Scaled Armor - Book 5 Variant

[jarednoble]

This diversion started in response to the oft-repeated idea of adding Book 5 armor to book 2 designs. The high guard armor rules are simple and seem to be a comfortable starting point when looking at armor for book 2.

Unfortunately, the rules are a bit _too_ simplistic. As was pointed out in the T5 forum, a large battleship that dedicates 10% of it tonnage to armor might have armor with a thickness in excess of the total length of a 10-ton fighter, but the fighter is considered equally well protected because it too dedicated 10% of it’s displacement tonnage to armor – even though it’s armor would probably be only 10 cm thick.

The suggestion was made that armor protection should to be based on the thickness of the armor, not the percentage of ship mass dedicated to that armor. I’m sure this is old ground for many folks, so bear with me.

MegaTraveller dodged the issue by ignoring armor volume, merely added to the vehicle’s weight. Essentially MegaTraveller displacement tonnage was only the _interior_ displacement of the craft. The merits of this approach are open for debate, but it is clearly different from High Guard, where every system uses dTons (perhaps because that’s the only property to choose from, since book2 and high guard both ignore mass/weight).

I think TNE, using FFS, tried to be more scientific about it by getting rather involved in calculating ship and armor volume, but in all honesty, TNE never interested me enough to look at too closely. I have a copy of FFS, but haven’t spent much time looking at it.

Over the course of a few posts I'll detail the steps I took to re-examine the book 5 armor rules, and what emerged.

 

[jarednoble]

This diversion started in response to the oft-repeated idea of adding Book 5 armor to book 2 designs. The high guard armor rules are simple and seem to be a comfortable starting point when looking at armor for book 2.

Unfortunately, the rules are a bit _too_ simplistic. As was pointed out in the T5 forum, a large battleship that dedicates 10% of it tonnage to armor might have armor with a thickness in excess of the total length of a 10-ton fighter, but the fighter is considered equally well protected because it too dedicated 10% of it’s displacement tonnage to armor – even though it’s armor would probably be only 10 cm thick.

The suggestion was made that armor protection should to be based on the thickness of the armor, not the percentage of ship mass dedicated to that armor. I’m sure this is old ground for many folks, so bear with me.

MegaTraveller dodged the issue by ignoring armor volume, merely added to the vehicle’s weight. Essentially MegaTraveller displacement tonnage was only the _interior_ displacement of the craft. The merits of this approach are open for debate, but it is clearly different from High Guard, where every system uses dTons (perhaps because that’s the only property to choose from, since book2 and high guard both ignore mass/weight).

I think TNE, using FFS, tried to be more scientific about it by getting rather involved in calculating ship and armor volume, but in all honesty, TNE never interested me enough to look at too closely. I have a copy of FFS, but haven’t spent much time looking at it.

Over the course of a few posts I'll detail the steps I took to re-examine the book 5 armor rules, and what emerged.

 

[jarednoble]

Step 1 - What values does the current system create?

Find the radius of a sphere whose volume equals the total ship displacement. Then find the radius of a sphere whose volume equals the ship displacement _after_ removing the hg-computed armor tonnage. The difference in radius is the armor thickness.

Observations:
• By selecting _any_ armor in high guard you automatically pay a “displacement tax” equal to 1 factor of armor. In these calculations I remove this 1-factor penalty from the thickness calculations. Perhaps this is a “bracing” or “reinforcement” necessary to attach armor? At any rate, if it is included in the armor calculations, it becomes very difficult to reconcile the first level in protection with each of the next 14 levels, which are all considered identically.
• The armor thickness varies based on the ship’s displacement. Smaller ships have thinner armor for the same factor. For ships from 100-2000 dTons, the thickness ranges from 2.32 cm to 6.30 cm for factor 1 armor.
• Each successive Armor factor is a little bit thicker than the previous, which makes sense, since we are “filling-in” from the outside of the sphere, and each successive inner layer has the same volume applied to a smaller (inner) surface area. This difference in thickness is actually very small – the difference between the each adjacent armor factor and the next is less than 1%.

Interesting Tidbit 1:
At 1000 dTons and TL 14-15, the thickness of factor 1 armor is .050005 meters, or 5 cm. This is directly derived from HG displacement values, using the assumption above to negate the “armor tax”, and idealized for a sphere to make life easy. 1000 dTons seems a comfortable middle ground for a “small-ship” universe. Military ships smaller than this would typically be lightly armored escorts, while serious combat ships would just be showing up at this range.

 

[jarednoble]

Step 1 - What values does the current system create?

Find the radius of a sphere whose volume equals the total ship displacement. Then find the radius of a sphere whose volume equals the ship displacement _after_ removing the hg-computed armor tonnage. The difference in radius is the armor thickness.

Observations:
• By selecting _any_ armor in high guard you automatically pay a “displacement tax” equal to 1 factor of armor. In these calculations I remove this 1-factor penalty from the thickness calculations. Perhaps this is a “bracing” or “reinforcement” necessary to attach armor? At any rate, if it is included in the armor calculations, it becomes very difficult to reconcile the first level in protection with each of the next 14 levels, which are all considered identically.
• The armor thickness varies based on the ship’s displacement. Smaller ships have thinner armor for the same factor. For ships from 100-2000 dTons, the thickness ranges from 2.32 cm to 6.30 cm for factor 1 armor.
• Each successive Armor factor is a little bit thicker than the previous, which makes sense, since we are “filling-in” from the outside of the sphere, and each successive inner layer has the same volume applied to a smaller (inner) surface area. This difference in thickness is actually very small – the difference between the each adjacent armor factor and the next is less than 1%.

Interesting Tidbit 1:
At 1000 dTons and TL 14-15, the thickness of factor 1 armor is .050005 meters, or 5 cm. This is directly derived from HG displacement values, using the assumption above to negate the “armor tax”, and idealized for a sphere to make life easy. 1000 dTons seems a comfortable middle ground for a “small-ship” universe. Military ships smaller than this would typically be lightly armored escorts, while serious combat ships would just be showing up at this range.

 

[jarednoble]

Step 2: New volume formulas based on fixed thickness
Using the 5cm value from “Interesting Tidbit 1” (above), I recomputed armor volume based on a fixed thickness of 5cm per armor factor.
The approach I took was to start with a sphere of the ships total volume, shrink it’s radius by 5 cm per armor level, then recomputed the volume of this inner sphere. The armor volume is the difference between the two.

Observations:
• Since I based the 5cm value on the HG values for a 1000 dTon hull, I normalized the results to this value. For any hull size/armor level combination, the formula outputs a volume multiplier. Simply multiply this number times the HG “percent of hull per armor factor” to get an accurate value.
• This “Armor Scaling Factor” or ASF ranges from 2.416 at 100 dTons, down to .586 at 5000 dTons, each for factor 1 armor. So factor 1 armor on a 100 dTon scout ship takes 2.4% of the ship volume instead of 1% while still giving the same level of protection.
• When applied to small craft the ASF increases rapidly. A 10-ton fighter will need to spend 4.5% of its tonnage for factor 1 armor – half a ton if you allow fractional accounting. If not, the minimum of 1 ton of armor is only sufficient to give your fighter factor 2 armor, not factor 10. In fact factor 15 armor on a 10 ton fighter will take 54.9% of available tonnage.
• This volume formula is ugly. It’s no sweat for a spreadsheet to handle, but it would be a challenge to do it by hand for each design.

Interesting Tidbit 2:
The only change to standard high guard construction rules is the addition of a single multiplier to the armor volume calculation.

 

[jarednoble]

Step 2: New volume formulas based on fixed thickness
Using the 5cm value from “Interesting Tidbit 1” (above), I recomputed armor volume based on a fixed thickness of 5cm per armor factor.
The approach I took was to start with a sphere of the ships total volume, shrink it’s radius by 5 cm per armor level, then recomputed the volume of this inner sphere. The armor volume is the difference between the two.

Observations:
• Since I based the 5cm value on the HG values for a 1000 dTon hull, I normalized the results to this value. For any hull size/armor level combination, the formula outputs a volume multiplier. Simply multiply this number times the HG “percent of hull per armor factor” to get an accurate value.
• This “Armor Scaling Factor” or ASF ranges from 2.416 at 100 dTons, down to .586 at 5000 dTons, each for factor 1 armor. So factor 1 armor on a 100 dTon scout ship takes 2.4% of the ship volume instead of 1% while still giving the same level of protection.
• When applied to small craft the ASF increases rapidly. A 10-ton fighter will need to spend 4.5% of its tonnage for factor 1 armor – half a ton if you allow fractional accounting. If not, the minimum of 1 ton of armor is only sufficient to give your fighter factor 2 armor, not factor 10. In fact factor 15 armor on a 10 ton fighter will take 54.9% of available tonnage.
• This volume formula is ugly. It’s no sweat for a spreadsheet to handle, but it would be a challenge to do it by hand for each design.

Interesting Tidbit 2:
The only change to standard high guard construction rules is the addition of a single multiplier to the armor volume calculation.

 

[jarednoble]

Step 3: Streamline the Process
While playing around with the values produced by the formula used in Step 2 I started looking for ways to simplify the process further. I quickly realized that the most important factor in the formula was the cube root of the total volume. I experimented with a few possibilities and landed on a formula that is just about as simple as you could hope for while retaining a cube root. This new formula is 10 divided by the cube root of the ship’s dTons.

Observations:
• For most values, the ASF generated by this simplified formula deviates from the complex formula by less than 1%.
• The values that deviate most from the ‘accurate’ ASF are those in the extremely small tonnages. The ‘complex’ ASF for a 20 ton armor 1 craft is 3.651 vs a simplified ASF of 3.684.
• The simplified ASF does not track the changing volume of successive armor layers, since the calculation does not consider armor factor. It therefore tends to compound the slight deviation that is apparent at armor value 1. The same 20 dTon craft with factor 15 armor would have a ‘complex‘ ASF of 45.826, versus a simplified ASF of 55.261. I don’t see this as a problem – it is just slightly more aggressive in its effects.

 

[jarednoble]

Step 3: Streamline the Process
While playing around with the values produced by the formula used in Step 2 I started looking for ways to simplify the process further. I quickly realized that the most important factor in the formula was the cube root of the total volume. I experimented with a few possibilities and landed on a formula that is just about as simple as you could hope for while retaining a cube root. This new formula is 10 divided by the cube root of the ship’s dTons.

Observations:
• For most values, the ASF generated by this simplified formula deviates from the complex formula by less than 1%.
• The values that deviate most from the ‘accurate’ ASF are those in the extremely small tonnages. The ‘complex’ ASF for a 20 ton armor 1 craft is 3.651 vs a simplified ASF of 3.684.
• The simplified ASF does not track the changing volume of successive armor layers, since the calculation does not consider armor factor. It therefore tends to compound the slight deviation that is apparent at armor value 1. The same 20 dTon craft with factor 15 armor would have a ‘complex‘ ASF of 45.826, versus a simplified ASF of 55.261. I don’t see this as a problem – it is just slightly more aggressive in its effects.

 

[jarednoble]

Rules for using Scaled Armor
All the standard high-guard construction rules apply. Once you have determined the hull percentage required for the desired armor level, multiply by the Armor scaling factor, which is found by looking on the Armor Scaling Factor table or computed as 10/(cube root of vessel dTons). Do not round any numbers until after you have completed all multiplication, then round only once.

Converting existing designs:
Any existing design can be easily converted by dividing it’s existing armor factor by the ASF for that ship size and recording its new armor factor. This is of course a quick-and-dirty approach that does not provide a perfect fit, and does not address cost differences (10 tons of factor 2 armor costs 5MCr, while 10 tons of factor 7 armor costs 10 MCr).

Note: this method may result in giving heavily armored vessels larger than 1000 tons an AF larger than its construction TL. I don't have a quick and dirty response for how should this be handled. One approach is to cap the AF as normal, then just dump the remaining tonnage into hangarage, cargo or fuel.

Definitions:
1 Armor level is the equivalent of 5 cm of TL 14 plating material.
Max Armor level: Ship construction TL (Same as HG)
Base Armor Displacement: Based on TL (Same as HG)
TL 7-9: 4+4a
TL 10-11: 3+3a
TL 12-13: 2+2a
TL 14+: 1+a
Cost: MCr .3+.1a per ton of armor. (Same as HG)

Effects:
A 1000-ton craft can be armored armor exactly the same as HG. Smaller craft have to dedicate an increasingly large percentage of their tonnage to achieve the same protection level, while large craft require a decreasing percentage of their tonnage to achieve a given armor value. A 100 Ton scout ship requires 2.15 times the high guard volume percentage for the same protection, while a 20 ton launch requires 3.68 times the percentage.

At the other extreme, a 5000 ton battlecruiser (remember this is for a small-ship universe) requires only .58 times the high guard volume percentage for its armor.

If this is extended to a large-ship universe, 50 kTon vessels require .27% per level, 100 kTon require .22%, and 1 mTon vessels require only .1% of ship mass per armor level.

 

[jarednoble]

Rules for using Scaled Armor
All the standard high-guard construction rules apply. Once you have determined the hull percentage required for the desired armor level, multiply by the Armor scaling factor, which is found by looking on the Armor Scaling Factor table or computed as 10/(cube root of vessel dTons). Do not round any numbers until after you have completed all multiplication, then round only once.

Converting existing designs:
Any existing design can be easily converted by dividing it’s existing armor factor by the ASF for that ship size and recording its new armor factor. This is of course a quick-and-dirty approach that does not provide a perfect fit, and does not address cost differences (10 tons of factor 2 armor costs 5MCr, while 10 tons of factor 7 armor costs 10 MCr).

Note: this method may result in giving heavily armored vessels larger than 1000 tons an AF larger than its construction TL. I don't have a quick and dirty response for how should this be handled. One approach is to cap the AF as normal, then just dump the remaining tonnage into hangarage, cargo or fuel.

Definitions:
1 Armor level is the equivalent of 5 cm of TL 14 plating material.
Max Armor level: Ship construction TL (Same as HG)
Base Armor Displacement: Based on TL (Same as HG)
TL 7-9: 4+4a
TL 10-11: 3+3a
TL 12-13: 2+2a
TL 14+: 1+a
Cost: MCr .3+.1a per ton of armor. (Same as HG)

Effects:
A 1000-ton craft can be armored armor exactly the same as HG. Smaller craft have to dedicate an increasingly large percentage of their tonnage to achieve the same protection level, while large craft require a decreasing percentage of their tonnage to achieve a given armor value. A 100 Ton scout ship requires 2.15 times the high guard volume percentage for the same protection, while a 20 ton launch requires 3.68 times the percentage.

At the other extreme, a 5000 ton battlecruiser (remember this is for a small-ship universe) requires only .58 times the high guard volume percentage for its armor.

If this is extended to a large-ship universe, 50 kTon vessels require .27% per level, 100 kTon require .22%, and 1 mTon vessels require only .1% of ship mass per armor level.

 

[The Oz]

Quite an excellent piece of work, Imix!

Have you considered any way of allowing for the different surface areas of different configurations? If you need a place to start at, you might consider looking at the ship design rules from GT:Interstellar Wars. They insert a multiplier for armor tonnage needed based on the surface area of the hull, and that multiplier varies in size based on the hull configuration.

 

[The Oz]

Quite an excellent piece of work, Imix!

Have you considered any way of allowing for the different surface areas of different configurations? If you need a place to start at, you might consider looking at the ship design rules from GT:Interstellar Wars. They insert a multiplier for armor tonnage needed based on the surface area of the hull, and that multiplier varies in size based on the hull configuration.

 

[jarednoble]

Thanks. I did consider it, but for the initial foundation I left it out, since I was looking for a minimum tweak to the existing High Guard system.

If I remember correctly, MT has a configuration multiplier that affects armor mass and cost, and I know the configuration multiplier from FFS affects armor volume - and thereby mass and cost as well.

If using any kind of book 5 tweak that applies a configuration multiplier to the hull, I would think that the same multiplier should apply to the required armor volume.

I think that the FFS idea of configuration/Streamlining creating waste space and modifying the hull/armor values is an intriguing concept for an updated High Guard.

For HG style construction, I wouldn't want to directly introduce surface area - it isn't used for any of drive/antenna, etc. style calculations. I haven't checked it out yet, but my instinct is that the ASF, which scales with ship size, combined with a simple configuration multiplier, will give a reasonable approximation to a value that is derived from the surface area.


I'll see if I can find a copy of GT:Interstellar Wars to take a look.

 

[jarednoble]

Thanks. I did consider it, but for the initial foundation I left it out, since I was looking for a minimum tweak to the existing High Guard system.

If I remember correctly, MT has a configuration multiplier that affects armor mass and cost, and I know the configuration multiplier from FFS affects armor volume - and thereby mass and cost as well.

If using any kind of book 5 tweak that applies a configuration multiplier to the hull, I would think that the same multiplier should apply to the required armor volume.

I think that the FFS idea of configuration/Streamlining creating waste space and modifying the hull/armor values is an intriguing concept for an updated High Guard.

For HG style construction, I wouldn't want to directly introduce surface area - it isn't used for any of drive/antenna, etc. style calculations. I haven't checked it out yet, but my instinct is that the ASF, which scales with ship size, combined with a simple configuration multiplier, will give a reasonable approximation to a value that is derived from the surface area.


I'll see if I can find a copy of GT:Interstellar Wars to take a look.

 

[atpollard]

From a strict game balance perspective, can a 100 or 200 dTon ship (like most players have) afford yet another space penalty in their over crowded hulls. Since most small starships cannot operate at a profit with their current passenger/cargo capacity, the real game effect will be to push ships further into the red or leave them without the option of armor.

 

[atpollard]

From a strict game balance perspective, can a 100 or 200 dTon ship (like most players have) afford yet another space penalty in their over crowded hulls. Since most small starships cannot operate at a profit with their current passenger/cargo capacity, the real game effect will be to push ships further into the red or leave them without the option of armor.

 

[Anthony]

There's no particular reason it should be possible to damage capital ships with turret weapons. I would probably use a log scale for armor. At TL 15, here's one possible scaling:
1% (armor 0) is a base of 0
2% (armor 1) is a base of 2
3% (armor 2) is a base of 3
4% (armor 3) is a base of 4
6% (armor 5) is a base of 5
8% (armor 7) is a base of 6
11%(armor 10) is a base of 7
16%(armor 15) is a base of 8
Then adjust by size:
300-1000 dtons: +1
1k-3k dtons: +2
3k-10k dtons: +3
10k-30k dtons: +4
30k-100k dtons: +5
100k-300k dtons: +6
300k-1M dtons: +7
If you want dreadnaughts to be really impervious, you can put break points at 2/5/10 instead of 3/10, giving a +11 for 500k dtons and putting a Tigress at armor 19.

 

[Anthony]

There's no particular reason it should be possible to damage capital ships with turret weapons. I would probably use a log scale for armor. At TL 15, here's one possible scaling:
1% (armor 0) is a base of 0
2% (armor 1) is a base of 2
3% (armor 2) is a base of 3
4% (armor 3) is a base of 4
6% (armor 5) is a base of 5
8% (armor 7) is a base of 6
11%(armor 10) is a base of 7
16%(armor 15) is a base of 8
Then adjust by size:
300-1000 dtons: +1
1k-3k dtons: +2
3k-10k dtons: +3
10k-30k dtons: +4
30k-100k dtons: +5
100k-300k dtons: +6
300k-1M dtons: +7
If you want dreadnaughts to be really impervious, you can put break points at 2/5/10 instead of 3/10, giving a +11 for 500k dtons and putting a Tigress at armor 19.

 

[jarednoble]

Originally posted by atpollard:
From a strict game balance perspective, can a 100 or 200 dTon ship (like most players have) afford yet another space penalty in their over crowded hulls. Since most small starships cannot operate at a profit with their current passenger/cargo capacity, the real game effect will be to push ships further into the red or leave them without the option of armor.

Well, I don't believe that they will be left "without the option of armor", but rather "with lighter armor options". The trade/economic system not functioning for small ships is, I believe, a separate issue. The fact that it may be broken now won't be impacted by this change.

The intent of this change is to make the ship-building options a little more consistent and reasonable (for certain definitions of reasonable ) .

 

[jarednoble]

Originally posted by atpollard:
From a strict game balance perspective, can a 100 or 200 dTon ship (like most players have) afford yet another space penalty in their over crowded hulls. Since most small starships cannot operate at a profit with their current passenger/cargo capacity, the real game effect will be to push ships further into the red or leave them without the option of armor.

Well, I don't believe that they will be left "without the option of armor", but rather "with lighter armor options". The trade/economic system not functioning for small ships is, I believe, a separate issue. The fact that it may be broken now won't be impacted by this change.

The intent of this change is to make the ship-building options a little more consistent and reasonable (for certain definitions of reasonable ) .