Diagrams
Overview
This chapter provides boiler plate elements for diagrams: scales with values and title as well as grid elements are available for these types:
- linear
- logarithmic with various unit lengths
- powers and roots
- trigonometric functions
- projective scale
Samples of diagrams created with these elements
demonstrate usage and style.1)
1
Make construction lines visible in FrameMaker with View >
Color > Views : Graphic-construction.
Graphic elements
Graphic elements
Scales for diagrams
The following scales can be used for nice diagrams. All scales
comprise these elements:
ƒ
ƒ
ƒ
ƒ
Adjust a scale to your
needs
Tic marks
Axis (the spine) - not present in all templates
Figures (using character format x-figure)
Title (using character format x-title)
To adjust a scale to your needs (e.g. to make an inch ruler):
This scale is 100mm long with tics at each mm
0
1
2
3
4
5
6
7
8
9
10
This scale is 4 inches long with tics at each 1/10 inch
0
1
2
3
4
ƒ Make a copy of the desired scale (in this case, the linear
scale).
ƒ Ungroup the elements (you get the basic elements).
ƒ Use a large zoom factor for positioning.
ƒ Do not use spacing smaller than 2mm in diagrams when
printed on an ordinary laser printer.
Note:
Adjust the tic marks2)
Be very careful manipulating the ungrouped tic marks!
Remember that there is only one undo in FrameMaker. The
arrangement of the tic marks is the core of the boilerplate
scales!
ƒ Adjust the length of the tic-mark cluster (100mm P
254mm)
ƒ Ungroup the tic mark cluster and delete all unneeded tic
marks
ƒ Group the tic marks
Adjust the figures
ƒ
ƒ
ƒ
ƒ
Adjust the title
Ungroup the Figures
Remove the un-needed figures
Redistribute the figures horizontally
Group the figures
ƒ Select the title text and change it
ƒ Select the title and then the tic marks
ƒ Align the title to the tic marks
Put it together again
ƒ Select all four elements of the adjusted scale
ƒ Group the elements to prevent accidental misalignment.
2
1–2
An object may not have its centre of gravity outside a frame (or it will no
more belong to the frame). Hence it may be necessary to first ungroup
the tic mark cluster and remove any unneeded tics, re-group and adjust
the length.
Scales and grid elements
Scales and grid elements
Linear scales
2009-06-11
Linear scales can be set up with FrameMaker tools without
much work. For your convenience, some items are prepared
here.
mm ruler (180 mm total length)
0
1
2
3
4
5
6
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
1
7
8
9
10
11
12
13
14
15
16
17
1
mm ruler (180 mm total length)
Inch ruler with 1/10 divisions
10
100
9
90
8
80
7
70
6
60
5
50
4
40
3
30
2
20
1
10
0
0
2
0
0
1
3
2
3
5
0
mm ruler
cm ruler
1
10
6
7
2 x 5 divisions
15
8
9
20
10
5 x 6 divisions
5
30
1–3
5
5
5 x 4 divisions (quarters of any kind)
0
0
4
4
5
E:\FM-course\handout\Aside\diagrams.fm
0
10
60
10
11
25
7
12
30
15
20
15
5 x 7 divisions (weekdays)
6 x 5 divisions (months)
6
90
120
1
Scales and grid elements
Linear grids
The grids have these properties:
ƒ Divisions at 1 cm, line 0.3 pt, black
ƒ Subdivisions at 0.2 cm, line 0.3 pt, 40% gray
6-divisions for months, years etc.
7-divisions for weekdays
4-divisions for quarters of any kind
1–4
1–5
5
5
103
5
102 2
102 2
5
5
103 2
103 2
5
5
104 2
104 2
5
5
5
105
105
104
5
Logarithmic unit = 2cm, 5 cycles
5
2
Logarithmic unit = 10cm
101 2
5
5
100 2
2
5
Logarithmic unit = 2cm, 5 cycles
102
5
101 2
5
5
5
2
104 2
Logarithmic unit = 2.5cm, 4 cycles
2
101
2
5
104
2
100 2
2
5
5
100
2
103 2
103
5
103
5
5
2
2
102
102
5
102
5
2
LU = 10/3cm, 3 cycles
2
Logarithmic unit = 2.5cm, 4 cycles
Logarithmic unit = 5cm, 2 cycles
101
101
102
2
2
5
101
101
100
100
2
LU = 2 cm, 5 cycles
102 2
101
LU = 2.5cm, 4 cycles
5
5
5
Logarithmic unit = 5cm, 2 cycles
5
2
101 2
102
2
100
5
101
2
101
101
5
5
5
100 2
Logarithmic unit = 5cm, 2 cycles
2
2
5
100
2
5
2
Logarithmic unit = 10cm
100
5
2009-06-11
100
100
2
100
5
Logarithmic unit = 10cm
Logarithmic unit = 20cm
5
100
2
2
100
Logarithmic unit = 20cm
E:\FM-course\handout\Aside\diagrams.fm
100
100
2
100
Logarithmic scales
Logarithmic scales
101
102
103
104
105
Scales and grid elements
Logarithmic grids
1, 2 and 5 - line 0.6 pt, black
3, 4, 6, 7, 8, 9 - line 0.3 pt, black
Subdivisions 0.3 pt, 40% gray
Logarithmic unit = 10 cm
Logarithmic unit = 10 cm (1 cycle)
Logarithmic unit = 5 cm (2 cycles)
Logarithmic unit = 4 cm (3 cycles)
Logarithmic unit = 10/3 cm (3 cycles)
Logarithmic unit = 5 cm
Logarithmic unit = 2.5 cm (4 cycles)
Logarithmic unit = 2 cm (6 cycles)
1–6
Powers
Powers
0 2
4
6
8
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x=
0
4
6
10
t3/1000,
11
unit = 10cm
Roots
0
10
20
30
40
x=
12
unit = 10cm
8
x=
E:\FM-course\handout\Aside\diagrams.fm
10
t2/100,
0
1
10
100
200
x=
1–7
50
t1/2/10,
150
200
unit = 10cm
300 400
t1/3,
100
600
unit = 1cm
800 1000
2000
3000
Scales and grid elements
Trigonometric functions
0
10
20
30
40
50
60
70
90
x = sin t [degrees], unit = 15 cm
0
10
20
30
40
45
50
55
x = tan t [degrees], unit = 10 cm
Projective scale
5
10
x = (5t+1) / (t+5), unit = 3.125cm, l= 15cm
1–8
20
50
8
1000
0
100
Projective scales result from the perspective distortion of a
linear scale. For a given length there exist an infinite number
of scales. For these scales the unit has no direct relation to
any length on the scale.
Examples
Examples
E:\FM-course\handout\Aside\diagrams.fm
2009-06-11
Installes CPU power [MIPS] on the VS/MVS systems of OBR
Diagram
10
5
2
1
0.5
0.2
0.1
1975
1980
1985
Source: Klaus Daube, OBR-DTA report 27, Zürich 1988-05-06
Nomograph of Ohm’s law
P = U • I; R = U/I
100
2
Example:
101
5
I [A] current
I= 2 [A]
U= 230 [V]
P
P= 460 [W]
R= 115 [Ω]
P [W] power
100
100
100
1–9
2
5
2
2
101
2
5
101
5
102
2
U [V] voltage
5
101
2
5
5
102
R [Ω] resistance
2
103
2
5
2
5
5
104
103
102
Examples
Nomograph of flow properties
General formula
Formula with
dimensions
Constants
π
Q = v --- d 2
4
π
Q[dm³/min] = v[m/s]60[s/min]10[dm/m] --- d 2 [mm²]10 –4 [dm²/mm²]
4
1 USgal = 3.785 dm3; 1 ft = 0.305 m
Q
v
[m/s]
[ft/s]
3
[m /h]
3
[dm /s]
[gal/min]
100
10
30
200
50
20
5
200
100
2
20
1
2
10
0.5
0.5
0.2
2
0.05
20
1/2
2
0.02
0.05
0.01
0.5
0.02
1
1
3/8
10
0.5
0.1
1/4
0.2
5
0.1
0.005
0.05
0.01
1/8
0.002
0.005
0.001
1 – 10
3/4
0.1
1
Example
1
5
1
0.2
0.2
50
50
10
5
5
2
500
10
2
100
20
5
10
4
1000
50
100
20
DN
[inch] [mm]
3
0.02
0.7
Q= 30 dm3/min., DN 15 P v = 2.8 m/s (exactly: 2.83) or 9.3 ft/
s.
Density of gases
Density of gases
273 [°C ]
273 + t [°C]
Formula
For temperatures aroung 0 °C be valid:ρ t = ρ 0 -----------------------------
Constants
1 [lb/cft] = 16.02 [kg/m 3]; 1 [psia] = 0.069 [bar]
ρ
3
[lb/cft] [kg/m ]
2009-06-11
50
2
1
3
1
20
4
5 6
7
9
10
10
2
0.5
8
5
0.2
11
2
0.1
0.05
1
0.5
E:\FM-course\handout\Aside\diagrams.fm
0.02
0.01
0.2
0.1
pe
Example
[bar] 0.02
0.5
0.05
1
0.1
2
0.2
5
0.5
10
1
20
2
50
5
100
10
200
20
Nr
German
English
Nr
German
English
1
Chlorgas
Chlorine
7
Acetylene
Acetylene
2
Butan
Butane
8
Ammoniak
Ammonia
3
Porpan
Propane
9
Methan
Methane
4
Kohlendioxyd
Carbon dioxide
10
Stadtgas
City gas
5
Luft
Air
11
Wasserstoff
Hydrogen
6
Stickstoff
Nitrogen
Density of acetylen (7) ati 12 [bar] absolute pressure is
13 [kg/m 3] at 0 [°C].
At 50 [°C] it is according to the formula 11 [kg/m 3].
1 – 11
30
[psia]
Examples
Nomograph for enlacement friction
Enlacement friction is present for example in
ƒ A rope round a capstan in a harbour (friction with slip)
ƒ A rope turned in 8-shape round 2 bollards in a harbour
(initially friction with slip, then without slip)
ƒ Leather band on pulley
μα
0.8
0.9
1.0
5 10 7 2
0.7
0.6
e μα
105
T0
5 10 6 2
Bollards: an 8-turn ≈ 500°
100
T
μ
0.5
5 10 5 2
104
5
T = T0 e
5 108
General formula
100
10
5 10 2 2
5
0.2
Tension T 0
Tension T
0.3
5 10 3 2
103
5 10 4 2
2
0.4
1
2
1
0
1
Angle α in turns
2
2
3
5 10 2
10
0.1
1100
1000
900
800
700
600
500
400
Angle α in degrees
Example
Note:
300
200
100
0
μ = 0.3, α = 1000° (2 8-turns): e μα ≈ 200; T0= 50 P T = 10’000
T0 and T use the same dimension: kg, lb, ton or whatever.
Some values for μ
without slip, dry
Material-pair
Steel - steel
Metal on wood
Leather on metal
with slip, dry
μ
0.15
1 – 12
Steel-steel
0.5 …0.6 Metal on wood
0.6
Textile on cast iron
Steel rope on bollard
Material-pair
Leather on metal
Textile on cast iron
0.15
Steel rope on capstan
μ
0.1
0.2…0.5
0.25
0.3…0.5
0.13