Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/209

Air	(Hutton)	$C=.7$	Shape not stated.
’’	(Langley)	$C=.7$	Square planes.
’’	(Dines)	$C=.66$	Circular and other “compact” forms.
’’	(Dines)	$C=.76$	Rectangular lamina 16:1 ratio.
Water	(Beaufoy, Froude)	$C=.55$	Shape not stated.

§ 137. Deductions from Comparison of Theory and Experiment.— The method of the Newton medium may he dismissed on the grounds of faulty hypothesis; the prop, xxxvii. method may be discarded as being certainly unsound; the Torricellian method is based on a tacit assumption that the fluid in proximity to the front face of the plane is destitute of velocity, which we know is not true, except at one point or on one line. The Helmholtz method alone stands on a scientific basis, and at present this gives a result in but one special case.

We are in want of data; let us assume data and develop the method. The results can be corrected for more reliable figures when such have been ascertained.

Data assumed:—

Helmholtz' result for infinite lamina	$C=.44.$
Dines' determination for plane 16 inches $\times$ 1 inch assumed as for infinite lamina	$C=.76$	(Air).
Beaufoy's result augmented 10 per cent. for infinite lamina. (Water)	$C=.60.$

These values are plotted in Fig. 87, in which abscissae represent viscosity (kinematic), and ordinates values of $C$; that is, where $V$ is constant, ordinates are proportional to kinematic pressure.

Drawing tangents to this curve at $a$ and $b$, we can deduce the values of the indices $q$ and $r$ in the general equation of §§ 35 and 42,—

$R=c\ \nu ^{q}\ l^{r}\ V^{r}.$

The result given by the curve as drawn is as follows:

Water: $R=c\ \nu ^{.07}\ l^{1.93}\ V^{1.93}.$

Air: $R=c\ \nu ^{.1}\ l^{1.9}\ V^{1.9}.$

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