abhik wrote:Because every few weeks somebody comes up asking why sloped armor is not used in the Arjun and how that makes it inferior etc, i have made two easy to understand explanatory images to show that sloped armor is not all that is made out to be (esp. by discovery channel etc.). Here's a short sloped armor 101 (or rather basic geometry 101)
For the same weight the 'Line of Sight' thickness(and hence the level of protection) will be the same for a slab of both sloped and non sloped armor.
There are only a handful of modern tanks that use significantly sloped armor.
A sloped armour plate provides better protection than a vertical armour plate of the same thickness.
- This is due to two reasons.
1)The first is because the sloped armour is wider from a horizontal view than the vertical armour, and
2)thus the shells fired at it will have to travel a greater distance through the armour.
While the sloped armour seems superior in terms of relative thickness alone, this does not justify the use of sloped armour to same steel, as the same amount of steel is needed to achieve the same protection. This is because the sloped armour plate will have to be longer to cover the same height
The actual bonus comes from the shells deflecting. The more sloped an armour plate is, the more likely it is that the incoming shell will deflect.
Very simple physical model of the slope effect. Kinetic energy absorbed by armour is proportional to the square of the sine of angle (maximal for 90°). Friction and deformation of target are neglected
http://en.wikipedia.org/wiki/File:Slope ... -slide.png
How a groove caused by projectile impact increases the effective incident angle
http://en.wikipedia.org/wiki/File:Armor ... groove.png
Illustration of some possible effects that can occur when a projectile impacts sloped armour
http://en.wikipedia.org/wiki/File:Proje ... ffects.jpg
The second aspect of slope is the asymmetrical force acting on the penetrator. When a projectile strikes a sloped plate, the side of the penetrator closest to the plate will suffer more force, erosion, and damage than the opposing side. This puts an unbalanced force on the rod, turning it in towards the plate – and then into the opposite direction. The penetrator takes a longer overall route through the armor, resulting in less penetration of sloped armor. (See: Rheinmetall Handbook on Weaponry [figure 1128] (1982))
Exactly how likely the projectile is going to deflect depends on:
Firstly, all projectiles will ricochet. The real question is at what angle and velocity do they ricochet.
- A complex model has been developed to predict the angle at which a projectile is expected to ricochet, this is called the ‘critical ricochet angle’ (See: J. Phys. D. Appl. Phys. Vol 12-1979 pp. 1825—1829.)
The critical ricochet angle is measured from the vertical plane [i.e. 90° is horizontal].
- A rod of 10:1 L/d [Length to rod Diameter ratio] @ 1.7km/s should ricochet at ~78° when made of steel,
Tates Ricochet formula.
J Phys D Appl. Phys. Vol 12-1979pp 1825-1829. "A.Tate's" ricochet law and the formula is as follows .
p xV² (L² + 1) / p
------ x ------- x 1 + / ------ x 0.6666 = tan³ + [modifier] =the ‘critical ricochet angle’
Y L / t
Where ....
p = projectile density (g/cm³)
t = target density (g/ccm³
V= striking velocity (km/s)
L= L/d ratio (rod length to diameter)
Y= projectile yield strength
Modifiers to the ‘tan value’....
- 0.9 for each T/d above 1:1
+ 0.3 if the projectile has a sharp nose (> 60° cone)
-0.3 if the projectile has a blunt nose (< 30 ° cone)
-0.1 if the projectile is spinning.
Projectile Yield strengh is usually
Steel rod ~1.9 to ~1.7 ‘GPa’ or BHN = 600 - 500
WHA/DU rod ~1.6 to ~1.4‘GPa’ or BHN= 450 -400
HVAP ~ 1100m/s ….
8.4 x 1.1² 4.0² +1 / 8.4
--------- x ------- x 1 + / ------------- x 0.667 = tan³ + modifier + 0.3 – 0.1 – 0.9 [ - 1.8]
2.0 4.0 / 7.8 [ 4.8]
5.06 x 4.25 x 2.03 [ 2.32] x 0.67 + 0.2/ - 0.7/ - 1.6=
43.6 x 0.67 = 29.2 cube root = 3.15 + 0.2= 3.35 = Tan of 18° or 72° Vs T/d 1:1
43.6 x 0.67= 29.2 cube root = 3.15 –0.7 = 2.45 = Tan of 22° or 68° Vs T/d 2:1
49.9 x 0.67= 33.4 cube root = 3.30 – 1.6 = 1.7 = Tan of 30° or 60° Vs T/d 3:1 comp
Steel 44mm 10:1 L/d APFSDS ~ 1700m/s ….
7.8 x 1.7² 10.0² +1 / 7.8
--------- x ------- x 1 + / ------------- x 0.667 = tan³ + modifier 0 /- 1.2/- 3.3
2.0 10.0 / 7.8 [ 4.8]
11.27 x 10.1 x 2 x 0.67 = Tan³ = 5.52 = 10° or 80°= 85±7°
11.27 x 10.1 x 2 x 0.67 = Tan³ = 5.52 - 1.2 = 4.32 = 13°or 77° = 82°±7°
11.27 x 10.1 x 2.27 x 0.67= Tan³ = 5.77 - 3.3= 2.47 = 22°= 68° = 73°±7°
Steel 41mm 18:1 L/d APFSDS ~ 1700m/s ….
7.8 x 1.7² 18.0² +1 / 7.8
--------- x ------- x 1 + / ------------- x 0.667 = tan³ + modifier 0 /- 1.8/- 3.6
2.0 18.0 / 7.8 [ 4.8]
11.27 x 18.05 x 2 x 0.67 = Tan³ = 6.73 = 9° or 81°= 86±7°
11.27 x 18.05 x 2 x 0.67 = Tan³ - 1.8 = 4.9 = 12°or 78° = 83°±7°
11.27 x 18.05 x 2.27 x 0.67= Tan³ - 3.6=3.42 = 16°= 74° = 79°±7°
Steel 41mm 9:1 L/d APFSDS ~ 1500m/s ….
7.8 x 1.5² 9.0² +1 / 7.8
--------- x ------- x 1 + / ------------- x 0.667 = tan³ + modifier 0 /- 1.8/- 3.6
2.0 9.0 / 7.8 [ 4.8]
8.77 x 9.11 x 2 x 0.67 = Tan³ = 4.9 = 12° or 78°= 83±7°
8.77 x 9.11 x 2 x 0.67 = Tan³ = 4.9 - 1.8 = 3.1= 18°or 72° = 77°±7°
8.77 x 9.11 x 2.27 x 0.67= Tan³ =5.1-3.6= 1.51 = 33°= 57° = 62°±7°
DU 32mm 10:1 L/d APFSDS ~ 1600m/s ….
17x 1.6² 10.0² +1 / 17
--------- x ------- x 1 + / ------------- x 0.667 = tan³ + modifier - 0.4 /- 1.8 /- 4.9
1.3 10.0 / 7.8 [ 4.8]
33.5 x 10.1 x 2.48 x 0.67 = Tan³ 8.6 –0.4 = 8.2 = 7° or 83°= 88±7°
33.5 x 10.1 x 2.48 x 0.67 = Tan³ 8.6 – 1.8 = 6.8 = 9°or 81° = 86°±7°
33.5 x 10.1 x 2.88 x 0.67= Tan³ 9.05 –4.9 = 5.6 = 10°= 80° = 85°±7
DU 25mm 20:1 L/d APFSDS ~ 1400m/s ….
17x 1.4² 20.0² +1 / 17
--------- x ------- x 1 + / ------------- x 0.667 = tan³ + modifier - 0.9 /- 2.7 /- 7.0
1.3 20.0 / 7.8 [ 4.8]
25.6 x 20.05 x 2.48 x 0.67 = Tan³ 10.0 –0.9 = 9.1 = 6° or 84°= 89±7°
25.6 x 20.05 x 2.48 x 0.67 = Tan³ 10.0 – 2.7 = 7.3 = 8°or 82° = 87°±7°
25.6 x 20.05 x 2.88 x 0.67= Tan³ 10.44 –7.0 = 3.44 = 16°= 74° = 79°±7°
DU 25mm 20:1 L/d APFSDS ~ 1600m/s ….
17x 1.6² 20.0² +1 / 17
--------- x ------- x 1 + / ------------- x 0.667 = tan³ + modifier - 0.9 /- 2.7 /- 7.0
1.3 20.0 / 7.8 [ 4.8]
33.5 x 20.05 x 2.48 x 0.67 = Tan³ 10.9 –0.9 = 10.0 = 5° or 85°= 90±7°
33.5 x 20.05 x 2.48 x 0.67 = Tan³ 10.9– 2.7 = 8.2 = 7°or 83° = 88°±7°
33.5 x 20.05 x 2.88 x 0.67= Tan³ 11.44 –7.0 = 4.44 = 13°= 77° = 82°±7°
DU 25mm 30:1 L/d APFSDS ~ 1400m/s ….
17x 1.4² 30.0² +1 / 17
--------- x ------- x 1 + / ------------- x 0.667 = tan³ + modifier - 0.9 /- 2.7 /- 7.0
1.3 30.0 / 7.8 [ 4.8]
25.6 x 30.03 x 2.48 x 0.67 = Tan³ 11.4 –0.9 = 10.5 = 5-6° or 85°= 90±7°
25.6 x 30.03 x 2.48 x 0.67 = Tan³ 11.4 – 2.7 = 8.68 = 6-7°or 84° = 89°±7°
25.6 x 30.03 x 2.88 x 0.67= Tan³ 12.01 –7.0 = 4.95 = 11°= 79° = 84°±7°
DU 25mm 30:1 L/d APFSDS ~ 1600m/s ….
17x 1.6² 30.0² +1 / 17
--------- x ------- x 1 + / ------------- x 0.667 = tan³ + modifier - 0.9 /- 2.7 /- 7.0
1.3 30.0 / 7.8 [ 4.8]
33.5 x 30.03 x 2.48 x 0.67 = Tan³ 12.47 –0.9 = 11.57 = 5° or 85°= 90±7°
33.5 x 30.03 x 2.48 x 0.67 = Tan³ 12.47 – 2.7 = 9.77 = 6°or 84° = 89°±7°
33.5 x 30.03 x 2.88 x 0.67 = Tan³ 13.1 –7.0 = 6.1 = 9°= 81° = 86°±7°
[note 4 ] The effect of ricochet on AP shot
For a 820m/s 3.5:1 L/d Steel APCBC sharp capped shot-the figures should be .......
[PRE]
At muzzle Vs 1:1 T/d thats 64 -74° .
At 2000m Vs 1:1 T/d thats 62 -75° .
At muzzle Vs 2:1 T/d thats 51 -61° .
At 2000m Vs 2:1 T/d thats 40 -50° .
APFSDS Vs
Vs 1:1 T/d at 1000m = 82.6 ±5°
Vs 5:1 T/d at 1000m = 76.5 ±5°