Page:Aerial Flight - Volume 2 - Aerodonetics - Frederick Lanchester - 1908.djvu/397

of the curves (where they overlap) as shown. In the example given the calculation is as follows:—

Suspension from origin O₁ gives t₁ = .29.

Now, $\lambda ^{2}=l\left(g\left({\frac {t}{\pi }}\right)^{2}-l\right)$, from which it is evident that A falls to zero when $l_{1}=o$ (i.e., at origin), and when $l_{1}=g\left({\frac {t_{1}}{\pi }}\right)^{2}$ that is

$l_{1}=32\cdot 2\left({\frac {\cdot 29}{3\cdot 14}}\right)^{2}=\cdot 274.$

Suspension from $O_{2},t=\cdot 36$

$g\left({\frac {t}{\pi }}\right)^{2}=32\cdot 2\left({\frac {\cdot 36}{3\cdot 14}}\right)=\cdot 424.$

These values give l₁ and l₂ respectively for $\lambda ^{2}$ = o laid off from O₁ and O₂. The intersection evidently lies between these points. We proceed to plot this portion of each curve as follows:—

 

$l_{1}.$		$\lambda ^{2}$
$\cdot 25$	$\lambda ^{2}=\cdot 25\times (\cdot 274-\cdot 25)$	$=\cdot 0060$
$\cdot 24$	$\lambda ^{2}=\cdot 24\times (\cdot 274-\cdot 24)$	$=\cdot 0081$
$\cdot 23$	$\lambda ^{2}=\cdot 23\times (\cdot 274-\cdot 23)$	$=\cdot 0101$

 

And similarly for the curve of $l_{2}$. The ordinates representing these plottings are shown in the figure.

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