Reposting this from Axis-history forum where I originally posted it
I challenged myself to run some numbers and used a very primitive 'tank' to demonstrate my findings.
Firstly I started with my 'unsloped tank' a simple 3x3x6 meter box. With 100mm frontal armor, 80mm side/rear armor, and 20mm belly/roof armor.
Basically a super simplified and boxier tiger tank.
3 meters wide, 6 long, 3 tall
Volume 54m^3
Surface area+volume of armor
Front surface area=9m^2 Volume (0.1m thick) = 0.9m^3
Rear surface area 9m^2 Volume (0.08m thick) = 0.72m^3
Side surface area (each) = 18m^2 Volume (0.08m thick) = 1.44m^3
Roof/belly area (each) =18m^2 Volume (0.02m thick)= 0.36m^3
Total armor volume 5.22m^3
Weight assuming density of iron/steel is 7800kg per cubic meter 40716kg
I gave this tank a simple 60 degree UFP and LFP
Volume of UFP and LFP (11.691)
Rest of tank volume = (30.618)
Total volume of tank now = 42.309m/3
Area of tank
UFP+LFP=18m/2 Volume (0.05m thick) = 0.9m^3
Rear surface area 9m^2 Volume (0.08m thick) = 0.72m^3
Roof/Belly (each) = 10.206m^2 Volume (0.02m thick) = 0.20412m^3
Sides (each) =3.89712+10.206= 14.10312m^2 Volume (0.08m thick) = 1.1282496m^3
Total armor volume 4.2847392m^3
Weight assuming density of iron/steel is 7800kg per cubic meter 33421kg
Non-sloped tank is 1.27632418634 more volumous than sloped tank
Non-sloped tank is 1.21827593429 heavier than sloped tank
So the unsloped tank actually more efficient for it's volume, without further alterations. But I thought "Wait a minute what happens if I expand this tank to the same volume?"
To do this I did some maths and the thing had to be approximately 8% larger in all dimensions.
Sloped tank enlarged to 54m^3
Overall length 6.50836024248
Overall width/height 3.25418012124
Volume of UFP and LFP (14.9219127787)
Rest of tank volume = (39.0797645404)
Total volume of tank now = 54.0016773191m/3
Area of tank
UFP+LFP=21.178204229m^2 Volume (0.05m thick) = 1.05891021145m^3
Rear surface area 10.5896882615m^2 Volume (0.08m thick) = 0.84717506091m^3
Roof/Belly (each) = 12.0090969413m^2 Volume (0.02m thick) = 0.24018193882m^3
Sides (each) =4.58546+12.0090969413= 16.5945569413m^2 Volume (0.08m thick) = 1.3275645553m^3
Total armor volume 5.0415782606m^3
Weight assuming density of iron/steel is 7800kg per cubic meter 39324kg
So now the tank has identical LOS frontal armor (depending on the projectile MORE durable), the same volume, and is a good 800 kilograms lighter.
However it is now a fair bit larger and this is a VERY simple model. But hopefully it puts some points across. Thank you.
I challenged myself to run some numbers and used a very primitive 'tank' to demonstrate my findings.
Firstly I started with my 'unsloped tank' a simple 3x3x6 meter box. With 100mm frontal armor, 80mm side/rear armor, and 20mm belly/roof armor.
Basically a super simplified and boxier tiger tank.
3 meters wide, 6 long, 3 tall
Volume 54m^3
Surface area+volume of armor
Front surface area=9m^2 Volume (0.1m thick) = 0.9m^3
Rear surface area 9m^2 Volume (0.08m thick) = 0.72m^3
Side surface area (each) = 18m^2 Volume (0.08m thick) = 1.44m^3
Roof/belly area (each) =18m^2 Volume (0.02m thick)= 0.36m^3
Total armor volume 5.22m^3
Weight assuming density of iron/steel is 7800kg per cubic meter 40716kg
I gave this tank a simple 60 degree UFP and LFP
Volume of UFP and LFP (11.691)
Rest of tank volume = (30.618)
Total volume of tank now = 42.309m/3
Area of tank
UFP+LFP=18m/2 Volume (0.05m thick) = 0.9m^3
Rear surface area 9m^2 Volume (0.08m thick) = 0.72m^3
Roof/Belly (each) = 10.206m^2 Volume (0.02m thick) = 0.20412m^3
Sides (each) =3.89712+10.206= 14.10312m^2 Volume (0.08m thick) = 1.1282496m^3
Total armor volume 4.2847392m^3
Weight assuming density of iron/steel is 7800kg per cubic meter 33421kg
Non-sloped tank is 1.27632418634 more volumous than sloped tank
Non-sloped tank is 1.21827593429 heavier than sloped tank
So the unsloped tank actually more efficient for it's volume, without further alterations. But I thought "Wait a minute what happens if I expand this tank to the same volume?"
To do this I did some maths and the thing had to be approximately 8% larger in all dimensions.
Sloped tank enlarged to 54m^3
Overall length 6.50836024248
Overall width/height 3.25418012124
Volume of UFP and LFP (14.9219127787)
Rest of tank volume = (39.0797645404)
Total volume of tank now = 54.0016773191m/3
Area of tank
UFP+LFP=21.178204229m^2 Volume (0.05m thick) = 1.05891021145m^3
Rear surface area 10.5896882615m^2 Volume (0.08m thick) = 0.84717506091m^3
Roof/Belly (each) = 12.0090969413m^2 Volume (0.02m thick) = 0.24018193882m^3
Sides (each) =4.58546+12.0090969413= 16.5945569413m^2 Volume (0.08m thick) = 1.3275645553m^3
Total armor volume 5.0415782606m^3
Weight assuming density of iron/steel is 7800kg per cubic meter 39324kg
So now the tank has identical LOS frontal armor (depending on the projectile MORE durable), the same volume, and is a good 800 kilograms lighter.
However it is now a fair bit larger and this is a VERY simple model. But hopefully it puts some points across. Thank you.