Page:Aerial Flight - Volume 2 - Aerodonetics - Frederick Lanchester - 1908.djvu/392

Curve No. 9. (Tumbler.)

$H_{n}=64.\qquad H_{1}=16.\qquad \cos \Theta _{1}=-1.$

$C=4\times \left(-1-{\frac {16}{192}}\right)=-4\cdot 333$.

Lowest point on curve,

${\frac {H}{192}}+{\frac {-4\cdot 333}{\sqrt {H}}}=1$

whence

$H=245$.

Curve No. 10. (Tumbler.)

$H_{n}=64.\qquad H_{1}=36.\qquad \cos \Theta _{1}=-1.$

$C=6\times \left(-1-{\frac {36}{192}}\right)=-7\cdot 125$.

Lowest point on curve,

${\frac {H}{192}}+{\frac {-7\cdot 125}{\sqrt {H}}}=1$

whence

$H=275.$

Curve No. 11. (Tumbler.)

$H_{n}=64.\qquad H_{1}=50.\qquad \cos \Theta _{1}=-1.$

$C={\sqrt {50}}\times \left(-1-{\frac {50}{192}}\right)=-8\cdot 91$.

Lowest point on curve,

${\frac {H}{192}}+{\frac {-8\cdot 91}{\sqrt {H}}}=1$

whence

$H=292.$

Curve No. 12.

$H_{n}=64.\qquad H_{1}=100.\qquad \cos \Theta _{1}=-1.$

$C=10\times \left(-1-{\frac {100}{192}}\right)=-15\cdot 21$.

Lowest point on curve,

${\frac {H}{192}}+{\frac {-15\cdot 21}{\sqrt {H}}}=1$

whence

$H=348.$

The calculated values of r for the preparation of trammels for the plotting of the curves as above are appended.