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Pacific Historian
I received this in an e-mail today.
WORLD WAR 2 FIGHTER ARMAMENT EFFECTIVENESS
© Anthony G Williams Emmanuel Gustin (with
acknowledgements to Henning Ruch)
Revised 28 June 2004
The comparative effectiveness of fighter guns in the
Second World War is a subject of perennial fascination
(and a great deal of argument) among technical
military historians. This is an attempt to take a
fresh and objective look at the evidence in order to
draw up comparative tables of cartridge
destructiveness, gun power and gun efficiency. The
effectiveness of typical day fighter armament fits is
also considered.
CARTRIDGE DESTRUCTIVENESS
There are two types of energy that may be transmitted
to the target; kinetic and chemical. The kinetic
energy is a function of the projectile weight and the
velocity with which it hits the target. This velocity
in turn depends on three factors: The muzzle velocity,
the ballistic properties of the projectile, and the
distance to the target. There are therefore two fixed
elements in calculating the destructiveness of a
projectile, its weight and chemical (high explosive or
incendiary) content, and one variable element, its
velocity. The key issue is the relationship between
these three factors.
A high muzzle velocity will provide a short flight
time, which is advantageous in increasing the hit
probability and extending the effective range, and
will also improve the penetration of AP rounds.
However, it might not add much to destructiveness, as
unless an AP projectile hits armour plate (and not
much of the volume of an aircraft was protected by
this), a higher velocity just ensures that a neater
hole is punched through the aircraft; the extra
kinetic energy is wasted. Also, if the projectile is
primarily relying on HE blast or incendiary effect,
the velocity with which it strikes the target is
almost immaterial. Provided that it hits with
sufficient force to penetrate the skin and activate
the fuze, the damage inflicted will remain constant.
In contrast, AP projectiles lose effectiveness with
increasing distance.
It is sometimes argued that a projectile with a high
muzzle velocity and a good ballistic shape (which
reduces the rate at which the initial velocity is
lost) provides a longer effective range. To some
extent this is true, but the greatest limitation on
range in air fighting in the Second World War was the
difficulty in shooting accurately. The problem of
hitting a target moving in three dimensions from
another also moving in three dimensions (and probably
at a different speed and on a different heading)
requires a complex calculation of range, heading and
relative speed, while bearing in mind the flight time
and trajectory of the projectiles. Today, such a
problem can easily be solved by a ballistic computer
linked to a radar or laser rangefinder, but at the
time we are examining, the "radar" was the human
eyeball and the "ballistic computer" the human brain.
The range, heading and speed judgements made by the
great majority of pilots were notoriously poor, even
in training. And this was without considering the
effects of air turbulence, G-forces when manoeuvring,
and the stress of combat. These factors limited the
effective shooting range to around 400 m against
bombers (longer in a frontal attack) and against
fighters more like 250 m.
For all of these reasons muzzle energy (one half of
the projectile weight multiplied by the square of the
velocity) has not been used to calculate kinetic
damage as this would overstate the importance of
velocity. Instead, momentum (projectile weight
multiplied by muzzle velocity) was used as an estimate
of the kinetic damage inflicted by the projectile. It
might be argued that even this overstates the
importance of velocity in the case of HE shells, as
noted above, but the effect of velocity in improving
hit probability is one measure of effectiveness which
needs acknowledging, so it is given equal weighting
with projectile weight.
Chemical energy is generated by the high explosive or
incendiary material carried by most WW2 air-fighting
projectiles. First, there is the difference between HE
and incendiary material, which were often mixed (in
very varying proportions) in the same shell. HE
delivers instant destruction by blast effect (plus
possibly setting light to inflammable material within
its blast radius), incendiaries burn on their passage
through the target, setting light to anything
inflammable they meet on the way. The relationship
between the effectiveness of HE and incendiary
material is difficult to assess. Bearing in mind that
fire was the big plane-killer, there appears to be no
reason to rate HE as more important, so they have been
treated as equal.
The comparison between kinetic and chemical energy is
the most difficult and complicated subject to tackle.
This complexity is revealed by the example of a strike
by a delay-fuzed HEI cannon projectile. This will
first inflict kinetic damage on the target as it
penetrates the structure. Then it will inflict
chemical (blast) damage as the HE detonates. Thirdly,
the shell fragments sent flying by the explosion will
inflict further kinetic damage (a thin-walled shell
will distribute lots of small fragments, a
thick-walled shell fewer but larger chunks), and
finally the incendiary material distributed by the
explosion may cause further chemical (fire) damage.
There will therefore always be a degree of
arbitrariness in any attempt to compare kinetic and
chemical energy, as it all depends on exactly where
the projectile strikes, the detail design of the
projectile and its fuze, and on the type of aircraft
being attacked. To allow a simple comparison, we will
reduce all these factors to an increase in
effectiveness directly proportional to the chemical
content of the projectile. We assign to projectiles
that rely exclusively on kinetic energy an
effectiveness factor of 100%. For projectiles with a
chemical content, we increase this by the weight
fraction of explosive or incendiary material, times
ten. This chosen ratio is based on a study of many
practical examples of gun and ammunition testing, and
we will see below that it at least approximately
corresponds with the known results of ammunition
testing.
To illustrate how this works: a typical cannon shell
consists of 10% HE or incendiary material by weight.
Multiplying this by ten gives a chemical contribution
of 100%, adding the kinetic contribution of 100% gives
a total of 200%. In other words, an HE/I shell of a
given weight that contains 10% chemicals will generate
twice the destructiveness of a plain steel shot of the
same weight and velocity. If the shell is a
high-capacity one with 20% chemical content, it will
be three times as destructive. If it only has 5%
content, the sum will be 150%, so it will be 50% more
destructive, and so on.
WORLD WAR 2 FIGHTER ARMAMENT EFFECTIVENESS
© Anthony G Williams Emmanuel Gustin (with
acknowledgements to Henning Ruch)
Revised 28 June 2004
The comparative effectiveness of fighter guns in the
Second World War is a subject of perennial fascination
(and a great deal of argument) among technical
military historians. This is an attempt to take a
fresh and objective look at the evidence in order to
draw up comparative tables of cartridge
destructiveness, gun power and gun efficiency. The
effectiveness of typical day fighter armament fits is
also considered.
CARTRIDGE DESTRUCTIVENESS
There are two types of energy that may be transmitted
to the target; kinetic and chemical. The kinetic
energy is a function of the projectile weight and the
velocity with which it hits the target. This velocity
in turn depends on three factors: The muzzle velocity,
the ballistic properties of the projectile, and the
distance to the target. There are therefore two fixed
elements in calculating the destructiveness of a
projectile, its weight and chemical (high explosive or
incendiary) content, and one variable element, its
velocity. The key issue is the relationship between
these three factors.
A high muzzle velocity will provide a short flight
time, which is advantageous in increasing the hit
probability and extending the effective range, and
will also improve the penetration of AP rounds.
However, it might not add much to destructiveness, as
unless an AP projectile hits armour plate (and not
much of the volume of an aircraft was protected by
this), a higher velocity just ensures that a neater
hole is punched through the aircraft; the extra
kinetic energy is wasted. Also, if the projectile is
primarily relying on HE blast or incendiary effect,
the velocity with which it strikes the target is
almost immaterial. Provided that it hits with
sufficient force to penetrate the skin and activate
the fuze, the damage inflicted will remain constant.
In contrast, AP projectiles lose effectiveness with
increasing distance.
It is sometimes argued that a projectile with a high
muzzle velocity and a good ballistic shape (which
reduces the rate at which the initial velocity is
lost) provides a longer effective range. To some
extent this is true, but the greatest limitation on
range in air fighting in the Second World War was the
difficulty in shooting accurately. The problem of
hitting a target moving in three dimensions from
another also moving in three dimensions (and probably
at a different speed and on a different heading)
requires a complex calculation of range, heading and
relative speed, while bearing in mind the flight time
and trajectory of the projectiles. Today, such a
problem can easily be solved by a ballistic computer
linked to a radar or laser rangefinder, but at the
time we are examining, the "radar" was the human
eyeball and the "ballistic computer" the human brain.
The range, heading and speed judgements made by the
great majority of pilots were notoriously poor, even
in training. And this was without considering the
effects of air turbulence, G-forces when manoeuvring,
and the stress of combat. These factors limited the
effective shooting range to around 400 m against
bombers (longer in a frontal attack) and against
fighters more like 250 m.
For all of these reasons muzzle energy (one half of
the projectile weight multiplied by the square of the
velocity) has not been used to calculate kinetic
damage as this would overstate the importance of
velocity. Instead, momentum (projectile weight
multiplied by muzzle velocity) was used as an estimate
of the kinetic damage inflicted by the projectile. It
might be argued that even this overstates the
importance of velocity in the case of HE shells, as
noted above, but the effect of velocity in improving
hit probability is one measure of effectiveness which
needs acknowledging, so it is given equal weighting
with projectile weight.
Chemical energy is generated by the high explosive or
incendiary material carried by most WW2 air-fighting
projectiles. First, there is the difference between HE
and incendiary material, which were often mixed (in
very varying proportions) in the same shell. HE
delivers instant destruction by blast effect (plus
possibly setting light to inflammable material within
its blast radius), incendiaries burn on their passage
through the target, setting light to anything
inflammable they meet on the way. The relationship
between the effectiveness of HE and incendiary
material is difficult to assess. Bearing in mind that
fire was the big plane-killer, there appears to be no
reason to rate HE as more important, so they have been
treated as equal.
The comparison between kinetic and chemical energy is
the most difficult and complicated subject to tackle.
This complexity is revealed by the example of a strike
by a delay-fuzed HEI cannon projectile. This will
first inflict kinetic damage on the target as it
penetrates the structure. Then it will inflict
chemical (blast) damage as the HE detonates. Thirdly,
the shell fragments sent flying by the explosion will
inflict further kinetic damage (a thin-walled shell
will distribute lots of small fragments, a
thick-walled shell fewer but larger chunks), and
finally the incendiary material distributed by the
explosion may cause further chemical (fire) damage.
There will therefore always be a degree of
arbitrariness in any attempt to compare kinetic and
chemical energy, as it all depends on exactly where
the projectile strikes, the detail design of the
projectile and its fuze, and on the type of aircraft
being attacked. To allow a simple comparison, we will
reduce all these factors to an increase in
effectiveness directly proportional to the chemical
content of the projectile. We assign to projectiles
that rely exclusively on kinetic energy an
effectiveness factor of 100%. For projectiles with a
chemical content, we increase this by the weight
fraction of explosive or incendiary material, times
ten. This chosen ratio is based on a study of many
practical examples of gun and ammunition testing, and
we will see below that it at least approximately
corresponds with the known results of ammunition
testing.
To illustrate how this works: a typical cannon shell
consists of 10% HE or incendiary material by weight.
Multiplying this by ten gives a chemical contribution
of 100%, adding the kinetic contribution of 100% gives
a total of 200%. In other words, an HE/I shell of a
given weight that contains 10% chemicals will generate
twice the destructiveness of a plain steel shot of the
same weight and velocity. If the shell is a
high-capacity one with 20% chemical content, it will
be three times as destructive. If it only has 5%
content, the sum will be 150%, so it will be 50% more
destructive, and so on.
