. Divide AF by three, to give A12F.
Draw radials C1 and C2. With centre E and radius
EC, strike an arc at D on the centre line. Divide AE by
three to give A12E. Draw line D1 to strike C1 at G,
and line D2 to strike C2 at H. Bisect HC and extend
the bisecting line down to give I on the centre line.
Draw a line from H to I. Now bisect GH and extend
the bisecting line down to cut the springing line at K
and line HI at J. IJK are the three centres to form half
of the semi- ellipse. The other two centres are trans-
ferred as follows: with centre E, transfer K to give L on
the springing line; draw a horizontal line from J to M
and beyond; with centre M, strike an arc from J to give
the centre N. To transfer the normal lines G and H,
strike arc CP, equal to CH, then BR, equal to AG. To
describe the semi- ellipse, draw sector- shapes AG from
centre K, GH from centre J, HCP from centre I, PR
from centre N, and RB from centre L.

DEPRESSED SEMI- ELLIPTICAL

ARCHED SHAPE

Figure 8.5(i): To achieve this arched shape, a very
shallow rise is used. The geometry is exactly the same

To G

F

A

H

K

G

E

C

L

I

J

B

Figure 8.5 (i) Depressed, approximate

semi- ellipse by three- centred method.

L K J I H G F E

AB

C Tangent

Normal

90º

D

Figure 8.6 (a) Equilateral Gothic arched shape.