大跨径桥梁箱形桥板结构在风荷载下的作用机理

1、外文资料翻译译文大跨径桥梁箱形桥板结构在风荷载下的作用机理弗朗西斯科理查德里摘要：近 35 年来，作为桁架和板梁的替代品，箱梁已经被广泛用来加强悬索桥桥板的 刚度。不管是结构方面还是空气动力学方面，它的优良性能都已被广泛的认同。最 近，箱梁的一种改进型式多室箱梁已经发展起来， 而这被看作是在目前条件下桥板 空气动力学的技术发展现状。然而，老式的桁架和平板梁依然还在应用之中，而且 与箱梁相比常常更受到大家的关注，特别是在北美和东亚地区。这篇论文将探讨箱 形桥板的空气动力性能。并通过分析桥面板压力分布的平均值和波动以及跟桥板位 移特征的关系， 对这种风载作用机制进行了研究。关键词：桥板；箱形梁；桥

2、梁空气动力学；桥梁气动弹性力学；风洞测试1.近 200 年之内缆索支撑桥梁中的桁架梁，板梁和箱梁为了适当限制重力作用下悬索桥的挠度并使其在风载作用下正常工作，应该给悬索桥提供多大的刚度呢？这似乎已经是在过去的200 年中，如果不能说是主要的话题的话，也是悬索桥设计者们经常争论的一个话题。在亚洲和南美，未加劲结构 已经存在大约 5000 年了，而这一方法被引入欧洲而后在 17 世纪才开始在北美被使 用。这种未加劲悬索桥原理非常简单， 但它只能用于桥梁的跨度较小短的情况而且 由于它的可变形性较大，所以它不适合车辆交通。所以，在18 世纪中期，当悬索桥梁开始在欧洲和北美建造时，很明显，除了悬索外，还

3、必须要给这种结构增加刚 度。但那时， 给悬索桥提供刚度的最适当的方法是什么呢？附加的刚度可来自于对 悬吊体系或者桥面板的修改，这两种解决方案都已经研究并实现。第一个以加劲梁 为特征的悬索桥跨度仅仅为 21 米，由美国的芬力在 1801 年设计和完成，在该设计 中，在桥板上增加了一个纵向支撑的托梁。作为一种选择，可以在桥塔和桥板之间 增加支柱，以提供桥梁的刚度。后面的这个技术被内维亚大量的运用，但后来几乎 被放弃，由于这被证明不如使用加劲梁更为有效。更复杂的加劲缆索体系已经被加 以研究，例如，莫扎奇为横跨墨西拿海峡所做的设计，就是以悬吊和缆索支撑混合 为特征的体系，其中，为限制顺风向的位移而增加

4、了两个水平的悬吊缆索。现在看 来似乎除了少量小跨度的反例，悬索桥梁所需的弯曲刚度必须来自于桥面板已经称 为大家的共识。桁架梁从芬力时代开始就被不间断地运用着， 而且现在仍然是加强桥板刚度最 受欢迎的结构。然而，给桥板添加桁架梁，从根本上改变了其几何特征，而且也会 对其空气动力学性能产生影响。越高的桁架梁可以产生更大的拉力，整个19 世纪许多事故的发生正是由于这个原因，主要归因于狂风的袭击。作为桁架梁的一个替换，20 世纪 20 年代在德国出现了平板梁，然后在法国和 美国被采用。使用板梁可以允许设计更薄的桥板，所以减小了拉力，随之而来的结 果就是，减小了支撑缆索和桥塔的尺寸，因而使得结构更轻便、

5、更便宜。另外，它 在审美学上的吸引力对平板梁悬索桥在欧洲和北美的流行作出了贡献。平板梁桥板已经被用于中等跨度的桥梁，从跨径378 米的雷恩哈德的Rodenkirchen 桥，到 1939 年完成的跨径 701 米的安曼的布朗克斯-白石桥。大约 1 年后，莫塞弗的 853 米的塔科马纽约湾海峡桥在 1940 年 7 月 1 日开放通车，129 天 后的 11 月7 日倒塌。拉力减小了，随之而来的就是在风载作用下的震动反应，但 是 H 形断面的空气动力性能结合平板的弹性给其带来了一个完全不同的特性，而这 在以前是没有被认识到的。虽然没有被认识到，但很可能已经在别的桥面板中经历 过了这种情况。基于从

6、塔科马事故中得到的认识，许多过去的其它桥梁事故被重新 思考，其中一些就是归因于其相似的空气动力性特（例如1826 年泰尔福德的米乃海峡桥遭遇的毁坏）。即使意识到了这些是不能免除可能的空气弹性变形的特性， 悬索桥设计者们又 回到了桁架梁结构，直到 1959 年，当罗伯茨吉尔波特主持设计赛文横跨桥时， 提出了一个完全新式的桥板构想：箱形梁桥板。箱形梁和桁架梁的设计水平都得到 了发展，但是 7 年后的 1966 年，具有 3 米高的箱形桥板的 988 米的赛文桥建成了。 这个桥板的构想结合了所有要求的特征，也就是高扭转刚度，低拉力，空气弹性变 形的稳定性，还有经济性和美学要求，这一构想似乎已经实现。

7、而这似乎也完成了 伊丽莎白莫克的美好理想。既然一个桥梁的实体归结于它的结构， 那么桥梁建筑的 艺术就归结于对那些最有效的利用所给材料的力学和特殊性能的结构形式的潜在 的美学的鉴赏。箱形断面的高抗扭转刚度允许减小梁的高度， 这再与改进的外形相结合就带来 了低拉力的效果。在平板梁的情况下，可以减小悬吊缆索和桥塔的尺寸，这就使结 构物的重量得以减小，从而降低了其成本。然而，对于箱形桥板，这种成本的减小， 不会伴随带来差的空气弹性变形性能。在赛文桥的情况下，箱形梁结构的总成本结 果比桁架梁要低 10%，但是测量发现这种桥板可以在 240km/h的风速下保持稳定， 相比， 塔科马桥只能承受 35km/h

8、的风速（在风洞实验中，直到桥梁破还）。近 35 年中，箱形梁已经在全世界被广泛并成功地应用于悬索桥，其跨度可达到丹麦的斯道波特桥的 1624 米，但是老的桁架梁和板梁仍然在使用之中，而且与箱 形梁相比经常更受到大家的喜欢，特别是在北美和东亚地区。如果不是从19世纪初到第二次世界大战期间的120年之间它们的结构已经被放 弃了，很可能已经会重演跟另外一种形式的悬索桥相似的历史。19 世纪初，在欧洲也设计并建造了一些的单纯缆索支撑桥梁，但几次因风造成的失败之后，这种结构 就从桥梁结构的清单中消失了。 1955 年迪斯邱吉尔的斯卓恩桑德桥（183 米）在瑞 典建成，因而开始了悬索桥的崭新时代。由于跨度

9、更小并且支撑体系的刚度更高（如 果跟悬吊体系相比） ， 缆索支撑桥梁比悬浮桥梁更趋向坚硬， 而且它的桥板相比更 不容易受到风载的作用。缆索支撑桥梁通常是以平板或者箱形梁桥板为特征的， 它 们都显示出跟悬索桥桥板相似的空气动力学特性。下列的悬索桥和缆索支撑桥桥板 将作为大跨度桥梁桥板被提及和谈论。2.大跨度桥梁桥面板的空气动力学性能和风洞测试的作用暴露风中结构的设计中荷载选择的第一个标准早在1759 年就由斯莫顿发表了，在随后的一个半世纪中许多著名的工程师都在评估风荷载对结构的作用机理， 并解 释随之引起的结构反应。尽管他们做出了努力，但是19 世纪所有的桥梁倒塌事故都被简单的归因于“由风引起的

10、失败”， 因为风和结构交互作用机构的一致解释是 没有用的，而且为对这些失败作一个更深层次的物理解释所做的努力在今天看来几 乎是天真的。两个至关重要的问题被忽略了，而且直到20 世纪中期才被认识到，这两个问题是：（a） 风载作用的动力学特征以及跟柔韧结构的动力性能的相互作用 和 （b）存在一定形式的能够从根本上改变激发模式的空气弹性变形性能。结构上的失败前后都有发生，但塔科马桥的倒塌可以称为空前的转折点，从此 开始了一个结构工程的新时代。在桥梁倒塌原因分析的必要性的刺激下，桥梁空气 动力性能的研究有了新的推动力， 这提供了对空气弹性变形的相互作用在大跨度桥 梁动力性能的作用的更清晰的理解。事实上

11、，负责调查评估失败原因的卡莫迪成员 并没有达成完全的共识，最后的报告中还存在一些矛盾。然而，很明显那时在空气 动力学和空气弹性变形方面所取得的知识已经使工程师们做好了理解大跨度桥梁 桥板摆振动性的特征的准备。20 年后，达文波特所做的先导性工作，使人们开始理解大气扰动以及它对弹性 结构的影响，特别使对悬索桥的影响。他介绍了处理结构风荷载荷盖然论的方法，而且给振动模型反应的评估引入了空气动力学准入和细长结构的联合认同的概念。基于稳定的空气动力学，从准静态运动方程中发现了扭转和垂直振动的纵向耦合，并依靠空气动力学系数挑选出了可能不稳定形式。20 世纪 60 年代，由于斯肯兰的努力，人们开始了对振动

12、的数学处理工作。已 经介绍的新特点是以下两个方面的运用， 即用不稳定空气动力学来描述桥梁桥板的 行为特征和运用实验方法测量不稳定空气动力学系数。所谓的振动导数也得到了发 展。在分析风对大跨度桥梁的作用的理论背景发展的同时，实验技术也得到了确立。在气流中放置模型结构来测量空气动力的方法可以追溯到19 世纪末。那时，爱明哥在烟囱通风管中完成了第一个“风洞”实验。 最初风洞试验只是应用于土木工程 学的目的，比空气重的飞行器还没有实现。20 世纪，航天工程师们开始了风洞的研 究，土木工程师则利用那些设备的有利条件来测试建筑结构。1955 年，杰森发现了在平滑流和大气湍流中测试风荷载的差异，但是西安大略

13、大学的达文波特，用了十 多年时间在 1965 年建立了第一个界面层风洞土木工程实验室。20 世纪 70 年代初，所有成果显示大跨度桥面板的空气动力学设计是有效的，建立的完全擅振理论和界面层风洞是有利于提供实验要求的输入数据和验证分析 输出。但是，这些成就并不能表示哪种桥板（桁架梁、平板梁和箱形梁）是最终的 首选。平板梁虽然不被应用于悬索桥，但因为经济原因其仍被看作是斜拉桥的不错 选择。箱形梁在全世界被广泛应用于斜拉桥，但是在欧洲主要被用于悬索桥，桁架 梁主要是在北美和东亚主要被用于悬索桥（尽管中国好象不在这一普遍趋势之列）接下来的部分将介绍箱形梁桥板断面的空气动力学特性， 桥面板的三维整体性

14、能是断面的空气动力学性能与翼展方向空气动力学激发的相关性的结合。本文将把 重点放在对桥板起作用的断面力的结构上，关于力的翼展方向性的资料可以别处找 到，例如在文献12和关于它的参考书中。例如将提到关于佛罗里达州坦帕市的阳光高架桥的桥板就是来自西安大略大学 边界层风洞实验室最近进行的风洞实验的结果。关于此结果的报告在此只是一个摘要，更详细的情况作者将会在另一篇论文中论述。3.在边界层风洞实验室进行的阳光高架桥断面模型的风洞试验1982 年在阳光高架桥的设计阶段，边界层风洞实验室筹划设计并测试了一个桥 板的受压断面模型（图 1）和一个空气弹性变形的复制品。最近，为了更深入的分 析箱形梁上的空气动力

15、的结构对断面模型进行了进一步的测试。阳光高架桥是一个主桥跨度为 364m 宽 29m 高 4.27m 的预应力混凝土连续箱 形梁桥板的斜拉桥。由于单平面支柱的存在，桥板中心线的调整，桥板抗扭刚度只 来源于梁的刚度，而其抗弯刚度则来自于梁的抗弯刚度和支撑刚度的结合。结果是 以上四个要素将桥的首要弯曲和扭转的固有频率分开。首要弯曲频率为0.31Hz 首要扭转频率为 1.25Hz。建成于 1986 年的阳光高架桥在风载的作用下具有良好的性图 1.阳光高架桥模型横断面受压区位置1999 年和 2000 年在箱形梁桥板空气动力学研究工程的框架内，边界层风洞实 验室对桥的断面模型进行新的测试。平滑流测试先

16、后在固定和可动模型上进行。48个压强的压力作用在确定好的比例为 1:80 的断面模型的两断面中间跨度点周围 2cm 处。所用的压力模型在风激振的可动桥板上允许空气动力的测量。固定的模型测试在边界层风洞实验室（I）中进行。测量桥面板压力，并且测力 传感器还被用来测量作用在模型上的总的空气动力。另外，记录下模型某一尾流位 置的风速水平和竖直方向的合成。可动模型的测试是在边界层风洞实验室（II）中进行，分别用激光位移转换器、加速度计和测力传感器同时测量了桥板压力、 模型垂直和扭转的位移和加速度和支 撑弹性力。另外，风速分别在尾迹模型的七个位置和一个逆流位置用两个组合热电 阻风速计来测量。关于测试的更

17、多细节的信息和更完整的结果在文献【14, 15】中给出附件 2:外文原文（复印件）Juumikl of Wind Enmecringand Industrial Aerudynamtcs 91 (2005) 141 I 1430晒w * .u llitv iier.c Dni/liKate/ju ciiiOn the wind loading mechanism of kmg-spanbridge deck box sectionsI rancesco Ricciardelli*I)cfJiff ItmHl iff Mct hiinii itnd. I tlii ersitLThis seem

18、s to huve IKVHone of. inot the muinsubject of dcbulc among supctision bridge designersaver the past bvo ccnlui its. UnifGcned suspensionlinks existed in Aiii and South Aincriicu for wiinc 5000 years, and the idea wus exported to Europe umi thccito Norih .mcricu starting in tlie 17th ccnLury UntUilTc

19、nt?uspciisioi-i bridges arc simple in principle,however Ihdr is lx)und to rathershortTd.: 4-39-%SS75267:GIK:+39-96i5-8752l.E-muii Heiress: fria?iuiij ing. imnire.it (F. Ricciarddli).(H67-6I05 5 - see front mumr 4 2005 Elswcvicr Ltd. AW riighl ed)_ d0i：IO/IOlfi;jjwd.a.2m.W.OI IJQLHNALDfwind engineeri

20、ng -AND r屈即噱rf副痂诚怯f血函!1412F. Ricckirdclli / J. Wiful Eng. Ind Acrodyn. 91 (2003) 1411 1430spans and unsuitable for vehicular traflic. due to their deformability Therefore, when in the mid-18th centurysuspension bridges started to be built in Europe and North America, it became clear that some source

21、 ofstiffiiess had to be added to the structure, other than the suspension chains (or cables)But then, what is the most appropriate way to provide stiffness to a suspension bridge? Additional stiffnesscan come from modifications to the suspension system or to the deck, both solutions having been stud

22、ied andimplemented The first suspension bridge featuring a stiffening girder was a mere 21 m span, designed byFinley and completed in 1801 in the United States, in which a longitudinal braced joist was added to the deck 1 As an alternative, stays can be added between the tower and the deck, which pr

23、ovide stiffness to the bridgeThis latter technique was largely used by Navicr 2. but then almost abandoned, as it proved less cfTcctivc thanthe use of a stiffening girder. More complicated stiffening cable systems have been studied, like, for example,that proposed by Musmeci for the Messina Strait c

24、rossing, featuring a hybrid suspension cable-slaycd system towhich two horizontal suspension cables were added to limit the alongwind displacements. Today it seems that,except for a few, small span counterexamples, it has been accepted that the required flexural stiffiiess of asuspension bridge has

25、to come from the deck.Truss girders have been used uninterruptedly since Finleys times, and still remain the most popular systemfor stiffening suspension bridge decks The addition of truss girders to the deck, however, radically changes itsgeometry, and this affects theaerodynamic behaviour Larger d

26、rag forces arc associated with deep truss gilders,which caused a number of Hiilures occurred throughout the i9lh century, mainly due to gust buffetingAs an alternative to truss girders, plate girders appeared in Germany in the second decade of the 20lh century,and were later adopted in France and in

27、 the United States The use of plate girders allows to design shallowerdecks, and therefore reduce drag forces As a consequence, the size the supporting cables and of the towers canalso be reduced, bringing lighter and cheaper structures In addition, their appealing aesthetics contributed tothe diffu

28、sion of plate girder suspension bridges in Europe and North America.Plate girder decks had been used for mediumspan bridges, upto the378 m Leonhards Rodcnkirchcn Bridge,until 701 in Ammans Bronx Whitestone Bridge completed in 1939 About one year latci MoissefTs 853 mTacoma Narrows Bridge was opened

29、to traffic on July 1. 1940. which collapsed 129 days later, on November 7.Drag had been reduced, and with it the alongwind buffeting response, but the aerodynamics of the H-shapedsection, combined with the flexibility of the deck brought to light a totally different behaviour, never recognisedbefore

30、 Never recognised, but most probably already experienced by other bridge decks Based on theknowledge gained from the Tacoma failure, many other bridge failures of the past were revisited, and some ofthem ascribed to a similar aeroclastic behaviour (as an example the damage suffered by Tcllords Mcnai

31、 StraitsBridge in 1826).Even though aware that these are not exempt from a possible acroelastic behaviour, suspension bridgedesigners moved back to truss girders, until 1959, when Gilbert Roberts of Freeman Fox and Partners, in chargeof the design of the SevernF. Riccuirdclli I J. Wiiul Eng. Ind Acr

32、odyn. 91 (2(X)3) 1411-14301413crossing bridge put forward the idea of a totally new type of deck: the box girder deck The designs of boxgirder and truss girder alternates were both developed, but seven years later, in 1966, the 988 m Severn Bridgewas completed featuring a 3 m deep box deck. The idea

33、 of a bridge deck that could combine all the desiredcharacteristics, i.e. high torsional stiffness, low drag, acroelastic stability, together with economy and aesthetics,seemed to have been realized, which appeared the fulfilment of Elizabeth Mocks ideal of beauty 3:Since the reality of a bridge lie

34、s in its structure, the art of bridge building lies in the recognition of the beautylatent in those structural fonns that most effectively exploit the strength and special properties of a givenmaterial The high torsional stiffiicss of box sections allows reducing the girder depth, which, combined wi

35、th thestreamlined shape brings low drag forces As in the case of the plate girders, the size of the suspension cablesand of the towers can be reduced, bringing a decrease of the structure weight and, there lore, of its cost. For boxgirder decks, however, this cost reduction is not accompanied by a p

36、oor aeroclastic behaviour. In the case of theSevern bridge, the overall cost of the structure for the box girder alternate proved to be 10% lower than for thetruss girder alternate, but the deck was measured to be stable up to a wind speed of 240 km/h, as opposed to amere 35 km/h measured (in the wi

37、nd tunnel, after its collapse) for the Tacoma bridge 4.In the last 35 years, box girders have been extensively and successfully used for suspension bridges all overthe world, with spans up to the 1624 m of the Storcbajlt Bridge in Denmark, but the older truss and plate girdersare still in use, and h

38、ave often been preferred to box girders, especially in North America and in eastern Asia.Probably it would have been possible to trace a similar history for the other form of cable supported bridge,the cable-stayed bridge, if their construction hadnt been discontinued for almost 120 years, between t

39、he early19th century and World War II. Pure cable-stayed bridges were designed and a few built in Europe at thebeginning of the 19th century, but after some failures due to wind, they disappeared from the rex:rLoire ofbridge slruulures In 1955 DisuhingurS Slidinsuiid bridge (183 in) was completed in

40、 Sweden, initiating a newera for cable-stayed bridges 5 Due to the smaller spans and to the higher stiffiicss of the stay system (ifcompared to the suspension system), cable-stayed bridges tend to be stiffer than suspension bridges, and theirdecks only comparatively less prone to the wind action. Ca

41、ble-staved bridges usually feature either plate or boxgirder decks, whose aerodynamics show similar characteristics to those of suspension bridge decks. In thefollowing suspension and cable-stayed bridge decks will be addressed, and referred to as long-span bridgedecks.2. The aerodynamics of long-sp

42、an bridge decks and the role of wind tunnel testingThe first criteria for the choice of the loads to be included in the design of wind exposed structures werepublished by S meat on as early as 1759 6, and in the1414F. Ricckirdelli I J. Wirui Eng. /nd Acroclyn. 91 (2(X)3) 1411 1430following one and a

43、 half century distinguished engineers devoted themselves to the problem of assessing themechanism of the wind loading of structures, and to interpret the consequent structural response. In spite of theirefTorts, all the bridge collapses of the 19th century were simply classified as failures due to w

44、ind* as aconsistent explanation of the wind-structure interaction mechanism was not available, and the attempts towardsa deeper interpretation of the physics underlying the failures appear today almost naive Two crucial issueswere ignored, and wont be recognised till the mid-20th century, namely (a)

45、 the dynamic nature of the windaction and its interaction with the dynamics of flexible structures, and (b) the existence some forms ofacroclastic behaviour which arc able to radically modify the excitation patterns.Structural failures had occurred before and occurred after but the collapse of the T

46、acoma bridge became anunprecedented milestone which started a new era for structural engineering. Stimulated by the necessity ofclarify ing the causes of the collapse, new impetus was given to research on bridge aerodynamics, which broughta much more aware understanding of the role of acroclastic in

47、teraction in the dynamic behaviour of long-spanbridges. Indeed, the agreement between the members of the Carmody Board (O.H. Amman. Th. von Karmanand G Woodruff), in charge of the investigation to asses the causes of the failure, was not fbll, and manycontradictions were included in the final report

48、 7. However, it was clear that the knowledge achieved at thattime in aerodynamics and aeroclasticity was such that engineers were ready for the understanding of the natureof the flutter behaviour of long-span bridge decks Two decades later the pioneering work of Davenport brought to the understandin

49、g of the structure of theatmospheric turbulence and of its effects on flexible structures, in particular on suspension bridges 8.9. Theprobabilistic approach to the treatinent of the wind loading of structures was introduced and the concepts ofaerodynamic admittance and of joint acceptance of a slen

50、der structure were added to the models for theevaluation of the buffeting response The coupling of longitudinal, torsional and vertical vibrations was foundfrom the quasi-stcady equations of motion, based on stationary aerodynamics and the possible types ofinstability were singled out. depending on

51、the values of the aerodynamic coefficientsThe mathematical treatment of flutter came also in the 1960s, due the work of Scanian. The new feature tohave been introduced was the use of nonstationary aerodynamics to characterise the behaviour of bridge decks,and experimental techniques for the measurem

52、ent of the nonstationarj aerodynamic coefficients, the so calledflutter derivatives, were developed 10.The development of the theoretical background for the analysis of the action of wind on long-span bridgeswas paralleled by the establishment of experimental techniques. The idea of placing a model

53、structure in an airflow, to measure the aerodynamic forces, dates back to the end of the 19th century, when Irmingcr ran the firstwind tunnel* tests in a chimney ventilation duct. Heavier-than-air flight had not yet been achieved, and in thebeginning wind tunnel tests were only for civil engineering

54、 purposes. In the 20th century wind tunnel started tobe built by aeronautical engineers, and civil engineers took advantage of these facilities forF. RiccMrdclli / J. Wifkl Eng. /nd Acro(h n. 91 (2(X)3) 1411 14301415testing civil structures The discrepancies between the wind forces measured in smoot

55、h flow and those arisingfrom a real atmospheric turbulent flow were recognised by Jensen in 1955. but it took 10 more years before thefirst boundary layer wind tunnel for civil engineering testing was built by Davenport at the University ofWestern Ontario, in 1965By the beginning of the 1970s all th

56、e tools for the aerodynamic design of long-span bridge decks wereavailable: flutter and buffeting theories had been established and boundary layer wind tunnels were available toprovide the required experimental input data and to validate the outcomes lhe analyses. These achievements,however, did not

57、 indicate which type of deck (truss girder, plate girder and box girder) was to be ultimatelypreferred. Plate girders were abandoned for suspension bridge, but are still considered appealing forcable-stayed bridges, for economical reasons 11). Box girders arc widely used all over the world forcable-

58、stayed bridges and, mainly in Europe for suspension bridges. Truss girders arc in use for suspensionbridges, mainly in North America and in eastern Asia (though China seems to be away from this general trend).In the following sections the aerodynamic characteristics of box girder decks will be addre

59、ssed The overall3-dimensional behaviour of the bridge deck is a combination of the sectional aerodynamic behaviour and of thespanwise correlation othe aerodynamic excitation .In this paper emphasis will be put on the structure of thesectional forces acting on the deck. Information about the spanwisc

60、 correlation of the forces can be foundelsewhere, for example in 12 and reference thereof.As an example, results will be presented regarding the deck of the Sunshine Skyway Bridge, Tampa, FL,deriving from wind tunnel tests recently carried out on a section model at the Boundary Layer Wind TunnelLaborato