{"id":559878,"date":"2024-11-05T18:25:27","date_gmt":"2024-11-05T18:25:27","guid":{"rendered":"https:\/\/pdfstandards.shop\/product\/uncategorized\/esdu-tm-1692012\/"},"modified":"2024-11-05T18:25:27","modified_gmt":"2024-11-05T18:25:27","slug":"esdu-tm-1692012","status":"publish","type":"product","link":"https:\/\/pdfstandards.shop\/product\/publishers\/esdu\/esdu-tm-1692012\/","title":{"rendered":"ESDU TM 169:2012"},"content":{"rendered":"<p>ESDU TM 169 provides a brief background to the development of<br \/>\nthe compressible form of the Helmbold-Diederich equation for wing<br \/>\nlift-curve slope, a simple analytical equation which was in common<br \/>\nuse prior to the advent of more reliable methods such as the<br \/>\nlifting-surface theory which was used to derive the data in ESDU<br \/>\n70011.<\/p>\n<p>In its original form, involving only wing aspect ratio and sweep<br \/>\nto define the planform, the chordwise position of the wing sweep<br \/>\nwas undefined, consistent with its infinite swept wing basis. The<br \/>\nearliest uses of the Helmbold-Diederich equation adopted the sweep<br \/>\nof the quarter-chord line (commonly used to define planform sweep)<br \/>\nwhereas later uses employed the half-chord sweep in an attempt to<br \/>\neliminate the effects of wing taper, not otherwise accounted for.<br \/>\nComparisons are given of predictions using the Helmbold-Diederich<br \/>\nequation with both quarter-chord sweep and half-chord sweep against<br \/>\nthe lifting-surface theory data for 80 planforms used in developing<br \/>\nESDU 70011. The comparisons show that neither form has a maximum<br \/>\nerror much less than 10%, although the half-chord sweep form is<br \/>\nrather better, albeit with some bias.<\/p>\n<p>The residual effects of wing taper are shown to be largely<br \/>\naccounted for using empirical corrections similar to those<br \/>\ndetermined by Isaacs. The improved version of the<br \/>\nHelmbold-Diederich equation, using half-chord sweep, provides an<br \/>\nerror band of about +2% to \u20133% when compared with the data from<br \/>\nESDU 70011. Removal of just 10% of the 80 planforms (those with the<br \/>\nmost extreme sweeps) corrects the slight bias to give an accuracy<br \/>\nof \u00b12%.<\/p>\n","protected":false},"excerpt":{"rendered":"<p><b>Wing lift-curve slope in inviscid subsonic flow: Improvements to the Helmbold-Diederich equation and comparison with data from ESDU 70011<\/b><\/p>\n<table style=\"width: 100%\" border=\"0\" cellspacing=\"0\" cellpadding=\"0\">\n<tbody>\n<tr>\n<td>Published By<\/td>\n<td>Publication Date<\/td>\n<td>Number of Pages<\/td>\n<\/tr>\n<tr>\n<td><a href=\"https:\/\/pdfstandards.shop\/product-category\/publishers\/esdu\/\"><b>ESDU<\/b><\/a><\/td>\n<td>2012-03-01<\/td>\n<td>34<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"featured_media":559889,"template":"","meta":{"rank_math_lock_modified_date":false,"ep_exclude_from_search":false},"product_cat":[2675],"product_tag":[],"class_list":{"0":"post-559878","1":"product","2":"type-product","3":"status-publish","4":"has-post-thumbnail","6":"product_cat-esdu","8":"first","9":"instock","10":"sold-individually","11":"shipping-taxable","12":"purchasable","13":"product-type-simple"},"_links":{"self":[{"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/product\/559878","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/product"}],"about":[{"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/types\/product"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/media\/559889"}],"wp:attachment":[{"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/media?parent=559878"}],"wp:term":[{"taxonomy":"product_cat","embeddable":true,"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/product_cat?post=559878"},{"taxonomy":"product_tag","embeddable":true,"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/product_tag?post=559878"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}