|
|
| Line 232: |
Line 232: |
| | 0.1m | | | 0.1m |
| |} | | |} |
| ===Useful Formulas===
| |
| <h4 id="cone">Cone====
| |
|
| |
| A cone's volume depends on two factors: r (Radius) and h (height)
| |
|
| |
| <math display = 'block'>
| |
| <mrow>
| |
| <mi>v</mi>
| |
| <mo>=</mo>
| |
| <mi>π</mi>
| |
| <msup>
| |
| <mi>r</mi>
| |
| <mn>2</mn>
| |
| </msup>
| |
| <mfrac>
| |
| <mi>h</mi>
| |
| <mn>3</mn>
| |
| </mfrac>
| |
| </mrow>
| |
| </math>
| |
|
| |
| Often, when using a cone, the caster is trying to determine either the r or the h. The same formula can be modified as follows:
| |
|
| |
| <math display = 'block'>
| |
| <mtable columnalign='left' linebreak='true'>
| |
| <mtr>
| |
| <mtd>
| |
| <mrow></mrow>
| |
| </mtd>
| |
| </mtr>
| |
| <mtr>
| |
| <mtd>
| |
| <mi>h</mi>
| |
| <mo>=</mo>
| |
| <mfrac>
| |
| <mrow>
| |
| <mn>3</mn>
| |
| <mi>v</mi>
| |
| </mrow>
| |
| <mrow>
| |
| <mi>π</mi>
| |
| <msup>
| |
| <mi>r</mi>
| |
| <mn>2</mn>
| |
| </msup>
| |
| </mrow>
| |
| </mfrac>
| |
| </mtd>
| |
| </mtr>
| |
| </mtable>
| |
| </math>
| |
|
| |
| or
| |
|
| |
| <math display = 'block'>
| |
| <mrow>
| |
| <mi>r</mi>
| |
| <mo>=</mo>
| |
| <mroot>
| |
| <mfrac>
| |
| <mi mathvariant='italic' fontfamily='Times New Roman'>3v</mi>
| |
| <mrow>
| |
| <mi>π</mi>
| |
| <mi>h</mi>
| |
| </mrow>
| |
| </mfrac>
| |
| <mrow></mrow>
| |
| </mroot>
| |
| </mrow>
| |
| </math></div></div></div>
| |
| <div class='s3_column s3_column_right'><div id='stacks_out_25_page135' class='stacks_out'><div id='stacks_in_25_page135' class='stacks_in markdown_stack'><h4 id="dome">Dome====
| |
|
| |
| Sphere's have the problem that, in many instances, the bottom of the sphere is below ground. The caster doesn't really need a full sphere, a dome is sufficient. The formula for a dome depends on whether the caster is using a full half sphere or a smaller cap. The volume of the spherical cap and the area of the curved surface may be calculated using combinations of
| |
|
| |
| * The radius r of the sphere
| |
| * The radius a of the base of the cap
| |
| * The height h of the cap
| |
|
| |
| <h4 id="half-sphere">Half-Sphere====
| |
|
| |
| <h4 id="smallercap">Smaller Cap====
| |
|
| |
| <math display = 'block'>
| |
| <mrow>
| |
| <mi>v</mi>
| |
| <mo>=</mo>
| |
| <mfrac>
| |
| <mrow>
| |
| <mi>π</mi>
| |
| <msup>
| |
| <mi>h</mi>
| |
| <mn>2</mn>
| |
| </msup>
| |
| </mrow>
| |
| <mn>3</mn>
| |
| </mfrac>
| |
| <mfenced open = '(' close = ')'>
| |
| <mrow>
| |
| <mn>3</mn>
| |
| <mi>r</mi>
| |
| <mo>−</mo>
| |
| <mi>h</mi>
| |
| </mrow>
| |
| </mfenced>
| |
| </mrow>
| |
| </math></div></div><div id='stacks_out_27_page135' class='stacks_out'><div id='stacks_in_27_page135' class='stacks_in image_stack'>
| |
| <div class='centered_image' >
| |
| <img class='imageStyle' src='files/stacks-image-b6515ea.png' alt='Stacks Image 28' />
| |
| </div>
| |
|
| |
| </div></div></div>
| |
| </div></div></div></div></div></div></div></div></div></div></div>
| |
|
| |
|
| |
|
| |
| <script data-cfasync="true" src="../../rw_common/themes/foundation/foundation.min.js?rwcache=630554602"></script>
| |
| <script>
| |
| <script type="text/javascript" async
| |
| src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.0/MathJax.js?config=TeX-MML-AM_CHTML">
| |
| </script>
| |
| </script>
| |
|
| |
| </body>
| |
| </html>
| |
Revision as of 23:37, 26 December 2020
Potential Drain Chart
| Drain
|
Range
meters
|
Area of Effect
cubic meters
|
| 1
|
2
|
3
|
| 2
|
4
|
9
|
| 3
|
8
|
27
|
| 4
|
16
|
81
|
| 5
|
32
|
243
|
| 6
|
64
|
729
|
| 7
|
128
|
2,187
|
| 8
|
256
|
6,561
|
| 9
|
512
|
19,683
|
| 10
|
1,024
|
59,049
|
| 11
|
2,048
|
177,147
|
| 12
|
4,096
|
531,441
|
| 13
|
8,192
|
1,594,323
|
| 14
|
16,384
|
4,782,969
|
| 15
|
32,768
|
14,348,907
|
| 16
|
65,536
|
43,046,721
|
| 17
|
131,072
|
129,140,163
|
| 18
|
262,144
|
387,420,489
|
| 19
|
524,288
|
1,162,261,467
|
| 20
|
1,048,576
|
3,486,784,401
|
Area of Effect Shapes
| Drain
|
Sphere
m Radius
|
Cube
m per side
|
Cylinder Radius
3m High
|
| 1
|
1
|
1
|
1.75
|
| 2
|
1
|
2
|
3
|
| 3
|
2
|
3
|
5.25
|
| 4
|
3
|
4
|
9.25
|
| 5
|
4
|
6
|
16
|
| 6
|
6
|
9
|
27.75
|
| 7
|
8
|
13
|
48
|
| 8
|
12
|
19
|
83
|
| 9
|
17
|
27
|
143.5
|
| 10
|
24
|
39
|
248.5
|
| 11
|
35
|
56
|
430.75
|
| 12
|
50
|
81
|
746
|
| 13
|
72
|
117
|
1 km
|
| 14
|
105
|
168
|
2 km
|
| 15
|
151
|
243
|
4 km
|
| 16
|
217
|
350
|
7 km
|
| 17
|
314
|
505
|
11 km
|
| 18
|
452
|
729
|
20 km
|
| 19
|
652
|
1,051
|
34 km
|
| 20
|
941
|
1,516
|
60 km
|
Area of Effect Nuances
Caster’s do not have to use circles or cubes. They can shape the spell how they want. The general rule is that you need to be able to visualize the area. For example, a circular area with three “holes” is easy to imagine. Picking all the friendly soldiers on the battlefield is not. A caster can visualize a number of holes equal to their Quickness
The chart below shows the minimum sides of an area that a caster can use. In other words, a caster cannot create spell with a 0m side and therefore make the spell infinitely large.
| Magical Theory Skill
|
Minimum Side
|
Magical Theory Skill
|
Minimum Side
|
| 1
|
1m
|
6
|
0.5m
|
| 2
|
0.9m
|
7
|
0.4m
|
| 3
|
0.8m
|
8
|
0.3m
|
| 4
|
0.7m
|
9
|
0.2m
|
| 5
|
0.6m
|
10+
|
0.1m
|