Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/281

a position to obtain numerical values for the best values of the angle $\beta$ for aerofoils of different aspect value. Table IV. illustrates the process of calculation in the case of the pterygoid aerofoil $\xi$ being taken as = .03.

Table III.

Plausible Values, $\kappa$ and $\epsilon .$

$n.$	$\kappa .$	$\epsilon .$
3 4 5 6 7 8 — 10 — 12	1.00 (?) 1.03 (?) 1.064 (?) 1.10 (?) 1.12 (?) 1.14 (?) — 1.175 (?) — 1.195 (?)	.48 (?) .54 (?) .59 (?) .62 (?) .65 (?) .68 (?) — .72 (?) — .75 (?)

Table IV.

$\beta$ values for $\gamma =$ minimum.

Calculated from Equation, $\beta _{1}={\sqrt {\frac {2\ \xi \ C}{\kappa \ (1\,{\boldsymbol {-}}\,\epsilon ^{2})}}}$ for $\xi =.03.$

$n.$	$\kappa \,(?).$	$\epsilon \,(?).$	$\epsilon ^{2}.$	$1-\epsilon ^{2}.$	$\kappa (1{\boldsymbol {-}}\epsilon ^{2}).$	$C.$	$\xi .$	$2\,\xi \,C.$	$\beta _{1}^{2}.$	$\beta _{1}.$	$\beta _{1}^{\ \circ }.$
3 4 5 6 7 8 — 10 — 12	1.00 1.03 1.064 1.10 1.12 1.14 — 1.175 — 1.195	.48 .54 .59 .62 .65 .68 — .72 — .75	.23 .291 .348 .384 .422 .462 — .518 — .562	.770 .709 .652 .616 .578 .538 — .482 — .438	.770 .730 .695 .678 .648 .614 — .567 — .523	.685 .700 .71 .72 .725 .73 — .74 — .75	.03 .03 .03 .03 .03 .03 — .03 — .03	.0411 .0420 .0426 .0432 .0435 .0438 — .0444 — .0450	.0534 .0575 .0612 .0638 .0671 .0715 — .0783 — .0861	.231 .240 .247 .252 .259 .268 — .280 — .293	13.2° 13.75° 14.14° 14.4° 14.8° 15.0° — 16.0° — 16.8°

Table V. gives the results for values of $\xi$ equal .025, .020, .015 and .010 in the respective

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