Chapter 6 Basic Geometric Constructions 207
5. Line EB is the approximate length of the
circumference of Circle O. The error of
this line is equal to less than 1″ in 20,000″ ″
or .005%. This error is well within the
accuracy range of mechanical drafting
instruments.
Using the Equal Chord Method
1. Circle X is given, Figure 6-58B.
2. Draw Line YZ to an approximate length.
3. Using dividers, divide one-quarter of
the circle into an equal number of chord
lengths. The accuracy of the projection
is increased when a greater number of
chords is used.
4. Lay off on Line YZ four times the
number of chord lengths in the quarter
circle. The length of Line YZ is the
required approximate length of Circle
X. This method is not as accurate as the
construction method.
Lay Off the Length
of the Circumference
of a Circle
Using the Construction Method
Laying off the circumference of a circle
is also referred to as locating the true length
or rectified length. fi The rectifi length of a fied
curved surface (such as a circle) is the length
of the surface laid out on a straight line.
1. Circle O is given, Figure 6-58A.
2. Draw Line AB tangent to the point where
the vertical centerline crosses the circle.
The length of the line should be equal to
three times the diameter of the circle.
3. Locate Point C where the horizontal cen-
terline crosses the circle. With the center
at Point C, strike an arc of a radius equal
to that of the circle. This arc will intersect
the circle at Point D. (Note that Point D is
on the opposite side of the circle center as
Point A.)
4. From Point D, draw Line ED perpendicu-
lar to the vertical centerline.
Figure 6-58. Laying off the rectifi length of a circle. fied
A—Using the construction method. This method is accu-
rate to .005%. B—Using the equal chord method. This
method is not as accurate as the construction method.
3D
D
B
C
D
O
E
A
Rectified length
A
B
X
Y Z
Figure 6-59. To calculate the circumference of a
circle, multiply the diameter by pi (3.1416). The result
is a very accurate calculation.
3.00‡
Diameter (d) = 3‡
Circumference = od
Circumference = 3.1416
¶3‡
= 9.4248 ‡
The circumference of a circle may also be
calculated very accurately by multiplying the
diameter by pi (π). The approximate value
of pi is 3.1416. Use the calculated circum-
ference and lay off the length on a straight
line. See Figure 6-59 for an example of this
calculation.
Calculate and Lay
Off the Length of the
Circumference of a Circle
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Chapter 6 Basic Geometric Constructions 207
5. Line EB is the approximate length of the
circumference of Circle O. The error of
this line is equal to less than 1″ in 20,000″ ″
or .005%. This error is well within the
accuracy range of mechanical drafting
instruments.
Using the Equal Chord Method
1. Circle X is given, Figure 6-58B.
2. Draw Line YZ to an approximate length.
3. Using dividers, divide one-quarter of
the circle into an equal number of chord
lengths. The accuracy of the projection
is increased when a greater number of
chords is used.
4. Lay off on Line YZ four times the
number of chord lengths in the quarter
circle. The length of Line YZ is the
required approximate length of Circle
X. This method is not as accurate as the
construction method.
Lay Off the Length
of the Circumference
of a Circle
Using the Construction Method
Laying off the circumference of a circle
is also referred to as locating the true length
or rectified length. fi The rectifi length of a fied
curved surface (such as a circle) is the length
of the surface laid out on a straight line.
1. Circle O is given, Figure 6-58A.
2. Draw Line AB tangent to the point where
the vertical centerline crosses the circle.
The length of the line should be equal to
three times the diameter of the circle.
3. Locate Point C where the horizontal cen-
terline crosses the circle. With the center
at Point C, strike an arc of a radius equal
to that of the circle. This arc will intersect
the circle at Point D. (Note that Point D is
on the opposite side of the circle center as
Point A.)
4. From Point D, draw Line ED perpendicu-
lar to the vertical centerline.
Figure 6-58. Laying off the rectifi length of a circle. fied
A—Using the construction method. This method is accu-
rate to .005%. B—Using the equal chord method. This
method is not as accurate as the construction method.
3D
D
B
C
D
O
E
A
Rectified length
A
B
X
Y Z
Figure 6-59. To calculate the circumference of a
circle, multiply the diameter by pi (3.1416). The result
is a very accurate calculation.
3.00‡
Diameter (d) = 3‡
Circumference = od
Circumference = 3.1416
¶3‡
= 9.4248 ‡
The circumference of a circle may also be
calculated very accurately by multiplying the
diameter by pi (π). The approximate value
of pi is 3.1416. Use the calculated circum-
ference and lay off the length on a straight
line. See Figure 6-59 for an example of this
calculation.
Calculate and Lay
Off the Length of the
Circumference of a Circle

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