Ballistics, 2nd Edition

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

viv− )]e

(8.265)

But with the fact that (h · i) = I

P

p/I

T

as shown earlier, then we can write

()() ()()(hi iv ee⋅×=−+−+

Ip

I

iv iv

Ip

I

iv iv

Ip

I

iv

P

T

P

T

P

T

23 32 131132 1222

13

− 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

ee

⋅=

++

)

P

T

P

T

P

T

Ip

I

i

Ip

I

i

Ip

I

i

11 22

33

(8.268)

In Equation 8.258, we need

() ()()(vi

eee

ee×= =− +− ...