1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
|
<html>
<h1>Simulation of thermals</h1>
<h2>1. Revisions of this document</h2>
<table cellpadding="3" border="1">
<tr>
<td>January 2005</td>
<td>Jens Wilhelm Wulf</td>
<td>Wrote first version</td>
</tr>
<tr>
<td>02.02.2006</td>
<td>Jens Wilhelm Wulf</td>
<td>Added revision history and section about how to set up the sim to
test certain things. Minor updates.</td>
</tr>
<tr>
<td>26.02.2006</td>
<td>Jens Wilhelm Wulf</td>
<td>Description of thermal simulation version 3</td>
</tr>
</table>
<h2>2. Implementation of thermals</h2>
<p>
CRRCSim provides several methods of how thermals are simulated.
The one to use must be selected using <tt>THERMAL_CODE</tt> in <tt>crrc_config.h</tt> before compilation.
Newer methods may be selected without recompilation.
</p>
<h3>2.1 The original CRRCSim method</h3>
See the following picture showing the vertical velocity
of the airmass due to thermals in a fixed altitude:
<img src="thermals_old.png"/><br>
In my opinion there are some important issues about this:
<ul>
<li>
Very high gradient between 'outside of thermal' and 'inside thermal'.
</li>
<li>
Inside the thermal air is rising with constant speed. No need to
center inside, just stay anywhere inside.
</li>
<li>
Somewhere around a thermal air has to drop. The old implementation
distributes this volume on full parts of the grid -- you can see those
ugly steps where you'd assume something like zero velocity.
Again, these are gradients of the wind field.
</li>
</ul>
<p>
So it's all about the gradient. If the simulation of the plane is done
well, you'd expect it to show those gradients. If the left wing is in an
area where the vertical velocity of the air is different from what the
right wing sees, the plane should roll to one side or the other.
</p>
<p>
The old implementation let's your plane roll when you come near a
thermal, but it will also do so at those steps on the floor!
</p>
<h3>2.2 The second method</h3>
<p>
In my opinion the old implementation is not that realistic. Obviously,
there won't be such high gradients in moving air.
Furthermore air moves down near a thermal -- but surely not in a
rectangular grid.
</p>
<p>
Except for the area near ground, both the old and the new method describe
thermals which are mostly independent of altitude.
</p>
<p>
I began with creating a mathematical description of the profile of a
thermal -- the function of vertical velocity along the way from its core
to the outside. Some important points:
<ul>
<li>
Integrated over the whole area of a thermal, the volume of raising air
has to be equal to the volume of falling air.
</li>
<li>
Vertical velocity is zero on the edges of the thermal.
Its first derivation should be steady.
</li>
</ul>
Doing some math resulted in the program <tt>table.cpp</tt> which can be
used to create such profiles.
Some possible results are in <tt>thermalprofile.h</tt> and can be
selected using preprocessor definitions. By exchanging this
file, other profiles can easily be used.
</p>
<p>
Similar to the old method, the vertical velocity is zero near the ground
and rises linearly until it reaches its full strength at a certain
altitude.
</p>
<p>
A new feature of this method is that a thermals strength slowly
decreases to zero instead of just disappearing when the thermal dies.
</p>
<p>
<b>There is one aspect of thermals which isn't modeled by the new method
yet:</b> horizontal wind, which exists at least in the lower part of the
thermal (vacuum cleaner effect). There is some code modeling this in the old method, but I
didn't understand why it is done just like this.
</p>
<img src="thermals_new.png"/><br>
<h4>2.2.1 Thermal profiles selectable at compile time</h4>
There is <tt>THERMPROF</tt> in <tt>thermalprofile.h</tt>. It can be defined as:
<p>
<tt>#define THERMPROF 0</tt><br>
<img src="thermprof0.png"/><br>
</p>
<p>
<tt>#define THERMPROF 2</tt><br>
<img src="thermprof2.png"/><br>
</p>
<p>
<tt>#define THERMPROF 3</tt><br>
<img src="thermprof3.png"/><br>
</p>
All those profiles have a velocity distribution which is not nearly as
sharp as the one of the old thermal simulation. To make the feeling inside
of the thermal as easy, its diameter and/or strength has to be enlarged.
<h3>2.3 Comparison</h3>
<img src="comparison.png"/><br>
<p>
X axis is relative radius, Y axis is relative upward velocity of
airmass. If you don't touch thermal parameters in CRRCSim and only
change the type, thermals will relate to each other as shown above.
</p>
<p>
It is easy to see that thermalling with <tt>THERMPROF=0</tt> is hard if
parameters are left unchanged.
</p>
<p>
The same holds for <tt>THERMPROF=1</tt>, which is a proposal by Ulf
Gerber (see below). <br>
Let's compare diameters: traditionally, radius is 50ft in CRRCSim. We
assume that this relates to x=1 in the diagram.<br>
The whole radius of this thermal is at 2.6 in the diagram, which means
2.6*50ft=130ft=39.6m.<br>
However, Ulf Gerber states that a typical thermal has a radius of 50m (in a
height of 50m above ground), including downwind.
To get this 'Ulf Gerber Standard Thermal' in CRRCSim, you have to set the radius to
50ft*50m/39.6m=63ft. But this will still be less powerful than the
traditional CRRCSim thermal.
</p>
<p>
<tt>THERMPROF=2</tt> and <tt>THERMPROF=3</tt> are only different
regarding the area of downwind. Both have an effect similar to the old
method if you enlarge the thermal's diameter using a factor in the range of
1.2 to 1.3.
</p>
<h3>2.4 The third method</h3>
<p>
The new thermal does not only take into account that 'what goes up must come
down', but that it has to find its way from this inside to the outside
(upper end of the thermal) and back again (lower end of thermal, vacuum
cleaner effect).
</p>
<p>
<img src="thermalv3_schalen1.png"/><br>
The picture above shows some curves which, when rotated around the
y-axis (center of thermal), create some shells inside of which air
circulates. Basically a thermal is characterized by the shape of those
curves and the vertical velocity at y=0.5 (bold black line).
</p>
<p>
The distribution of velocity along this line can be varied.
</p>
<p>
One curve consists of two parts. One describes the inner
part where air moves upwards, the other one describes the outer part
where air moves downwards.
<br>
Every part consists of a straight line in the middle part (its length can
be zero as well), an ellipsis at the upper end and an ellipsis at the lower end.
<br>
The shape of those curves can be varied to some extend, as shown by the next picture.
Here not only one half of a thermal is shown.
<img src="thermalv3_schema.png"/><br>
</p>
<p>
To use the new version you have to insert some lines into your <tt>crrcsim.xml</tt>.
Find the lines where thermal characteristics for davis are described:
<pre>
<locations>
<location name="DAVIS">
...
<thermal strength_mean="5" strength_sigma="1" radius_mean="70"
radius_sigma="10" density="3.0000001e-06" lifetime_mean="240" lifetime_sigma="60" />
</pre>
</p>
<p>
Now, as a starting point, change that to
<pre>
<locations>
<location name="DAVIS">
...
<thermal strength_mean="5" strength_sigma="1"
radius_mean="70" radius_sigma="10"
density="3.0000001e-06" lifetime_mean="240" lifetime_sigma="60">
<v3 vRefExp="2" dz_m="50" height_m="600"
fileA="schalen.dat" fileB="feld.dat" fileC="vel.dat">
<inside>
<upper r_m="30" sl_r="0.8" sl_dz_r="0.2" />
<lower r_m="20" sl_r="0.8" sl_dz_r="0.2" />
</inside>
<outside>
<upper r_m="65" sl_r="0" sl_dz_r="0.7" />
<lower r_m="65" sl_r="0" sl_dz_r="0.7" />
</outside>
</v3>
</thermal>
</pre>
Here you can adjust the shape of a thermal.<br>
Only an average thermal is described here. In CRRCSim, thermals do vary to some degree.
</p>
<p>
The values ending in <tt>_m</tt> are absolute values in meters, those ending in <tt>_r</tt>
are relative values in the range 0 to 1.
</p>
<p>
<tt>vRefExp</tt> describes upwards velocity profile at average height.
1 lets velocity rise linearily; a value of 2 makes sense.
Bigger numbers result in a more 'blocky' profile.
</p>
<p>
<tt>fileA</tt>, <tt>fileB</tt> and <tt>fileC</tt> instruct CRRCSim to write out some data
files which show thermal characteristics. You can use GNUPlot to view those files; it is available for
Windows, too.
</p>
<p>
I do use a file <tt>schalen.gnuplot</tt> to view <tt>schalen.dat</tt>.
The picture above (red lines showing the curves) has been created using it.
Just execute <tt>gnuplot schalen.gnuplot</tt> to view. You can
zoom using the right mouse button, hitting <tt>a</tt> shows everything again.
<tt>schalen.gnuplot</tt> looks like this:
<pre>
set grid x
set grid y
set size ratio -1
set key off
plot 'schalen.dat' with lines
pause -1 "plb"
</pre>
</p>
<p>
I do use a file <tt>vel.gnuplot</tt> to view <tt>vel.dat</tt>.
Just execute <tt>gnuplot vel.gnuplot</tt> to view. You can
zoom using the right mouse button, hitting <tt>a</tt> shows everything again.
<tt>vel.gnuplot</tt> looks like this:
<pre>
set grid x
set grid y
set key off
plot 'vel.dat' with lines
pause -1 "plb"
</pre>
</p>
<h2>3. Effect on aircraft</h2>
<pre>
W_atmo_X shows strong effect -- OK
Why are there two transformations in crrc_aero.cpp?
G_32 shows strong effect
W_body_Y shows strong effect -- OK
That does not affect CL_left and CL_right, although this vertical flow
should clearly change the effective alpha.
Even changing CL_left and CL_right does not let the aircraft roll. They
only change stalling behaviour.
Conclusion: having a more realistic windfield is not of much use, the
current model does not respond to it. Is it wrong or just not implemented?
I think CL_left and CL_right should be affected (which is not the case)
and they in turn should let the aircraft roll (which is not the case).
</pre>
<h2>4. How to test</h2>
<h3>4.1 Fixed enviroment</h3>
<p>
There is a switch <tt>THERMAL_TEST</tt> in <tt>windfield.cpp</tt>. To
get a thermal at a fixed position, set this to <tt>1</tt> (heading towards
the thermals edge) or <tt>2</tt>
(flying straight into thermal).
</p>
<p>
Fly at Davis and set:
<table>
<tr><td>wind direction</td><td>180</td></tr>
<tr><td>wind velocity</td> <td>0 ft/s</td></tr>
<tr><td>launch altitude</td> <td>50 ft</td></tr>
<tr><td>launch relative velocity</td><td>1</td></tr>
<tr><td>launch angle</td> <td>0 rad</td></tr>
</table>
</p>
<h3>4.2 Thermal Screenshot</h3>
<p>
Use <tt>DEBUG_THERMAL_SCRSHOT</tt> in <tt>crrc_config.h</tt>.
Take a look at the notes in that file. There is another define <tt>DEBUG_THERMAL_SCRSHOT_FORMAT</tt>
which can be used to adjust the format of the output file to various
plotting programs. See <tt>windfield.cpp</tt>.
</p>
<hr width="100%"/>
<h3>Links</h3>
<p>
<em>Das Thermikbuch fr Modellflieger</em> written by Markus Lisken and
Ulf Gerber, Verlag fr Technik und Handwerk, Baden-Baden.
</p>
</html>
|
