ESDU TM 169
ESDU TECHNICAL MEMORANDUM Wing lift-curve slope in inviscid subsonic flow: Improvements to the Helmbold-Diederich equation and comparison with data from ESDU 70011
Abstract:ESDU TM 169 provides a brief background to the development of the compressible form of the Helmbold-Diederich equation for wing lift-curve slope, a simple analytical equation which was in common use prior to the advent of more reliable methods such as the lifting-surface theory which was used to derive the data in ESDU 70011.
In its original form, involving only wing aspect ratio and sweep to define the planform, the chordwise position of the wing sweep was undefined, consistent with its infinite swept wing basis. The earliest uses of the Helmbold-Diederich equation adopted the sweep of the quarter-chord line (commonly used to define planform sweep) whereas later uses employed the half-chord sweep in an attempt to eliminate the effects of wing taper, not otherwise accounted for. Comparisons are given of predictions using the Helmbold-Diederich equation with both quarter-chord sweep and half-chord sweep against the lifting-surface theory data for 80 planforms used in developing ESDU 70011. The comparisons show that neither form has a maximum error much more than 10%, although the half-chord sweep form is rather better, albeit with some bias.
The residual effects of wing taper are shown to be largely accounted for using empirical corrections similar to those determined by Isaacs. The improved version of the Helmbold-Diederich equation, using half-chord sweep, provides an error band of about +2% to -3% when compared with the data from ESDU 70011. Removal of just 10% of the 80 planforms (those with the most extreme sweeps) corrects the slight bias to give an accuracy of ±2%.
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