Page:Aerial Flight - Volume 2 - Aerodonetics - Frederick Lanchester - 1908.djvu/390

Appendix V

Calculations for the Plotting of the Phugoid Chart

 

(The reference numbers correspond to those given in Fig. 42 and the Frontispiece.)

Curve No. 1 is the special case of the straight flight path.

Curves Nos. 2 and 3 are plotted by the approximate method of § 31.

Curve No. 4. (Inflected type.)

$H_{n}=64.\qquad H_{1}=25.\qquad \cos \Theta _{1}=1.$

For highest and lowest points on the curve, cos θ₁ = 1, and

${\begin{aligned}C&={\sqrt {H_{1}}}\left(\cos \Theta _{1}-{\frac {H_{1}}{3H_{n}}}\right)\\&=5\times \left(1-{\frac {25}{192}}\right)=4\cdot 35\end{aligned}}$.

For highest and lowest points on the curve, $\cos \Theta _{1}=1$, and

${\frac {H}{192}}+{\frac {4\cdot 35}{\sqrt {H}}}=1$

the solution of which gives alternative values of II (compare § 28).

H = 25, highest point of curve (already known).

H  = 113.5, lowest point on curve (value required).

Point of Inflection.—This is given by § 28, Equation (15).

${\begin{aligned}H_{i}&=\left({\frac {3H_{n}C}{2}}\right)^{\tfrac {2}{3}}\\&=\left({\frac {192\times 4\cdot 35}{2}}\right)^{2}=56\end{aligned}}$

 

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