Clark Y Joukovski 11 G¨ottingen 628 Eppler 793 Naca 0012 RAE 104 SC 20406 NLF 015 Whitcomb
Parametric Airfoil Catalog, Part I
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 I
Archer A18 to G¨
ottingen 655
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 a18 . . . 7 a18sm . . . 8 a63a108c . . . 9 ag03 . . . 10 ag04 . . . 11 ag09 . . . 13 ag10 . . . 14 ag11 . . . 15 ag12 . . . 16 ag13 . . . 17 ag14 . . . 18 ag16 . . . 19 ag17 . . . 20 ag18 . . . 21 ag19 . . . 22 ag24 . . . 23 ag25 . . . 24 ag26 . . . 25 ag27 . . . 26 ag35 . . . 27 ag36 . . . 28 ag37 . . . 29 ag38 . . . 30 ag44ct02r . . . 31 ag45c03 . . . 32 ag45ct02r . . . 33 ag46c03 . . . 34 ag46ct02r . . . 35 ag47c03 . . . 36 ag47ct02r . . . 37 ag455ct02r . . . 38 ah21-7 . . . 39 ah21-9 . . . 40 ah63k127 . . . 41 ah79k132 . . . 42 ah79k135 . . . 43 ah85l120 . . . 44 ah93w145 . . . 45 ah79100a . . . 51 ah79100b . . . 52 ah79100c . . . 53 ah80129 . . . 54 ah80136 . . . 55 ah80140 . . . 56 ah82150a . . . 57 ah82150f . . . 58 ah83150q . . . 59 ah83159 . . . 60 ah93156 . . . 61 ah93157 . . . 62 ah94145 . . . 63 ah94156 . . . 64 ah95160 . . . 65 ames01 . . . 66 ames02 . . . 67 ames03 . . . 68 amsoil1 . . . 69 amsoil2 . . . 70 aquilasm . . . 71 arad6 . . . 72 arad10 . . . 73 arad20 . . . 74 as5045 . . . 75 as5046 . . . 76 as5048 . . . 77 atr72sm . . . 78 avistar . . . 79 b29root . . . 80 b29tip . . . 81 b707e . . . 82 b737a . . . 83 b737b . . . 84 b737d . . . 85 bacj . . . 86 bacxxx . . . 87 be50 . . . 88 boe106 . . . 89 bqm34 . . . 90 c5a . . . 91 c5b . . . 92 c5c . . . 93 c141a . . . 94 c141b . . . 95 c141c . . . 96 c141d . . . 97 c141e . . . 98 c141f . . . 99 cast102 . . . 100 clarkk . . . 101 clarkv . . . 102 clarkx . . . 103 clarky . . . 104 clarkyh . . . 105
cr001sm . . . 111 curtisc72 . . . 112 dae11 . . . 113 dae21 . . . 114 dae31 . . . 115 dae51 . . . 116 davis-corrected . . . 117 davis . . . 118 daytonwright6 . . . 119 defcnd1 . . . 120 defcnd2 . . . 121 defcnd3 . . . 122 df101 . . . 123 dillner2032c . . . 124 doa5 . . . 125 du8608418 . . . 126 e66 . . . 127 e67 . . . 128 e168 . . . 129 e169 . . . 130 e171 . . . 131 e174 . . . 132 e176 . . . 133 e178 . . . 134 e180 . . . 135 e182 . . . 136 e184 . . . 137 e186 . . . 138 e193 . . . 139 e195 . . . 140 e197 . . . 141 e201 . . . 142 e203 . . . 143 e205 . . . 144 e207 . . . 145 e209 . . . 146 e210 . . . 147 e211 . . . 148 e212 . . . 149 e214 . . . 150 e216 . . . 151 e220 . . . 152 e221 . . . 153 e222 . . . 154 e224 . . . 155 e226 . . . 156 e228 . . . 157 e230 . . . 158 e231 . . . 159 e326 . . . 160 e327 . . . 161 e331 . . . 162 e332 . . . 163 e334 . . . 164 e335 . . . 165 e342 . . . 171 e343 . . . 172 e360 . . . 173 e361 . . . 174 e374 . . . 175 e385 . . . 176 e387 . . . 177 e392 . . . 178 e393 . . . 179 e395 . . . 180 e396 . . . 181 e397 . . . 182 e399 . . . 183 e403 . . . 184 e417 . . . 185 e422 . . . 186 e426 . . . 187 e428 . . . 188 e431 . . . 189 e432 . . . 190 e433 . . . 191 e434 . . . 192 e435 . . . 193 e471 . . . 194 e472 . . . 195 e473 . . . 196 e474 . . . 197 e475 . . . 198 e476 . . . 199 e477 . . . 200 e478 . . . 201 e479 . . . 202 e502 . . . 203 e542 . . . 204 e543 . . . 205 e544 . . . 206 e545 . . . 207 e546 . . . 208 e548 . . . 209 e550 . . . 210 e552 . . . 211 e554 . . . 212 e556 . . . 213 e557 . . . 214 e558 . . . 215 e559 . . . 216 e560 . . . 217 e561 . . . 218 e562 . . . 219 e580 . . . 220 e583 . . . 221 e584 . . . 222 e587 . . . 223 e591 . . . 224 e593 . . . 225
e636 . . . 231 e637 . . . 232 e638 . . . 233 e639 . . . 234 e642 . . . 235 e654 . . . 236 e655 . . . 237 e656 . . . 238 e657 . . . 239 e662 . . . 240 e664 . . . 241 e668 . . . 242 e682 . . . 243 e694 . . . 244 e715 . . . 245 e748 . . . 246 e793 . . . 247 e817 . . . 248 e836 . . . 249 e837 . . . 250 e838 . . . 251 e851 . . . 252 e852 . . . 253 e853 . . . 254 e854 . . . 255 e856 . . . 256 e857 . . . 257 e874 . . . 258 e1098 . . . 259 e1200 . . . 260 e1210 . . . 261 e1211 . . . 262 e1212 . . . 263 e1212mod . . . 264 e1213 . . . 265 e1214 . . . 266 e1230 . . . 267 e1233 . . . 268 ea61012 . . . 269 eh0009 . . . 270 eh1070 . . . 271 eh1090 . . . 272 eh1590 . . . 273 eh2010 . . . 274 eh2012 . . . 275 eiffel385 . . . 276 eiffel428 . . . 277 eppler793 . . . 278 falcon . . . 279 fg2 . . . 280 fg3 . . . 281 fg4 . . . 282 fx2 . . . 283 fx08s176 . . . 284 fx66a175 . . . 285 fx84w140 . . . 291 fx84w150 . . . 292 fx84w175 . . . 293 fx84w218 . . . 294 fx05188 . . . 295 fx05191 . . . 296 fx60100 . . . 297 fx60100sm . . . 298 fx60126 . . . 299 fx60157 . . . 300 fx60160 . . . 301 fx60177 . . . 302 fx61140 . . . 303 fx61147 . . . 304 fx601261 . . . 305 fx711530 . . . 306 fxl142k . . . 307 fxm2 . . . 308 fxs03182 . . . 309 fxs21158 . . . 310 giiia . . . 311 giiib . . . 312 giiic . . . 313 giiid . . . 314 giiie . . . 315 giiif . . . 316 giiig . . . 317 giiih . . . 318 giiii . . . 319 giiij . . . 320 giiik . . . 321 giiil . . . 322 gm15sm . . . 323 goe07k . . . 324 goe08k . . . 325 goe11k . . . 326 goe14k . . . 327 goe15k . . . 328 goe16k . . . 329 goe29b . . . 330 goe54 . . . 331 goe55 . . . 332 goe57 . . . 333 goe79 . . . 334 goe81 . . . 335 goe92 . . . 336 goe114 . . . 337 goe115 . . . 338 goe116 . . . 339 goe117 . . . 340 goe118 . . . 341 goe121 . . . 342 goe122 . . . 343 goe123 . . . 344 goe124 . . . 345
goe144 . . . 351 goe147 . . . 352 goe155 . . . 353 goe164 . . . 354 goe165 . . . 355 goe167 . . . 356 goe173 . . . 357 goe174 . . . 358 goe176 . . . 359 goe177 . . . 360 goe178 . . . 361 goe180 . . . 362 goe182 . . . 363 goe184 . . . 364 goe190 . . . 365 goe195 . . . 366 goe199 . . . 367 goe210 . . . 368 goe217 . . . 369 goe222 . . . 370 goe223 . . . 371 goe225 . . . 372 goe226 . . . 373 goe227 . . . 374 goe229 . . . 375 goe233 . . . 376 goe234 . . . 377 goe239 . . . 378 goe240 . . . 379 goe242 . . . 380 goe255 . . . 381 goe256 . . . 382 goe257 . . . 383 goe264 . . . 384 goe265 . . . 385 goe269 . . . 386 goe276 . . . 387 goe277 . . . 388 goe278 . . . 389 goe279 . . . 390 goe280 . . . 391 goe281 . . . 392 goe282 . . . 393 goe284 . . . 394 goe285 . . . 395 goe286 . . . 396 goe287 . . . 397 goe288 . . . 398 goe289 . . . 399 goe290 . . . 400 goe298 . . . 401 goe300 . . . 402 goe301 . . . 403 goe303 . . . 404 goe304 . . . 405 goe331 . . . 411 goe332 . . . 412 goe335 . . . 413 goe342 . . . 414 goe346 . . . 415 goe358 . . . 416 goe359 . . . 417 goe360 . . . 418 goe361 . . . 419 goe362 . . . 420 goe363 . . . 421 goe364 . . . 422 goe365 . . . 423 goe366 . . . 424 goe367 . . . 425 goe368 . . . 426 goe369 . . . 427 goe371 . . . 428 goe372 . . . 429 goe373 . . . 430 goe374 . . . 431 goe381 . . . 432 goe383 . . . 433 goe385 . . . 434 goe387 . . . 435 goe389 . . . 436 goe392 . . . 437 goe393 . . . 438 goe394 . . . 439 goe395 . . . 440 goe396 . . . 441 goe397 . . . 442 goe398 . . . 443 goe399 . . . 444 goe400 . . . 445 goe402 . . . 446 goe403 . . . 447 goe405 . . . 448 goe409 . . . 449 goe410 . . . 450 goe411 . . . 451 goe413 . . . 452 goe414 . . . 453 goe416a . . . 454 goe417 . . . 455 goe418 . . . 456 goe419 . . . 457 goe420 . . . 458 goe423 . . . 459 goe424 . . . 460 goe425 . . . 461 goe426 . . . 462 goe427 . . . 463 goe428 . . . 464 goe430 . . . 465
goe438 . . . 471 goe439 . . . 472 goe442 . . . 473 goe445 . . . 474 goe446 . . . 475 goe447 . . . 476 goe449 . . . 477 goe450 . . . 478 goe456 . . . 479 goe457 . . . 480 goe458 . . . 481 goe459 . . . 482 goe460 . . . 483 goe464 . . . 484 goe477 . . . 485 goe478 . . . 486 goe479 . . . 487 goe480 . . . 488 goe481a . . . 489 goe483 . . . 490 goe484 . . . 491 goe492 . . . 492 goe493 . . . 493 goe494 . . . 494 goe495 . . . 495 goe496 . . . 496 goe497 . . . 497 goe498 . . . 498 goe499 . . . 499 goe500 . . . 500 goe501 . . . 501 goe502 . . . 502 goe504 . . . 503 goe506 . . . 504 goe508 . . . 505 goe517 . . . 506 goe526 . . . 507 goe527 . . . 508 goe528 . . . 509 goe529 . . . 510 goe532 . . . 511 goe533 . . . 512 goe534 . . . 513 goe535 . . . 514 goe546 . . . 515 goe547 . . . 516 goe548 . . . 517 goe549 . . . 518 goe550 . . . 519 goe553 . . . 520 goe559 . . . 521 goe563 . . . 522 goe564 . . . 523 goe565 . . . 524 goe567 . . . 525 goe596 . . . 531 goe598 . . . 532 goe599 . . . 533 goe600 . . . 534 goe601 . . . 535 goe602 . . . 536 goe602m . . . 537 goe604 . . . 538 goe610bm . . . 539 goe611 . . . 540 goe613 . . . 541 goe615 . . . 542 goe617 . . . 543 goe619 . . . 544 goe620 . . . 545 goe621 . . . 546 goe622 . . . 547 goe623 . . . 548 goe624 . . . 549 goe626 . . . 550 goe627 . . . 551 goe628 . . . 552 goe629 . . . 553 goe630 . . . 554 goe645 . . . 555 goe646 . . . 556 goe647 . . . 557 goe648 . . . 558 goe650 . . . 559 goe654 . . . 560 goe655 . . . 561
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 that a lot of historical airfoils needed to be preprocessed
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 control points and control vectors. The control points
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
Handling the control point coordinates directly when specifying an airfoil is not user friendly. The
coordi-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
in itself a fraction of the chord length and need not to
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 to present a large set of airfoils. This approach would
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. One example of a wing profile that needs preprocessing is
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 curvature between were evaluated Notably many of the
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 attack and post-stall behaviour, which cannot be
cap-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 Inc., New York, 1959
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: Archer A18 F1C free flight airfoil(original) Reference: UIUC
Figure 8: Wing profile with camber and thickness dis-tribution.
Table 5: Geometrical properties
Maximum Thickness: 7.3716 % @0.26C Maximum Camber: 3.8388 % @0.49C Trailing Edge Gap: 0.6139 %C Upper nose radius: 0.87604 %C Lower nose radius: Inf %C Boat-Tail Angle: 8.305 deg Release Angle: 8.7462 deg Nose Incidence: 5.1754 deg Camber deflection: 13.9216 deg
Table 6: Controlpoints 1 -0.0030695 0.51761 0.035689 0.22225 -0.017479 0.075281 -0.017479 0 -0.017479 0 -0.0027967 0 0 0 0.034595 0.20492 0.071454 0.34893 0.071454 0.52472 0.071454 0.74869 0.060622 1 0.0030695
Table 7: Base 64 representation:
faWReK FKH1nJtP
Control points Base64 RMS position error: 3.139 4.145 ects RMS curvature error: 82.32 81.84 % CD error -6 -6.3 dcts Cm error -4 16 mcts Upper transition point 16.75 16.76 %
Figure 9: Error distribution of vertical position and curvature of the parameter curve.
Information: Archer A18 F1C free flight airfoil (smoothed) Reference: UIUC
Figure 11: Wing profile with camber and thickness dis-tribution.
Table 9: Geometrical properties
Maximum Thickness: 7.3004 % @0.26C Maximum Camber: 3.8292 % @0.48C Trailing Edge Gap: 0.6139 %C Upper nose radius: 0.80441 %C Lower nose radius: 0.7243 %C Boat-Tail Angle: 8.6557 deg Release Angle: 8.7335 deg Nose Incidence: 4.6017 deg Camber deflection: 13.3351 deg
Table 10: Controlpoints 1 -0.0030695 0.50962 0.034711 0.22382 -0.017479 0.075281 -0.017479 0.026042 -0.017479 0 -0.011214 0 0 0 0.031215 0.1817 0.071454 0.37893 0.071454 0.4767 0.071454 0.73763 0.063939 1 0.0030695
Table 11: Base 64 representation:
chYKeopFKH4oKtP
Control points Base64 RMS position error: 1.613 3.97 ects RMS curvature error: 33.8 33.06 % CD error -0.4 -42.1 dcts Cm error -11 38 mcts Upper transition point 1.59 0.11 %
Figure 12: Error distribution of vertical position and curvature of the parameter curve.
Information: NASA/AMES modification of the NACA 63A-108 airfoil
Reference: UIUC
Figure 14: Wing profile with camber and thickness dis-tribution.
Table 13: Geometrical properties
Maximum Thickness: 7.7324 % @0.32C Maximum Camber: 0.44446 % @0.17C Trailing Edge Gap: 0.7 %C Upper nose radius: 7.3484 %C Lower nose radius: 0.96721 %C Boat-Tail Angle: 2.6362 deg Release Angle: -1.8163 deg Nose Incidence: 8.1186 deg Camber deflection: 6.3023 deg
Table 14: Controlpoints 1 -0.0035 0.67387 -0.021359 0.53376 -0.034625 0.34988 -0.034625 0.043735 -0.034625 0 -0.016793 0 0 0 0.017524 0.0062687 0.0428 0.30015 0.0428 0.65936 0.0428 0.89177 0.002559 1 0.0035
Table 15: Base 64 representation:
a-TgSf3WSPUsDsS
Control points Base64 RMS position error: 3.074 5.126 ects RMS curvature error: Inf Inf % CD error 1.5 1.7 dcts Cm error 12 19 mcts Upper transition point -1.95 -2.4 %
Figure 15: Error distribution of vertical position and curvature of the parameter curve.
Information: Drela AG03 (flat aft bottom) airfoil Reference: UIUC
Figure 17: Wing profile with camber and thickness dis-tribution.
Table 17: Geometrical properties
Maximum Thickness: 6.2362 % @0.24C Maximum Camber: 2.0801 % @0.33C Trailing Edge Gap: 0.12109 %C Upper nose radius: 0.91155 %C Lower nose radius: 0.28905 %C Boat-Tail Angle: 6.2667 deg Release Angle: 2.5067 deg Nose Incidence: 10.4494 deg Camber deflection: 12.9561 deg
Table 18: Controlpoints 1 -0.000605 0.24106 -0.011456 0.14104 -0.013042 0.11285 -0.013042 0.032851 -0.013042 0 -0.0074338 0 0 0 0.018966 0.062535 0.051261 0.28141 0.051261 0.45191 0.051261 0.6626 0.035301 1 0.000605
Table 19: Base 64 representation:
YxSPWjsHCGr4HjD
Control points Base64 RMS position error: 0.57 4.651 ects RMS curvature error: 64.95 Inf % CD error -0.8 2.8 dcts Cm error 2 -1 mcts Upper transition point 0.03 -0.11 %
Figure 18: Error distribution of vertical position and curvature of the parameter curve.
Information: Drela AG04 airfoil Reference: UIUC
Figure 20: Wing profile with camber and thickness dis-tribution.
Table 21: Geometrical properties
Maximum Thickness: 6.431 % @0.22C Maximum Camber: 1.7383 % @0.4C Trailing Edge Gap: 0.134 %C Upper nose radius: 0.11324 %C Lower nose radius: 0.38937 %C Boat-Tail Angle: 5.4372 deg Release Angle: 2.54 deg Nose Incidence: 4.8897 deg Camber deflection: 7.4297 deg
Table 22: Controlpoints 1 -0.00067001 0.41458 -0.0024952 0.31306 -0.018619 0.12471 -0.018619 0.037228 -0.018619 0 -0.010154 0 0 0 0.0032762 0.014218 0.047906 0.28091 0.047906 0.46682 0.047906 0.70227 0.028073 1 0.00067001
Table 23: Base 64 representation:
E8SRUisIOIk2GjD
Control points Base64 RMS position error: 0.772 3.504 ects RMS curvature error: 78.17 77.96 % CD error 0.1 0 dcts Cm error -8 -5 mcts Upper transition point 0 -0.47 %
Figure 21: Error distribution of vertical position and curvature of the parameter curve.
Information: Drela AG08 airfoil Reference: UIUC
Figure 23: Wing profile with camber and thickness dis-tribution.
Table 25: Geometrical properties
Maximum Thickness: 5.8158 % @0.2C Maximum Camber: 1.7887 % @0.38C Trailing Edge Gap: 0.1599 %C Upper nose radius: 0.14748 %C Lower nose radius: 0.49865 %C Boat-Tail Angle: 5.5484 deg Release Angle: 2.8292 deg Nose Incidence: 4.0776 deg Camber deflection: 6.9068 deg
Table 26: Controlpoints 1 -0.0007995 0.35178 -0.00017682 0.25139 -0.016274 0.10702 -0.016274 0.013992 -0.016274 0 -0.0069976 0 0 0 0.0037576 0.014361 0.045229 0.2797 0.045229 0.46324 0.045229 0.75563 0.024775 1 0.0007995
Table 27: Base 64 representation:
F8SQTc3HKHi2GkE
Control points Base64 RMS position error: 1.235 3.282 ects RMS curvature error: 53.77 58.42 % CD error -0.2 -0.1 dcts Cm error -8 -8 mcts Upper transition point 0.45 0.28 %
Figure 24: Error distribution of vertical position and curvature of the parameter curve.
Information: Drela AG09 airfoil Reference: UIUC
Figure 26: Wing profile with camber and thickness dis-tribution.
Table 29: Geometrical properties
Maximum Thickness: 4.8323 % @0.19C Maximum Camber: 1.7992 % @0.33C Trailing Edge Gap: 0.1953 %C Upper nose radius: 0.13559 %C Lower nose radius: 0.58733 %C Boat-Tail Angle: 4.3115 deg Release Angle: 2.3245 deg Nose Incidence: 3.0164 deg Camber deflection: 5.3409 deg
Table 30: Controlpoints 1 -0.00097652 0.18565 0.0014228 0.1208 -0.012956 0.053016 -0.012956 0.014118 -0.012956 0 -0.007435 0 0 0 0.0034204 0.012943 0.041311 0.25799 0.041311 0.44519 0.041311 0.70899 0.023779 1 0.00097652
Table 31: Base 64 representation:
F8RQSkuDFGj6FjF
Control points Base64 RMS position error: 1.638 7.178 ects RMS curvature error: Inf Inf % CD error 1.4 1.5 dcts Cm error -5 6 mcts Upper transition point 0.05 0.6 %
Figure 27: Error distribution of vertical position and curvature of the parameter curve.
Information: Drela AG10 airfoil Reference: UIUC
Figure 29: Wing profile with camber and thickness dis-tribution.
Table 33: Geometrical properties
Maximum Thickness: 4.6276 % @0.17C Maximum Camber: 1.6779 % @0.3C Trailing Edge Gap: 0.3617 %C Upper nose radius: 0.70733 %C Lower nose radius: 1.2777 %C Boat-Tail Angle: 3.9621 deg Release Angle: 2.2757 deg Nose Incidence: 4.7855 deg Camber deflection: 7.0612 deg
Table 34: Controlpoints 1 -0.0018085 0.19456 0.0023339 0.13144 -0.012762 0.052895 -0.012762 0.0020376 -0.012762 0 -0.0041661 0 0 0 0.015276 0.049489 0.039103 0.23424 0.039103 0.33993 0.039103 0.6342 0.029035 1 0.0018085
Table 35: Base 64 representation:
ZxPJRV9DFFu6EjJ
Control points Base64 RMS position error: 2.221 6.221 ects RMS curvature error: Inf Inf % CD error 1.5 1.4 dcts Cm error -12 -2 mcts Upper transition point -0.04 1.08 %
Figure 30: Error distribution of vertical position and curvature of the parameter curve.
Information: Drela ag11 Airfoil Reference: UIUC
Figure 32: Wing profile with camber and thickness dis-tribution.
Table 37: Geometrical properties
Maximum Thickness: 5.8281 % @0.25C Maximum Camber: 2.2378 % @0.3C Trailing Edge Gap: 0.23211 %C Upper nose radius: 1.0233 %C Lower nose radius: 0.48629 %C Boat-Tail Angle: 6.3025 deg Release Angle: 2.7502 deg Nose Incidence: 11.8638 deg Camber deflection: 14.614 deg
Table 38: Controlpoints 1 -0.0011605 0.12818 -0.0072634 0.12818 -0.0085929 0.062559 -0.0085929 0.022776 -0.0085929 0 -0.0085929 0 0 0 0.017122 0.042974 0.051424 0.27237 0.051424 0.49516 0.051424 0.80514 0.021303 1 0.0011605
Table 39: Base 64 representation:
V1RUW oEEEa HkG
Control points Base64 RMS position error: 1.697 3.676 ects RMS curvature error: Inf Inf % CD error -0.7 0.4 dcts Cm error -9 -19 mcts Upper transition point 0.35 -0.71 %
Figure 33: Error distribution of vertical position and curvature of the parameter curve.
Information: Drela AG12 airfoil Reference: UIUC
Figure 35: Wing profile with camber and thickness dis-tribution.
Table 41: Geometrical properties
Maximum Thickness: 6.2467 % @0.21C Maximum Camber: 1.8519 % @0.43C Trailing Edge Gap: 0.0942 %C Upper nose radius: 0.29309 %C Lower nose radius: 0.39563 %C Boat-Tail Angle: 3.5704 deg Release Angle: 3.557 deg Nose Incidence: 5.4867 deg Camber deflection: 9.0437 deg
Table 42: Controlpoints 1 -0.000471 0.58904 0.012241 0.32192 -0.017368 0.1367 -0.017368 0.1121 -0.017368 0 -0.017195 0 0 0 0.007639 0.029865 0.047421 0.27642 0.047421 0.33811 0.047421 0.50871 0.046411 1 0.000471
Table 43: Base 64 representation:
K4SFU-MJOH-mElC
Control points Base64 RMS position error: 0.57 4.006 ects RMS curvature error: 23.77 20 % CD error 0 -1.1 dcts Cm error 1 15 mcts Upper transition point -0.08 1.09 %
Figure 36: Error distribution of vertical position and curvature of the parameter curve.
Information: Drela AG13 airfoil Reference: UIUC
Figure 38: Wing profile with camber and thickness dis-tribution.
Table 45: Geometrical properties
Maximum Thickness: 5.8377 % @0.21C Maximum Camber: 1.9847 % @0.43C Trailing Edge Gap: 0.0948 %C Upper nose radius: 0.15829 %C Lower nose radius: 0.34629 %C Boat-Tail Angle: 3.7275 deg Release Angle: 3.7369 deg Nose Incidence: 6.2355 deg Camber deflection: 9.9724 deg
Table 46: Controlpoints 1 -0.000474 0.54498 0.014407 0.31541 -0.014817 0.11427 -0.014817 0.020217 -0.014817 0 -0.0068317 0 0 0 0.0037237 0.01314 0.046611 0.28113 0.046611 0.49014 0.046611 0.8484 0.015341 1 0.000474
Table 47: Base 64 representation:
F8STUe0HPGVqElC
Control points Base64 RMS position error: 0.746 3.442 ects RMS curvature error: 21.55 22.19 % CD error -0.4 -0.5 dcts Cm error -1 -8 mcts Upper transition point 0.67 1.14 %
Figure 39: Error distribution of vertical position and curvature of the parameter curve.
Information: Drela AG14 airfoil Reference: UIUC
Figure 41: Wing profile with camber and thickness dis-tribution.
Table 49: Geometrical properties
Maximum Thickness: 5.3797 % @0.2C Maximum Camber: 2.1006 % @0.41C Trailing Edge Gap: 0.0956 %C Upper nose radius: 0.20363 %C Lower nose radius: 0.46443 %C Boat-Tail Angle: 2.5983 deg Release Angle: 3.4341 deg Nose Incidence: 6.6902 deg Camber deflection: 10.1242 deg
Table 50: Controlpoints 1 -0.000478 0.54239 0.016581 0.24845 -0.01217 0.089637 -0.01217 0.0050921 -0.01217 0 -0.0039707 0 0 0 0.0050753 0.018974 0.045611 0.26974 0.045611 0.54821 0.045611 0.97943 0.0021814 1 0.000478
Table 51: Base 64 representation:
H6RYTV7GLFDmDlC
Control points Base64 RMS position error: 0.583 4.503 ects RMS curvature error: 20.49 20.58 % CD error 0 -0.3 dcts Cm error 4 18 mcts Upper transition point -0.21 -0.82 %
Figure 42: Error distribution of vertical position and curvature of the parameter curve.
Information: Drela AG16 airfoil Reference: UIUC
Figure 44: Wing profile with camber and thickness dis-tribution.
Table 53: Geometrical properties
Maximum Thickness: 7.1257 % @0.23C Maximum Camber: 1.8923 % @0.46C Trailing Edge Gap: 0.0929 %C Upper nose radius: 0.38526 %C Lower nose radius: 0.47317 %C Boat-Tail Angle: 4.2561 deg Release Angle: 3.9528 deg Nose Incidence: 4.6057 deg Camber deflection: 8.5585 deg
Table 54: Controlpoints 1 -0.0004645 0.62188 0.011582 0.35229 -0.021861 0.15 -0.021861 0.1455 -0.021861 0 -0.021424 0 0 0 0.010942 0.046612 0.051721 0.28899 0.051721 0.39848 0.051721 0.57165 0.046097 1 0.0004645
Table 55: Base 64 representation:
O1SKW-CKPJ4kFmC
Control points Base64 RMS position error: 0.504 3.053 ects RMS curvature error: 16.44 20.4 % CD error 0.1 0.8 dcts Cm error -2 -8 mcts Upper transition point -0.56 -2.3 %
Figure 45: Error distribution of vertical position and curvature of the parameter curve.
Information: Drela AG17 airfoil Reference: UIUC
Figure 47: Wing profile with camber and thickness dis-tribution.
Table 57: Geometrical properties
Maximum Thickness: 6.4999 % @0.22C Maximum Camber: 2.0372 % @0.45C Trailing Edge Gap: 0.0939 %C Upper nose radius: 0.33128 %C Lower nose radius: 0.38325 %C Boat-Tail Angle: 3.9266 deg Release Angle: 3.9986 deg Nose Incidence: 6.0635 deg Camber deflection: 10.0621 deg
Table 58: Controlpoints 1 -0.0004695 0.59646 0.013871 0.32561 -0.017646 0.13694 -0.017646 0.11914 -0.017646 0 -0.017646 0 0 0 0.0086 0.033488 0.050086 0.28915 0.050086 0.42436 0.050086 0.611 0.041094 1 0.0004695
Table 59: Base 64 representation:
L4TMV IJOIzlEmC
Control points Base64 RMS position error: 0.447 5.281 ects RMS curvature error: 21.13 23.58 % CD error -0.1 -0.5 dcts Cm error -2 -13 mcts Upper transition point -0.22 0.69 %
Figure 48: Error distribution of vertical position and curvature of the parameter curve.
Information: Drela AG18 airfoil Reference: UIUC
Figure 50: Wing profile with camber and thickness dis-tribution.
Table 61: Geometrical properties
Maximum Thickness: 5.8638 % @0.21C Maximum Camber: 2.1825 % @0.44C Trailing Edge Gap: 0.0948 %C Upper nose radius: 0.22085 %C Lower nose radius: 0.32579 %C Boat-Tail Angle: 3.6509 deg Release Angle: 4.021 deg Nose Incidence: 7.2609 deg Camber deflection: 11.2819 deg
Table 62: Controlpoints 1 -0.000474 0.54809 0.016852 0.3181 -0.013804 0.096885 -0.013804 0.072651 -0.013804 0 -0.012562 0 0 0 0.0047717 0.015465 0.048451 0.28931 0.048451 0.44443 0.048451 0.6416 0.037172 1 0.000474
Table 63: Base 64 representation:
G8TOV5QGQGwpEmC
Control points Base64 RMS position error: 0.397 2.922 ects RMS curvature error: 20.92 22.8 % CD error 0 -0.2 dcts Cm error -2 -11 mcts Upper transition point -0.03 1.38 %
Figure 51: Error distribution of vertical position and curvature of the parameter curve.
Information: Drela AG19 profile Reference: UIUC
Figure 53: Wing profile with camber and thickness dis-tribution.
Table 65: Geometrical properties
Maximum Thickness: 5.4039 % @0.2C Maximum Camber: 2.2958 % @0.42C Trailing Edge Gap: 0.0954 %C Upper nose radius: 0.16958 %C Lower nose radius: 0.29661 %C Boat-Tail Angle: 3.3048 deg Release Angle: 4.1143 deg Nose Incidence: 8.1149 deg Camber deflection: 12.2292 deg
Table 66: Controlpoints 1 -0.000477 0.53884 0.01935 0.25592 -0.01147 0.083848 -0.01147 0.072714 -0.01147 0 -0.01147 0 0 0 0.0018582 0.0030542 0.047306 0.28942 0.047306 0.45507 0.047306 0.65678 0.035138 1 0.000477
Table 67: Base 64 representation:
D-TPU IFMFunEmC
Control points Base64 RMS position error: 0.908 2.946 ects RMS curvature error: 25.17 27.39 % CD error -0.2 -0.6 dcts Cm error -5 -4 mcts Upper transition point 0.97 1.77 %
Figure 54: Error distribution of vertical position and curvature of the parameter curve.
Information: AG24 Bubble Dancer DLG by Mark Drela Reference: UIUC
Figure 56: Wing profile with camber and thickness dis-tribution.
Table 69: Geometrical properties
Maximum Thickness: 8.4185 % @0.26C Maximum Camber: 2.232 % @0.45C Trailing Edge Gap: 0.0971 %C Upper nose radius: 0.48654 %C Lower nose radius: 0.47278 %C Boat-Tail Angle: 4.0698 deg Release Angle: 5.3831 deg Nose Incidence: 5.9859 deg Camber deflection: 11.3689 deg
Table 70: Controlpoints 1 -0.0004855 0.78905 0.011856 0.39277 -0.023806 0.17708 -0.023806 0.11797 -0.023806 0 -0.019283 0 0 0 0.014478 0.064627 0.06255 0.31499 0.06255 0.58855 0.06255 0.88291 0.01573 1 0.0004855
Table 71: Base 64 representation:
PyUabzVLRKSWFoC
Control points Base64 RMS position error: 0.631 4.258 ects RMS curvature error: 18.03 20.46 % CD error 0.5 1.1 dcts Cm error -5 -2 mcts Upper transition point -0.43 -1.13 %
Figure 57: Error distribution of vertical position and curvature of the parameter curve.
Information: AG25 Bubble Dancer DLG by Mark Drela Reference: UIUC
Figure 59: Wing profile with camber and thickness dis-tribution.
Table 73: Geometrical properties
Maximum Thickness: 7.5788 % @0.25C Maximum Camber: 2.4182 % @0.45C Trailing Edge Gap: 0.0963 %C Upper nose radius: 0.4144 %C Lower nose radius: 0.41098 %C Boat-Tail Angle: 4.3626 deg Release Angle: 5.3241 deg Nose Incidence: 6.8875 deg Camber deflection: 12.2116 deg
Table 74: Controlpoints 1 -0.0004815 0.72414 0.014665 0.34085 -0.019003 0.1501 -0.019003 0.10207 -0.019003 0 -0.016723 0 0 0 0.011777 0.050208 0.059926 0.3156 0.059926 0.57181 0.059926 0.8617 0.018703 1 0.0004815
Table 75: Base 64 representation:
N1UYa3UKOIVbFoC
Control points Base64 RMS position error: 0.417 4.012 ects RMS curvature error: 12.22 12.91 % CD error 0.1 0.4 dcts Cm error -2 -2 mcts Upper transition point 0.13 -0.38 %
Figure 60: Error distribution of vertical position and curvature of the parameter curve.
Information: AG26 Bubble Dancer DLG by Mark Drela Reference: UIUC
Figure 62: Wing profile with camber and thickness dis-tribution.
Table 77: Geometrical properties
Maximum Thickness: 6.8375 % @0.24C Maximum Camber: 2.5649 % @0.44C Trailing Edge Gap: 0.0999 %C Upper nose radius: 0.40075 %C Lower nose radius: 0.36598 %C Boat-Tail Angle: 4.5466 deg Release Angle: 5.0101 deg Nose Incidence: 7.8733 deg Camber deflection: 12.8835 deg
Table 78: Controlpoints 1 -0.0004995 0.62383 0.017482 0.31741 -0.015296 0.10998 -0.015296 0.069288 -0.015296 0 -0.013002 0 0 0 0.010201 0.038946 0.057438 0.31627 0.057438 0.50477 0.057438 0.72377 0.035804 1 0.0004995
Table 79: Base 64 representation:
L3USZ1YHPHniFnD
Control points Base64 RMS position error: 0.315 5.753 ects RMS curvature error: 19.31 19.78 % CD error 0.3 1 dcts Cm error 0 -4 mcts Upper transition point -0.44 -1.14 %
Figure 63: Error distribution of vertical position and curvature of the parameter curve.
Information: AG27 Bubble Dancer DLG by Mark Drela Reference: UIUC
Figure 65: Wing profile with camber and thickness dis-tribution.
Table 81: Geometrical properties
Maximum Thickness: 6.1212 % @0.22C Maximum Camber: 2.6939 % @0.43C Trailing Edge Gap: 0.1035 %C Upper nose radius: 0.066651 %C Lower nose radius: 16.9447 %C Boat-Tail Angle: 4.1799 deg Release Angle: 4.7444 deg Nose Incidence: 7.2214 deg Camber deflection: 11.9658 deg
Table 82: Controlpoints 1 -0.00051751 0.51098 0.022154 0.28019 -0.012895 0.079122 -0.012895 6.636e-005 -0.012895 0 -0.0027379 0 0 0 0.001851 0.0077103 0.054524 0.31772 0.054524 0.53295 0.054524 0.80092 0.024377 1 0.00051751
Table 83: Base 64 representation:
C9UUXO FOGcqFnD
Control points Base64 RMS position error: 0.371 6.741 ects RMS curvature error: 22.21 25.4 % CD error 0.4 0.4 dcts Cm error 7 7 mcts Upper transition point -0.8 -0.8 %
Figure 66: Error distribution of vertical position and curvature of the parameter curve.
Information: AG35 - Not so good fit. Reference: UIUC
Figure 68: Wing profile with camber and thickness dis-tribution.
Table 85: Geometrical properties
Maximum Thickness: 8.7243 % @0.28C Maximum Camber: 2.3805 % @0.37C Trailing Edge Gap: 0.24889 %C Upper nose radius: 0.6654 %C Lower nose radius: 0.7988 %C Boat-Tail Angle: 41.5742 deg Release Angle: 19.2444 deg Nose Incidence: 6.3739 deg Camber deflection: 25.6183 deg
Table 86: Controlpoints 1 -0.0012445 0.35219 -0.018691 0.25219 -0.022407 0.17008 -0.022407 0.014579 -0.022407 0 -0.0088112 0 0 0 0.017463 0.068748 0.066862 0.31591 0.066862 0.57871 0.066862 0.99811 0.0028315 1 0.0012445
Table 87: Base 64 representation:
RxUZsZ6LGKC2t-G
Control points Base64 RMS position error: 2.47 8.015 ects RMS curvature error: Inf Inf % CD error 1.2 2.1 dcts Cm error -58 -84 mcts Upper transition point -0.58 -1.12 %
Figure 69: Error distribution of vertical position and curvature of the parameter curve.
Information: AG46 Reference: UIUC
Figure 71: Wing profile with camber and thickness dis-tribution.
Table 89: Geometrical properties
Maximum Thickness: 8.1678 % @0.28C Maximum Camber: 2.2378 % @0.35C Trailing Edge Gap: 0.26691 %C Upper nose radius: 0.52526 %C Lower nose radius: 0.85103 %C Boat-Tail Angle: 9.4311 deg Release Angle: 3.2997 deg Nose Incidence: 5.2392 deg Camber deflection: 8.5389 deg
Table 90: Controlpoints 1 -0.0013346 0.34869 -0.017432 0.24869 -0.020814 0.16994 -0.020814 0.016336 -0.020814 0 -0.0096272 0 0 0 0.014821 0.062726 0.062778 0.31615 0.062778 0.42013 0.062778 0.6665 0.048296 1 0.0013346
Table 91: Base 64 representation:
PyUKbe5LGJw2LlH
Control points Base64 RMS position error: 0.899 3.694 ects RMS curvature error: Inf Inf % CD error 0.6 1.2 dcts Cm error -2 -16 mcts Upper transition point -1.17 -1.71 %
Figure 72: Error distribution of vertical position and curvature of the parameter curve.
Information: N/A Reference: N/A
Figure 74: Wing profile with camber and thickness dis-tribution.
Table 93: Geometrical properties
Maximum Thickness: 7.7335 % @0.27C Maximum Camber: 2.2045 % @0.34C Trailing Edge Gap: 0.35071 %C Upper nose radius: 0.88948 %C Lower nose radius: 0.59804 %C Boat-Tail Angle: 10.1333 deg Release Angle: 3.8549 deg Nose Incidence: 8.3885 deg Camber deflection: 12.2434 deg
Table 94: Controlpoints 1 -0.0017535 0.35094 -0.015482 0.25094 -0.018345 0.16989 -0.018345 0.026545 -0.018345 0 -0.010288 0 0 0 0.022021 0.081779 0.060398 0.30209 0.060398 0.47148 0.060398 0.82934 0.028544 1 0.0017535
Table 95: Base 64 representation:
XuTQaj1LGIs2LlJ
Control points Base64 RMS position error: 1.016 2.592 ects RMS curvature error: Inf Inf % CD error 0.8 1.6 dcts Cm error -8 -4 mcts Upper transition point -0.71 -1.6 %
Figure 75: Error distribution of vertical position and curvature of the parameter curve.
Information: AG38 - Sequential flat top. Reference: UIUC
Figure 77: Wing profile with camber and thickness dis-tribution.
Table 97: Geometrical properties
Maximum Thickness: 7.09 % @0.27C Maximum Camber: 2.1139 % @0.34C Trailing Edge Gap: 0.46973 %C Upper nose radius: 0.96108 %C Lower nose radius: 0.65407 %C Boat-Tail Angle: 9.8477 deg Release Angle: 4.0734 deg Nose Incidence: 8.5099 deg Camber deflection: 12.5833 deg
Table 98: Controlpoints 1 -0.0023511 0.35859 -0.013357 0.25859 -0.015859 0.15767 -0.015859 0.020048 -0.015859 0 -0.0088358 0 0 0 0.023723 0.086492 0.055832 0.31472 0.055832 0.44798 0.055832 0.8073 0.033007 1 0.0023511
Table 99: Base 64 representation:
btUMYj3KIHk2LmM
Control points Base64 RMS position error: 0.99 2.97 ects RMS curvature error: Inf Inf % CD error 0.3 1 dcts Cm error -13 -24 mcts Upper transition point -0.69 -0.7 %
Figure 78: Error distribution of vertical position and curvature of the parameter curve.
Information: Drela AG44ct -02f airfoil Reference: UIUC
Figure 80: Wing profile with camber and thickness dis-tribution.
Table 101: Geometrical properties
Maximum Thickness: 7.2978 % @0.24C Maximum Camber: 1.9711 % @0.35C Trailing Edge Gap: 0.0534 %C Upper nose radius: 0.55571 %C Lower nose radius: 0.38892 %C Boat-Tail Angle: 6.0413 deg Release Angle: 2.521 deg Nose Incidence: 8.5092 deg Camber deflection: 11.0302 deg
Table 102: Controlpoints 1 -0.000267 0.63271 -0.0034701 0.34543 -0.018389 0.16335 -0.018389 0.089844 -0.018389 0 -0.015263 0 0 0 0.012551 0.042522 0.055628 0.27448 0.055628 0.41942 0.055628 0.51942 0.046894 1 0.000267
Table 103: Base 64 representation:
O1SNY0sKOI1jHjB
Control points Base64 RMS position error: 1.635 4.322 ects RMS curvature error: 88.77 75.82 % CD error -0.2 -0.3 dcts Cm error 15 10 mcts Upper transition point -0.39 0.95 %
Figure 81: Error distribution of vertical position and curvature of the parameter curve.
Information: Drela AG45c -03f airfoil Reference: UIUC
Figure 83: Wing profile with camber and thickness dis-tribution.
Table 105: Geometrical properties
Maximum Thickness: 6.9341 % @0.23C Maximum Camber: 2.056 % @0.32C Trailing Edge Gap: 0.089404 %C Upper nose radius: 0.68748 %C Lower nose radius: 0.36316 %C Boat-Tail Angle: 2.8362 deg Release Angle: 2.5406 deg Nose Incidence: 9.1188 deg Camber deflection: 11.6595 deg
Table 106: Controlpoints 1 -0.00044702 0.84572 0.0025761 0.25739 -0.016272 0.13659 -0.016272 0.084686 -0.016272 0 -0.014156 0 0 0 0.016085 0.056449 0.054761 0.26295 0.054761 0.45884 0.054761 0.55884 0.030977 1 0.00044702
Table 107: Base 64 representation:
TxRRX3YJJHzNDjC
Control points Base64 RMS position error: 1.928 4.224 ects RMS curvature error: 87.7 88.93 % CD error -0.5 -1.1 dcts Cm error 20 26 mcts Upper transition point -0.39 -0.02 %
Figure 84: Error distribution of vertical position and curvature of the parameter curve.
Information: Drela AG45ct -02f airfoil Reference: UIUC
Figure 86: Wing profile with camber and thickness dis-tribution.
Table 109: Geometrical properties
Maximum Thickness: 6.9066 % @0.24C Maximum Camber: 1.877 % @0.33C Trailing Edge Gap: 0.0622 %C Upper nose radius: 0.64802 %C Lower nose radius: 0.33101 %C Boat-Tail Angle: 4.9582 deg Release Angle: 2.2012 deg Nose Incidence: 8.7934 deg Camber deflection: 10.9945 deg
Table 110: Controlpoints 1 -0.000311 0.66001 -0.0019602 0.3403 -0.017269 0.15022 -0.017269 0.088631 -0.017269 0 -0.014679 0 0 0 0.015506 0.055655 0.052819 0.26292 0.052819 0.44337 0.052819 0.54337 0.037694 1 0.000311
Table 111: Base 64 representation:
TxRQX1aKOH0gGjC
Control points Base64 RMS position error: 1.456 6.225 ects RMS curvature error: 92.91 75.5 % CD error 0 -0.6 dcts Cm error 16 14 mcts Upper transition point -0.82 -0.08 %
Figure 87: Error distribution of vertical position and curvature of the parameter curve.
Information: Drela AG46c -03f airfoil Reference: UIUC
Figure 89: Wing profile with camber and thickness dis-tribution.
Table 113: Geometrical properties
Maximum Thickness: 6.0359 % @0.23C Maximum Camber: 1.7305 % @0.32C Trailing Edge Gap: 0.079396 %C Upper nose radius: 0.7473 %C Lower nose radius: 0.32371 %C Boat-Tail Angle: 2.3184 deg Release Angle: 2.3813 deg Nose Incidence: 8.6922 deg Camber deflection: 11.0735 deg
Table 114: Controlpoints 1 -0.00039698 0.89349 0.0018752 0.27658 -0.014689 0.1229 -0.014689 0.077426 -0.014689 0 -0.012926 0 0 0 0.016951 0.057676 0.047087 0.26216 0.047087 0.47656 0.047087 0.57657 0.026595 1 0.00039698
Table 115: Base 64 representation:
XxRTU3YILGzJDjC
Control points Base64 RMS position error: 1.853 4.31 ects RMS curvature error: 86.88 80.23 % CD error -0.8 -1.1 dcts Cm error 13 -7 mcts Upper transition point -0.08 0.32 %
Figure 90: Error distribution of vertical position and curvature of the parameter curve.
Information: Drela AG46ct -02f airfoil Reference: UIUC
Figure 92: Wing profile with camber and thickness dis-tribution.
Table 117: Geometrical properties
Maximum Thickness: 6.0803 % @0.23C Maximum Camber: 1.7152 % @0.32C Trailing Edge Gap: 0.0793 %C Upper nose radius: 0.63476 %C Lower nose radius: 0.33084 %C Boat-Tail Angle: 3.1401 deg Release Angle: 2.5804 deg Nose Incidence: 8.2892 deg Camber deflection: 10.8696 deg
Table 118: Controlpoints 1 -0.0003965 0.87999 0.0017202 0.24385 -0.015231 0.1365 -0.015231 0.10101 -0.015231 0 -0.014926 0 0 0 0.013702 0.044364 0.047085 0.26215 0.047085 0.41713 0.047085 0.50752 0.036134 1 0.0003965
Table 119: Base 64 representation:
T0RNU-RJIG1KEjC
Control points Base64 RMS position error: 1.848 3.968 ects RMS curvature error: 83.73 77.17 % CD error -0.7 -1.6 dcts Cm error 24 22 mcts Upper transition point -0.3 0.13 %
Figure 93: Error distribution of vertical position and curvature of the parameter curve.
Information: Drela AG47c -03f airfoil Reference: UIUC
Figure 95: Wing profile with camber and thickness dis-tribution.
Table 121: Geometrical properties
Maximum Thickness: 5.0652 % @0.23C Maximum Camber: 1.3685 % @0.32C Trailing Edge Gap: 0.069288 %C Upper nose radius: 1.0218 %C Lower nose radius: 0.25118 %C Boat-Tail Angle: 3.1028 deg Release Angle: 1.7923 deg Nose Incidence: 9.7223 deg Camber deflection: 11.5146 deg
Table 122: Controlpoints 1 -0.00034644 0.72118 -0.00053732 0.27908 -0.01318 0.12359 -0.01318 0.087941 -0.01318 0 -0.01315 0 0 0 0.011766 0.029761 0.038643 0.2659 0.038643 0.48035 0.038643 0.58035 0.020088 1 0.00034644
Table 123: Base 64 representation:
T4RTQ SILGzZDhC
Control points Base64 RMS position error: 1.602 6.302 ects RMS curvature error: Inf Inf % CD error -0.6 -0.3 dcts Cm error 21 27 mcts Upper transition point -0.1 -1.19 %
Figure 96: Error distribution of vertical position and curvature of the parameter curve.
Information: Drela AG47ct -02f airfoil Reference: UIUC
Figure 98: Wing profile with camber and thickness dis-tribution.
Table 125: Geometrical properties
Maximum Thickness: 5.0109 % @0.2C Maximum Camber: 1.334 % @0.33C Trailing Edge Gap: 0.069302 %C Upper nose radius: 1.5382 %C Lower nose radius: 0.25118 %C Boat-Tail Angle: 3.7209 deg Release Angle: 2.101 deg Nose Incidence: 12.7206 deg Camber deflection: 14.8216 deg
Table 126: Controlpoints 1 -0.00034651 0.72071 -0.00054082 0.27896 -0.01318 0.12358 -0.01318 0.087959 -0.01318 0 -0.013151 0 0 0 0.012521 0.029276 0.037867 0.26588 0.037867 0.42966 0.037867 0.52966 0.027645 1 0.00034651
Table 127: Base 64 representation:
V4ROQ SILG0ZEiC
Control points Base64 RMS position error: 1.536 4.959 ects RMS curvature error: Inf 91.7 % CD error -0.2 0.1 dcts Cm error 20 26 mcts Upper transition point -0.8 -1.41 %
Figure 99: Error distribution of vertical position and curvature of the parameter curve.
Information: Drela AG47ct -02f airfoil Reference: UIUC
Figure 101: Wing profile with camber and thickness distribution.
Table 129: Geometrical properties
Maximum Thickness: 6.4629 % @0.23C Maximum Camber: 1.8645 % @0.32C Trailing Edge Gap: 0.084402 %C Upper nose radius: 0.58885 %C Lower nose radius: 0.3227 %C Boat-Tail Angle: 3.5673 deg Release Angle: 2.6828 deg Nose Incidence: 9.0365 deg Camber deflection: 11.7193 deg
Table 130: Controlpoints 1 -0.00042201 0.8476 0.00197 0.25994 -0.015703 0.13673 -0.015703 0.080672 -0.015703 0 -0.013505 0 0 0 0.012275 0.038382 0.050471 0.2637 0.050471 0.42269 0.050471 0.5227 0.037705 1 0.00042201
Table 131: Base 64 representation:
Q2ROW2aJJH0NEkC
Control points Base64 RMS position error: 1.599 5.74 ects RMS curvature error: 90.26 94.22 % CD error -0.5 0.2 dcts Cm error 17 5 mcts Upper transition point -0.19 -0.29 %
Figure 102: Error distribution of vertical position and curvature of the parameter curve.
Information: Andrew Hollom AH 21 airfoil (7 Reference: UIUC
Figure 104: Wing profile with camber and thickness distribution.
Table 133: Geometrical properties
Maximum Thickness: 9.0217 % @0.35C Maximum Camber: 2.2717 % @0.58C Trailing Edge Gap: 0 %C Upper nose radius: 1.2939 %C Lower nose radius: 0.55902 %C Boat-Tail Angle: 8.5473 deg Release Angle: 12.0864 deg Nose Incidence: 8.4152 deg Camber deflection: 20.5015 deg
Table 134: Controlpoints 1 0 0.94178 0.007989 0.53283 -0.026163 0.25509 -0.026163 0.18366 -0.026163 0 -0.026163 0 0 0 0.045185 0.23669 0.065727 0.39727 0.065727 0.48498 0.065727 0.7761 0.065727 1 0
Table 135: Base 64 representation:
raZJc SQYL IKzA
Control points Base64 RMS position error: 0.775 2.128 ects RMS curvature error: 20.94 22.37 % CD error 0.8 1.7 dcts Cm error -4 -5 mcts Upper transition point -0.95 -2.49 %
Figure 105: Error distribution of vertical position and curvature of the parameter curve.
Information: Andrew Hollom AH 21 airfoil (original 9 Reference: UIUC
Figure 107: Wing profile with camber and thickness distribution.
Table 137: Geometrical properties
Maximum Thickness: 6.9745 % @0.35C Maximum Camber: 1.7394 % @0.58C Trailing Edge Gap: 0 %C Upper nose radius: 0.76099 %C Lower nose radius: 0.35479 %C Boat-Tail Angle: 7.7118 deg Release Angle: 9.1924 deg Nose Incidence: 6.3248 deg Camber deflection: 15.5172 deg
Table 138: Controlpoints 1 0 0.93404 0.0061614 0.54915 -0.020163 0.25509 -0.020163 0.1301 -0.020163 0 -0.017542 0 0 0 0.031239 0.19236 0.050727 0.39727 0.050727 0.49371 0.050727 0.78112 0.050727 1 0
Table 139: Base 64 representation:
mgZKW3fQZJ JJuA
Control points Base64 RMS position error: 1.251 4.294 ects RMS curvature error: 18.9 17.93 % CD error 0.8 -0.8 dcts Cm error -3 6 mcts Upper transition point -2.39 -3.43 %
Figure 108: Error distribution of vertical position and curvature of the parameter curve.
Information: Althaus AH 63-K-127/24 airfoil for use with flaps (K)
Reference: UIUC
Figure 110: Wing profile with camber and thickness distribution.
Table 141: Geometrical properties
Maximum Thickness: 12.7016 % @0.42C Maximum Camber: 3.754 % @0.45C Trailing Edge Gap: 0 %C Upper nose radius: 0.80776 %C Lower nose radius: 0.38153 %C Boat-Tail Angle: 7.2212 deg Release Angle: 6.977 deg Nose Incidence: 9.7159 deg Camber deflection: 16.6929 deg
Table 142: Controlpoints 1 0 0.79049 0.012324 0.78992 -0.0263 0.37059 -0.0263 0.2483 -0.0263 0 -0.0263 0 0 0 0.030733 0.17539 0.10098 0.43474 0.10098 0.63509 0.10098 0.73509 0.049517 1 0
Table 143: Base 64 representation:
TlcXq VYqLt IqA
Control points Base64 RMS position error: 5.624 6.583 ects RMS curvature error: 50.43 49.22 % CD error 0.6 0.4 dcts Cm error 97 98 mcts Upper transition point -5.44 -5.07 %
Figure 111: Error distribution of vertical position and curvature of the parameter curve.
Information: Althaus AH 6-407 airfoil Reference: UIUC
Figure 113: Wing profile with camber and thickness distribution.
Table 145: Geometrical properties
Maximum Thickness: 13.2012 % @0.4C Maximum Camber: 3.6792 % @0.4C Trailing Edge Gap: 0 %C Upper nose radius: 0.56806 %C Lower nose radius: 0.83926 %C Boat-Tail Angle: 8.5694 deg Release Angle: 4.8172 deg Nose Incidence: 5.8891 deg Camber deflection: 10.7062 deg
Table 146: Controlpoints 1 0 0.83607 0.0015234 0.83607 -0.02924 0.43474 -0.02924 0.085303 -0.02924 0 -0.021847 0 0 0 0.021256 0.1193 0.1028 0.40245 0.1028 0.65086 0.1028 0.75086 0.039914 1 0
Table 147: Base 64 representation:
NsabrvycsMt KnA
Control points Base64 RMS position error: 5.534 8.047 ects RMS curvature error: 49.62 50.2 % CD error -1 -1 dcts Cm error 121 104 mcts Upper transition point -5.15 -4.31 %
Figure 114: Error distribution of vertical position and curvature of the parameter curve.
Information: Althaus AH 79-K-135/20 airfoil for use with flaps (K)
Reference: UIUC
Figure 116: Wing profile with camber and thickness distribution.
Table 149: Geometrical properties
Maximum Thickness: 13.4838 % @0.4C Maximum Camber: 3.0551 % @0.41C Trailing Edge Gap: 0 %C Upper nose radius: 0.61238 %C Lower nose radius: 0.6081 %C Boat-Tail Angle: 8.9066 deg Release Angle: 4.14 deg Nose Incidence: 6.2982 deg Camber deflection: 10.4382 deg
Table 150: Controlpoints 1 0 0.80797 -0.0010499 0.80797 -0.03693 0.37059 -0.03693 0.30008 -0.03693 0 -0.034879 0 0 0 0.022397 0.12287 0.09796 0.40245 0.09796 0.65402 0.09796 0.75402 0.037171 1 0
Table 151: Base 64 representation:
Prabp7MYrQt KmA
Control points Base64 RMS position error: 4.873 5.963 ects RMS curvature error: 52.71 54.14 % CD error -3.7 -4.2 dcts Cm error 96 95 mcts Upper transition point -4.73 -4.5 %
Figure 117: Error distribution of vertical position and curvature of the parameter curve.
Information: Althaus AH 85-L-120/17 symmetrical airfoil Reference: UIUC
Figure 119: Wing profile with camber and thickness distribution.
Table 153: Geometrical properties
Maximum Thickness: 12.1092 % @0.44C Maximum Camber: -3.4043e-005 % @0.81C Trailing Edge Gap: 0.16 %C Upper nose radius: 0.53477 %C Lower nose radius: 0.53477 %C Boat-Tail Angle: 8.3674 deg Release Angle: 0.00065455 deg Nose Incidence: 0 deg Camber deflection: 0.00065455 deg
Table 154: Controlpoints 1 -0.0008 0.79081 -0.017154 0.75818 -0.06055 0.43474 -0.06055 0.17971 -0.06055 0 -0.025312 0 0 0 0.025312 0.17971 0.06055 0.43474 0.06055 0.75818 0.06055 0.79076 0.017158 1 0.0008
Table 155: Base 64 representation:
blckablcka22KgE
Control points Base64 RMS position error: 1.683 3.57 ects RMS curvature error: 19.95 17.77 % CD error -1 -0.9 dcts Cm error -3 -2 mcts Upper transition point 3.3 3.02 %
Figure 120: Error distribution of vertical position and curvature of the parameter curve.
Information: Althaus AH 93-W-145 airfoil for use on wind turbines (W)
Reference: UIUC
Figure 122: Wing profile with camber and thickness distribution.
Table 157: Geometrical properties
Maximum Thickness: 14.4707 % @0.35C Maximum Camber: 3.9019 % @0.38C Trailing Edge Gap: 0.195 %C Upper nose radius: 1.2431 %C Lower nose radius: 1.3124 %C Boat-Tail Angle: 8.7316 deg Release Angle: 10.1715 deg Nose Incidence: 5.9352 deg Camber deflection: 16.1067 deg
Table 158: Controlpoints 1 -0.000975 0.89902 0.0092925 0.62672 -0.035207 0.22223 -0.035207 0.12428 -0.035207 0 -0.032975 0 0 0 0.034918 0.14712 0.11118 0.37052 0.11118 0.49268 0.11118 0.92002 0.021715 1 0.000975
Table 159: Base 64 representation:
UmYMu7cOgPMRKvF
Control points Base64 RMS position error: 2.884 4.645 ects RMS curvature error: 84.55 82.73 % CD error 2.2 1.8 dcts Cm error 32 40 mcts Upper transition point -4.49 -4.05 %
Figure 123: Error distribution of vertical position and curvature of the parameter curve.
Information: Althaus AH 93-W-174 airfoil for use on wind turbines (W)
Reference: UIUC
Figure 125: Wing profile with camber and thickness distribution.
Table 161: Geometrical properties
Maximum Thickness: 17.4475 % @0.32C Maximum Camber: 3.9126 % @0.38C Trailing Edge Gap: 0 %C Upper nose radius: 1.7815 %C Lower nose radius: 2.0808 %C Boat-Tail Angle: 6.2892 deg Release Angle: 8.9863 deg Nose Incidence: 4.2294 deg Camber deflection: 13.2157 deg
Table 162: Controlpoints 1 0 0.84886 0.015463 0.613 -0.050272 0.22221 -0.050272 0.18218 -0.050272 0 -0.050272 0 0 0 0.043819 0.16167 0.1259 0.33928 0.1259 0.49336 0.1259 0.59336 0.087406 1 0
Table 163: Base 64 representation:
WhWP1 MOgVyZHuA
Control points Base64 RMS position error: 2.753 6.669 ects RMS curvature error: 78.48 83.07 % CD error -0.3 -0.4 dcts Cm error 40 15 mcts Upper transition point -1.06 -0.24 %
Figure 126: Error distribution of vertical position and curvature of the parameter curve.
Information: N/A Reference: UIUC
Figure 128: Wing profile with camber and thickness distribution.
Table 165: Geometrical properties
Maximum Thickness: 21.2437 % @0.33C Maximum Camber: 3.0646 % @0.39C Trailing Edge Gap: 0 %C Upper nose radius: 2.753 %C Lower nose radius: 3.3159 %C Boat-Tail Angle: 16.1904 deg Release Angle: 7.4024 deg Nose Incidence: 3.0573 deg Camber deflection: 10.4597 deg
Table 166: Controlpoints 1 0 0.84803 -0.0018376 0.5608 -0.076241 0.30873 -0.076241 0.05013 -0.076241 0 -0.033289 0 0 0 0.04945 0.13324 0.13643 0.33916 0.13643 0.42374 0.13643 0.52374 0.13206 1 0
Table 167: Base 64 representation:
XmVI5c1TXg9WSrA
Control points Base64 RMS position error: 6.18 7.484 ects RMS curvature error: 95.88 97.91 % CD error 1.4 2.2 dcts Cm error -7 -6 mcts Upper transition point -2.4 -3.02 %
Figure 129: Error distribution of vertical position and curvature of the parameter curve.
