Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/405

Rh {| align="center" style="text-align: center; width: 100%"
 * align="right" width="1%" | Or, || width="1%" | $$V_1 = 15\ \mbox{ft. /sec.}$$ || width="1%" |
 * || $$V_2 = 12.5\ \mbox{ft. /sec.}$$ ||
 * || $$\gamma_1 = \frac{7.5}{47} = .160$$ || align="left" |
 * || $$\gamma_2 = \frac{7.5}{35} = 2.14$$ ||
 * || $$x_1 + y_1 = .160 \times 5.25 = .84$$ || align="right" | (1)
 * || $$x_2 + y_2 = .214 \times 5.25 = 1.12$$ || align="right" | (2)
 * colspan="3" align="left" | Now we know that $$x = n\ V^2$$ and $$y = \frac{m}{V^2}$$ where $$n$$ and $$m$$ are constants,
 * align="right" | or, || $$x_1 = 15^2 n, \quad y_1 = \frac{m}{15^2}$$ || align="right" | (3)
 * || $$x_2 = 12.5^2 n, \quad y_2 = \frac{m}{12.5^2}$$ || align="right" | (4)
 * align="right" | By (1) and (3) || $$15^2 n + \frac{m}{15^2} = .84$$ || align="right" | (5)
 * align="right" | By (2) and (4) || $$12.5^2 n + \frac{m}{12.5^2} = 1.12$$ || align="right" | (6)
 * align="right" | || $$12.5^2 n + \frac{(.84 - 15^2 n) \times 15^2}{12.5^2}$$ ||
 * align="right" | || $$156\ n - 325\ n = 1.12 - 1.21$$ ||
 * align="left" | or, || $$169\ n = .09$$ ||
 * || $$n = .000532$$ ||
 * align="left" | or, || $$x = .000532\ V^2\ \mbox{grams.}$$ ||
 * }
 * || $$x_2 = 12.5^2 n, \quad y_2 = \frac{m}{12.5^2}$$ || align="right" | (4)
 * align="right" | By (1) and (3) || $$15^2 n + \frac{m}{15^2} = .84$$ || align="right" | (5)
 * align="right" | By (2) and (4) || $$12.5^2 n + \frac{m}{12.5^2} = 1.12$$ || align="right" | (6)
 * align="right" | || $$12.5^2 n + \frac{(.84 - 15^2 n) \times 15^2}{12.5^2}$$ ||
 * align="right" | || $$156\ n - 325\ n = 1.12 - 1.21$$ ||
 * align="left" | or, || $$169\ n = .09$$ ||
 * || $$n = .000532$$ ||
 * align="left" | or, || $$x = .000532\ V^2\ \mbox{grams.}$$ ||
 * }
 * align="left" | or, || $$169\ n = .09$$ ||
 * || $$n = .000532$$ ||
 * align="left" | or, || $$x = .000532\ V^2\ \mbox{grams.}$$ ||
 * }
 * align="left" | or, || $$x = .000532\ V^2\ \mbox{grams.}$$ ||
 * }
 * }

multiplying by $$\frac{144}{16}$$ to obtain grams per square foot, and by $$\frac{32.2}{453.6}$$ to convert to British absolute units, we have—

But normal plane pressure is given by expression—

In the foregoing calculation no allowance has been made for