Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/408

$=189-26.9$

$=162.1$

This is the value of $m$ for $y$ expressed in grams; for $y$ in poundals this becomes—

$m=11.5$

and for the aeroplanes in question,

$A=.111$  and  $W=.372$

∴ $\quad c={\frac {.372^{2}}{.111\times 11.5\times .0546}}=1.98$

This is about the value as determined directly by Duchemin, Dines and Langley for the square plane; it is probably too low for a plane of $n=4$ as used in these experiments.

Example.—Planes 3 and 4.

	$m=17^{2}\times (.875-17^{2}\ n)$
where	$n=.000724$
whence	$m=192.5$
or, when absolute units are employed, $m=13.6.$
	$A=.111\quad W=.418.$
∴	$c={\frac {.418\times .418}{.111\times 13.6\times .0546}}=2.11$

a result which is still probably less than the true value.

Calculation of $\beta .$

$\beta ={\frac {y}{W}}={\frac {m}{W\ V^{2}}}$

Taking planes 3 and 4.

Plane No. 3.

$\beta ={\frac {192.5}{5.9\times 289}}=.112\quad$$\quad \beta ^{\circ }=6.5^{\circ }$

or,

Plane No. 4.

$\beta ={\frac {192.5}{5.9\times 169}}=.193\quad$$\quad \beta ^{\circ }=11.1^{\circ }$

386