# Question about armor angling and slope

### #1 Posted 06 February 2013 - 10:42 PM

Example:

My frontal armor is 100mm thick and sloped at 60°. I present my frontal plate at a 20° angle to the enemy gun.

What is the effective armor value?

Would really appreciate it if someone could explain how to calculate this, thx.

### #2 Posted 06 February 2013 - 10:47 PM

EDIT: Or do you mean the math behind it?

EDIT2:

effective armor slope: armor/cos(X degrees from vertical - normalisation)

100/cos(60-5) = 174 mm

effective armor angle: effective armor slope /cos(X degrees away from enemy - normalisation)

174/cos(20-5) = 180 mm

PS: I think 5 degrees is ap normalization.

PPS: The matter of sine or cosine may change if you have other definitions for the angleing and slope.

**Edited by az879, 06 February 2013 - 11:00 PM.**

### #4 Posted 06 February 2013 - 10:57 PM

Not everyone is a math professor.

**Edited by The_SlayeR, 06 February 2013 - 11:10 PM.**

### #5 Posted 06 February 2013 - 10:58 PM

Therefore hypot = adjacent / cos(theta)

Apply this twice.

100mm at 60degrees is (100/cos(60)) = 200mm effective.

200mm at 20degress is (200/cos(20)) ==

**213mm effective**.

[EDIT] If you then want to apply normalization, reverse this equation to get the compound angle, subtract your normalization value, and work out the armour again...

cos(theta) = 100/ 213

theta = 62degress

effective armour = (100/cos(62-5)) =

**183mm effective after 5 degrees of shell normalization**

**Edited by CitizenSoldier, 07 February 2013 - 10:52 AM.**

### #6 Posted 06 February 2013 - 11:00 PM

You got premium ammo to counter all that.

Since this is close to 0.0006% simulation game (only tank names are so-so true and linked to real world), that armor means nothing. The game is based on RNG and Player Balance system. So just an advice, forget those numbers, the only thing you want to know is when you see the red sillouette, you shoot there. If server has chosen that you should win, you will hit. If you need to be balanced, you will miss. Easy as that.

### #8 Posted 06 February 2013 - 11:12 PM

kejmo, on 06 February 2013 - 11:00 PM, said:

You got premium ammo to counter all that.

Since this is close to 0.0006% simulation game (only tank names are so-so true and linked to real world), that armor means nothing. The game is based on RNG and Player Balance system. So just an advice, forget those numbers, the only thing you want to know is when you see the red sillouette, you shoot there. If server has chosen that you should win, you will hit. If you need to be balanced, you will miss. Easy as that.

+1 to you. @OP: listen to what he says. Armor angling is good in practice, forget about the statistics and calculations..its an arcade game, not a simulator.

### #9 Posted 06 February 2013 - 11:24 PM

az879, on 06 February 2013 - 10:47 PM, said:

EDIT: Or do you mean the math behind it?

EDIT2:

effective armor slope: armor/cos(X degrees from vertical - normalisation)

100/cos(60-5) = 174 mm

effective armor angle: effective armor slope /cos(X degrees away from enemy - normalisation)

174/cos(20-5) = 180 mm

PS: I think 5 degrees is ap normalization.

PPS: The matter of sine or cosine may change if you have other definitions for the angleing and slope.

CitizenSoldier, on 06 February 2013 - 10:58 PM, said:

Therefore hypot = adjacent / cos(theta)

Apply this twice.

100mm at 60degrees is (100/cos(60)) = 200mm effective.

200mm at 20degress is (200/cos(20)) ==

**213mm effective**.

Thx for the math answers guys, appreciate it!

### #10 Posted 06 February 2013 - 11:31 PM

### #11 Posted 06 February 2013 - 11:36 PM

kejmo, on 06 February 2013 - 11:00 PM, said:

You got premium ammo to counter all that.

Since this is close to 0.0006% simulation game (only tank names are so-so true and linked to real world), that armor means nothing. The game is based on RNG and Player Balance system. So just an advice, forget those numbers, the only thing you want to know is when you see the red sillouette, you shoot there. If server has chosen that you should win, you will hit. If you need to be balanced, you will miss. Easy as that.

**Edited by tomogaso, 06 February 2013 - 11:37 PM.**

### #12 Posted 06 February 2013 - 11:36 PM

az879, on 06 February 2013 - 10:47 PM, said:

EDIT: Or do you mean the math behind it?

EDIT2:

effective armor slope: armor/cos(X degrees from vertical - normalisation)

100/cos(60-5) = 174 mm

effective armor angle: effective armor slope /cos(X degrees away from enemy - normalisation)

174/cos(20-5) = 180 mm

PS: I think 5 degrees is ap normalization.

PPS: The matter of sine or cosine may change if you have other definitions for the angleing and slope.

Actually that's 'wrong'. The normalization is not applied individually to each axis but to the end result, unless WG calculates it wrongly obviously which I highly doubt.

First you must calculate what the actual impact angle is. Take a plane, rotate it first 60 degrees on one axis and 20 degrees on another axis. The total rotation is actually surprisingly little. It becomes 61 degrees total.

The effective armor thickness is 183.5mm in this case while with calculating the normalization separately for each axis it becomes 180.5mm

The difference is small but we have to be precise

Quote

ang1r = 60/180*pi;

ang2r = 20/180*pi;

nval = 5/180*pi;

R1 = [ 1,0,0 ; 0,cos(ang1r), -sin(ang1r) ; 0,sin(ang1r),cos(ang1r) ];

R2 = [ cos(ang2r), 0, sin(ang2r);0, 1, 0;-sin(ang2r), 0, cos(ang2r)];

nw = ic*R1*R2;

ang = acos(dot(nw,ic));

ang/pi*180

I used this piece of matlab code to calculate the rotation. I hope I wrote that matrix correctly

### #13 Posted 06 February 2013 - 11:40 PM

az879, on 06 February 2013 - 11:31 PM, said:

QFT +1

### #14 Posted 06 February 2013 - 11:41 PM

### #15 Posted 06 February 2013 - 11:44 PM

sharpneli, on 06 February 2013 - 11:36 PM, said:

First you must calculate what the actual impact angle is. Take a plane, rotate it first 60 degrees on one axis and 20 degrees on another axis. The total rotation is actually surprisingly little. It becomes 61 degrees total.

The effective armor thickness is 183.5mm in this case while with calculating the normalization separately for each axis it becomes 180.5mm

The difference is small but we have to be precise

I used this piece of matlab code to calculate the rotation. I hope I wrote that matrix correctly

Ok, so how exactly do you calculate that the total rotation becomes 61°? Sry if it's in that piece of code, but I couldn't really read it.

### #17 Posted 06 February 2013 - 11:54 PM

DarthFreddy, on 06 February 2013 - 11:44 PM, said:

The gist is that the normalization must be calculated at the total rotation angle, not just at the end result. So we simply must first calculate what the total angle is and then normalize that.

It works that at first the impact is at 0 degrees angle. Then it rotates it by 60 degrees on one axis and then 20 degrees on another. I do this by multiplying the incoming vector with 2 rotation matrices. First of them rotates it 60 degrees on one axis and second rotates it 20 degrees on another axis. Check http://en.wikipedia....Rotation_matrix for more info. Then I simply take a dot product with the resulting vector and the original vector and use arccos to get the angle. All that /180*pi stuff is just in order to convert degrees to radians.

Truly practical example: Put your finger straight against your palm. Now turn your palm forwards a bit, that is the first rotation. Then turn it sideways, that is the second rotation. The dot product simply calculates the resulting angle of your finger against that surface.

There may be a simpler way to do it but I'm too stupid and lazy to figure one out. If one learns linear algebra it tends to become the default mode of thinking

### #18 Posted 07 February 2013 - 12:04 AM

CitizenSoldier, on 06 February 2013 - 10:58 PM, said:

Therefore hypot = adjacent / cos(theta)

Apply this twice.

100mm at 60degrees is (100/cos(60)) = 200mm effective.

200mm at 20degress is (200/cos(20)) ==

**213mm effective**.

Don't forget normalization. -5/8 degrees depending on shell type (AP/APCR)

### #19 Posted 07 February 2013 - 03:23 AM

### #20 Posted 07 February 2013 - 09:42 AM

0° 100% = x1

10° 101.54% = x1,015

20° 106.42% = x1,064

30° 115.47% = x1,115

40° 130.54% = x1,305

50° 155.57% = x1,556

60° 200% = x2

70° 292.38% = x1

> 70° Ricochet

More detailed table inside the spoiler:

So if you have 60 vertical angle and 20 lateral angle for for a 100m thick armor the actual thickness is 100mm x2 x1,064 = 213mm. From that figure we can figure out that the overall multiplier is x2,13 (213mm / 100mm) and then we just go look at that angle table again and we see that x2,13 is somewhere between 61 and 63 degrees.Let's just use 62 degrees.

To apply normalization to this number we can simply deduct the normalization angle from that 63 degrees to get the actual effective thickness. So if we assume that ap shell has 4 degrees of normalization then 62-4 = 58 degrees. Again, lets just look at our table. 58 degrees means approximately x1,9 multiplier for our 100m thickness. So the effective thickess is 190mm.