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The principle of armor piercing

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Hi, developers, this is an article about the principle of armor piercing. I think it could help you for the "Tank Crews". Another article about the T-34/76 and T-34-85 protection and 85mm gun firepower is here:





As a main theme, the armor vs gun is an important thing for every tank, so expound the armor piercing principle is important for us. Of course, this is not necessary to read other chapters, you can skip this chapter and go straight to the next chapter. But as a basic knowledge about “armor vs gun”, I highly recommend you read this chapter.


When talking about the armor piercing, we often thing it is a simple process and easy to calculate by some formulas, but it is a whole wrong view, the process of armor piercing is very complex.





Chapter 1 The summary of armor-piercing principle

1. Development of armor-piercing projectile types and armor types

(1) Rolled Homogeneous Armor (RHA) and Armor-Piercing projectile (AP)

Rifling emerged in the 1840s, high-speed spin shells were sharping steadily, and armor-piercing shells became possible. Sharped armor piercing projectiles appeared in the 1960s, the process of piercing mainly by extrusion, can effectively deal with low hardness homogeneous steel armor, used to attack the rising armor warship.


(2) Face Hardened Armor (FHA) and Armor-Piercing Capped (APC)

In the 1880s, Countries began to use hardened armor on warships

A sharped armor-piercing projectile is prone to fragmentation and failure when it strikes a surface hardened armor, so its armor-piercing ability is greatly reduced. In the 1890s, Rear Admiral Makarov of Saudi Arabia put a low-hardness steel cap in front of the sharped bullet and designed a cap-pierced bullet. But after Makarov died in the Japanese-Russian War, the APC was paid attention to by the Russian authorities and was distributed in 1907. The Royal Navy had issued APCs in 1904. APC projectile can effectively deal with surface hardened armor, but the penetration force is greatly reduced when the angle is large, so it is not easy to break through warship armor during long-range curved firing.


(3) Slope armor, clearance armor and armor-piercing carbide ballistic cap (APCBC)

After World War I, blunt cap by the surface hardened appeared. The blunt cap behaves better when the angle is larger than the cuspidal cap. In order to improve the aerodynamic shape, a thin hood was added to the cap, this is APCBC. The hood is thin and has no effect on armor- piercing. The warship began to use a double-layer surface hardened armor to fight APCBC shell. The thinner outer armor causes the cap to work ahead of time, and the thicker inner armor breaks the projectile.


(4) High hardness armor and armor piercing blunt cap (APBC)

In the 1930s, for many countries, tank armor became generally high in hardness, and the Soviets developed blunt-headed armor-piercing projectiles. The armor-piercing process of APBC is dominated by shear and punch, it can effectively deal with high hardness armor, surface hardening armor effect is also good, but for low hardness armor effect is general. Because of the aerodynamic shape, APBC need to have wind caps. In addition, APBC have good effects on large angle sloped armor and multi-layer armor. However, APBC are sensitive to T/D value than AP, so when used in small caliber guns, it doesn't work well. That’s also a reason why Soviet aspire large caliber guns for their tanks, the APBC shells are basic ammo type for their tanks.


Fig 1-01 Force condition of bullet impact on armor plate


(5) Armor-piercing discarding sabot (APDS)

There was a way to “large caliber gun shot small caliber shell” in the 1930s, this will increase the initial velocity and range of the shell. Since the diameter of the projectile is relatively small, APDS projectiles are required to fit the caliber of the gun by sabot. The sabot does not participate in armor piercing, in order to reduce the dead weight, the quality of the sabot is relatively small, and has a negative impact on the storage speed, so after the loading, the sabot will be separated from the cartridge core. In 1940, the Frenchman developed a cemented carbide core (usually tungsten carbide) for shell removal. Because the diameter of the projectile is small and the core hardness is high, the perforation is very small, which can reduce the kinetic energy loss and effectively deal with the vertical armor with low hardness. But France was soon defeated. In World War II, only the British were equipped with a hard-metal core of the APDS ammunition. However, the problem of incomplete de-hulling led to poor firing accuracy of the shell-piercing projectile, which was not resolved until the end of the war.


(6) Armor-piercing-composite rigid/ Hyper-Velocity Armor Piercing (APCR/HVAP)

In order to reduce the kinetic energy loss during armor piercing, the Germans developed cemented carbide subcaliber armor piercing projectiles before 1940. The body of this armor-piercing projectile is made of high-hardness alloy (usually tungsten carbide) with a smaller diameter and a very small perforation, which can reduce kinetic energy loss and effectively deal with low-hardness vertical armor. In order to prevent fragmentation, the front end of the projectile needs to be covered with a cap. Since the diameter of the projectile is far smaller than the caliber of the gun, it is necessary to add the sabot. For conical cannon, the receptacle is retractable. In addition, there are non-cemented carbide subcaliber armor piercers (APNCR), but very rare.



2. The value of Thickness/Diameter

Thickness/ Diameter value, also known as "T/D" or "B/D", is the ratio of armor thickness to the diameter of armor-piercing projectiles. The diameter here is actually another expression of the mass of the projectile. In theory, the greater the density and the ratio of length to diameter of the rigid projectile, the better, because the kinetic energy can be concentrated on the smallest possible area and the loss of kinetic energy can be reduced. However, spin projectiles need to maintain a sufficiently large axial moment of inertia, so that the ratio of length to diameter cannot be too large (according to the formula for calculating the moment of inertia, when the mass is far from the axis of rotation, the moment of inertia is greater). So, this ratio is only for steel spin-stabilized projectiles.



3. Process of armor piercing

The current armor piercing process is similar and is a combination of multiple destruction processes. But different T/D values, projectile types and armor types will change the proportion of each process.


(1) Impact

During a high-speed impact armor (especially a surface hardened armor), the projectile may break down due to stress concentration. High-hardness projectile are easy to break down. If left uncontrolled, the crack extends throughout the projectile and invalidatas the projectile. The tip stress of normal AP is very concentrated, so the it should not be made too sharp, the shoulder is usually caused by circular arc, the smaller the radius of the arc busbar, the more dispersed the stress.


Adding a cap to the tip can disperse the stress to the shoulder and prevent the body from breaking. The cap is usually made of low-hardness material so that it does not cause too much resistance to the body.


APBC do not have a tip and do not cause stress concentration, so blunt-headed bullets do not need to be capped. In addition, in order to enhance the effect of adiabatic shear, APBC should not be added the cap.


(2) Adiabatic shear failure

As the projectile began to penetrate the armor, the temperature at the point of contact rose sharply. The armor at the point of contact was melted because the time was very short and the heat was too late to spread. As the projectile advances intermittently, the armor surface is cut off and the adiabatic shear process ends. The contact point area of the sharped projectile (normal AP) is very small and round; if the angle is larger, the contact area will be larger and triangular. The contact point of blunt head projectile (APBC) is circular and the kinetic energy loss is larger. For high hardness armor, adiabatic shear time is shorter and kinetic energy loss is smaller. As a result, the kinetic energy loss of APBC projectiles is relatively large when shearing low hardness armor.


(3) Layer crack damage

The projectile also produces shock waves when it hits the armor. Because the sound speed in the steel is fast and the attenuation of the unit distance is very small, the shock wave usually reaches the back of the armor more quickly and reflects than the projectile. The reflected wave peak interferes with the subsequent wave peak, resulting in local stress concentration. When the armor has poor toughness (usually too high hardness or improper heat treatment). This stress separates the back armor from the armor body, and in severe cases causes the back armor to collapse in the form of a diskette. The form of destruction is the same as that of the armor buster. Spallation damage can turn a single armor into a double armor, which makes it more vulnerable to flushing damage. If a fall occurs, dished debris has a lot of damage, and the armor thickness will be smaller.


(4) Extrusion failure

When the heat generated by friction is not enough to melt the projectile, the projectile begins to squeeze the armor, and the armor is squeezed sideways. The extrusion resistance increases with the increase of armor hardness. For ductile armor, the extruded armor produces a circle of bulge around the perforated perimeter. When the hardness of the projectile is higher, the deformation of the extrusion process is smaller, the diameter of the bullet hole is smaller, and the kinetic energy loss is smaller. The DeMarre formula is suitable for simulating the extrusion process of rigid projectile to ductile armor.


The extrusion process of the sharped projectile (AP and APCBC) accounts for a large proportion, which is also the main process of kinetic energy loss. When the radius of busbar is large, the extrusion resistance is smaller.


The proportion of extrusion process of blunt head projectile (APBC) is small, and the kinetic energy loss is very small. The proportion of extrusion process also decreases with the decrease of T/D value.


(5) Positive rotation and negative rotation

When the thickness of armor on one side of the armor path is small, the radial pressure of the projectile is unbalanced and a deflecting moment is produced, which makes the projectile deflect towards the small thickness side. This effect is evident when the impact angle is large. Because the outer pressure is small, the projectile deflects to the outside of the armor, that is, negative rotation. The larger the radius of the bus, the greater the torque. When the negative positive moment action time is longer, the projectile will jump. However, when the mass of projectile is large, the deflection to jump requires greater angular momentum, larger radius of deflection path, and thicker armor to provide deflection torque. In other words, the higher the T/D value, the more obvious the negative deflection. The deflecting moment of blunt-headed projectile is much smaller than that of sharped-headed projectile, so the negative rotation is not obvious. When the angle of impact is not large, it can even make the projectile deflect in the direction of vertical armor and positive rotation.


The AP is easy to jump, so there is a blunt cap hardened through the surface (APCBC). The deflection moment produced by the blunt cap can also make the projectile turn positive when the angle is small, but when the angle is large, the torque of the cap to the projectile makes the projectile turn negative. Therefore, in the case of large impact angle, the armor-piercing path of APBC projectiles is smaller than that of AP projectiles.


(6) Self-blunt and self-sharpening

The steel body of projectile may be torn during penetration. Especially the charge body, the strength is relatively low, the chamber damage may cause the aftereffect to be affected. The fracture groove can control the position of the bullet body fracture and protect the medicine chamber. The fracture groove of different shapes can control the shape of the projectile after fracture, which can be sharped or blunt.


The velocity of long-rod armor-piercing projectile is still very high in the process of penetration. The friction heat between projectile and armor causes heat, the projectile is melted, the length becomes shorter, and the shape of projectile changes. This process occurs only when the projectile has a high speed, usually a long-rod armor-piercing projectile with a speed greater than 1200m/s. Because the metal between the projectile and the armor is molten, the projectile can be regarded as liquid, the same principle as the HEAT.


For tungsten projectiles, because the melting point is relatively high, the length change is small, the front end of the bullet is self-blunted, becomes mushroom-shaped, the perforation is increased, and the kinetic energy loss is increased.


For uranium projectiles, the melting point is relatively low, the length varies greatly, and the front end of the projectile is self-sharpened and needle-shaped because of falling off. The self-sharpening effect can also be achieved by adjusting the molecular structure of some tungsten projectiles.


With the increase of armor hardness, the resistance of self-blunt and self-sharpening process increases. Multi-material composite armor can cause a complex process, which is not detailed here


(7) Plugging damage

When the residual thickness of the armor is small, the T/D value decreases and the armor is cut off to form a plug. The process of getting the plug out of the armor by the projectile is the plugging. The kinetic energy loss of projectile is very small in the process of plugging. Krupp formula is suitable for simulating the plugging process. The percentage of the plugging process of a sharped bullet (AP and APCBC) is relatively small. The smaller the T/D value, or the higher the armor hardness, the greater the percentage of the plugging. The plugging process of blunt head projectile accounts for a large proportion, which is the main process of armor piercing. The proportion of the flush process also increases with the decrease of T/D value. So the armor-piercing power of blunt-headed bullets is sensitive to the T/D value.


(8) Second rotation

When the piercing path is not perpendicular to the armor on the back of the armor, the radial pressure imbalance and deflection will occur when the projectile passes through the armor. The projectile deflects perpendicular to the armor so that the length of the path is smaller than the thickness of the armor, but the residual thickness of the armor is small at this time, so this rotation is not of much help to the armor-piercing.


For the shaped projectile, two deflections in the slope armor result in a S-shaped path longer than the horizontal thickness of the armor. Each deflection also loses kinetic energy, so the sharp-headed projectile is not conducive to dealing with large angle sloped armor.


For the blunt projectile, the first deflection is very small, the length of the piercing path is small, the kinetic energy of deflection loss is also small, and the second deflection makes the armor-piercing path smaller than the horizontal thickness, so it is advantageous to deal with the large angle sloped armor.


All kinds of projectile which used kinetic energy to piercing armor in WWII, will lost its kinetic energy in above 8 steps. That is mean, for slope armor, no matter what kind of kinetic energy projectiles in WWII, the resistance will large than its horizontal thickness. That’s why so many tanks use slope armor after T-34.





Chapter 2 The characterization of armor-piercing phenomenon and bulletproof ability

In WWII, the most widely used bullets are kinetic energy bullets, like AP, APC, APBC, APCBC and APCR, all of them are using the kinetic energy to penetrate the armor plate, so in this chapter, I will focus on the principle of kinetic energy, some other types bullets like HEAT will be also included.


The kinetic energy bullets penetrate the armor plate by directly impact, the process of impact is very complex. The kinetic energy of a projectile (W) before impacting armor is:


In this formula, “m” is projectile mass, “Vc” is velocity of projectile impact armor.


The kinetic energy of the projectile is consumed in many aspects during the armor piercing process, including damage to the armor, deformation of the projectile itself, elastic vibration of the armor plate, collision and friction heating, etc. Among them, damage to armor is the main work.


From a mechanical point of view, there are several possible stresses for armor damage:

(1) Ductile extrusion: σx=F/π*d^2

(2) Annular shear: τ=F/π*d*b

(3) Tensile stress rupture:

Radial direction: σn

Circumference: σm

In above formulas, “F” is the force of a projectile on armor, “d” is projectile diameter(caliber), “b” is armor thickness.


When the projectile collides with the armor, these kinds of stresses occur at the same time. Any stress reaching the limit will cause damage to the armor. Which kind of stress damage will vary depending on the material properties and size of the projectile and armor. The form of movement after the armor-piercing projectile impact the target, there will be three possibilities, namely penetration, embedding and ricochet. There are also three possible forms of armor-piercing projectile after impact with the target: integrity, deformation, and rupture. The actual forms of armor damage are as follows:



Fig 2-01 The forms of armor damage

(a) Ductile reaming (Ductile damage)

Mainly due to the effect of extrusion stress σx, the metal is extruded plastic flow by projectile, some of them are stacked at the entrance, others are extruded from the outlet, and the pore diameter of the metal is about equal to the diameter of the projectile. This usually happens when the armor is thick and tough, the projectile is sharp and hard, and the armor thickness b is slightly greater than caliber d.


(b) Plugging perforation (Punch damage)

Mainly due to the destruction caused by the failure of shear stress τ, the armor is punched out of a large cylindrical plug by the projectile, and its outlet is slightly larger than the projectile diameter d. This usually happens when the medium-thickness armor has considerable hardness, the warhead is blunt, and the armor plate thickness is slightly less than the projectile diameter.


(c) Petal shaped hole (Petal shaped damage)

Mainly due to the effect of the circumferential tensile stress σm, radial cracks appear, and the armor plate rolls to the rear of the hole. The hole diameter is approximately equal to the diameter of the projectile d. This generally occurs when the armor is thin and tough, and when the projectile speed is low.


(d) Block caving (Broken block damage)

When the armor is not too thick and the toughness is poor, the radial stress σn is the main cause of circular cracks, and the armor is pierced into a large hole several times the diameter of the projectile.


(e) Fragment in armor back (Layer crack/ Slabbing damage)

When the strength of the thicker armor is sufficient and the toughness is insufficient, the shock stress wave caused by the projectile hitting can cause the back of the armor to collapse and break up and fly out to kill. At this time, the hole in front of the board is not large, and it may not penetrate.


The actual phenomenon of armor piercing may also be a different combination of the above. Generally, Under the condition of the thickness and hardness of the armor, armor-piercing bullets are mainly composed of the first two conditions. That is, the first ductile reaming, when the armor projectile remaining thickness is a little smaller than the diameter of the projectile, then punching into the hole. For thin armor, perforation is generally petal or punching, depending on the relative ratio of projectile diameter to armor thickness. The reason why the block caving is unusual is that the over-hard and brittle thin armor is difficult to be machined and prone to crack, so it is not suitable for cutting and welding the hull body. The HESH destroys the armor mainly with the slabbing damage, which is a special form of damage that does not penetrate the armor. In the general armor-piercing projectile armor, except for the metal defects in the armor's back, it rarely appears.


In order to calculate and test the anti-penetration ability of projectile, it is necessary to have a kind of metrology standard to show the resistance to projectile. The practical representation is expressed separately for each particular plate, that is, the resistance of a armor to be "Vc to a certain projectile" for a certain gun. The Vc was confirmed in a large number of firing experiments in the grounding tests. In the test, use a certain gun and projectile to fire at a certain target plate, and gradually increase the quantity of the projectile to increase the velocity of the projectile until it has just penetrated the plate (or the drop point is near the back of the plate, for example, within 5m). The Vc of the projectile is used to indicate the resistance of the armor plate. Of course, the thicker the plate and the better the material, the higher the Vc is required to penetrate. To indicate the ability of a certain armor to resist projectiles of different calibres. This method of representation can ensure that it conforms to the reality and is accurate and reliable, so it has been used all the time. As long as a few accurate values are obtained in the shooting tests, the different plate thickness, projectile diameter and velocity can be calculated according to the law. The method of calculation is shown in the following section.


For thinner plates, such as the deck below 30mm, a gun is generally used to test fire (if the caliber is too large, it must penetrate the armor and no critical velocity can be tested). But the projectile cannot change the propellant, that is, the initial velocity of the projectile from the tube opening is fixed, and it cannot be changed. Therefore, it is necessary to use the air resistance in the projectile flight to cause a large velocity drop, that is, to change the distance S to get different hit speeds. As a result, the resistance at this time, becomes resistance to "a bullet (penetration) minimum distance" to denote. In the experiment, it is sometimes inconvenient to change the distance, or fixed distance to change the hit angle of the target. The larger the hit angle α is, the more difficult it is to penetrate the target plate. Therefore, the bullet resistance can be expressed by the α angle of a certain projectile at a certain distance (penetration).


In either of these ways, there is also a question that what is the standard of penetration. There are usually two standards:

(1) Back strength limit

When the armor is impacted by projectile, in order to damage the continuity of the metal on the back of armor, that is, the maximum velocity when there is no crack, no protuberance, etc., is expressed in terms of m/s or the corresponding distance (m) or angle.

(2) Penetration strength limit

The armor won’t be penetrated when impacted by a projectile, that is, the maximum speed at which the shell consumes up energy and the armor does not appear to have holes. Denoted by m/s or corresponding distance m or angle.

The first is more about the toughness/ tenacity of the armor, and the second is more about the strength of the armor. The velocity value of the second standard is generally greater than the veloocity value of the first, and it is also the standard for starting to have a killing aftereffect. The penetration strength limit is mainly used at now.





Chapter 3 The basic formula for calculating the resistance

1. The basic formula for vertical armor resistance

(1) Krupp formula

In Krupp formula, the armor is considered according to the larger projectile, the thinner armor, that is, the lower b/d value, and the armor is destroyed by the projectile in the form of a slug. According to this assumption, the work dW of the force R per stroke dx distance in the thrust process is a variable. In the formula, the resistance R is proportional to the remaining thickness of the deck during the flush process, that is:


From 0 to b integral, get the total work that completely washed the plug off:

W=π*d*τ∫b→0 xdx=τ*π*d*(b^2/2)

But the dynamic source of work is the kinetic energy of the projectile.


Get the so-called Krupp formula:

Vc=sqrt(τ*π)*d^0.5*b*m^(-0.5)=K*d^0.5*b*m^(-0.5)  (Formula 3-1)

K=sqrt(τ*π) known as the armor anti-ballistic coefficient, depending on armor material


Krupp formula is a more primitive formula for armor-piercing. It is only suitable for low-speed projectiles to judge armor-piercing when a value is small, it is not used now, but it is the basis for understanding armor-piercing calculation.


(2) DeMarre formula

For the case where the thickness of the armor that usually needs to be calculated is larger than the diameter of the projectile, the armor is not punched at the beginning, but is mainly ductile(extrusion). During the piercing process, the speed of the bullet decreases, the shape of the projectile gradually becomes dull, and the remaining armor is slightly smaller than the projectile diameter. Only then, the plug was rushed out. The entire armor-piercing process is close to the compliance of the extrusion and the punching.


If the extrusion damage is considered completely, the total work of the damage armor should be:


Get the:



Comparing Krupp's formula, except K is different, (d^0.5)*b change to (d*b^0.5). Therefore, the DeMarre formula can be understood as considering the combination of punch and extrusion. That is, the damage resistance is proportional to the geometric average, which the circumference (shear stress) of the ram and the value of the circular area (compressive stress). Based on experience, modify to:


DeMarre formula:

Vc=K*b^0.7*d^0.75*m^(-0.5)      (Formula 3-2)

or: b=Vc^1.43*m^0.715/(K^1.43*d^1.07)      (Formula 3-3)

In the formula, b and d are commonly used for “dm (=100 mm)”, Vc is calculated by “m/s”, and m is calculated by “Kg”.


At this time, the armor anti-ballistic coefficient K becomes a comprehensive coefficient representing the physical properties of the armor material, which should be determined by the firing test, it cannot be calculated according to a certain stress.


The recommended K values from datas are as follows:

Low carbon steel plate: 1530

Nickel steel plate: 1900

Generally homogeneous armor: 2000-2400 (the lower value is suitable for low carbon or medium hardness armor, while the higher value is suitable for high hardness thin armor)

Surface treated (face hard) armor 2400-2600

DeMarre formula has been widely used up to now, and it is the main basic formula for calculating the anti-ballistic ability.


There are also many other formulas for calculating the anti-ballistic ability, but most of them are based on Krupp formula and DeMarre formula, so I won’t list them at here.



2. The basic formula for slope armor resistance

Due to the high initial velocity and low trajectory extension of anti-tank projectiles, it can be considered as a horizontal target. When the armor is slope to a β angle with the horizontal plane, the α angle between the projectile centerline and the normal of the armor plate is also called "normal angle" or "impact angle", which is the common angle used in the calculation of the ballistic ability. α and β angles are complementary angles to each other.


When the armor is sloped, the range through which the projectile passes through the armor increases as the thickness of the armor increases to b/cosα, will increase the resistance. The formula for slope armor is:

Vc=K*b^0.7*d^0.75/(m^0.5*cosα^n)      (Formula 3-4)


The experimental results show that n>0.7, it is related to the relative thickness of Cb=b/d, armor type and the shape of projectile.


Why is n > 0.7 and changed? Mainly because of the impact of the "ricochet" factor, when the projectile contacts and begins to destroy the slope armor, the armor has a reaction to the projectile, slow down the projectile, and the projectile has the inertia force forward. Force of reaction and inertia force of projectile make up force couple. When α is not large, especially for blunt-headed armor-piercing projectiles (APBC), this force couple will make the projectile rotate in the direction of decreasing α angle, which is called the positive effect, which is beneficial to armor-piercing. When the α angle is large, the direction of the couple will make the projectile rotate in the direction of the α angle, and the penetration distance will be increased. Even when the force couple is large enough to make the projectile reflect and jump off the surface of the armor, the so-called "ricochet" is formed.


When the hardness of the armor is low, the projectile is prone to hit into a pit on the armor, that is, the direction of the reaction force is less likely to form a ricochet. Or when the armor is thinner, the less strong the reaction to the projectile, the less likely it is to form a ricochet. That is why the larger the Cb, or the harder the armor is, the higher the n value is.


When designing projectiles, in order to avoid forming a blunt-topped head shape, it can also avoid sharp-headed projectiles so easily broken that they can't be penetrated. The diameter of the blunt head is even up to 0.8d, often with a sharped head of thin windbreak cap to reduce the flight resistance. The windbreak cap is destroyed at the first touch, and it does not work on armor-piercing. Some projectiles are capped with cemented carbide on the head (APC or APCBC). The purpose is also to improve the performance of armor piercing.


As the against armor piercing side, the armor material and its manufacturing process have also been improving. Under the conditions of price and processing permit, it is necessary to have a large n-value to cause the projectile to ricochet. In addition, while increasing the thickness of armor to increase the Cb, a smaller and smaller β angle has been used, that is, increasing the α angle when hit to cause the projectile to ricochet. No matter how the angle β of the armor changes, the horizontal thickness of the armor is the same, and the cross-section area and mass are the same. But the larger the α, the more likely to cause a ricochet, which is why sloping armor is better than vertical armor against armor-piercing projectiles. The speed of the modern long-rod overspeed armor-piercing projectile (APFSDS) has doubled. When hitting armor at high speed, it is often the ever-forming fragments to ricochet, while the rest of the rod-shaped projectile will continue to penetrate forward, and the positive effect is stronger than that of the ordinary armor-piercing projectile. When the velocity of projectile is not too high, the calculation result of DeMarre formula is not different from the actual situation. Its accuracy often depends on the selection of K value. The source of K value is based on experiments, and many complicated practical factors have been included, which can guarantee the accuracy of calculation. However, such tests are destructive, and K values may not necessarily be obtained for each batch or armor calculated. Therefore, some improvement attempts to reflect the general mechanical properties of armor and projectile materials in the formula. One is K.A. Belkin formula:


σs : Armor yield limit, kg/mm^2.


φ: coefficient reflecting relative mass of projectile and relative thickness of armor, the value is 6.16*Cm/Cb=6.16*m/(b*d^2).


K1: considering the structural characteristics of projectile and the force coefficient of armor, when the value of b/d is not too different, the K1 value of ordinary armor-piercing projectile shooting homogeneous armor can be used the recommended value of the following table:

AP (head bus radius=1.5-2.0d): 0.95~1.05

APBC (passivation diameter=0.6 × 0.7d, head bus radius=1.5/2.0d): 1.20~1.30

APCBC: 0.9~0.95


K1 values can also be calculated using the following formula:

AP: K1=0.9427*Cb^0.5(2.6*i/(1+φ)+0.333)

APBC: K1=0.9427*Cb^0.5(2.2*i/(1+φ)+0.333)

The “i” is a projectile shape coefficient:

For AP: i=8/n1*sqrt(2*n1-1)

For APBC: i=8-5n1/(15*n1)*sqrt((1-n1)*(2*n1-n2-1)+n2^2)

For APCBC: i=(0.9~0.95)*8/(n1*sqrt(2*n1-1))

“n1”: curvature radius of projectile head/diameter of projectile, r/d

“n2”: passivation diameter of projectile head/diameter of projectile, d*/d


Belkin's formula can be applied to one of the deformations of DeMarre formula. Its application is not as extensive as that of DeMarre formula or the above-mentioned formulas for calculating slope armor.



3. The standard of penetration determination

For a gun, its penetration is needed to test by massive shootings, but because the many influential factor, the tests results are floating, so a standard to determine the penetration are necessary.


Most Countries are used this standard:

For numbers of a type projectile, at a certain distance, shot a certain thickness of a certain type armor plate, it will have different percent can penetration:

IP: Initial the armor penetration thickness, for example: 20%

CP: Confirm the armor penetration thickness, for example: 80%


Different Countries standards are different, and for different thickness, the armor type maybe different, and IP and CP also different for Countries. Usually, the test armors are not the standard requested type, so it need to convert the actual datas as the standards, it means the penetration in battle of a certain gun maybe higher than the data sheets, because its test standards are strict.


Some Countries standards:


The definition of the penetration: the whole projectile pass through the armor plate

CP: 80%

Armor type: RHA

Hardness (BHN): 250-380.



The definition of the penetration: a meaningful designated part of the projectile must pass through the plate

CP: 50%

Armor type: RHA

Hardness (BHN):

6-13mm: 330-370

38, 51, 63mm: 240

76-127mm: 220-240

Above 127mm: 220



The definition of the penetration: the whole projectile pass through the armor plate

CP: 50%

Armor type: RHA

Hardness (BHN):

5-15mm: 435-465

16-30mm: 338-382

31-50mm: 323-368

51-80mm: 309-338

81-120mm: 279-309

121-150mm: 235-265

151-275mm: 206-235


We can see the USSR used the strictest standards for penetration determination, that’s a reason why USSR guns’ penetration look like “lower” than other Countries.



Chapter 4 American misunderstanding of USSR APBC

In American reports (like AD011426) from their tests about Soviet tanks in 1950s had many misunderstandings. One of them is about USSR APBC.

1. The purpose of the USSR using APBC

The US believes that the Soviet APBC is mainly used to deal with the large angle sloped armor. This is obviously a mistake, when the Soviets popularized APBC projectiles in the 1930s, large sloped armor had not yet become popular.


Of course, Americans also found that blunt-headed bullets have a better effect on high-hardness armor. However, they believe that the blunt head "ensures the integrity of the warhead is not damaged," and, like the principle of the cap. They had not found the most important principle of blunt-headed projectiles: the instantaneous high-temperature shear and extrusion.



2. The purpose of circular groove on APBC

Americans believe that the role of "circular grooves" on APBC is to "create more debris." In fact, the role of the circular grooves is to control the position of the warhead fracture and protect the charge of HE. Obviously, the circular grooves are not helpful for armor piercing.


In AD011426, it’s mentioned that the targets can be solved by most of the AP projectiles, will also can be solved well by APBC bullets, this may because one of the properties of a blunt-headed bullet. When the blunt head projectile hits the surface of the armor, it will change the metallic phase of the armor to martensite, the hardness will be higher, the toughness will become worse, and the armor will be more easily to extrusion. Of course, if the armor is inherently low in hardness, it will not be hard to go there after being converted to martensite.



3. The puzzle about the low hardness of Soviet armor-piercing projectiles

Americans say they don't understand the low hardness of Soviet-made armor-piercing projectiles. First of all, why should the US-made armor-piercing projectiles add more "carbon"? Because the American armor has very low hardness and good toughness, it is not easy to produce impingement damage, but the penetration resistance is small, so it can not effectively resist the sharped projectile. On the other hand, when the sharped projectile hits the armor surface, it will have some deformation, make the caliber larger, and increase the penetration resistance. To control deformation, Americans add more "carbon" to armor-piercing bullets, increasing hardness. At the same time, "carbon" also makes the warhead toughness worse, when it impact armor at the high-speed, it is easy to break, so the US normal AP projectiles usually do not charge. When faced with high-hardness or slope armor, the performance of this high-carbon, cap-less armor-piercing projectile is very poor. In March 1942, British forces carried out shooting tests on captured tanks in North Africa. It was found that the M72 armor piercing projectile launched by M2 could only penetrate the surface hardened armor of the 50mm at 500m distance. Then, it is obvious that the low hardness of the Soviet armor piercing projectile is to prevent the body from breaking, especially to resist the tangential shear stress during the impact on the slope armor. It is also mentioned that blunt-headed bullets are "almost broken" during armor piercing, which should be the normal work of the broken ring (circular groove).



4. The wrong views about the performance of AP and APBC against slope armor

In AD011426, it mentioned that, when dealing with large angle sloping armor, regardless of the alloy composition and physical properties, the whole piece of sharped projectile will lead to the sharp head rupture at the moment of impact, and this (sharp head bumped into blunt head) state, it will be very effective against the slope surface. Considering that the sharp head will be ruptured in impact, the blunt-head bullets used by the Russians may not be necessary. Of course, when using the APHE bullets, the blunt-head bullet is very effective in ensuring the penetration of the explosion and the debris killing through the armor.


Americans stumbled to find that their high-carbon AP had a special effect on sloping armor. This is because "the moment of impact will cause a sharp head to break" and become a blunt head. As a result, they thought it was "less necessary" for the Soviets to use blunt-headed bullets with relatively poor vertical penetration in order to deal with sloping armor. Aside from the Soviet motive to use blunt-headed bullets, the problem of deal with sloping armor was not in all cases capable of breaking the sharped-headed bullets in the right position, speed, incidence, armor hardness all have an impact, and there's no special fracture slot, so this fracture position is uncontrollable. The way of sharp head impact to blunt head, its scope of application is quite limited.


It can be seen that until the 1950s, Americans still had a lot of misunderstandings about Soviet blunt-headed armor-piercing bullets of the 1930s.


With regard to the generality of blunt-headed projectiles, AD011426 only gives good results for large-angle sloping armor and high-hardness armor, especially for large-angle sloping armor. But, in principle, the versatility of blunt-headed bullets goes far beyond that:


Normal AP with no cap-- advantages: low hardness armor; disadvantage: high hardness armor, surface hardened armor, large angle sloping armor.


APC or APCBC-- advantages: low hardness armor, surface hardened armor; disadvantage: high hardness armor, double-layer high hardness armor (or double-layer surface hardened armor), large angle sloping armor.


APBC-- Advantages: high hardness armor, surface hardened armor, double-layer armor, large angle sloping armor; disadvantage: low hardness armor.


So obviously, APBC bullets are the most versatile. German using low-hardness armor in the later war was also targeted. In response, the Soviets distributing K-suffixed no cap AP from 1944. APBC bullets with AP bullets, there's no need to use APC or APCBC.


As for the post-war, the armors all over the world large using of nickel, they had good toughness, not easy to extrusion. And blunt-headed bullets are also sensitive to a value of T/D, so they are naturally be replaced by APCBC. However, due to the good effect for dealing with large-angle sloping armor, the US and the Soviet Union still used a long period of APBC bullets after the war.



Chapter 5 The transitory APBC in history

In the 1930s, anti-tank guns all over the world were small caliber high initial speed, AP shells were without cap. In the process of armor piercing, extrusion is the main. When the hardness of the armor is low, the compressive ability of armor is poor, and the resistance to the bullet is low, so the armor is easy to be pressed around by the bullet, thus forming a bulging perforation inside and outside the armor. When the caliber of the bullet is relatively small, it will even break because the stress is too concentrated. Although large caliber shells can produce punch effect instead of extrusion, but large caliber gun is heavy, difficult to produce, difficult to maneuvering, and difficult to be competent for anti-tank work.


So, the Soviet have developed a series of high-hardness armor represented by 8S. After heat treatment, the hardness of 8S had high hardness at 375~477HB, and also had well toughness, which can effectively resist the AP bullets at that time.


The high-hardness armor gave Soviet tanks well resistance performance in battle, but Soviet also worried that: if enemy also used high-hardness armor, how to deal it? The Soviets quickly found a solution by cutting off the tip of the shell and forming a 0.6~0.7 rate of the caliber at the front of the bullet. The blunt head AP for tank gun was born.


The appearance of T-34 has set off a craze of slope armor. When the projectile hit the slope armor, the projectiles were subjected to upward by elastic force, thus deflecting upward. When the deflection radius of the projectile is relatively small, the projectile slips out of a small crater and flies on the surface of the armor, which is called ricochet. When the deflection radius of the projectile is large, the back of the lower armor may lose its elasticity due to fracture, and the projectile will deflect down and break through the armor because of the lateral elastic force, which is called rotation effect. That is, when the projectile breaks through the slope armor, the path is S-shaped, and the path length is larger than the horizontal thickness of the armor. Moreover, the projectile also consumes a certain amount of kinetic energy in the process of two deflections.


Soviet found when the APBC projectiles squeeze the slope armor, the direction of the elastic force is closer to the center of gravity of the projectiles, resulting in the upward deflection angle of the projectiles becomes smaller, the energy loss is relatively small, and the passage path is also relatively short. If the slope angle is small, the APBC can even rotate straight on the surface of the armor. So the APBC become the standard ammo for most Soviet guns, like 45mm, 57mm, 76.2mm, 85mm guns.


From 1940s, most German tanks armor hardness were 280~360HB, at the beginning of 1941, the front armor of Panzer III H start using the FHA (Face hardened armor), which had 600HB surface hardness. For the face hardened armor, the thin surface hardening layer can’t break the APBC, but even more easily be cut off. And the thickness of the non-hardened layer is much lower than the caliber of the bullet, which aggravates the plugging. The same thing also happened in Panzer IV.


But in Tiger I, it was different. The side armor of Tiger I was 255~265HB. When the 76mm APBC (BR-350A) begins to shear cut the low hardness armor, the deformation of the armor is larger and the shear force becomes smaller, so it is difficult for the bullet to cut out the complete fragments. When the armor deformation reaches a certain extent, the armor piercing process becomes mainly extrusion. Another important reason, the ahead working of the fracture ring also affects the integrity of the bullet, which makes it difficult for the bullet to move forward. To solve that, Soviet designed BR-350B APBC, the weight up to 6.5kg, fracture ring was change very small and move to the nose, it was hard to fragment. The BR-350B quickly instead of the BR-350A, which could help T-34/76 penetrate Tiger I from side.


After WWII, former allies stood on both sides of the Iron Curtain. Because the immature heat treatment process in high hardness armor, Americans still use a low hardness armor, which was only about 210HB. The main target of APBC was gone, although the APBC still had a good performance in against low hardness armor, but the APCBC will perform better. Soviet came back on the way of APCBC, the APBC became a transitory ammo type in history.

Edited by zyss
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Very interesting, thanks.

I wonder if there is a Calculator to put the Caliber, ammo type, armour and distance and see if there is or not penetration ... :gamer:

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