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G. L
eng,
ME
Dep
t, N
US
1. A
erod
ynam
ics a
nd F
irep
ower
or h
ow to
“sl
ug”
the
enem
y fr
om a
dis
tanc
e
G. L
eng,
ME
Dep
t, N
US
Quo
tabl
e Q
uote
Cpt
Lidd
ell-H
art*
“It i
s the
fire
pow
er, a
nd fi
re p
ower
alo
ne,
that
arr
ives
at t
he c
orre
ct ti
me
and
plac
e th
at c
ount
s in
the
mod
ern
war
”
* Si
r Bas
il H
enry
Lid
dell-
Har
t (31
Oct
189
5–29
Jan
1970
) En
glis
hm
ilita
ry h
isto
rian
know
n fo
r his
idea
s on
arm
oure
dw
arfa
rean
d st
rate
gic
theo
ry
G. L
eng,
ME
Dep
t, N
US
Stal
in –
“Art
iller
y is
the
God
of W
ar”
•U
SSR
-V
ladi
mir
Tria
ndaf
ilov
(192
9),
“Cha
ract
er o
f the
Ope
ratio
ns
of M
oder
n Ar
mie
s” e
stim
ated
th
at 5
0-60
gun
s/km
of f
ront
ne
eded
for b
reak
dow
n of
en
emy
defe
nses
.
•W
W2
(194
4) R
ussi
an a
rmie
s us
ed 2
00-3
00 g
uns/
km o
f fr
ont f
or 2
hr b
arra
ge
Ref
: W
alte
r S. D
unn
Jr, “
Hitl
er’s
Nem
esis
: Th
e R
ed A
rmy,
193
0-19
45”,
Pra
eger
, 199
4
G. L
eng,
ME
Dep
t, N
US
Fire
pow
er
The
rate
of e
nerg
yde
liver
edfr
om p
oint
A to
poi
nt B
fo
r des
truc
tive
purp
oses
Que
stio
n : S
o ho
w m
uch
ener
gy c
an b
e de
liver
ed b
y m
oder
n w
eapo
n sy
stem
s ?
G. L
eng,
ME
Dep
t, N
US
Exa
mpl
e : F
H20
00 F
ield
How
itzer
G. L
eng,
ME
Dep
t, N
US
Exa
mpl
e : P
rim
us S
elf P
rope
lled
Art
iller
y
G. L
eng,
ME
Dep
t, N
US
Exa
mpl
e : M
107
155m
m P
roje
ctile
Wei
ght
Leng
th (e
xclu
ding
fuze
)60
5.3
mm
B
ody
diam
eter
154.
89 m
m
Driv
ing
band
dia
met
er15
7.98
mm
Payl
oad
: C
ompo
sitio
n B
: 6.
985
kgTN
T :
6.62
kg
Supp
lem
enta
ry c
harg
e :
0.13
6 kg
TN
T
Rang
e
G. L
eng,
ME
Dep
t, N
US
Exa
mpl
e : X
M98
2 E
xten
ded
Ran
ge A
mm
o•
Join
t dev
elop
men
t by
Bof
ors&
Ray
theo
n
•B
ased
on
stan
dard
155
mm
pro
ject
ile
•C
anar
ds a
erod
ynam
ic c
ontro
ls
•G
PS/IN
S un
it
•C
EP*
= 10
m ra
dius
at a
dis
tanc
e of
50k
m
G. L
eng,
ME
Dep
t, N
US
Ene
rgy
of a
155
mm
HE
pro
ject
ile
Con
side
r the
kin
etic
ene
rgy
for t
he 1
75m
m R
omac
hSP
K.E
.= = =
Ass
umin
g a
payl
oad
frac
tion
of
The
chem
ical
ene
rgy
=
Tota
l ene
rgy
≈
G. L
eng,
ME
Dep
t, N
US
Ene
rgy
of a
GPM
G c
artr
idge
Car
trid
ge, 7
.62m
m, A
P, M
61
Wei
ght(
cartr
idge
) :
Wei
ght (
proj
ectil
e):
M60
mac
hine
gun
Max
eff
ectiv
e ra
nge
Muz
zle
velo
city
: R
ates
of f
ire:
G. L
eng,
ME
Dep
t, N
US
Ene
rgy
of a
GPM
G c
artr
idge
Con
side
r the
kin
etic
ene
rgy
for a
7.6
2mm
M61
AP
proj
ectil
e
K.E
.= = =
Sust
aine
d ra
te o
f fire
is
Muz
zle
“pow
er”
= =
G. L
eng,
ME
Dep
t, N
US
Gal
ileiG
alile
o (1
564-
1642
)
•D
ialo
gues
Con
cern
ing
Two
New
Sci
ence
s–
“ A
proj
ectil
e w
hich
is c
arri
ed b
y a
unifo
rm h
oriz
onta
l m
otio
n co
mpo
unde
d w
ith a
nat
ural
ly a
ccel
erat
ed v
ertic
al
mot
ion
desc
ribe
s a p
ath
whi
ch is
a se
mi-p
arab
ola.
”
G. L
eng,
ME
Dep
t, N
US
Art
iller
y Pr
ojec
tile
Tra
ject
ory
G. L
eng,
ME
Dep
t, N
US
Fact
ors a
ffec
ting
a re
al tr
ajec
tory
or w
hat G
alile
o di
dn’t
cons
ider
•A
ir re
sist
ance
-ae
rody
nam
ic d
rag
•A
ir di
stur
banc
es –
cros
s win
d, g
ust
•V
aria
ble
atm
osph
eric
pro
perti
es w
ith a
ltitu
de
•D
rift c
ause
d by
pro
ject
ile sp
in
•Ea
rth’s
rota
tion
G. L
eng,
ME
Dep
t, N
US
Bal
listic
coe
ffic
ient
-a
mea
sure
of a
ir r
esis
tanc
e
C=
m/A
=
sect
iona
l den
sity
Cd
form
fact
or
C :
ba
llist
ic c
oeff
icie
nt
m :
m
ass o
f pro
ject
ileA
: cr
oss-
sect
iona
l are
a of
pro
ject
ileC
d:
drag
coe
ffic
ient
(ai
r res
ista
nce)
Not
e : t
he b
allis
tic “
coef
ficie
nt”
has u
nits
of k
g/m
2
G. L
eng,
ME
Dep
t, N
US
Bal
listic
coe
ffic
ient
of 1
55m
m H
E p
roje
ctile
For t
he M
107
155m
m H
E pr
ojec
tile
mas
s =
diam
eter
=
C
d(e
stim
ated
)=
The
balli
stic
coe
ffic
ient
= =
G. L
eng,
ME
Dep
t, N
US
Bal
listic
coe
ffic
ient
of a
bul
let
In S
.I. u
nits
, bal
listic
coe
ffic
ient
= =
G. L
eng,
ME
Dep
t, N
US
Eff
ect o
f air
res
ista
nce
Sim
ulat
ed 1
55m
m H
E tra
ject
ory
Traj
ecto
ry p
aram
eter
s for
max
rang
e
elev
atio
n :
25 d
egra
nge
: 17
.5 k
mtim
e of
flig
ht :
51 s
max
ord
inat
e :
≈3.
5 km
G. L
eng,
ME
Dep
t, N
US
Wor
k ag
ains
t air
res
ista
nce
-los
s of k
inet
ic e
nerg
y
time
s
| V |
m/s
G. L
eng,
ME
Dep
t, N
US
Com
pari
son
: 88m
m P
ak43
Ant
i Tan
k G
un
Muz
zle
velo
city
:
AP
proj
ectil
e:
Pene
tratio
n
:
G. L
eng,
ME
Dep
t, N
US
Sim
ulat
ed 8
8mm
Arm
our
Pier
cing
(AP)
traj
ecto
ry
Traj
ecto
ry p
aram
eter
s (C
D=
0.25
)
elev
atio
n :
0.65
deg
rang
e :
2 50
0mm
ax o
rdin
ate
: ≈
8 m
time
of fl
ight
: 2.
5 s
G. L
eng,
ME
Dep
t, N
US
Com
pari
son
: E
nerg
y lo
ss a
gain
st a
ir r
esis
tanc
e
| V |
m/s
time
s
KE
of A
P pr
ojec
tile
at im
pact
= =
G. L
eng,
ME
Dep
t, N
US
Spin
ning
of a
rtill
ery
proj
ectil
es•
Spin
ning
= f
light
stab
ility
•A
chie
ved
by a
rifle
d ba
rrel
and
co
rres
pond
ing
rota
ting
band
on
proj
ectil
e
•Ex
ampl
e –
155m
m h
owitz
er–
Rifl
ing
of g
un b
arre
l
Cor
resp
ondi
ng ro
tatin
g ba
nd
G. L
eng,
ME
Dep
t, N
US
Aer
odyn
amic
con
sequ
ence
s of s
pinn
ing
The
Mag
nus e
ffect
*
* G
. Mag
nus ,
“On
the
devi
atio
n of
pro
ject
iles;
and
on
a re
mar
kabl
e ph
enom
enon
of r
otat
ing
bodi
es."
, M
emoi
rs o
f the
Roy
al A
cade
my,
Ber
lin,
1852
.
G. L
eng,
ME
Dep
t, N
US
Spin
ning
and
shel
l dri
ft
V
g
G. L
eng,
ME
Dep
t, N
US
Poin
t to
Pond
er
Seas
oned
old
gun
ner :
“ Sh
ell d
rift i
s alw
ays t
o th
e le
ft “
G. L
eng,
ME
Dep
t, N
US
App
licat
ion
exam
ple
