Clark Y Joukovski 11 G¨ottingen 628 Eppler 793 Naca 0012 RAE 104 SC 20406 NLF 015 Whitcomb
Parametric Airfoil Catalog, Part II
An Aerodynamic and Geometric Comparison Between Parametrized and Point Cloud Airfoils Tomas Melin
Copyright c 2013, Tomas Melin
Published by:
Fluid and Mechatronic Systems,
Department of Management and Engineering, The Institute of Technology,
Link¨oping University, Link¨oping, Sweden
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Parametric Airfoil Catalog
Part II
G¨
ottingen 673 to YS930
An Aerodynamic and Geometric Comparison Between Parametrized and Point Cloud Airfoils.
Tomas Melin
Research Associate
Fluid and Mechatronic Systems,
Department of Management and Engineering,
The Institute of Technology,
Link¨
oping University,
Link¨
oping, Sweden
1 Acknowledgements 1 2 Introduction 1 3 Background 1 4 Method 2 4.1 Model . . . 2 4.2 Parameterization . . . 2 4.3 Base change . . . 4
4.4 Reproducing known airfoils . . . 4
5 Discussion 5 6 Software 6 7 Airfoil Catalog 6 goe673 . . . 7 goe675 . . . 8 goe676 . . . 9 goe677 . . . 10 goe679 . . . 11 goe681 . . . 12 goe682 . . . 13 goe683 . . . 14 goe685 . . . 15 goe692 . . . 16 goe693 . . . 17 goe703 . . . 18 goe704 . . . 19 goe711 . . . 20 goe735 . . . 21 goe738 . . . 22 goe758 . . . 23 goe766 . . . 24 goe767 . . . 25 goe769 . . . 26 goe770 . . . 27 goe775 . . . 28 goe776 . . . 29 goe780 . . . 30 goe795 . . . 31 goe795sm . . . 32 goe797 . . . 33 goe801 . . . 34 goe802 . . . 35 goe803h . . . 36 goe804 . . . 37 gs1 . . . 38 hobie . . . 39 hobiesm . . . 40 hor20 . . . 41 hq07 . . . 42 hq09 . . . 43 hq208 . . . 50 hq209 . . . 51 hq259b . . . 52 hq309 . . . 53 hq358 . . . 54 hq359 . . . 55 hq1010 . . . 56 hq1012 . . . 57 hq1510 . . . 58 hq1511 . . . 59 hq1512 . . . 60 hq1585 . . . 61 hq2010 . . . 62 hq2012 . . . 63 hq2090sm . . . 64 hq2195 . . . 65 hq2510 . . . 66 hq2511 . . . 67 hq2590sm . . . 68 hq3010 . . . 69 hq3011 . . . 70 hq3012 . . . 71 hq3013 . . . 72 hq3014 . . . 73 hq3015 . . . 74 hq3510 . . . 75 hq3512 . . . 76 hq3513 . . . 77 hq3514 . . . 78 hq3518 . . . 79 hsnlf213 . . . 80 ht08 . . . 81 ht12 . . . 82 ht22 . . . 83 ht23 . . . 84 isa571 . . . 85 isa960 . . . 86 isa961 . . . 87 isa962 . . . 88 joukovski11 . . . 89 joukovski12 . . . 90 k1 . . . 91 k2 . . . 92 k3 . . . 93 k3311 . . . 94 kc135a . . . 95 kc135b . . . 96 kc135c . . . 97 kc135d . . . 98 l188root . . . 99 l188tip . . . 100 l7769 . . . 101 la2573a . . . 102 la5055 . . . 103
ls421 . . . 110 ls421mod . . . 111 lwk79100 . . . 112 lwk80080 . . . 113 lwk80100 . . . 114 lwk80120k25 . . . 115 lwk80150k25 . . . 116 m3 . . . 117 m6 . . . 118 m11 . . . 119 m12 . . . 120 m665 . . . 121 ma409 . . . 122 ma409sm . . . 123 marske1 . . . 124 marske2 . . . 125 marske3 . . . 126 marske4 . . . 127 marske5 . . . 128 marske7 . . . 129 mb253515sm . . . 130 mh18 . . . 131 mh20 . . . 132 mh22 . . . 133 mh23 . . . 134 mh24 . . . 135 mh25 . . . 136 mh26 . . . 137 mh27 . . . 138 mh30 . . . 139 mh32 . . . 140 mh42 . . . 141 mh43 . . . 142 mh44 . . . 143 mh45 . . . 144 mh46 . . . 145 mh49 . . . 146 mh60 . . . 147 mh61 . . . 148 mh62 . . . 149 mh64 . . . 150 mh70 . . . 151 mh78 . . . 152 mh80 . . . 153 mh81 . . . 154 mh82 . . . 155 mh83 . . . 156 mh84 . . . 157 mh91 . . . 158 mh92 . . . 159 mh93 . . . 160 mh94 . . . 161 mh95 . . . 162 mh102 . . . 163 mh115 . . . 170 mh116 . . . 171 mh117 . . . 172 mh120 . . . 173 mh121 . . . 174 mh200 . . . 175 mh201 . . . 176 miley . . . 177 mrc-16 . . . 178 mrc-20 . . . 179 ms317 . . . 180 mue139 . . . 181 n5h10 . . . 182 n5h15 . . . 183 n5h20 . . . 184 n6h15 . . . 185 n8h12 . . . 186 n9 . . . 187 n10 . . . 188 n11 . . . 189 n0011sc . . . 190 n12 . . . 191 n13 . . . 192 n14 . . . 193 n22 . . . 194 n24 . . . 195 n64215 . . . 196 naca0002mod . . . 197 naca0004mod . . . 198 naca0006mod . . . 199 naca0008mod . . . 200 naca0009sm . . . 201 naca0010mod . . . 202 naca0012mod . . . 203 naca0014mod . . . 204 naca0016mod . . . 205 naca0018mod . . . 206 naca0020mod . . . 207 naca0022mod . . . 208 naca0024mod . . . 209 naca0026mod . . . 210 naca0028mod . . . 211 naca0030mod . . . 212 naca64a010 . . . 213 naca64a210 . . . 214 naca66-018 . . . 215 naca632a015 . . . 216 naca747a315 . . . 217 naca747a415 . . . 218 naca000834 . . . 219 naca001034 . . . 220 naca001034a08cli0.2 . . . 221 naca001035 . . . 222 naca001064 . . . 223
naca1116mod . . . 230 naca1118mod . . . 231 naca1120-mod . . . 232 naca1122-mod . . . 233 naca1124-mod . . . 234 naca001234 . . . 235 naca001264 . . . 236 naca001264a08cli0.2 . . . 237 naca2408mod . . . 238 naca2415 . . . 239 naca6409mod . . . 240 naca16006 . . . 241 naca16009 . . . 242 naca16012 . . . 243 naca16015 . . . 244 naca16018 . . . 245 naca16021 . . . 246 naca23012 . . . 247 naca23015 . . . 248 naca23018 . . . 249 naca23021 . . . 250 naca63010a . . . 251 naca63012a . . . 252 naca63015a . . . 253 naca63206 . . . 254 naca63210a . . . 255 naca63212 . . . 256 naca63215 . . . 257 naca63215b . . . 258 naca63412 . . . 259 naca63415 . . . 260 naca64008a . . . 261 naca64012 . . . 262 naca64012a . . . 263 naca64015 . . . 264 naca64015a . . . 265 naca64108 . . . 266 naca64110 . . . 267 naca64206 . . . 268 naca64208 . . . 269 naca64209 . . . 270 naca64210 . . . 271 naca64212 . . . 272 naca64212mb . . . 273 naca65209 . . . 274 naca65210 . . . 275 naca65410 . . . 276 naca66206 . . . 277 naca66209 . . . 278 naca632615 . . . 279 naca633018 . . . 280 naca633218 . . . 281 naca633418 . . . 282 naca633618 . . . 283 naca643418 . . . 290 naca643618 . . . 291 naca644221 . . . 292 naca644421 . . . 293 naca651212 . . . 294 naca651412 . . . 295 naca652215 . . . 296 naca652415 . . . 297 naca652415a05 . . . 298 naca653218 . . . 299 naca654221 . . . 300 naca654421 . . . 301 naca654421a05 . . . 302 naca661212 . . . 303 naca662215 . . . 304 naca662415 . . . 305 naca663218 . . . 306 naca663418 . . . 307 naca664221 . . . 308 naca671215 . . . 309 nacacyh . . . 310 nacam2 . . . 311 nacam3 . . . 312 nacam6 . . . 313 nacam12 . . . 314 nasasc2-0714 . . . 315 ncambre . . . 316 nl722343 . . . 317 nl722362 . . . 318 nlf0115 . . . 319 nlf0215f . . . 320 nlf414f . . . 321 nlf415 . . . 322 nlf416 . . . 323 nlr1t . . . 324 nlr7301 . . . 325 nn7mk20 . . . 326 npl9510 . . . 327 npl9615 . . . 328 npl9626 . . . 329 npl9627 . . . 330 nplx . . . 331 oa206 . . . 332 oa209 . . . 333 oa213 . . . 334 oaf095 . . . 335 oaf102 . . . 336 oaf117 . . . 337 oaf128 . . . 338 oaf139 . . . 339 p51droot . . . 340 p51dtip . . . 341 p51hroot . . . 342 p51htip . . . 343
r1080 . . . 350 r1082 . . . 351 r1082t . . . 352 rae69ck . . . 353 rae100 . . . 354 rae101 . . . 355 rae102 . . . 356 rae103 . . . 357 rae104 . . . 358 rae2822 . . . 359 rae5212 . . . 360 rae5213 . . . 361 rae5214 . . . 362 rae5215 . . . 363 raf6 . . . 364 raf25 . . . 365 raf27 . . . 366 raf28 . . . 367 raf30 . . . 368 raf30md . . . 369 raf31 . . . 370 raf32 . . . 371 raf32md . . . 372 raf34 . . . 373 raf38 . . . 374 raf48 . . . 375 raf69 . . . 376 raf89 . . . 377 rc08b3 . . . 378 rc10b3 . . . 379 rc10n1 . . . 380 rc12b3 . . . 381 rc12n1 . . . 382 rc0864c . . . 383 rcsc2 . . . 384 rg8 . . . 385 rg12 . . . 386 rg12a . . . 387 rg12a189 . . . 388 rg14 . . . 389 rg14a147 . . . 390 rg15 . . . 391 rg15a111 . . . 392 rg15a213 . . . 393 rg149 . . . 394 rg1410 . . . 395 rg1495 . . . 396 rhodesg30 . . . 397 rhodesg32 . . . 398 rhodesg34 . . . 399 rhodesg36 . . . 400 s3 . . . 401 s102b . . . 402 s102s . . . 403 s1048 . . . 410 s2027 . . . 411 s2046 . . . 412 s2048 . . . 413 s2050 . . . 414 s2055 . . . 415 s2060 . . . 416 s2062 . . . 417 s2091 . . . 418 s3002 . . . 419 s3010 . . . 420 s3014 . . . 421 s3016 . . . 422 s3021 . . . 423 s3024 . . . 424 s3025 . . . 425 s4022 . . . 426 s4053 . . . 427 s4061 . . . 428 s4062 . . . 429 s4083 . . . 430 s4110 . . . 431 s4158 . . . 432 s4180 . . . 433 s4233 . . . 434 s4310 . . . 435 s4320 . . . 436 s5010 . . . 437 s5020 . . . 438 s6061 . . . 439 s6062 . . . 440 s6063 . . . 441 s7012 . . . 442 s7055 . . . 443 s7075 . . . 444 s8025 . . . 445 s8035 . . . 446 s8036 . . . 447 s8037 . . . 448 s8038 . . . 449 s8052 . . . 450 s8055 . . . 451 s8064 . . . 452 s8065 . . . 453 s8066 . . . 454 s9000 . . . 455 s9026 . . . 456 s9027 . . . 457 s9032 . . . 458 s9033 . . . 459 s9037 . . . 460 sa7035 . . . 461 sa7036 . . . 462 sa7038 . . . 463
sc20406 . . . 470 sc20410 . . . 471 sc20412 . . . 472 sc20414 . . . 473 sc20518 . . . 474 sc20606 . . . 475 sc20610 . . . 476 sc20612 . . . 477 sc20614 . . . 478 sc20706 . . . 479 sc20710 . . . 480 sc20712 . . . 481 sc20714 . . . 482 sc21006 . . . 483 sc21010 . . . 484 sd2030 . . . 485 sd2083 . . . 486 sd5060 . . . 487 sd6060 . . . 488 sd6080 . . . 489 sd7003 . . . 490 sd7032 . . . 491 sd7034 . . . 492 sd7037 . . . 493 sd7043 . . . 494 sd7062 . . . 495 sd7080 . . . 496 sd7084 . . . 497 sd7090 . . . 498 sd8000 . . . 499 sd8020 . . . 500 sd8040 . . . 501 sg6040 . . . 502 sg6041 . . . 503 sg6042 . . . 504 sg6043 . . . 505 sg6050 . . . 506 sg6051 . . . 507 sm701 . . . 508 sokolov . . . 509 spicasm . . . 510 ssca07 . . . 511 ssca09 . . . 512 stcyr24 . . . 513 stcyr172 . . . 514 stcyr234 . . . 515 strand . . . 516 tempest1 . . . 517 tsagi-r3a . . . 518 tsagi8 . . . 519 tsagi12 . . . 520 ua79sf18 . . . 521 uag8814320 . . . 522 ui1720 . . . 523 usa40 . . . 530 usa40b . . . 531 usa41 . . . 532 usa45 . . . 533 usa45m . . . 534 usa46 . . . 535 usa48 . . . 536 usa49 . . . 537 usa50 . . . 538 usa51 . . . 539 usa98 . . . 540 usnps4 . . . 541 v13006 . . . 542 v13009 . . . 543 v23010 . . . 544 vr1 . . . 545 vr7 . . . 546 vr7b . . . 547 vr8 . . . 548 vr9 . . . 549 vr11x . . . 550 vr12 . . . 551 vr13 . . . 552 vr14 . . . 553 vr15 . . . 554 wb13535sm . . . 555 whitcomb . . . 556 ys900 . . . 557 ys915 . . . 558 ys930 . . . 559
This collection of parametrized airfoils would not have been possible without the prior work of several indi-viduals. Many thanks goes to Prof. Michael Selig at University of Illinois at Urbana-Champaign for supply-ing the original point cloud airfoil database on which this work is based. All my appreciation to Brenda Kul-fan from Boeing for her inspiring work on class function / shape function transformation technique. My warm thanks tho the research team at Link¨oping University: Anton Jonz´en, Chetan Nangunoori, Jacob Bj¨arkmar, Jo-han Karl´en, Svante L¨othgren and Vijaykumar Govin-darajan.
The author also wishes to thank the sponsors: VIN-NOVA and the industrial partner Saab AB for their funding through Nationella Flygtekniska Frsksprogram-met, NFFP5.
2
Introduction
This book is intended to serve as a reference for students, engineers and researchers requiring a parametrized air-foil that can model existing airair-foils well as providing a significant design space for optimisation. The pro-posed method covers at least one thousand of the known profiles used in aeronautics today, while enabling many more. The method uses 15 parameters defining a wing profile. This way many existing airfoils can be mod-elled with close tolerance. In the following volumes, the parametrized airfoils are compared with the origi-nal point cloud data. The comparison is made for ge-ometrical and aerodynamic similarity, but is should be noted that the point clouds used may in some instances not be representative for the original airfoil due to round off errors, discretisation error and other other unknown errors. The parametrisation is intended for two dimen-sional airfoils but the method can easily be extended to a three dimensional wing.
The coordinate resolution becomes infinite and point dis-tribution becomes a non-issue by employing a functional parametric description with built-in smoothing and in-terpolation. In order to facilitate this, some basic as-sumptions regarding the shape of an airfoil are made: The airfoil is assumed to have one distinct top and bot-tom point, the chord line has a length of exactly one, forming the x-axis of the profile, the trailing edge is as-sumed to be either sharp, i.e. with a y-coordinate of zero for both top and bottom sides, or blunt with the y coor-dinates of the top and bottom trailing edges being sym-metric around the chord line. These assumptions means
lower sides both ended at x=1.
3
Background
A fundamental part of aircraft design involves wing air-foil optimization, establishing an outer shape of the wing which has good aerodynamic performance for the design mission, good internal volume distribution for fuel and systems and which also serves as an efficient structural member supporting the load of the weight of the air-craft. The underlying idea with this parametrization is to couple an appropriate number of parameters, balanc-ing the need of geometric accuracy with the necessity of few airfoil parameters in order to facilitate en expedient optimisation, with the intrinsic value of having param-eters that makes sense for a human; such as thickness, camber and trailing edge thickness. Several approaches to parametrization of wing profiles can be found in the literature.
Airfoils can be described by point clouds as done in most airfoil libraries [1]. The number of parameters is twice as large as the number of points used (x and y coordi-nates) and in the case of aerodynamic optimization this parametrization will most certainly be not well behaved, since no smoothing function is included and must there-fore be employed. Other problems may arise for the fact that the airfoils sometimes are defined with too few co-ordinate points and/or too few decimals, a problem oc-curring especially with old airfoils. On the other hand, the design space that this kind of parametrization allows representing is extremely large, as any and all shapes can be reproduced, even degenerate ones.
Airfoils can also be represented by mathematical func-tions. Among the most common representatives of this category are indeed the NACA 4-, 5- and 6-digits for-mulations [2] [3]. Compared to point clouds, they could be said to represent the opposite case: they are very well behaving parametrizations, but they cannot cover a very large design space, since they only provide four to six parameters respectively to be tuned. The NACA 4 digit series is particularly interesting as the parameters are a part of the name of the airfoil. In the case of the 5- and 6 digit series, the name is instead constructed from the airfoils aerodynamic characteristic and geome-try. Another known set of theoretically defined airfoils are the Joukowski profiles [4]. Using the conformal map-ping method, airfoils with a round nose and sharp trail-ing edge can be represented. Sadly the method is not to recommend for trying to match known airfoils and the design space it describes is quite confined to airfoils with often poor performances.
rameters at will. Also the formulation is not restricted to round nose and sharp trailing edge profiles, but can describe almost any shape.
4
Method
4.1
Model
The envelope of the airfoil is described by a set of para-metric Bezi´er curves, which are closely related to Bern-stein polynomials. The equation for an n-dimensional cubic Bezi´er curve is shown in equation 1. The cubic Bezi´er curve requires the four control points, P0 to P3
in order to be defined. The points P0 to P2 span the
first control vector, and P2 to P3 span the second
con-trol vector, as shown in figure 1. The Bezi´er is tangential to the control vectors at the start and endpoints of the curve. This behaviour will ensure that the leading edge is tangential with the z-axis and that the curve at top point of the airfoil is tangential with the x-axis. The
air-Figure 1: Generic cubic Bezi´er curve with the four con-trol points P0 to P3 marked. The Bezi´er is tangential
to the control vectors at the start and endpoints of the curve.
foil’s top and bottom curves are modelled individually by two cubic Bezi´er curves in parametric form being C1 continuous at the defined top and bottom points, as well as the leading edge. C1 continuity was selected over C2 continuity in order to allow curve fitting with many older airfoils which only exhibit C1 continuity.
¯
B = (1 − t)3P¯0+ 3t(1 − t)2P¯1+ 3t2(1 − t) ¯P2+ t3P¯3 (1)
When modelling modern profiles, the proposed method does allow C2 continuity as well. Figure 2 gives an ex-ample of a transonic wing airfoil, the Lockheed C-5A BL576, and show the outer envelope and the Bezi´er
Figure 2: Parametrized transonic wing airfoil with Bezi´er control points and control vectors, and the num-bering of the control points.
the curve, giving 26 variables when both x and y co-ordinates are taken into account. However when some symmetries and simplifications valid for wing profiles are taken into account the number of independent parame-ters are reduced to 14. Control point 1 and 13 always have the same x-coordinate, one, and the same absolute value of their y-coordinate is also equal as their average, the camber line, must be on the x-axis at the trailing edge. Control points 3,4 and 5 on the bottom side have the same y-coordinate. The same goes for the top side control points 9, 10 and 11. The leading edge points 6,7 and 8 all have an x-coordinate of zero. Table 1 show the dependent parameters for the control points.
Table 1: Coordinate dependency for the control points. Some always take the value one or zero, while others (a,b,c) always shares the same numerical while (xn yn )
are allowed any value.
Coordinate Point nr. X Y 1 1 a 2 x2 y2 3 x3 b 4 x4 b 5 x5 b 6 0 y6 7 0 0 8 0 y8 9 x9 c 10 x10 c 11 x11 c 12 x12 y12 13 1 −a
The control points for each of the investigated airfoils are available in this tabulated form in the results section of this book.
4.2
Parameterization
parameter transformations are done:
The lengths of the control vectors are limited to prevent degenerate cases. For example the upper leading edge control vector needs to be shorter than the distance be-tween the top point and the chord line to prevent leading edge overshoot. Figure 3 shows the bounding box lim-iting the range of the control vectors. None of the con-trol points are allowed outside of this box, furthermore the trailing edge control vectors, governed by the two control points nr.2 and nr.12 may never reach further forward than points nr.3 and nr.11 respectively. -Shown by the limit lines L1and L2 in figure 3. Thickness: The
Figure 3: Bounding box of the control vectors, together with the trailing edge vectors forward limits L1 and L2.
x and y coordinates of the top and bottom points (nr. 4 and nr.10) are kept as is and named upper thickness and upper thickness position and similarly for the lower side. The upper height is parametrized as a factor k4
times the maximum allowed upper thickness, 0.15, ac-cording to equation 2. As the lower side is treated in the same way, this means that the maximum thickness al-lowed with this parametrization is 30% of the chord. The difference between the upper and lower thickness then becomes the ram thickness. The ram thickness equals the airfoil thickness in case the thickness positions are equals. If the upper and lower thickness positions are not equal, the ram thickness will be slightly larger than the traditional airfoil thickness.
y9,10,11= hu= k5· 0.15 (2)
Control vectors: The upper leading edge control vec-tor spanned by its start point, the leading edge at [0 0] which is point nr.7, and point nr.8. The length of this vector is defined as a fraction k1 of the upper thickness
hu, according to equation 3 The constant k1is then only
allowed to be in the range [0..1], see figure 4. This en-sures that the part of the profile going from the leading edge to the top point does not overshoot the top points y value.
y8= k1· hu (3)
The top side of the airfoil is controlled by three param-eters, shown in figure 5. The top point position Pu is
Figure 4: Definition of the leading edge control vector parameters.
nr.10 to nr.9 has its length limited to a fraction, k2, of the
top point position in the same way in order to prevent an overshoot of the profile into negative x-coordinates. Likewise the control vector defined by points 10 to 11, the top to TE vector is a fraction k4 of the length
be-tween the upper thickness position (nr.10) and the trail-ing edge (x=1). The trailtrail-ing edge is defined by five
Figure 5: Definition of the top side control vector pa-rameters.
rameters, some shown in figure 6. The trailing edge gap g, is the distance between the upper and lower side of the airfoil at the trailing edge. It is parametrized accord-ing to equation 4, where Gmax is the maximum allowed
trailing edge gap of 5% of the chord.
g = k15· Gmax (4)
The release angle α, which is the angle between the cam-ber line tangent and the chord line at the trailing edge, is parametrized similarly according to equation 5. The release angle is a fraction k14 times the maximum
al-lowed release angle αmax of 0.35 radians ( about 20◦ ).
Is should be noted that the release angle may take on both positive and negative values.
α = k14· αmax (5)
The boat tail angle β, which is the angle between tan-gents of the upper and lower sides of the airfoil at the trailing edge is defined in equation 6. It is treated in a similar way to the release angle. The boat tail angle β is a factor k13times the maximum allowed boat tail angle
βmax of 1 radian ( about 57◦ ).
trol vectors together with the trailing edge gap, the boat tail angle and the release angle determines the position of control points nr. 2 and nr. 12. These lengths are are also parametrized according to equation 7. The length of the upper vector, V , is a fraction k11of the maximum
allowed length Vmax. The maximum allowed length is in
turn dependent on the bounding box of the airfoil and the position of the forward limit L1set by the x-position
of control point nr. 11.
V = k11,12· Vmax (7)
The parameters of the lower side of the airfoil are de-fined in the same manner as the upper side parameters, numbering the parameters in the same way from 6 to 10. With the five parameters defining the trailing edge, the number of parameters are now reduced to 15. See table 2. By the limits of the fractions many degenerate airfoils are now hard to impossible to generate. By using the chord length as normalizing agent, the parameters are also dimensionless and fully scalable.
Table 2: Parameter names and order.
Name Parameter Range
Upper side
Upper nose fraction k1 [0..1]
Upper forward fraction k2 [0..1]
Upper thickness position k3 [0..1]
Upper rearward fraction k4 [0..1]
Upper thickness k5 [0..1]
Lower side
Lower nose fraction k6 [0..1]
Lower forward fraction k7 [0..1]
Lower thickness position k8 [0..1]
Lower rearward fraction k8 [0..1]
Lower thickness k10 [0..1]
Trailing edge
Upper length fraction k11 [0..1]
Lower length fraction k12 [0..1]
Boat tail angle fraction k13 [0..1]
Release angle fraction k10 [0..1]
Trailing edge gap fraction k10 [0..1]
4.3
Base change
By listing the parameters k1 to k15 when rounded of
to the nearest tenth, a 15 digit number could be used
ification to the new base numbering has to be made as both zero and one needs to be modelled, and any double digit parameter is disallowed. The encoding follows the RFC3548 [6]. The series [0, 1, 2, .., 25, 26, ..., 51, 52, ...63] maps to [A, B, C, .., Z, a, ..., z, 0, ... ]. By rounding the base 10 multi-decimal parameter towards the closest 63:rd as shown in table 3, a reasonable accurate value can be stored in a single digit. With this system an
air-Table 3: Base change example.
Parameter 63:rds base 64 error
k1= 0 0 A 0 %
k2= 0.3333 21 V 0 %
k3= 0.5 32 g 1.6 %
k4= 0.7 44 s -0.3 %
k5= 1 63 0 %
foil with know parameters k1to k15can be expressed as
a single string. For example will the Naca747a415 profile shown in figure 6 be represented as the string shown in table 4
Table 4: Base 64 representation:
ggaQszVsoTL8DeA
4.4
Reproducing known airfoils
In many design cases it will not be appropriate to start with a generic airfoil for design optimization. Instead, by employing a known airfoil, whether it is a Clark-Y, NACA0012 or any other known airfoil there is a need of having the traditional airfoil shape expressed in the proposed parameters. Modelling known airfoils require slightly more work than creating new airfoils.
When fitting known wing profiles to the parametrization, the input data are sometimes in poor condition and in need of preprocessing. The point cloud must have its leading edge at [0 0] and the trailing edge cord have to end at [1 0], if the profile has a trailing edge gap, this should be symmetrically distributed around the [1 0]. If this is not the case som geometrical rotation, transla-tion and scaling will have to be employed. This means that some aerodynamic properties such has zero lift an-gle and stall anan-gle of attack will shift when comparing the parametrized airfoil with external aero data.
the x-axis, rather than letting the chord line define the x-axis.
A starting guess of parameters were created by evaluat-ing the profile radius at the leadevaluat-ing edge, top and bot-tom, at the upper maximum y- position and at the lower minimum y-position. Together with the trailing edge gap and the slope of the upper and lower sides of the airfoil at the trailing edge. The radius at these points are computed with a three point circle algorithm from which the length of the control vectors can be computed according to equation 8, where a is the outgoing control vector length and h the perpendicular distance to the next control point as shown in figure 7.
1 r =
2h
3a3 (8)
Figure 7: Definition radius parameters.
With the obtained starting guess, a standard optimiza-tion is run in MATLAB to fit the parameter curve to the corresponding point cloud. The mathematical method used is the built-in fsolve method, which in this case utilizes the Levenberg-Marquardt algorithm. The run is set to minimize the root mean square error of the verti-cal position of the coordinate points between parameter points and point cloud.
The optimization is nested in two layers in order to treat the parameter nature of the Bezi´er curve. The outer loop solves for the control parameters governing the curve segment in question and an inner loop solving for the curvilinear position parameter vector t, with respect to the x coordinate. As the original data points may have any distribution along the x-axis, it cannot be assumed that the t vector in equation 1 is evenly distributed. The optimization results is evaluated both from a geo-metrical point of view, were the error of vertical position of each point is plotted for the profile. The average RMS error for the profile is a general quality control. The av-erage RMS error was usually in the order of 10−4, ne-cessitating the use of the unit error counts (ects), where 1 ects = 10−4. Similarly, the curvature and error in
be assumed to be small.
To further investigate the correlation between the orig-inal data point cloud and the parametric wing pro-file, an aerodynamic study was performed utilizing the panel method XFOIL [8]. The original airfoil and the parametrized airfoil were both subjected to a CL sweep
ranging from −0.3 to 1 at a Reynolds number of 6 · 106.
The drag and moment coefficients were evaluated, as well as the boundary layer transition point for both profiles. The proposed parametrization method was tested on a set of over 1100 different airfoils. Results for these pro-files are presented in this report, in the catalog section. For each of the investigated airfoils the reported curva-ture distribution graph is truncated at the leading edge in order to give a better scale of the results for the rest of the profile. Each profile is reported on a separate page consisting of the following sections
• Full name, if one is available
• Data source, usually the UIUC [1] database, but also NACA or other sources.
• A geometry plot, showing both a scaled up y-axis with camber and thickness, as well as an axis equal profile plot.
• A geometrical data table containing maximum thickness, maximum thickness position etc... • Coordinates of the Bezi´er curve control points. • Base 64 parametrized airfoil name
• A table showing the average errors in position, cur-vature as well as errors in drag- and pitching mo-ment coefficient and transition point position for control point and parameter curves at a standard CL of 0.3
• A graph showing the position and curvature error over the entire profile.
• A figure showing the error in drag- and pitching moment coefficient as well as the error in transition point position for a range of lift coefficients.
5
Discussion
The conducted aerodynamic study covers only some aerodynamic phenomena in the linear domain of low speed flight. For a more thorough comparison higer or-der effects needs to be modelled. Notably stall angle of
at the top and bottom points. Adding this constraint to the method will reduce the number of free parame-ters with two, and also give a more traditional curvature continuity. However, the geometrical fitting of known airfoils would suffer in having a higher geometrical er-ror. For most known airfoils tested, the optimized cur-vature is indeed discontinuous, but with a very small step. This discontinuity does not appear to have a sig-nificant impact on the aerodynamic performance of the parametrized airfoil.
Some of the airfoils in the catalog have an improper set of control points. In the numerical optimisation used to compute the control points, some profiles got a zero length control vector at the trailing edge. While the geometric representation using the control points works, as well as creating the base 64 string, creating control points from the BM64 string will not work. The zero-length control vector destroys the information about its orientation.
6
Software
MATLAB code needed for evaluating the airfoils in the database, as well as an electronic version of the database will be available at:
Link¨oping University:
http://www.iei.liu.se/flumes/aircraft-design/ software
and at Redhammer Consulting: http://www.redhammer.se/software
References
[1] Michael Selig, UIUC Airfoil Coordinates Database, University of Illinois at Urbana-Champaign, Dept of Aerospace Engineering, Urbana, Illinois, http://www.ae.illinois.edu/m-selig/ads/coord database.html, webpage retrieved 2012-01-01
[2] E. N. Jacobs, K. E. Ward, & R. M. Pinkerton The characteristics of 78 related airfoil sections from tests in the variable-density wind tunnel, NACA Report No. 460,1933
[3] P. Marzocca. The NACA airfoil series, Clarkson Uni-versity, Retrieved 07-03-2009.
[4] R. Von Mises, Theory of Flight, Dover Publications
Data Encodings, Request for Comments: 3548, Net-work Working Group, The Internet Society, 2003. [7] Louden, F A , Collection of wind-tunnel data
on commonly used wing sections, NACA-TR-331, 93R20691,1930
[8] Drela, M, XFOIL - An analysis and design system for low Reynolds number airfoils, Proceedings of the Conference, Notre Dame, Germany; 5-7 June 1989. pp. 1-12. 1989.
7
Airfoil Catalog
Information: Gottingen 673 airfoil Reference: UIUC
Figure 8: Wing profile with camber and thickness dis-tribution.
Table 5: Geometrical properties
Maximum Thickness: 10.7812 % @0.35C Maximum Camber: 2.7651 % @0.47C Trailing Edge Gap: 0.4 %C Upper nose radius: 0.18724 %C Lower nose radius: 0.16614 %C Boat-Tail Angle: 13.5355 deg Release Angle: 6.1497 deg Nose Incidence: 5.2022 deg Camber deflection: 11.3519 deg
Table 6: Controlpoints 1 -0.002 0.68741 -0.0053721 0.49986 -0.02985 0.20121 -0.02985 0.064908 -0.02985 0 -0.008479 0 0 0 0.010842 0.094169 0.08057 0.39674 0.08057 0.47118 0.08057 0.68855 0.073432 1 0.002
Table 7: Base 64 representation:
JwZIhSqNYN5nPpK
Control points Base64 RMS position error: 2.2 4.457 ects RMS curvature error: Inf Inf % CD error 1.4 -1.3 dcts Cm error 2 -2 mcts Upper transition point -2.48 1.73 %
Figure 9: Error distribution of vertical position and curvature of the parameter curve.
Information: Gottingen 675 airfoil Reference: UIUC
Figure 11: Wing profile with camber and thickness dis-tribution.
Table 9: Geometrical properties
Maximum Thickness: 14.6311 % @0.29C Maximum Camber: 5.9429 % @0.45C Trailing Edge Gap: 0.35 %C Upper nose radius: 2.4084 %C Lower nose radius: 2.2406 %C Boat-Tail Angle: 15.7436 deg Release Angle: 8.4689 deg Nose Incidence: 12.2588 deg Camber deflection: 20.7277 deg
Table 10: Controlpoints 1 -0.00175 0.37714 0.004741 0.21775 -0.03335 0.07616 -0.03335 0.056358 -0.03335 0 -0.029014 0 0 0 0.032398 0.065372 0.13024 0.39547 0.13024 0.65942 0.13024 0.93386 0.021142 1 0.00175
Table 11: Base 64 representation:
Q0Zc33RFKOMyStJ
Control points Base64 RMS position error: 4.429 6.389 ects RMS curvature error: Inf Inf % CD error 0.4 1.8 dcts Cm error -11 4 mcts Upper transition point 1.11 0.31 %
Figure 12: Error distribution of vertical position and curvature of the parameter curve.
Information: Gottingen 676 (= M 12) Reference: UIUC
Figure 14: Wing profile with camber and thickness dis-tribution.
Table 13: Geometrical properties
Maximum Thickness: 11.8712 % @0.33C Maximum Camber: 2.024 % @0.29C Trailing Edge Gap: 0.3 %C Upper nose radius: 1.2313 %C Lower nose radius: 1.7655 %C Boat-Tail Angle: 16.7088 deg Release Angle: 1.1857 deg Nose Incidence: 2.3603 deg Camber deflection: 3.5459 deg
Table 14: Controlpoints 1 -0.0015 0.71216 -0.037703 0.44935 -0.0395 0.39994 -0.0395 0.061709 -0.0395 0 -0.02695 0 0 0 0.034413 0.14426 0.0795 0.30012 0.0795 0.47469 0.0795 0.57928 0.072206 1 0.0015
Table 15: Base 64 representation:
cgTQhr1aFR58ThI
Control points Base64 RMS position error: 2.164 3.226 ects RMS curvature error: Inf Inf % CD error -3.4 -2.9 dcts Cm error 3 -1 mcts Upper transition point 3.33 2.63 %
Figure 15: Error distribution of vertical position and curvature of the parameter curve.
Information: Gottingen 677 (= M 6) airfoil Reference: UIUC
Figure 17: Wing profile with camber and thickness dis-tribution.
Table 17: Geometrical properties
Maximum Thickness: 12.0186 % @0.32C Maximum Camber: 2.1969 % @0.29C Trailing Edge Gap: 0.4 %C Upper nose radius: 1.2483 %C Lower nose radius: 3.4365 %C Boat-Tail Angle: 16.8695 deg Release Angle: -0.46463 deg Nose Incidence: 0.9031 deg Camber deflection: 0.43847 deg
Table 18: Controlpoints 1 -0.002 0.81657 -0.030722 0.71657 -0.0385 0.39992 -0.0385 0.025042 -0.0385 0 -0.023952 0 0 0 0.034709 0.14476 0.082 0.30016 0.082 0.52017 0.082 0.58364 0.060294 1 0.002
Table 19: Base 64 representation:
bgTUin7ahQ3xTfK
Control points Base64 RMS position error: 2.688 4.503 ects RMS curvature error: Inf Inf % CD error -3.9 -2.7 dcts Cm error 20 1 mcts Upper transition point 3.67 3.01 %
Figure 18: Error distribution of vertical position and curvature of the parameter curve.
Information: Gottingen 679 airfoil Reference: UIUC
Figure 20: Wing profile with camber and thickness dis-tribution.
Table 21: Geometrical properties
Maximum Thickness: 18.3818 % @0.25C Maximum Camber: 4.4993 % @0.4C Trailing Edge Gap: 0 %C Upper nose radius: 3.6372 %C Lower nose radius: 2.7604 %C Boat-Tail Angle: 26.3561 deg Release Angle: 9.6257 deg Nose Incidence: 13.5989 deg Camber deflection: 23.2246 deg
Table 22: Controlpoints 1 0 0.73876 -0.016218 0.25203 -0.054051 0.15367 -0.054051 0.12294 -0.054051 0 -0.047564 0 0 0 0.044012 0.079887 0.13478 0.29083 0.13478 0.53305 0.13478 0.82797 0.072329 1 0
Table 23: Base 64 representation:
VtTW53NKHXhWsvA
Control points Base64 RMS position error: 4.503 7.94 ects RMS curvature error: Inf Inf % CD error 0.5 -0.6 dcts Cm error -1 -42 mcts Upper transition point -3.35 -1.67 %
Figure 21: Error distribution of vertical position and curvature of the parameter curve.
Information: Gottingen 681 airfoil Reference: UIUC
Figure 23: Wing profile with camber and thickness dis-tribution.
Table 25: Geometrical properties
Maximum Thickness: 16.9523 % @0.25C Maximum Camber: 4.3174 % @0.4C Trailing Edge Gap: 0 %C Upper nose radius: 2.5577 %C Lower nose radius: 2.6577 %C Boat-Tail Angle: 19.5605 deg Release Angle: 6.2279 deg Nose Incidence: 9.9021 deg Camber deflection: 16.13 deg
Table 26: Controlpoints 1 0 0.25766 -0.046084 0.1813 -0.04893 0.15306 -0.04893 0.10616 -0.04893 0 -0.04337 0 0 0 0.035869 0.07545 0.12576 0.29214 0.12576 0.4571 0.12576 0.61426 0.11067 1 0
Table 27: Base 64 representation:
SuTP14UKCV37WpA
Control points Base64 RMS position error: 3.029 5.277 ects RMS curvature error: 69.75 70.55 % CD error -4.3 -4.6 dcts Cm error 11 -3 mcts Upper transition point 0.1 1.2 %
Figure 24: Error distribution of vertical position and curvature of the parameter curve.
Information: Gottingen 682 airfoil Reference: UIUC
Figure 26: Wing profile with camber and thickness dis-tribution.
Table 29: Geometrical properties
Maximum Thickness: 10.79 % @0.26C Maximum Camber: 4.2621 % @0.41C Trailing Edge Gap: 0 %C Upper nose radius: 1.3079 %C Lower nose radius: 1.3468 %C Boat-Tail Angle: 12.7255 deg Release Angle: 7.048 deg Nose Incidence: 7.7968 deg Camber deflection: 14.8448 deg
Table 30: Controlpoints 1 0 0.45629 0.0065031 0.17259 -0.0225 0.1 -0.0225 0.052614 -0.0225 0 -0.021735 0 0 0 0.03137 0.11286 0.0945 0.3 0.0945 0.47546 0.0945 0.65122 0.08316 1 0
Table 31: Base 64 representation:
VnTQn9eGFK3pOqA
Control points Base64 RMS position error: 2.513 6.221 ects RMS curvature error: Inf Inf % CD error 4.7 5.2 dcts Cm error 16 34 mcts Upper transition point -7.56 -9.1 %
Figure 27: Error distribution of vertical position and curvature of the parameter curve.
Information: Gottingen 683 airfoil Reference: UIUC
Figure 29: Wing profile with camber and thickness dis-tribution.
Table 33: Geometrical properties
Maximum Thickness: 19.9 % @0.3C Maximum Camber: 2.9504 % @0.31C Trailing Edge Gap: 0 %C Upper nose radius: 3.0384 %C Lower nose radius: 3.5181 %C Boat-Tail Angle: 38.7074 deg Release Angle: -6.5984 deg Nose Incidence: 4.6442 deg Camber deflection: -1.9541 deg
Table 34: Controlpoints 1 0 0.89028 -0.053403 0.3842 -0.07 0.3 -0.07 0.16179 -0.07 0 -0.0616 0 0 0 0.048431 0.11579 0.129 0.3 0.129 0.48875 0.129 0.66268 0.07636 1 0
Table 35: Base 64 representation:
YmTR23sTIepwqVA
Control points Base64 RMS position error: 3.341 4.087 ects RMS curvature error: 31.13 31.08 % CD error -4 -4 dcts Cm error 32 45 mcts Upper transition point 0.63 0.28 %
Figure 30: Error distribution of vertical position and curvature of the parameter curve.
Information: Gottingen 685 airfoil Reference: UIUC
Figure 32: Wing profile with camber and thickness dis-tribution.
Table 37: Geometrical properties
Maximum Thickness: 13.2529 % @0.23C Maximum Camber: 4.2547 % @0.45C Trailing Edge Gap: 0 %C Upper nose radius: 1.9047 %C Lower nose radius: 1.8925 %C Boat-Tail Angle: 12.6695 deg Release Angle: 7.1632 deg Nose Incidence: 4.4905 deg Camber deflection: 11.6536 deg
Table 38: Controlpoints 1 0 0.35174 0.0093735 0.27396 -0.04155 0.15204 -0.04155 0.094265 -0.04155 0 -0.034486 0 0 0 0.045976 0.16646 0.10096 0.29505 0.10096 0.42913 0.10096 0.59631 0.096902 1 0
Table 39: Base 64 representation:
scTMq0YKJS84OrA
Control points Base64 RMS position error: 2.772 3.95 ects RMS curvature error: 78.53 79.53 % CD error 2.6 -3 dcts Cm error 13 -20 mcts Upper transition point -2.18 2.22 %
Figure 33: Error distribution of vertical position and curvature of the parameter curve.
Information: Gottingen 692 airfoil Reference: UIUC
Figure 35: Wing profile with camber and thickness dis-tribution.
Table 41: Geometrical properties
Maximum Thickness: 16.0837 % @0.33C Maximum Camber: 5.0253 % @0.44C Trailing Edge Gap: 0.5 %C Upper nose radius: 1.3587 %C Lower nose radius: 2.62 %C Boat-Tail Angle: 22.9183 deg Release Angle: 8.8411 deg Nose Incidence: 7.2281 deg Camber deflection: 16.0691 deg
Table 42: Controlpoints 1 -0.0025 0.27392 -0.035701 0.16941 -0.040245 0.1499 -0.040245 0.056415 -0.040245 0 -0.031391 0 0 0 0.022101 0.053925 0.1295 0.40032 0.1295 0.6248 0.1295 0.93473 0.026643 1 0.0025
Table 43: Base 64 representation:
L2aY2xnKBRM3atN
Control points Base64 RMS position error: 2.337 7.332 ects RMS curvature error: Inf Inf % CD error 0.2 -0.1 dcts Cm error 19 27 mcts Upper transition point 0.03 0.73 %
Figure 36: Error distribution of vertical position and curvature of the parameter curve.
Information: Gottingen 693 airfoil Reference: UIUC
Figure 38: Wing profile with camber and thickness dis-tribution.
Table 45: Geometrical properties
Maximum Thickness: 11.9613 % @0.34C Maximum Camber: 3.6218 % @0.43C Trailing Edge Gap: 0.5 %C Upper nose radius: 0.30703 %C Lower nose radius: 1.4902 %C Boat-Tail Angle: 17.4589 deg Release Angle: 5.697 deg Nose Incidence: 3.3786 deg Camber deflection: 9.0756 deg
Table 46: Controlpoints 1 -0.0025 0.90193 -0.0072038 0.21593 -0.0308 0.099923 -0.0308 0.073943 -0.0308 0 -0.027104 0 0 0 0.0081769 0.032666 0.0953 0.40024 0.0953 0.57808 0.0953 0.83768 0.043393 1 0.0025
Table 47: Base 64 representation:
F6aTo3RGINcLToN
Control points Base64 RMS position error: 2.266 3.903 ects RMS curvature error: Inf Inf % CD error -2.1 -2.1 dcts Cm error -31 -44 mcts Upper transition point 3.78 4.69 %
Figure 39: Error distribution of vertical position and curvature of the parameter curve.
Information: Gottingen 703 airfoil Reference: UIUC
Figure 41: Wing profile with camber and thickness dis-tribution.
Table 49: Geometrical properties
Maximum Thickness: 19.4363 % @0.32C Maximum Camber: 2.299 % @0.29C Trailing Edge Gap: 0 %C Upper nose radius: 3.7787 %C Lower nose radius: 3.6285 %C Boat-Tail Angle: 29.7938 deg Release Angle: 0 deg Nose Incidence: 4.81 deg Camber deflection: 4.81 deg
Table 50: Controlpoints 1 0 0.99357 -0.00171 0.78573 -0.075 0.4 -0.075 0.17709 -0.075 0 -0.065451 0 0 0 0.06388 0.16199 0.12 0.3 0.12 0.43179 0.12 0.60304 0.1056 1 0
Table 51: Base 64 representation:
hsTMy3jaog3CggA
Control points Base64 RMS position error: 3.755 4.541 ects RMS curvature error: 39.54 39.63 % CD error 0.7 0.8 dcts Cm error 92 64 mcts Upper transition point -3.72 -3.99 %
Figure 42: Error distribution of vertical position and curvature of the parameter curve.
Information: Gottingen 704 airfoil Reference: UIUC
Figure 44: Wing profile with camber and thickness dis-tribution.
Table 53: Geometrical properties
Maximum Thickness: 13.0008 % @0.29C Maximum Camber: 2.0662 % @0.31C Trailing Edge Gap: 0.55 %C Upper nose radius: 0.76654 %C Lower nose radius: 1.2672 %C Boat-Tail Angle: 18.3269 deg Release Angle: -1.0126 deg Nose Incidence: 3.5188 deg Camber deflection: 2.5062 deg
Table 54: Controlpoints 1 -0.00275 0.86409 -0.027145 0.77246 -0.04454 0.20077 -0.04454 0.076293 -0.04454 0 -0.025388 0 0 0 0.017611 0.060689 0.08565 0.29852 0.08565 0.60527 0.08565 0.70527 0.044963 1 0.00275
Table 55: Base 64 representation:
NyTckjnNtTvlUeO
Control points Base64 RMS position error: 4.699 6.27 ects RMS curvature error: Inf Inf % CD error -4.8 -4.8 dcts Cm error 26 25 mcts Upper transition point 3.09 3.01 %
Figure 45: Error distribution of vertical position and curvature of the parameter curve.
Information: Gottingen 711 airfoil Reference: UIUC
Figure 47: Wing profile with camber and thickness dis-tribution.
Table 57: Geometrical properties
Maximum Thickness: 14.853 % @0.3C Maximum Camber: 6.3051 % @0.31C Trailing Edge Gap: 1.4 %C Upper nose radius: 0.78451 %C Lower nose radius: 0.92836 %C Boat-Tail Angle: 21.6687 deg Release Angle: 10.4905 deg Nose Incidence: 17.2185 deg Camber deflection: 27.709 deg
Table 58: Controlpoints 1 -0.0070002 0.14092 -0.012156 0.044412 -0.012855 0.024911 -0.012855 0.020676 -0.012855 0 -0.011312 0 0 0 0.019404 0.071989 0.1373 0.30097 0.1373 0.57888 0.1373 0.81727 0.078336 1 0.0070002
Table 59: Base 64 representation:
JwTZ63LCBFi5Ywj
Control points Base64 RMS position error: 2.279 7.405 ects RMS curvature error: Inf Inf % CD error 6.2 0.5 dcts Cm error -10 19 mcts Upper transition point -5.94 -6.82 %
Figure 48: Error distribution of vertical position and curvature of the parameter curve.
Information: Gottingen 735 airfoil Reference: UIUC
Figure 50: Wing profile with camber and thickness dis-tribution.
Table 61: Geometrical properties
Maximum Thickness: 20.0582 % @0.29C Maximum Camber: 4.4019 % @0.31C Trailing Edge Gap: 0 %C Upper nose radius: 2.3472 %C Lower nose radius: 2.7451 %C Boat-Tail Angle: 15.6387 deg Release Angle: -3.5643 deg Nose Incidence: 13.4973 deg Camber deflection: 9.933 deg
Table 62: Controlpoints 1 0 0.88066 -0.024029 0.58481 -0.057 0.2 -0.057 0.162 -0.057 0 -0.05643 0 0 0 0.029126 0.054213 0.14425 0.3 0.14425 0.49188 0.14425 0.83099 0.012575 1 0
Table 63: Base 64 representation:
NzTS9-MNfYVbRaA
Control points Base64 RMS position error: 4.003 6.737 ects RMS curvature error: 19.74 20.75 % CD error -4.2 -4.2 dcts Cm error -3 -12 mcts Upper transition point 3.33 3.09 %
Figure 51: Error distribution of vertical position and curvature of the parameter curve.
Information: Gottingen 738 airfoil Reference: UIUC
Figure 53: Wing profile with camber and thickness dis-tribution.
Table 65: Geometrical properties
Maximum Thickness: 15.44 % @0.3C Maximum Camber: 2.125 % @0.3C Trailing Edge Gap: 0 %C Upper nose radius: 2.5258 %C Lower nose radius: 2.6688 %C Boat-Tail Angle: 12.7185 deg Release Angle: -3.332 deg Nose Incidence: 4.9499 deg Camber deflection: 1.6179 deg
Table 66: Controlpoints 1 0 0.95936 -0.0069403 0.55382 -0.05595 0.3 -0.05595 0.13625 -0.05595 0 -0.049236 0 0 0 0.038677 0.088837 0.09845 0.3 0.09845 0.53506 0.09845 0.7593 0.012729 1 0
Table 67: Base 64 representation:
ZsTVp3iTXYgIOaA
Control points Base64 RMS position error: 2.001 3.15 ects RMS curvature error: 19.76 20.62 % CD error -1.1 -1.1 dcts Cm error -7 11 mcts Upper transition point 1.27 0.93 %
Figure 54: Error distribution of vertical position and curvature of the parameter curve.
Information: Gottingen 758 airfoil Reference: UIUC
Figure 56: Wing profile with camber and thickness dis-tribution.
Table 69: Geometrical properties
Maximum Thickness: 13.9497 % @0.28C Maximum Camber: 4.6394 % @0.41C Trailing Edge Gap: 0 %C Upper nose radius: 1.5202 %C Lower nose radius: 1.8709 %C Boat-Tail Angle: 13.1212 deg Release Angle: 6.892 deg Nose Incidence: 10.1377 deg Camber deflection: 17.0297 deg
Table 70: Controlpoints 1 0 0.59123 0.0023642 0.38641 -0.0271 0.2 -0.0271 0.020148 -0.0271 0 -0.015852 0 0 0 0.037276 0.13711 0.11435 0.3 0.11435 0.4665 0.11435 0.56177 0.10483 1 0
Table 71: Base 64 representation:
ViTPwk5NPM6qPqA
Control points Base64 RMS position error: 2.332 6.336 ects RMS curvature error: Inf Inf % CD error 1.7 2 dcts Cm error 4 10 mcts Upper transition point -4.51 -5.33 %
Figure 57: Error distribution of vertical position and curvature of the parameter curve.
Information: Gottingen 766 airfoil Reference: UIUC
Figure 59: Wing profile with camber and thickness dis-tribution.
Table 73: Geometrical properties
Maximum Thickness: 12.0471 % @0.26C Maximum Camber: 1.4173 % @0.22C Trailing Edge Gap: 0 %C Upper nose radius: 3.2587 %C Lower nose radius: 1.4829 %C Boat-Tail Angle: 13.2973 deg Release Angle: 0.1775 deg Nose Incidence: 11.7416 deg Camber deflection: 11.9191 deg
Table 74: Controlpoints 1 0 0.59732 -0.045674 0.38317 -0.0465 0.3 -0.0465 0.048024 -0.0465 0 -0.021789 0 0 0 0.050524 0.1175 0.0743 0.25 0.0743 0.35708 0.0743 0.73631 0.031565 1 0
Table 75: Base 64 representation:
rhQJge1TIUb-PgA
Control points Base64 RMS position error: 2.357 3.852 ects RMS curvature error: 38.22 39.37 % CD error -2.7 -2.3 dcts Cm error -15 -26 mcts Upper transition point 4.55 4.35 %
Figure 60: Error distribution of vertical position and curvature of the parameter curve.
Information: Gottingen 767 airfoil Reference: UIUC
Figure 62: Wing profile with camber and thickness dis-tribution.
Table 77: Geometrical properties
Maximum Thickness: 12.007 % @0.21C Maximum Camber: 1.5004 % @0.19C Trailing Edge Gap: 0 %C Upper nose radius: 4.4262 %C Lower nose radius: 2.0604 %C Boat-Tail Angle: 10.3152 deg Release Angle: 0.2093 deg Nose Incidence: 12.9566 deg Camber deflection: 13.1659 deg
Table 78: Controlpoints 1 0 0.49884 -0.04339 0.28255 -0.0452 0.25 -0.0452 0.14874 -0.0452 0 -0.0452 0 0 0 0.06 0.122 0.075 0.2 0.075 0.31644 0.075 0.36907 0.059273 1 0
Table 79: Base 64 representation:
yZNJg aQDT68MgA
Control points Base64 RMS position error: 2.509 5.261 ects RMS curvature error: Inf Inf % CD error -4.5 -4.6 dcts Cm error 18 -1 mcts Upper transition point 1.53 1.83 %
Figure 63: Error distribution of vertical position and curvature of the parameter curve.
Information: Gottingen 769 airfoil Reference: UIUC
Figure 65: Wing profile with camber and thickness dis-tribution.
Table 81: Geometrical properties
Maximum Thickness: 13.7935 % @0.21C Maximum Camber: 4.7991 % @0.31C Trailing Edge Gap: 0 %C Upper nose radius: 0.35956 %C Lower nose radius: 3.1215 %C Boat-Tail Angle: 10.7049 deg Release Angle: 4.905 deg Nose Incidence: 14.899 deg Camber deflection: 19.804 deg
Table 82: Controlpoints 1 0 0.29498 -0.0055062 0.20295 -0.03042 0.05 -0.03042 0.040449 -0.03042 0 -0.029013 0 0 0 0.003462 0.005 0.1154 0.25 0.1154 0.42041 0.1154 0.60006 0.072374 1 0
Table 83: Base 64 representation:
C-QPw8MDKNr4MnA
Control points Base64 RMS position error: 2.379 4.984 ects RMS curvature error: Inf Inf % CD error NaN NaN dcts Cm error NaN NaN mcts Upper transition point NaN NaN %
Figure 66: Error distribution of vertical position and curvature of the parameter curve.
Information: Gottingen 770 airfoil Reference: UIUC
Figure 68: Wing profile with camber and thickness dis-tribution.
Table 85: Geometrical properties
Maximum Thickness: 20.99 % @0.3C Maximum Camber: 4.002 % @0.3C Trailing Edge Gap: 0.26 %C Upper nose radius: 6.8175 %C Lower nose radius: 1.326 %C Boat-Tail Angle: 19.3974 deg Release Angle: 3.6187 deg Nose Incidence: 26.4859 deg Camber deflection: 30.1047 deg
Table 86: Controlpoints 1 -0.0013 0.61164 -0.042666 0.51164 -0.06493 0.29992 -0.06493 0.12422 -0.06493 0 -0.033137 0 0 0 0.084462 0.15696 0.14497 0.30019 0.14497 0.45279 0.14497 0.55279 0.10716 1 0.0013
Table 87: Base 64 representation:
kfTO9gkTTczyWlH
Control points Base64 RMS position error: 3.677 5.905 ects RMS curvature error: Inf Inf % CD error -3.3 -2.8 dcts Cm error -9 -25 mcts Upper transition point 0.95 0.56 %
Figure 69: Error distribution of vertical position and curvature of the parameter curve.
Information: Gottingen 775 airfoil Reference: UIUC
Figure 71: Wing profile with camber and thickness dis-tribution.
Table 89: Geometrical properties
Maximum Thickness: 20.9999 % @0.3C Maximum Camber: -0.0088208 % @0.02C Trailing Edge Gap: 0.44 %C Upper nose radius: 4.7333 %C Lower nose radius: 4.8183 %C Boat-Tail Angle: 27.8072 deg Release Angle: 0.009479 deg Nose Incidence: -0.23013 deg Camber deflection: -0.22065 deg
Table 90: Controlpoints 1 -0.0022 0.77884 -0.056906 0.49067 -0.105 0.29977 -0.105 0.10587 -0.105 0 -0.058316 0 0 0 0.057171 0.10358 0.105 0.30023 0.105 0.49168 0.105 0.78011 0.056671 1 0.0022
Table 91: Base 64 representation:
ipTSsjoTRshhfgL
Control points Base64 RMS position error: 0.795 3.879 ects RMS curvature error: 15.9 16.2 % CD error -0.4 0.3 dcts Cm error -2 -7 mcts Upper transition point 0.64 0.22 %
Figure 72: Error distribution of vertical position and curvature of the parameter curve.
Information: Gottingen 776 airfoil Reference: UIUC
Figure 74: Wing profile with camber and thickness dis-tribution.
Table 93: Geometrical properties
Maximum Thickness: 24.9999 % @0.3C Maximum Camber: -0.014792 % @0.02C Trailing Edge Gap: 0.52 %C Upper nose radius: 6.6315 %C Lower nose radius: 6.802 %C Boat-Tail Angle: 33.0388 deg Release Angle: 0.016196 deg Nose Incidence: -0.38646 deg Camber deflection: -0.37027 deg
Table 94: Controlpoints 1 -0.0026 0.86912 -0.041377 0.53746 -0.125 0.29968 -0.125 0.10341 -0.125 0 -0.068477 0 0 0 0.066607 0.10035 0.125 0.30033 0.125 0.53849 0.125 0.87028 0.041113 1 0.0026
Table 95: Base 64 representation:
hqTW0ipTW0UUkgN
Control points Base64 RMS position error: 0.389 3.565 ects RMS curvature error: 3.86 4.39 % CD error -0.3 0.6 dcts Cm error 0 6 mcts Upper transition point 0.33 -0.64 %
Figure 75: Error distribution of vertical position and curvature of the parameter curve.
Information: Gottingen 780 airfoil Reference: UIUC
Figure 77: Wing profile with camber and thickness dis-tribution.
Table 97: Geometrical properties
Maximum Thickness: 12 % @0.5C Maximum Camber: 1 % @0.5C Trailing Edge Gap: 0 %C Upper nose radius: 0.14943 %C Lower nose radius: 0.30486 %C Boat-Tail Angle: 23.5464 deg Release Angle: -2.7028 deg Nose Incidence: -1.4073 deg Camber deflection: -4.1102 deg
Table 98: Controlpoints 1 0 0.82172 -0.046028 0.6235 -0.05 0.5 -0.05 0.28486 -0.05 0 -0.024061 0 0 0 0.015705 0.2476 0.07 0.5 0.07 0.64575 0.07 0.74575 0.040589 1 0
Table 99: Base 64 representation:
OggTefcgQVt6abA
Control points Base64 RMS position error: 2.242 3.4 ects RMS curvature error: Inf Inf % CD error -1.3 1.3 dcts Cm error 20 -18 mcts Upper transition point 0.03 -0.03 %
Figure 78: Error distribution of vertical position and curvature of the parameter curve.
Information: Gottingen 795 airfoil Reference: UIUC
Figure 80: Wing profile with camber and thickness dis-tribution.
Table 101: Geometrical properties
Maximum Thickness: 8.0457 % @0.32C Maximum Camber: 2.4134 % @0.42C Trailing Edge Gap: 0 %C Upper nose radius: 0.51053 %C Lower nose radius: 0.71539 %C Boat-Tail Angle: 17.1887 deg Release Angle: 4.3772 deg Nose Incidence: 3.0533 deg Camber deflection: 7.4305 deg
Table 102: Controlpoints 1 0 0.94354 -0.0041628 0.16352 -0.02065 0.14645 -0.02065 0.069239 -0.02065 0 -0.018172 0 0 0 0.017681 0.091856 0.06385 0.37059 0.06385 0.6068 0.06385 0.91712 0.019091 1 0
Table 103: Base 64 representation:
SvYYb3hJBJTNTmA
Control points Base64 RMS position error: 2.573 4.386 ects RMS curvature error: Inf Inf % CD error -8.3 NaN dcts Cm error -45 NaN mcts Upper transition point 13.1 61.12 %
Figure 81: Error distribution of vertical position and curvature of the parameter curve.
Information: Gottingen 795 airfoil (smoothed) Reference: UIUC
Figure 83: Wing profile with camber and thickness dis-tribution.
Table 105: Geometrical properties
Maximum Thickness: 8.0861 % @0.32C Maximum Camber: 2.4099 % @0.42C Trailing Edge Gap: 0 %C Upper nose radius: 0.55628 %C Lower nose radius: 0.65774 %C Boat-Tail Angle: 53.6737 deg Release Angle: 13.2018 deg Nose Incidence: 3.8096 deg Camber deflection: 17.0114 deg
Table 106: Controlpoints 1 0 0.98591 -0.0034185 0.15574 -0.020633 0.14645 -0.020633 0.051575 -0.020633 0 -0.015038 0 0 0 0.019043 0.09778 0.064007 0.3706 0.064007 0.6642 0.064007 0.99658 0.0028774 1 0
Table 107: Base 64 representation:
TuYebuoJBJDL70A
Control points Base64 RMS position error: 1.779 4.692 ects RMS curvature error: 61.36 63.47 % CD error 0.4 0.4 dcts Cm error -32 -32 mcts Upper transition point -0.58 0.03 %
Figure 84: Error distribution of vertical position and curvature of the parameter curve.
Information: Gottingen 797 airfoil Reference: UIUC
Figure 86: Wing profile with camber and thickness dis-tribution.
Table 109: Geometrical properties
Maximum Thickness: 15.9583 % @0.33C Maximum Camber: 4.8974 % @0.44C Trailing Edge Gap: 0.80001 %C Upper nose radius: 0.71277 %C Lower nose radius: 2.8613 %C Boat-Tail Angle: 21.0949 deg Release Angle: 8.045 deg Nose Incidence: 5.5006 deg Camber deflection: 13.5456 deg
Table 110: Controlpoints 1 -0.004 0.28233 -0.035365 0.18233 -0.0406 0.14984 -0.0406 0.030967 -0.0406 0 -0.027608 0 0 0 0.014323 0.035821 0.1276 0.40051 0.1276 0.56839 0.1276 0.80526 0.069508 1 0.004
Table 111: Base 64 representation:
H5aS1ryKCRh3YsU
Control points Base64 RMS position error: 2.719 6.313 ects RMS curvature error: Inf Inf % CD error 2.8 2.7 dcts Cm error -4 -13 mcts Upper transition point 0.18 1 %
Figure 87: Error distribution of vertical position and curvature of the parameter curve.
Information: Gottingen 801 (MVA 301) airfoil Reference: UIUC
Figure 89: Wing profile with camber and thickness dis-tribution.
Table 113: Geometrical properties
Maximum Thickness: 9.8948 % @0.26C Maximum Camber: 6.0637 % @0.37C Trailing Edge Gap: 0.4 %C Upper nose radius: 2.8749 %C Lower nose radius: 1.6695 %C Boat-Tail Angle: 11.3251 deg Release Angle: 8.7761 deg Nose Incidence: 18.3122 deg Camber deflection: 27.0883 deg
Table 114: Controlpoints 1 -0.002 0.22835 0.039974 0.12136 -0.011875 0.012476 -0.011875 0.0098563 -0.011875 0 -0.010474 0 0 0 0.05018 0.13138 0.109 0.30022 0.109 0.53291 0.109 0.68877 0.082133 1 0.002
Table 115: Base 64 representation:
sjTVu3NBHFv3NtK
Control points Base64 RMS position error: 3.583 6.406 ects RMS curvature error: Inf Inf % CD error -7.3 -7.1 dcts Cm error -28 -19 mcts Upper transition point 1.63 -0.9 %
Figure 90: Error distribution of vertical position and curvature of the parameter curve.
Information: Gottingen 802 airfoil Reference: UIUC
Figure 92: Wing profile with camber and thickness dis-tribution.
Table 117: Geometrical properties
Maximum Thickness: 9.9292 % @0.26C Maximum Camber: 6.0501 % @0.37C Trailing Edge Gap: 0.4 %C Upper nose radius: 2.7514 %C Lower nose radius: 1.6411 %C Boat-Tail Angle: 11.3251 deg Release Angle: 8.7761 deg Nose Incidence: 17.8457 deg Camber deflection: 26.6218 deg
Table 118: Controlpoints 1 -0.002 0.22835 0.039974 0.12136 -0.011875 0.012476 -0.011875 0.009981 -0.011875 0 -0.01045 0 0 0 0.050181 0.13138 0.109 0.30022 0.109 0.53291 0.109 0.68877 0.082133 1 0.002
Table 119: Base 64 representation:
sjTVu3NBHFv3NtK
Control points Base64 RMS position error: 3.583 6.406 ects RMS curvature error: Inf Inf % CD error -63 -7.1 dcts Cm error 0 -19 mcts Upper transition point 0.3 -0.9 %
Figure 93: Error distribution of vertical position and curvature of the parameter curve.
Information: Gottingen 803 (Hacklinger) airfoil Reference: UIUC
Figure 95: Wing profile with camber and thickness dis-tribution.
Table 121: Geometrical properties
Maximum Thickness: 5.9516 % @0.16C Maximum Camber: 6.6462 % @0.43C Trailing Edge Gap: 0.3 %C Upper nose radius: 0.34561 %C Lower nose radius: 1.5199 %C Boat-Tail Angle: 5.0685 deg Release Angle: 12.68 deg Nose Incidence: 10.67 deg Camber deflection: 23.35 deg
Table 122: Controlpoints 1 -0.0015 0.40338 0.10527 0.031494 -0.012523 0.014981 -0.012523 0.013183 -0.012523 0 -0.01102 0 0 0 0.0039194 0.0066671 0.0916 0.40014 0.0916 0.57952 0.0916 0.93614 0.018868 1 0.0015
Table 123: Base 64 representation:
D-aTm3IBBFMmGzI
Control points Base64 RMS position error: 6.776 10.493 ects RMS curvature error: Inf Inf % CD error 59.7 -1 dcts Cm error 117 74 mcts Upper transition point 0.07 0.61 %
Figure 96: Error distribution of vertical position and curvature of the parameter curve.
Information: Gottingen 804 (EA 8) airfoil Reference: UIUC
Figure 98: Wing profile with camber and thickness dis-tribution.
Table 125: Geometrical properties
Maximum Thickness: 6.1644 % @0.33C Maximum Camber: 6.2798 % @0.53C Trailing Edge Gap: 0 %C Upper nose radius: 0.56368 %C Lower nose radius: 0.16706 %C Boat-Tail Angle: 8.9735 deg Release Angle: 19.5969 deg Nose Incidence: 12.474 deg Camber deflection: 32.0708 deg
Table 126: Controlpoints 1 0 0.68606 0.084766 0.025975 -0.00582 0.025 -0.00582 0.023552 -0.00582 0 -0.0051216 0 0 0 0.022246 0.13169 0.0915 0.5 0.0915 0.53544 0.0915 0.80196 0.088518 1 0
Table 127: Base 64 representation:
QugFm3ECAC9VK A
Control points Base64 RMS position error: 7.497 8.665 ects RMS curvature error: Inf Inf % CD error -1.7 -0.3 dcts Cm error 55 35 mcts Upper transition point 2.81 3.12 %
Figure 99: Error distribution of vertical position and curvature of the parameter curve.
Information: Gluharoff/Sikorsky GS-1 airfoil Reference: UIUC
Figure 101: Wing profile with camber and thickness distribution.
Table 129: Geometrical properties
Maximum Thickness: 14.0463 % @0.26C Maximum Camber: 4.1371 % @0.46C Trailing Edge Gap: 0 %C Upper nose radius: 2.35 %C Lower nose radius: 2.5954 %C Boat-Tail Angle: 13.8138 deg Release Angle: 7.5616 deg Nose Incidence: 3.7202 deg Camber deflection: 11.2818 deg
Table 130: Controlpoints 1 0 0.55078 0.0051334 0.2805 -0.0417 0.15 -0.0417 0.1005 -0.0417 0 -0.0417 0 0 0 0.052974 0.17913 0.1065 0.3 0.1065 0.41985 0.1065 0.58726 0.1065 1 0
Table 131: Base 64 representation:
gaTLs VKKS nPrA
Control points Base64 RMS position error: 2.322 4.965 ects RMS curvature error: Inf Inf % CD error 3.4 3 dcts Cm error 22 34 mcts Upper transition point -5.89 -6.41 %
Figure 102: Error distribution of vertical position and curvature of the parameter curve.
Information: Hobie Hawk airfoil (Hobie Hawk R/C sailplane) Reference: UIUC
Figure 104: Wing profile with camber and thickness distribution.
Table 133: Geometrical properties
Maximum Thickness: 8.5154 % @0.25C Maximum Camber: 3.9712 % @0.44C Trailing Edge Gap: 0 %C Upper nose radius: 0.6273 %C Lower nose radius: 1.4629 %C Boat-Tail Angle: 8.2059 deg Release Angle: 7.4467 deg Nose Incidence: 4.0276 deg Camber deflection: 11.4743 deg
Table 134: Controlpoints 1 0 0.51653 0.028247 0.2401 -0.01778 0.1 -0.01778 0.013019 -0.01778 0 -0.011268 0 0 0 0.02154 0.11094 0.07911 0.35 0.07911 0.58935 0.07911 0.89088 0.022299 1 0
Table 135: Base 64 representation:
RrWYho3GKISoJrA
Control points Base64 RMS position error: 2.18 5.307 ects RMS curvature error: Inf Inf % CD error -5.8 -2.8 dcts Cm error -10 -25 mcts Upper transition point 13.91 13.14 %
Figure 105: Error distribution of vertical position and curvature of the parameter curve.
Information: Hobie Hawk airfoil (Hobie Hawk R/C sailplane) Reference: UIUC
Figure 107: Wing profile with camber and thickness distribution.
Table 137: Geometrical properties
Maximum Thickness: 8.5847 % @0.26C Maximum Camber: 3.8453 % @0.46C Trailing Edge Gap: 0 %C Upper nose radius: 0.28998 %C Lower nose radius: 0.46873 %C Boat-Tail Angle: 7.6831 deg Release Angle: 6.9335 deg Nose Incidence: 2.7549 deg Camber deflection: 9.6884 deg
Table 138: Controlpoints 1 0 0.50092 0.026959 0.25688 -0.020407 0.087552 -0.020407 0.034117 -0.020407 0 -0.010325 0 0 0 0.014408 0.10738 0.077671 0.34981 0.077671 0.49584 0.077671 0.66524 0.063709 1 0
Table 139: Base 64 representation:
MrWOggmGMJzqJqA
Control points Base64 RMS position error: 1.136 4.7 ects RMS curvature error: 43.52 43.72 % CD error -0.5 0 dcts Cm error 5 22 mcts Upper transition point 0.71 -1.14 %
Figure 108: Error distribution of vertical position and curvature of the parameter curve.
Information: ONERA HOR20 - Onera propeller blade airfoils Reference: UIUC
Figure 110: Wing profile with camber and thickness distribution.
Table 141: Geometrical properties
Maximum Thickness: 20.4193 % @0.24C Maximum Camber: 3.2632 % @0.5C Trailing Edge Gap: 1.35 %C Upper nose radius: 2.7924 %C Lower nose radius: Inf %C Boat-Tail Angle: 9.6051 deg Release Angle: 6.6228 deg Nose Incidence: -7.8298 deg Camber deflection: -1.207 deg
Table 142: Controlpoints 1 -0.00675 0.62385 0.0052042 0.37271 -0.082656 0.1797 -0.082656 0 -0.082656 0 -0.015151 0 0 0 0.037413 0.075192 0.12656 0.30405 0.12656 0.49202 0.12656 0.74362 0.058563 1 0.00675
Table 143: Base 64 representation:
TvTR1M MPiglLqi
Control points Base64 RMS position error: 3.16 6.711 ects RMS curvature error: 52.18 51.79 % CD error 3.3 3.5 dcts Cm error -125 -96 mcts Upper transition point 0.88 -0.69 %
Figure 111: Error distribution of vertical position and curvature of the parameter curve.
Information: Quabeck HQ 0/7 R/C sailplane airfoil Reference: UIUC
Figure 113: Wing profile with camber and thickness distribution.
Table 145: Geometrical properties
Maximum Thickness: 6.998 % @0.34C Maximum Camber: -3.4994e-007 % @0.55C Trailing Edge Gap: 0 %C Upper nose radius: 0.30327 %C Lower nose radius: 0.30327 %C Boat-Tail Angle: 4.9355 deg Release Angle: -9.0161e-007 deg Nose Incidence: 0 deg Camber deflection: -9.0161e-007 deg
Table 146: Controlpoints 1 0 0.75837 -0.010413 0.59968 -0.03499 0.33933 -0.03499 0.086752 -0.03499 0 -0.013244 0 0 0 0.013244 0.086752 0.03499 0.33933 0.03499 0.59968 0.03499 0.75837 0.010413 1 0
Table 147: Base 64 representation:
YvWZPYvWZPmmGgA
Control points Base64 RMS position error: 0.763 2.336 ects RMS curvature error: 83.64 80.4 % CD error 1.2 -1.2 dcts Cm error -1 3 mcts Upper transition point -1.15 1.17 %
Figure 114: Error distribution of vertical position and curvature of the parameter curve.
Information: Quabeck HQ 0/9 R/C sailplane airfoil Reference: UIUC
Figure 116: Wing profile with camber and thickness distribution.
Table 149: Geometrical properties
Maximum Thickness: 8.112 % @0.34C Maximum Camber: 0.0066685 % @0.82C Trailing Edge Gap: 0 %C Upper nose radius: 0.37183 %C Lower nose radius: 0.37183 %C Boat-Tail Angle: 5.651 deg Release Angle: 0.048879 deg Nose Incidence: 0 deg Camber deflection: 0.048879 deg
Table 150: Controlpoints 1 0 0.75816 -0.012082 0.59977 -0.04056 0.33933 -0.04056 0.087062 -0.04056 0 -0.015398 0 0 0 0.015398 0.087062 0.04056 0.33933 0.04056 0.59977 0.04056 0.75816 0.012083 1 0
Table 151: Base 64 representation:
YvWZRYvWZRmmGgA
Control points Base64 RMS position error: 0.87 4.254 ects RMS curvature error: Inf Inf % CD error -1.4 -1.1 dcts Cm error 0 -1 mcts Upper transition point 2.17 1.3 %
Figure 117: Error distribution of vertical position and curvature of the parameter curve.
Information: Quabeck HQ 0/10 R/C sailplane airfoil Reference: UIUC
Figure 119: Wing profile with camber and thickness distribution.
Table 153: Geometrical properties
Maximum Thickness: 10 % @0.34C Maximum Camber: 1.1056e-006 % @0.75C Trailing Edge Gap: 0 %C Upper nose radius: 0.62037 %C Lower nose radius: 0.62037 %C Boat-Tail Angle: 7.0477 deg Release Angle: -1.398e-005 deg Nose Incidence: 0 deg Camber deflection: -1.398e-005 deg
Table 154: Controlpoints 1 0 0.75848 -0.014873 0.59952 -0.05 0.33933 -0.05 0.087108 -0.05 0 -0.018981 0 0 0 0.018981 0.087108 0.05 0.33933 0.05 0.59952 0.05 0.75848 0.014873 1 0
Table 155: Base 64 representation:
YvWZVYvWZVmmIgA
Control points Base64 RMS position error: 1.088 3.47 ects RMS curvature error: Inf Inf % CD error 0 0.2 dcts Cm error 2 3 mcts Upper transition point -0.52 -1.38 %
Figure 120: Error distribution of vertical position and curvature of the parameter curve.
Information: Quabeck HQ 1.0/8 R/C sailplane airfoil Reference: UIUC
Figure 122: Wing profile with camber and thickness distribution.
Table 157: Geometrical properties
Maximum Thickness: 7.9775 % @0.34C Maximum Camber: 0.99442 % @0.51C Trailing Edge Gap: 0 %C Upper nose radius: 0.36632 %C Lower nose radius: 0.17986 %C Boat-Tail Angle: 5.9283 deg Release Angle: 2.4987 deg Nose Incidence: 3.837 deg Camber deflection: 6.3357 deg
Table 158: Controlpoints 1 0 0.74357 -0.0020833 0.59291 -0.03037 0.325 -0.03037 0.012294 -0.03037 0 -0.0038395 0 0 0 0.01287 0.067827 0.04945 0.35 0.04945 0.59881 0.04945 0.74599 0.024292 1 0
Table 159: Base 64 representation:
RzWYVI9VZNonHjA
Control points Base64 RMS position error: 0.802 2.053 ects RMS curvature error: 37.74 36.85 % CD error -2.5 -1.9 dcts Cm error -5 3 mcts Upper transition point 6.25 4.56 %
Figure 123: Error distribution of vertical position and curvature of the parameter curve.
Information: Quabeck HQ 1.0/9 R/C sailplane airfoil Reference: UIUC
Figure 125: Wing profile with camber and thickness distribution.
Table 161: Geometrical properties
Maximum Thickness: 8.9859 % @0.34C Maximum Camber: 0.99736 % @0.5C Trailing Edge Gap: 0 %C Upper nose radius: 0.47055 %C Lower nose radius: 0.33304 %C Boat-Tail Angle: 6.6141 deg Release Angle: 2.4879 deg Nose Incidence: 3.7895 deg Camber deflection: 6.2773 deg
Table 162: Controlpoints 1 0 0.74711 -0.003616 0.59254 -0.03536 0.325 -0.03536 0.052318 -0.03536 0 -0.010778 0 0 0 0.014945 0.071198 0.05455 0.35 0.05455 0.5971 0.05455 0.75668 0.024694 1 0
Table 163: Base 64 representation:
SyWYXU1VZPmnHjA
Control points Base64 RMS position error: 1.159 2.919 ects RMS curvature error: 39.54 45.36 % CD error -1.6 1.1 dcts Cm error -4 0 mcts Upper transition point 4.12 -2.83 %
Figure 126: Error distribution of vertical position and curvature of the parameter curve.
Information: Quabeck HQ 1.5/8 R/C sailplane airfoil Reference: UIUC
Figure 128: Wing profile with camber and thickness distribution.
Table 165: Geometrical properties
Maximum Thickness: 7.9651 % @0.34C Maximum Camber: 1.4847 % @0.53C Trailing Edge Gap: 0 %C Upper nose radius: 0.46804 %C Lower nose radius: 0.35347 %C Boat-Tail Angle: 6.2435 deg Release Angle: 3.6044 deg Nose Incidence: 5.204 deg Camber deflection: 8.8085 deg
Table 166: Controlpoints 1 0 0.72322 0.002332 0.5851 -0.02562 0.325 -0.02562 0.273 -0.02562 0 -0.025364 0 0 0 0.015734 0.079335 0.05408 0.35 0.05408 0.60065 0.05408 0.73408 0.031362 1 0
Table 167: Base 64 representation:
TwWZX-KVZLqqHlA
Control points Base64 RMS position error: 1.522 2.035 ects RMS curvature error: 47.34 47.65 % CD error -5.3 -4.8 dcts Cm error -24 -34 mcts Upper transition point 11.74 10.81 %
Figure 129: Error distribution of vertical position and curvature of the parameter curve.
Information: Quabeck HQ 1.5/9 R/C sailplane airfoil Reference: UIUC
Figure 131: Wing profile with camber and thickness distribution.
Table 169: Geometrical properties
Maximum Thickness: 8.9784 % @0.34C Maximum Camber: 1.4916 % @0.52C Trailing Edge Gap: 0 %C Upper nose radius: 0.62349 %C Lower nose radius: 0.29824 %C Boat-Tail Angle: 6.7414 deg Release Angle: 3.7627 deg Nose Incidence: 6.1624 deg Camber deflection: 9.925 deg
Table 170: Controlpoints 1 0 0.74544 0.0017415 0.58353 -0.03063 0.325 -0.03063 0.023325 -0.03063 0 -0.0068101 0 0 0 0.018953 0.086421 0.05921 0.35 0.05921 0.59551 0.05921 0.73311 0.033401 1 0
Table 171: Base 64 representation:
UvWYZO6VZNpmIlA
Control points Base64 RMS position error: 1.136 3.05 ects RMS curvature error: Inf Inf % CD error 0.8 1.1 dcts Cm error -8 3 mcts Upper transition point -1.03 -2.37 %
Figure 132: Error distribution of vertical position and curvature of the parameter curve.
