
278 Ballistics: Theory and Design of Guns and Ammunition
Now, also in Equation 8.257 is the term
()()( )[( )( )(hi iv ee⋅×=++−+− +hi hi hi iv iv iv iv i
11 22 33 23 32 131132 112 21 3
(8.265)
But with the fact that (h · i) = I
P
p/I
T
as shown earlier, then we can write
()() ()()(hi iv ee⋅×=−+−+
iv iv
iv iv
iv
P
P
P
23 32 131132 1222
− iv)e
(8.266)
Another relation we have to deal with is
() ()()(hi
eee
ee×= =− +− +
1
1
1
2
2
2
3
3
3
23 32 131132 12
h
i
h
i
h
i
hi hi hi hi hi −− hi
21 3
)e
(8.267)
The next relation we generate with the help of Equation 8.229 is
(hiie
⋅=
)
P
P
P
i
i
i
11 22
(8.268)
In Equation 8.258, we need
() ()()(vi
eee
ee×= =− +− ...