3 <title>Beech 99 -- Linear Model</title>
7 bgcolor="FFFFFF" text="000000" link="0800FF"
8 vlink="FF0000" alink="FF0FF8">
10 <font face="arial,helvetica">
13 Beech 99 -- Linear Model
14 </i></b></h1></center>
16 <b><i>Graduate Research done by <a href="http://fly.to/jeffscott/">Jeff Scott</a><br>
17 Advisor: <a href="http://www.uiuc.edu/ph/www/m-selig">Prof. Michael Selig</a><br>
18 Applied Aerodynamics Group<br>
19 Department of Aeronautical and Astronautical Engineering<br>
20 University of Illinois at Urbana-Champaign, Urbana, Illinois 61801<p>
22 Last updated April 11, 2000</i></b>
26 The linear aerodynamics model uses stability derivatives to approximate
27 actual aircraft behavior. The Beech 99 linear model is based on the
28 following flight conditions (low altitude cruise):
33 <table width="95%" border="1">
35 <td colspan="7" bgcolor="FFFFCC">
36 <font face="arial,helvetica" size="4"><b><center>
44 <font face="arial,helvetica">
50 <font face="arial,helvetica">
56 <font face="arial,helvetica">
62 <font face="arial,helvetica">
68 <font face="arial,helvetica">
74 <font face="arial,helvetica">
80 <font face="arial,helvetica">
89 <font face="arial,helvetica">
95 <font face="arial,helvetica">
101 <font face="arial,helvetica">
102 altitude above sea level
107 <font face="arial,helvetica">
113 <font face="arial,helvetica">
119 <font face="arial,helvetica">
125 <font face="arial,helvetica">
132 <font face="arial,helvetica">
133 <img src="../images/alpha.gif">
138 <font face="arial,helvetica">
144 <font face="arial,helvetica">
150 <font face="arial,helvetica">
156 <font face="arial,helvetica">
162 <font face="arial,helvetica">
168 <font face="arial,helvetica">
176 <font face="arial,helvetica">
177 V<sub><img src="../images/inf.gif"></sub>
182 <font face="arial,helvetica">
188 <font face="arial,helvetica">
189 velocity (true air speed)
194 <font face="arial,helvetica">
200 <font face="arial,helvetica">
206 <font face="arial,helvetica">
212 <font face="arial,helvetica">
220 <font face="arial,helvetica">
226 <font face="arial,helvetica">
232 <font face="arial,helvetica">
238 <font face="arial,helvetica">
244 <font face="arial,helvetica">
250 <font face="arial,helvetica">
256 <font face="arial,helvetica">
264 <font face="arial,helvetica">
270 <font face="arial,helvetica">
276 <font face="arial,helvetica">
277 center of gravity location
282 <font face="arial,helvetica">
283 % <img src="../images/cbar.gif">
288 <font face="arial,helvetica">
294 <font face="arial,helvetica">
300 <font face="arial,helvetica">
308 <font face="arial,helvetica">
314 <font face="arial,helvetica">
320 <font face="arial,helvetica">
326 <font face="arial,helvetica">
332 <font face="arial,helvetica">
338 <font face="arial,helvetica">
344 <font face="arial,helvetica">
352 <font face="arial,helvetica">
358 <font face="arial,helvetica">
364 <font face="arial,helvetica">
370 <font face="arial,helvetica">
376 <font face="arial,helvetica">
382 <font face="arial,helvetica">
388 <font face="arial,helvetica">
396 <font face="arial,helvetica">
402 <font face="arial,helvetica">
408 <font face="arial,helvetica">
409 pitching moment coefficient
414 <font face="arial,helvetica">
420 <font face="arial,helvetica">
426 <font face="arial,helvetica">
432 <font face="arial,helvetica">
442 The data input into the simulator is listed in the following tables:
447 <table width="95%" border="1">
449 <td colspan="7" bgcolor="FFFFCC">
450 <font face="arial,helvetica" size="4"><b><center>
458 <font face="arial,helvetica">
464 <font face="arial,helvetica">
470 <font face="arial,helvetica">
476 <font face="arial,helvetica">
482 <font face="arial,helvetica">
488 <font face="arial,helvetica">
494 <font face="arial,helvetica">
502 <font face="arial,helvetica">
508 <font face="arial,helvetica">
514 <font face="arial,helvetica">
520 <font face="arial,helvetica">
526 <font face="arial,helvetica">
532 <font face="arial,helvetica">
538 <font face="arial,helvetica">
546 <font face="arial,helvetica">
547 <img src="../images/cbar.gif">
552 <font face="arial,helvetica">
558 <font face="arial,helvetica">
559 wing mean aerodynamic chord
564 <font face="arial,helvetica">
570 <font face="arial,helvetica">
576 <font face="arial,helvetica">
582 <font face="arial,helvetica">
590 <font face="arial,helvetica">
596 <font face="arial,helvetica">
602 <font face="arial,helvetica">
608 <font face="arial,helvetica">
614 <font face="arial,helvetica">
620 <font face="arial,helvetica">
626 <font face="arial,helvetica">
635 <table width="95%" border="1">
637 <td colspan="7" bgcolor="FFFFCC">
638 <font face="arial,helvetica" size="4"><b><center>
639 Control Surface Geometry
646 <font face="arial,helvetica">
652 <font face="arial,helvetica">
658 <font face="arial,helvetica">
664 <font face="arial,helvetica">
670 <font face="arial,helvetica">
676 <font face="arial,helvetica">
682 <font face="arial,helvetica">
690 <font face="arial,helvetica">
691 <img src="../images/delta.gif">e<sub>max</sub>
696 <font face="arial,helvetica">
702 <font face="arial,helvetica">
703 maximum elevator deflection
708 <font face="arial,helvetica">
714 <font face="arial,helvetica">
720 <font face="arial,helvetica">
726 <font face="arial,helvetica">
734 <font face="arial,helvetica">
735 <img src="../images/delta.gif">e<sub>min</sub>
740 <font face="arial,helvetica">
746 <font face="arial,helvetica">
747 minimum elevator deflection
752 <font face="arial,helvetica">
758 <font face="arial,helvetica">
764 <font face="arial,helvetica">
770 <font face="arial,helvetica">
778 <font face="arial,helvetica">
779 <img src="../images/delta.gif">a<sub>max</sub>
784 <font face="arial,helvetica">
790 <font face="arial,helvetica">
791 maximum aileron deflection
796 <font face="arial,helvetica">
802 <font face="arial,helvetica">
808 <font face="arial,helvetica">
814 <font face="arial,helvetica">
822 <font face="arial,helvetica">
823 <img src="../images/delta.gif">a<sub>min</sub>
828 <font face="arial,helvetica">
834 <font face="arial,helvetica">
835 minimum aileron deflection
840 <font face="arial,helvetica">
846 <font face="arial,helvetica">
852 <font face="arial,helvetica">
858 <font face="arial,helvetica">
866 <font face="arial,helvetica">
867 <img src="../images/delta.gif">r<sub>max</sub>
872 <font face="arial,helvetica">
878 <font face="arial,helvetica">
879 maximum rudder deflection
884 <font face="arial,helvetica">
890 <font face="arial,helvetica">
896 <font face="arial,helvetica">
902 <font face="arial,helvetica">
910 <font face="arial,helvetica">
911 <img src="../images/delta.gif">r<sub>min</sub>
916 <font face="arial,helvetica">
922 <font face="arial,helvetica">
923 minimum rudder deflection
928 <font face="arial,helvetica">
934 <font face="arial,helvetica">
940 <font face="arial,helvetica">
946 <font face="arial,helvetica">
955 <table width="95%" border="1">
957 <td colspan="7" bgcolor="FFFFCC">
958 <font face="arial,helvetica" size="4"><b><center>
966 <font face="arial,helvetica">
972 <font face="arial,helvetica">
978 <font face="arial,helvetica">
984 <font face="arial,helvetica">
990 <font face="arial,helvetica">
996 <font face="arial,helvetica">
1002 <font face="arial,helvetica">
1010 <font face="arial,helvetica">
1016 <font face="arial,helvetica">
1022 <font face="arial,helvetica">
1023 weight at flight condition
1028 <font face="arial,helvetica">
1034 <font face="arial,helvetica">
1040 <font face="arial,helvetica">
1046 <font face="arial,helvetica">
1047 converted to Mass <br>[slug/ft<sup>3</sup>] in code
1054 <font face="arial,helvetica">
1060 <font face="arial,helvetica">
1066 <font face="arial,helvetica">
1072 <font face="arial,helvetica">
1078 <font face="arial,helvetica">
1084 <font face="arial,helvetica">
1090 <font face="arial,helvetica">
1098 <font face="arial,helvetica">
1104 <font face="arial,helvetica">
1110 <font face="arial,helvetica">
1116 <font face="arial,helvetica">
1122 <font face="arial,helvetica">
1128 <font face="arial,helvetica">
1134 <font face="arial,helvetica">
1142 <font face="arial,helvetica">
1148 <font face="arial,helvetica">
1154 <font face="arial,helvetica">
1160 <font face="arial,helvetica">
1166 <font face="arial,helvetica">
1172 <font face="arial,helvetica">
1178 <font face="arial,helvetica">
1186 <font face="arial,helvetica">
1192 <font face="arial,helvetica">
1198 <font face="arial,helvetica">
1199 lateral cross inertia
1204 <font face="arial,helvetica">
1210 <font face="arial,helvetica">
1216 <font face="arial,helvetica">
1222 <font face="arial,helvetica">
1231 <table width="95%" border="1">
1233 <td colspan="7" bgcolor="FFFFCC">
1234 <font face="arial,helvetica" size="4"><b><center>
1236 </center></b></font>
1242 <font face="arial,helvetica">
1248 <font face="arial,helvetica">
1254 <font face="arial,helvetica">
1260 <font face="arial,helvetica">
1266 <font face="arial,helvetica">
1272 <font face="arial,helvetica">
1278 <font face="arial,helvetica">
1286 <font face="arial,helvetica">
1292 <font face="arial,helvetica">
1293 simpleSingleMaxThrust
1298 <font face="arial,helvetica">
1304 <font face="arial,helvetica">
1310 <font face="arial,helvetica">
1316 <font face="arial,helvetica">
1322 <font face="arial,helvetica">
1323 estimated from C<sub>T<sub>x</sub></sub><br>
1331 <font face="arial,helvetica">
1337 <font face="arial,helvetica">
1343 <font face="arial,helvetica">
1349 <font face="arial,helvetica">
1355 <font face="arial,helvetica">
1361 <font face="arial,helvetica">
1367 <font face="arial,helvetica">
1368 max engine rating<br>
1377 <table width="95%" border="1">
1379 <td colspan="7" bgcolor="FFFFCC">
1380 <font face="arial,helvetica" size="4"><b><center>
1382 </center></b></font>
1388 <font face="arial,helvetica">
1394 <font face="arial,helvetica">
1400 <font face="arial,helvetica">
1406 <font face="arial,helvetica">
1412 <font face="arial,helvetica">
1418 <font face="arial,helvetica">
1424 <font face="arial,helvetica">
1432 <font face="arial,helvetica">
1433 C<sub>D<sub>0</sub></sub>
1438 <font face="arial,helvetica">
1444 <font face="arial,helvetica">
1445 drag coefficient at <img src="../images/alpha.gif">=0
1450 <font face="arial,helvetica">
1456 <font face="arial,helvetica">
1462 <font face="arial,helvetica">
1468 <font face="arial,helvetica">
1476 <font face="arial,helvetica">
1477 C<sub>D<sub><img src="../images/alpha.gif"></sub></sub>
1482 <font face="arial,helvetica">
1488 <font face="arial,helvetica">
1494 <font face="arial,helvetica">
1500 <font face="arial,helvetica">
1506 <font face="arial,helvetica">
1512 <font face="arial,helvetica">
1520 <font face="arial,helvetica">
1521 C<sub>D<sub><img src="../images/delta.gif">e</sub></sub>
1526 <font face="arial,helvetica">
1532 <font face="arial,helvetica">
1533 drag due to elevator
1538 <font face="arial,helvetica">
1544 <font face="arial,helvetica">
1550 <font face="arial,helvetica">
1556 <font face="arial,helvetica">
1557 <img src="../images/delta.gif">e positive down
1564 <font face="arial,helvetica">
1565 C<sub>L<sub>0</sub></sub>
1570 <font face="arial,helvetica">
1576 <font face="arial,helvetica">
1577 lift coefficient at <img src="../images/alpha.gif">=0
1582 <font face="arial,helvetica">
1588 <font face="arial,helvetica">
1594 <font face="arial,helvetica">
1600 <font face="arial,helvetica">
1608 <font face="arial,helvetica">
1609 C<sub>L<sub><img src="../images/alpha.gif"></sub></sub>
1614 <font face="arial,helvetica">
1620 <font face="arial,helvetica">
1626 <font face="arial,helvetica">
1632 <font face="arial,helvetica">
1638 <font face="arial,helvetica">
1644 <font face="arial,helvetica">
1652 <font face="arial,helvetica">
1653 C<sub>L<sub><img src="../images/alphadot.gif"></sub></sub>
1658 <font face="arial,helvetica">
1664 <font face="arial,helvetica">
1665 lift due to angle of attack rate
1670 <font face="arial,helvetica">
1676 <font face="arial,helvetica">
1682 <font face="arial,helvetica">
1688 <font face="arial,helvetica">
1696 <font face="arial,helvetica">
1697 C<sub>L<sub>q</sub></sub>
1702 <font face="arial,helvetica">
1708 <font face="arial,helvetica">
1709 lift due to pitch rate
1714 <font face="arial,helvetica">
1720 <font face="arial,helvetica">
1726 <font face="arial,helvetica">
1732 <font face="arial,helvetica">
1740 <font face="arial,helvetica">
1741 C<sub>L<sub><img src="../images/delta.gif">e</sub></sub>
1746 <font face="arial,helvetica">
1752 <font face="arial,helvetica">
1753 lift due to elevator
1758 <font face="arial,helvetica">
1764 <font face="arial,helvetica">
1770 <font face="arial,helvetica">
1776 <font face="arial,helvetica">
1777 <img src="../images/delta.gif">e positive down
1784 <font face="arial,helvetica">
1785 C<sub>m<sub>0</sub></sub>
1790 <font face="arial,helvetica">
1796 <font face="arial,helvetica">
1797 pitch moment coefficient at <img src="../images/alpha.gif">=0
1802 <font face="arial,helvetica">
1808 <font face="arial,helvetica">
1814 <font face="arial,helvetica">
1820 <font face="arial,helvetica">
1828 <font face="arial,helvetica">
1829 C<sub>m<sub><img src="../images/alpha.gif"></sub></sub>
1834 <font face="arial,helvetica">
1840 <font face="arial,helvetica">
1841 pitch moment due to angle of attack
1846 <font face="arial,helvetica">
1852 <font face="arial,helvetica">
1858 <font face="arial,helvetica">
1864 <font face="arial,helvetica">
1872 <font face="arial,helvetica">
1873 C<sub>m<sub><img src="../images/alphadot.gif"></sub></sub>
1878 <font face="arial,helvetica">
1884 <font face="arial,helvetica">
1885 pitch moment due to angle of attack rate
1890 <font face="arial,helvetica">
1896 <font face="arial,helvetica">
1902 <font face="arial,helvetica">
1908 <font face="arial,helvetica">
1916 <font face="arial,helvetica">
1917 C<sub>m<sub>q</sub></sub>
1922 <font face="arial,helvetica">
1928 <font face="arial,helvetica">
1929 pitch moment due to pitch rate
1934 <font face="arial,helvetica">
1940 <font face="arial,helvetica">
1946 <font face="arial,helvetica">
1952 <font face="arial,helvetica">
1960 <font face="arial,helvetica">
1961 C<sub>m<sub><img src="../images/delta.gif">e</sub></sub>
1966 <font face="arial,helvetica">
1972 <font face="arial,helvetica">
1973 pitching moment due to elevator
1978 <font face="arial,helvetica">
1984 <font face="arial,helvetica">
1990 <font face="arial,helvetica">
1996 <font face="arial,helvetica">
1997 <img src="../images/delta.gif">e positive down
2004 <font face="arial,helvetica">
2005 C<sub>Y<sub><img src="../images/beta.gif"></sub></sub>
2010 <font face="arial,helvetica">
2016 <font face="arial,helvetica">
2017 side force fue to sideslip angle
2022 <font face="arial,helvetica">
2028 <font face="arial,helvetica">
2034 <font face="arial,helvetica">
2040 <font face="arial,helvetica">
2048 <font face="arial,helvetica">
2049 C<sub>Y<sub>p</sub></sub>
2054 <font face="arial,helvetica">
2060 <font face="arial,helvetica">
2061 side force due to roll rate
2066 <font face="arial,helvetica">
2072 <font face="arial,helvetica">
2078 <font face="arial,helvetica">
2084 <font face="arial,helvetica">
2092 <font face="arial,helvetica">
2093 C<sub>Y<sub>r</sub></sub>
2098 <font face="arial,helvetica">
2104 <font face="arial,helvetica">
2105 side force due to yaw rate
2110 <font face="arial,helvetica">
2116 <font face="arial,helvetica">
2122 <font face="arial,helvetica">
2128 <font face="arial,helvetica">
2136 <font face="arial,helvetica">
2137 C<sub>Y<sub><img src="../images/delta.gif">a</sub></sub>
2142 <font face="arial,helvetica">
2148 <font face="arial,helvetica">
2149 side force due to aileron
2154 <font face="arial,helvetica">
2160 <font face="arial,helvetica">
2166 <font face="arial,helvetica">
2172 <font face="arial,helvetica">
2173 <img src="../images/delta.gif">a positive<br>right aileron up
2180 <font face="arial,helvetica">
2181 C<sub>Y<sub><img src="../images/delta.gif">r</sub></sub>
2186 <font face="arial,helvetica">
2192 <font face="arial,helvetica">
2193 side force due to rudder
2198 <font face="arial,helvetica">
2204 <font face="arial,helvetica">
2210 <font face="arial,helvetica">
2216 <font face="arial,helvetica">
2217 <img src="../images/delta.gif">r positive left
2224 <font face="arial,helvetica">
2225 C<sub>l<sub><img src="../images/beta.gif"></sub></sub>
2230 <font face="arial,helvetica">
2236 <font face="arial,helvetica">
2242 <font face="arial,helvetica">
2248 <font face="arial,helvetica">
2254 <font face="arial,helvetica">
2260 <font face="arial,helvetica">
2268 <font face="arial,helvetica">
2269 C<sub>l<sub>p</sub></sub>
2274 <font face="arial,helvetica">
2280 <font face="arial,helvetica">
2286 <font face="arial,helvetica">
2292 <font face="arial,helvetica">
2298 <font face="arial,helvetica">
2304 <font face="arial,helvetica">
2312 <font face="arial,helvetica">
2313 C<sub>l<sub>r</sub></sub>
2318 <font face="arial,helvetica">
2324 <font face="arial,helvetica">
2325 roll moment due to yaw rate
2330 <font face="arial,helvetica">
2336 <font face="arial,helvetica">
2342 <font face="arial,helvetica">
2348 <font face="arial,helvetica">
2356 <font face="arial,helvetica">
2357 C<sub>l<sub><img src="../images/delta.gif">a</sub></sub>
2362 <font face="arial,helvetica">
2368 <font face="arial,helvetica">
2369 roll moment due to aileron
2374 <font face="arial,helvetica">
2380 <font face="arial,helvetica">
2386 <font face="arial,helvetica">
2392 <font face="arial,helvetica">
2393 <img src="../images/delta.gif">a positive<br>right aileron up
2400 <font face="arial,helvetica">
2401 C<sub>l<sub><img src="../images/delta.gif">r</sub></sub>
2406 <font face="arial,helvetica">
2412 <font face="arial,helvetica">
2413 roll moment due to rudder
2418 <font face="arial,helvetica">
2424 <font face="arial,helvetica">
2430 <font face="arial,helvetica">
2436 <font face="arial,helvetica">
2437 <img src="../images/delta.gif">r positive left
2444 <font face="arial,helvetica">
2445 C<sub>n<sub><img src="../images/beta.gif"></sub></sub>
2450 <font face="arial,helvetica">
2456 <font face="arial,helvetica">
2457 weathercock stability
2462 <font face="arial,helvetica">
2468 <font face="arial,helvetica">
2474 <font face="arial,helvetica">
2480 <font face="arial,helvetica">
2488 <font face="arial,helvetica">
2489 C<sub>n<sub>p</sub></sub>
2494 <font face="arial,helvetica">
2500 <font face="arial,helvetica">
2506 <font face="arial,helvetica">
2512 <font face="arial,helvetica">
2518 <font face="arial,helvetica">
2524 <font face="arial,helvetica">
2532 <font face="arial,helvetica">
2533 C<sub>n<sub>r</sub></sub>
2538 <font face="arial,helvetica">
2544 <font face="arial,helvetica">
2550 <font face="arial,helvetica">
2556 <font face="arial,helvetica">
2562 <font face="arial,helvetica">
2568 <font face="arial,helvetica">
2576 <font face="arial,helvetica">
2577 C<sub>n<sub><img src="../images/delta.gif">a</sub></sub>
2582 <font face="arial,helvetica">
2588 <font face="arial,helvetica">
2589 yaw moment due to aileron
2594 <font face="arial,helvetica">
2600 <font face="arial,helvetica">
2606 <font face="arial,helvetica">
2612 <font face="arial,helvetica">
2613 <img src="../images/delta.gif">a positive<br>right aileron up
2620 <font face="arial,helvetica">
2621 C<sub>n<sub><img src="../images/delta.gif">r</sub></sub>
2626 <font face="arial,helvetica">
2632 <font face="arial,helvetica">
2633 yaw moment due to rudder
2638 <font face="arial,helvetica">
2644 <font face="arial,helvetica">
2650 <font face="arial,helvetica">
2656 <font face="arial,helvetica">
2657 <img src="../images/delta.gif">r positive left
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