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High Guard Armor Fix

T

tbeard1999

SOC-14 1K
I've just completed an analysis (and fix) of a *major* logical flaw in High Guard that causes some pretty strange tactics to be effective. In High Guard, each point of armor costs a certain percentage of tonnage (after a very modest "up front" penalty). The percentage varies with tech level, but not with hull size.

So, a 15 points of armor on a 20 ton TL15 fighter consumes 16% of tonnage -- 3.2 tons. The same percentage -- 16% -- is consumed by 15 points of armor on a 1 million ton dreadnought.

So incredibly high armor levels may be found on tiny fighters, which is completely non-intuitive. It also breaks the HG combat system, since clouds of ultra-high armored fighters must be engaged one at a time by spinal weapons to be destroyed.

The problem is the assumption that armor mass/volume scales linearly with volume. It does not. An analysis of spheres, cubes and 3D rectangular constructs reveals that when you double volume ("tonnage" in CT), you only increase surface area 1.6 times. This is why 50,000 ton wet navy battleships have far thicker armor than 5,000 ton destroyers. It's also why 70 ton MBTs can have far thicker armor than 10 ton APCs.

So here's my fix.

I started with the assumption that HG's armor percentages were roughly correct for 100,000 ton starships and then scaled armor values for other hull sizes from that point. Using a sphere as my assumed shape, and 14 cubic meters per “ton”, I calculated that if 1 point of armor on a 100,000 ton ship displaces 1000 tons, then the armor would be about 23cm thick. This gave me a basis to calculate the tonnage of armor for other sizes. (As an aside, the 100,000 ton sphere is 138m in diameter; a 1 million ton behemoth is 299m in diameter). Star Trek’s Fesarius would have been a 15 million ton starship in Traveller. The Death Star (~500km in diameter) would be about 5,000,000,000,000,000 tons.

[UPDATE -- SEE FORMULA POSTED AT THE END OF THIS THREAD FOR A FAR MORE ELEGANT SOLUTION THAN THIS CHART]

Hull Size...TL7-9....TL10-11....TL12-13....TL14+
10 ...80.4%....60.3%....40.2%....20.1%
20 ...64.8%....48.6%....32.4%....16.2%
30 ...57.0%....42.7%....28.5%....14.2%
40 ...52.0%....39.0%....26.0%....13.0%
50 ...48.4%....36.3%....24.2%....12.1%
60 ...45.7%....34.3%....22.9%....11.4%
70 ...43.5%....32.6%....21.8%....10.9%
80 ...41.7%....31.3%....20.8%....10.4%
90 ...40.1%....30.1%....20.1%....10.0%
100 ...38.8%....29.1%....19.4%....9.7%
200 ...31.0%....23.3%....15.5%....7.8%
300 ...27.2%....20.4%....13.6%....6.8%
400 ...24.7%....18.6%....12.4%....6.2%
500 ...23.0%....17.3%....11.5%....5.8%
600 ...21.7%....16.3%....10.8%....5.4%
700 ...20.6%....15.5%....10.3%....5.2%
800 ...19.7%....14.8%....9.9%....4.9%
900 ...19.0%....14.2%....9.5%....4.7%
1,000 ...18.3%....13.7%....9.2%....4.6%
2,000 ...14.6%....10.9%....7.3%....3.6%
3,000 ...12.8%....9.6%....6.4%....3.2%
4,000 ...11.6%....8.7%....5.8%....2.9%
5,000 ...10.8%....8.1%....5.4%....2.7%
6,000 ...10.2%....7.6%....5.1%....2.5%
7,000 ....9.7%....7.2%....4.8%....2.4%
8,000 ....9.2%....6.9%....4.6%....2.3%
9,000 ....8.9%....6.7%....4.4%....2.2%
10,000 ....8.6%....6.4%....4.3%....2.1%
15,000 ....7.5%....5.6%....3.8%....1.9%
20,000 ....6.8%....5.1%....3.4%....1.7%
25,000 ....6.3%....4.8%....3.2%....1.6%
30,000 ....6.0%....4.5%....3.0%....1.5%
35,000 ....5.7%....4.2%....2.8%....1.4%
40,000 ....5.4%....4.1%....2.7%....1.4%
45,000 ....5.2%....3.9%....2.6%....1.3%
50,000 ....5.0%....3.8%....2.5%....1.3%
55,000 ....4.9%....3.7%....2.4%....1.2%
60,000 ....4.7%....3.6%....2.4%....1.2%
65,000 ....4.6%....3.5%....2.3%....1.2%
70,000 ....4.5%....3.4%....2.3%....1.1%
75,000 ....4.4%....3.3%....2.2%....1.1%
80,000 ....4.3%....3.2%....2.2%....1.1%
85,000 ....4.2%....3.2%....2.1%....1.1%
90,000 ....4.1%....3.1%....2.1%....1.0%
95,000 ....4.1%....3.1%....2.0%....1.0%
100,000 ....4.0%....3.0%....2.0%....1.0%
105,000 ....3.9%....3.0%....2.0%....1.0%
110,000 ....3.9%....2.9%....1.9%....1.0%
115,000 ....3.8%....2.9%....1.9%....1.0%
120,000 ....3.8%....2.8%....1.9%....0.9%
125,000 ....3.7%....2.8%....1.9%....0.9%
130,000 ....3.7%....2.7%....1.8%....0.9%
135,000 ....3.6%....2.7%....1.8%....0.9%
140,000 ....3.6%....2.7%....1.8%....0.9%
145,000 ....3.5%....2.7%....1.8%....0.9%
150,000 ....3.5%....2.6%....1.7%....0.9%
155,000 ....3.5%....2.6%....1.7%....0.9%
160,000 ....3.4%....2.6%....1.7%....0.9%
165,000 ....3.4%....2.5%....1.7%....0.8%
170,000 ....3.4%....2.5%....1.7%....0.8%
175,000 ....3.3%....2.5%....1.7%....0.8%
180,000 ....3.3%....2.5%....1.6%....0.8%
185,000 ....3.3%....2.4%....1.6%....0.8%
190,000 ....3.2%....2.4%....1.6%....0.8%
195,000 ....3.2%....2.4%....1.6%....0.8%
200,000 ....3.2%....2.4%....1.6%....0.8%
205,000 ....3.1%....2.4%....1.6%....0.8%
210,000 ....3.1%....2.3%....1.6%....0.8%
215,000 ....3.1%....2.3%....1.6%....0.8%
220,000 ....3.1%....2.3%....1.5%....0.8%
225,000 ....3.1%....2.3%....1.5%....0.8%
230,000 ....3.0%....2.3%....1.5%....0.8%
235,000 ....3.0%....2.3%....1.5%....0.8%
240,000 ....3.0%....2.2%....1.5%....0.7%
245,000 ....3.0%....2.2%....1.5%....0.7%
250,000 ....2.9%....2.2%....1.5%....0.7%
255,000 ....2.9%....2.2%....1.5%....0.7%
260,000 ....2.9%....2.2%....1.5%....0.7%
265,000 ....2.9%....2.2%....1.4%....0.7%
270,000 ....2.9%....2.2%....1.4%....0.7%
275,000 ....2.9%....2.1%....1.4%....0.7%
280,000 ....2.8%....2.1%....1.4%....0.7%
285,000 ....2.8%....2.1%....1.4%....0.7%
290,000 ....2.8%....2.1%....1.4%....0.7%
295,000 ....2.8%....2.1%....1.4%....0.7%
300,000 ....2.8%....2.1%....1.4%....0.7%
350,000 ....2.6%....2.0%....1.3%....0.7%
400,000 ....2.5%....1.9%....1.3%....0.6%
450,000 ....2.4%....1.8%....1.2%....0.6%
500,000 ....2.3%....1.8%....1.2%....0.6%
550,000 ....2.3%....1.7%....1.1%....0.6%
600,000 ....2.2%....1.7%....1.1%....0.6%
650,000 ....2.1%....1.6%....1.1%....0.5%
700,000 ....2.1%....1.6%....1.0%....0.5%
750,000 ....2.0%....1.5%....1.0%....0.5%
800,000 ....2.0%....1.5%....1.0%....0.5%
850,000 ....2.0%....1.5%....1.0%....0.5%
900,000 ....1.9%....1.4%....1.0%....0.5%
950,000 ....1.9%....1.4%....0.9%....0.5%
1 mil. ....1.9%....1.4%....0.9%....0.5%


The percentage given is the percentage of tonnage required for 1 point of armor at the given tech level. Multiply this by the number of armor points desired. For simplicity, you might want to round these fractions off to the nearest 0.25% or 0.50%.

--Ty

This solves the problem of cast-iron fighters, although it does make heavy armor less costly for large vehicles. This is realistic, however.

This also makes it much harder for small escorts to have much armor, which gives civilian ships (i.e. what the players probably have) a better chance against the authorities.

The surface area relationship holds true for cubes and rectangular solids, although the latter can have more surface area than a sphere. I wouldn’t get into the effect configuration has on armor. Since spheres have the lowest surface area by volume; the result would likely be nothing but spherical starships, which look silly.

To get a better formatted table, you can copy this into Word and Replace (Edit menu: Replace...) the four periods with tabs (the tab character is ^t) for formatting. Then do the same replacement for three periods.
 
I've just completed an analysis (and fix) of a *major* logical flaw in High Guard that causes some pretty strange tactics to be effective. In High Guard, each point of armor costs a certain percentage of tonnage (after a very modest "up front" penalty). The percentage varies with tech level, but not with hull size.

So, a 15 points of armor on a 20 ton TL15 fighter consumes 16% of tonnage -- 3.2 tons. The same percentage -- 16% -- is consumed by 15 points of armor on a 1 million ton dreadnought.

So incredibly high armor levels may be found on tiny fighters, which is completely non-intuitive. It also breaks the HG combat system, since clouds of ultra-high armored fighters must be engaged one at a time by spinal weapons to be destroyed.

The problem is the assumption that armor mass/volume scales linearly with volume. It does not. An analysis of spheres, cubes and 3D rectangular constructs reveals that when you double volume ("tonnage" in CT), you only increase surface area 1.6 times. This is why 50,000 ton wet navy battleships have far thicker armor than 5,000 ton destroyers. It's also why 70 ton MBTs can have far thicker armor than 10 ton APCs.

So here's my fix.

I started with the assumption that HG's armor percentages were roughly correct for 100,000 ton starships and then scaled armor values for other hull sizes from that point. Using a sphere as my assumed shape, and 14 cubic meters per “ton”, I calculated that if 1 point of armor on a 100,000 ton ship displaces 1000 tons, then the armor would be about 23cm thick. This gave me a basis to calculate the tonnage of armor for other sizes. (As an aside, the 100,000 ton sphere is 138m in diameter; a 1 million ton behemoth is 299m in diameter). Star Trek’s Fesarius would have been a 15 million ton starship in Traveller. The Death Star (~500km in diameter) would be about 5,000,000,000,000,000 tons.

[UPDATE -- SEE FORMULA POSTED AT THE END OF THIS THREAD FOR A FAR MORE ELEGANT SOLUTION THAN THIS CHART]

Hull Size...TL7-9....TL10-11....TL12-13....TL14+
10 ...80.4%....60.3%....40.2%....20.1%
20 ...64.8%....48.6%....32.4%....16.2%
30 ...57.0%....42.7%....28.5%....14.2%
40 ...52.0%....39.0%....26.0%....13.0%
50 ...48.4%....36.3%....24.2%....12.1%
60 ...45.7%....34.3%....22.9%....11.4%
70 ...43.5%....32.6%....21.8%....10.9%
80 ...41.7%....31.3%....20.8%....10.4%
90 ...40.1%....30.1%....20.1%....10.0%
100 ...38.8%....29.1%....19.4%....9.7%
200 ...31.0%....23.3%....15.5%....7.8%
300 ...27.2%....20.4%....13.6%....6.8%
400 ...24.7%....18.6%....12.4%....6.2%
500 ...23.0%....17.3%....11.5%....5.8%
600 ...21.7%....16.3%....10.8%....5.4%
700 ...20.6%....15.5%....10.3%....5.2%
800 ...19.7%....14.8%....9.9%....4.9%
900 ...19.0%....14.2%....9.5%....4.7%
1,000 ...18.3%....13.7%....9.2%....4.6%
2,000 ...14.6%....10.9%....7.3%....3.6%
3,000 ...12.8%....9.6%....6.4%....3.2%
4,000 ...11.6%....8.7%....5.8%....2.9%
5,000 ...10.8%....8.1%....5.4%....2.7%
6,000 ...10.2%....7.6%....5.1%....2.5%
7,000 ....9.7%....7.2%....4.8%....2.4%
8,000 ....9.2%....6.9%....4.6%....2.3%
9,000 ....8.9%....6.7%....4.4%....2.2%
10,000 ....8.6%....6.4%....4.3%....2.1%
15,000 ....7.5%....5.6%....3.8%....1.9%
20,000 ....6.8%....5.1%....3.4%....1.7%
25,000 ....6.3%....4.8%....3.2%....1.6%
30,000 ....6.0%....4.5%....3.0%....1.5%
35,000 ....5.7%....4.2%....2.8%....1.4%
40,000 ....5.4%....4.1%....2.7%....1.4%
45,000 ....5.2%....3.9%....2.6%....1.3%
50,000 ....5.0%....3.8%....2.5%....1.3%
55,000 ....4.9%....3.7%....2.4%....1.2%
60,000 ....4.7%....3.6%....2.4%....1.2%
65,000 ....4.6%....3.5%....2.3%....1.2%
70,000 ....4.5%....3.4%....2.3%....1.1%
75,000 ....4.4%....3.3%....2.2%....1.1%
80,000 ....4.3%....3.2%....2.2%....1.1%
85,000 ....4.2%....3.2%....2.1%....1.1%
90,000 ....4.1%....3.1%....2.1%....1.0%
95,000 ....4.1%....3.1%....2.0%....1.0%
100,000 ....4.0%....3.0%....2.0%....1.0%
105,000 ....3.9%....3.0%....2.0%....1.0%
110,000 ....3.9%....2.9%....1.9%....1.0%
115,000 ....3.8%....2.9%....1.9%....1.0%
120,000 ....3.8%....2.8%....1.9%....0.9%
125,000 ....3.7%....2.8%....1.9%....0.9%
130,000 ....3.7%....2.7%....1.8%....0.9%
135,000 ....3.6%....2.7%....1.8%....0.9%
140,000 ....3.6%....2.7%....1.8%....0.9%
145,000 ....3.5%....2.7%....1.8%....0.9%
150,000 ....3.5%....2.6%....1.7%....0.9%
155,000 ....3.5%....2.6%....1.7%....0.9%
160,000 ....3.4%....2.6%....1.7%....0.9%
165,000 ....3.4%....2.5%....1.7%....0.8%
170,000 ....3.4%....2.5%....1.7%....0.8%
175,000 ....3.3%....2.5%....1.7%....0.8%
180,000 ....3.3%....2.5%....1.6%....0.8%
185,000 ....3.3%....2.4%....1.6%....0.8%
190,000 ....3.2%....2.4%....1.6%....0.8%
195,000 ....3.2%....2.4%....1.6%....0.8%
200,000 ....3.2%....2.4%....1.6%....0.8%
205,000 ....3.1%....2.4%....1.6%....0.8%
210,000 ....3.1%....2.3%....1.6%....0.8%
215,000 ....3.1%....2.3%....1.6%....0.8%
220,000 ....3.1%....2.3%....1.5%....0.8%
225,000 ....3.1%....2.3%....1.5%....0.8%
230,000 ....3.0%....2.3%....1.5%....0.8%
235,000 ....3.0%....2.3%....1.5%....0.8%
240,000 ....3.0%....2.2%....1.5%....0.7%
245,000 ....3.0%....2.2%....1.5%....0.7%
250,000 ....2.9%....2.2%....1.5%....0.7%
255,000 ....2.9%....2.2%....1.5%....0.7%
260,000 ....2.9%....2.2%....1.5%....0.7%
265,000 ....2.9%....2.2%....1.4%....0.7%
270,000 ....2.9%....2.2%....1.4%....0.7%
275,000 ....2.9%....2.1%....1.4%....0.7%
280,000 ....2.8%....2.1%....1.4%....0.7%
285,000 ....2.8%....2.1%....1.4%....0.7%
290,000 ....2.8%....2.1%....1.4%....0.7%
295,000 ....2.8%....2.1%....1.4%....0.7%
300,000 ....2.8%....2.1%....1.4%....0.7%
350,000 ....2.6%....2.0%....1.3%....0.7%
400,000 ....2.5%....1.9%....1.3%....0.6%
450,000 ....2.4%....1.8%....1.2%....0.6%
500,000 ....2.3%....1.8%....1.2%....0.6%
550,000 ....2.3%....1.7%....1.1%....0.6%
600,000 ....2.2%....1.7%....1.1%....0.6%
650,000 ....2.1%....1.6%....1.1%....0.5%
700,000 ....2.1%....1.6%....1.0%....0.5%
750,000 ....2.0%....1.5%....1.0%....0.5%
800,000 ....2.0%....1.5%....1.0%....0.5%
850,000 ....2.0%....1.5%....1.0%....0.5%
900,000 ....1.9%....1.4%....1.0%....0.5%
950,000 ....1.9%....1.4%....0.9%....0.5%
1 mil. ....1.9%....1.4%....0.9%....0.5%


The percentage given is the percentage of tonnage required for 1 point of armor at the given tech level. Multiply this by the number of armor points desired. For simplicity, you might want to round these fractions off to the nearest 0.25% or 0.50%.

--Ty

This solves the problem of cast-iron fighters, although it does make heavy armor less costly for large vehicles. This is realistic, however.

This also makes it much harder for small escorts to have much armor, which gives civilian ships (i.e. what the players probably have) a better chance against the authorities.

The surface area relationship holds true for cubes and rectangular solids, although the latter can have more surface area than a sphere. I wouldn’t get into the effect configuration has on armor. Since spheres have the lowest surface area by volume; the result would likely be nothing but spherical starships, which look silly.

To get a better formatted table, you can copy this into Word and Replace (Edit menu: Replace...) the four periods with tabs (the tab character is ^t) for formatting. Then do the same replacement for three periods.
 
Perhaps you might simplify the table a bit? Break it down to fewer categories? I know you'd lose some precision but you could make it easier to use and deal with the rounding troubles at the same time.

Maybe these categories:

Light fighters - 1 to 49 tons
Heavy fighters - 50 to 99 tons
Very Light ships - 100 to 499 tons
Light ships - 500 to 999 tons
Escorts - 1000 to 4999 tons
Destroyers - 5000 to 9999 tons
Light cruisers - 10000 to 49999 tons
Heavy cruisers - 50000 to 99999 tons
Battleships - 100000 to 499999 tons
Dreadnoughts - 500000 to 999999 tons
Leviathans - 1 million tons +

or some other set of ranges.
 
Perhaps you might simplify the table a bit? Break it down to fewer categories? I know you'd lose some precision but you could make it easier to use and deal with the rounding troubles at the same time.

Maybe these categories:

Light fighters - 1 to 49 tons
Heavy fighters - 50 to 99 tons
Very Light ships - 100 to 499 tons
Light ships - 500 to 999 tons
Escorts - 1000 to 4999 tons
Destroyers - 5000 to 9999 tons
Light cruisers - 10000 to 49999 tons
Heavy cruisers - 50000 to 99999 tons
Battleships - 100000 to 499999 tons
Dreadnoughts - 500000 to 999999 tons
Leviathans - 1 million tons +

or some other set of ranges.
 
Since it is a High Guard fix, how about a simple formula using the High Guard USP size code and TL?
 
Since it is a High Guard fix, how about a simple formula using the High Guard USP size code and TL?
 
Here's a version with the same basic range as HG:
Armor=A+S, where A is from armor factor:
</font><blockquote>code:</font><hr /><pre style="font-size:x-small; font-family: monospace;">AF 0 1 2 3 5 7 B F
A 0 2 3 4 5 6 7 8
Size 0 1 2-5 6-A B-E F-K L-P Q-R S-V
S -2 0 1 2 3 4 5 6 7</pre>[/QUOTE]If you want to make capital ships really tough, have S apply vs meson weapons.
 
Here's a version with the same basic range as HG:
Armor=A+S, where A is from armor factor:
</font><blockquote>code:</font><hr /><pre style="font-size:x-small; font-family: monospace;">AF 0 1 2 3 5 7 B F
A 0 2 3 4 5 6 7 8
Size 0 1 2-5 6-A B-E F-K L-P Q-R S-V
S -2 0 1 2 3 4 5 6 7</pre>[/QUOTE]If you want to make capital ships really tough, have S apply vs meson weapons.
 
Originally posted by atpollard:
Since it is a High Guard fix, how about a simple formula using the High Guard USP size code and TL?
Click to expand...
Man, I wish. :D

Here are the steps necessary to calculate the number:

1. Convert tons to cubic meters (T*3)

2. Determine radius in m from volume in m^3:
a. R^3 = Volume/(4/3*Pi)
b. R = cube root of R^3

3. Determine Surface Area in m^2 -- 4 * Pi * R^2

4. Assuming 1 point of TL15 armor is ~23.2cm thick, determine radius (in meters), then volume (in tons) of "inner sphere" after armor is taken into account:
R2 = R - .232
Where R = outer radius of sphere calculated in step 2.
V2 = (4/3 * Pi * R2^3)/14
Where V2 = volume remaining after armor in tons; 14 is the number of cubic meters per Traveller ton.

5. Subtract V2 from V1 to determine the tonnage of 1 point of armor.

I couldn't find a way to reduce that to a simple formula.

Note that there's a little distortion since each additional point of armor will take up a slightly smaller volume than the previious point of armor. This isn't significant and can be ignored.

Looks to me like the easiest solution is to reduce it to a simpler chart.

--Ty
 
Originally posted by atpollard:
Since it is a High Guard fix, how about a simple formula using the High Guard USP size code and TL?
Click to expand...
Man, I wish. :D

Here are the steps necessary to calculate the number:

1. Convert tons to cubic meters (T*3)

2. Determine radius in m from volume in m^3:
a. R^3 = Volume/(4/3*Pi)
b. R = cube root of R^3

3. Determine Surface Area in m^2 -- 4 * Pi * R^2

4. Assuming 1 point of TL15 armor is ~23.2cm thick, determine radius (in meters), then volume (in tons) of "inner sphere" after armor is taken into account:
R2 = R - .232
Where R = outer radius of sphere calculated in step 2.
V2 = (4/3 * Pi * R2^3)/14
Where V2 = volume remaining after armor in tons; 14 is the number of cubic meters per Traveller ton.

5. Subtract V2 from V1 to determine the tonnage of 1 point of armor.

I couldn't find a way to reduce that to a simple formula.

Note that there's a little distortion since each additional point of armor will take up a slightly smaller volume than the previious point of armor. This isn't significant and can be ignored.

Looks to me like the easiest solution is to reduce it to a simpler chart.

--Ty
 
Originally posted by The Oz:
Perhaps you might simplify the table a bit? Break it down to fewer categories? I know you'd lose some precision but you could make it easier to use and deal with the rounding troubles at the same time.

Maybe these categories:

Light fighters - 1 to 49 tons
Heavy fighters - 50 to 99 tons
Very Light ships - 100 to 499 tons
Light ships - 500 to 999 tons
Escorts - 1000 to 4999 tons
Destroyers - 5000 to 9999 tons
Light cruisers - 10000 to 49999 tons
Heavy cruisers - 50000 to 99999 tons
Battleships - 100000 to 499999 tons
Dreadnoughts - 500000 to 999999 tons
Leviathans - 1 million tons +

or some other set of ranges.
Click to expand...
Good idea. I had to add two categories and change your break points (the ranges vary significantly at the low end). Here's my version of your idea:

Base Armor Percentage (P)
1 to 29 tons -- 16%
30 to 59 tons -- 13%
60 to 99 tons -- 11%
100 to 199 -- 9%
200 to 299 -- 7.5%
300 to 499 -- 6%
500 to 999 -- 5%
1000 to 1999 -- 4%
2000 to 9,999 -- 3%
10,000 to 74,999 -- 2%
75000 to 149,999 -- 1%
150,000 to 449,000 -- 0.75%
450,000+ -- 0.5%

The indicated % is the tonnage of 1 point of armor at TL14-15. Armor of lower TLs is less efficient:

Armor Tech Level Adjustment (T)
7-9 -- x4
10-11 -- x3
12-13 -- x2
14-15 -- x1
16-17 -- x.75?

So, to determine the tonnage of armor, use this formula:

A x P x T x H

A - Points of Armor Desired
P - Armor Percentage
T - Armor Tech Level Adjustment
H - Hull Tonnage

Cost Per Ton:

Cost is MCr0.1 per ton for TL. Note that the indicated percentage is the total tonnage of the armor; there is no "up front" tonnage cost like in classic High Guard. Also, I ditched the MCr0.3 fixed cost for armor; this was probably a weak disincentive to armor smaller vessels.

Example -- TL12 50,000 ton fleet intruder. The designer wants it to have 5 points of armor.

5 x 2% x 2 x 50,000 = 10,000 tons

This armor belt will cost (0.1 x 10,000) = MCr1000.

--Ty
 
Originally posted by The Oz:
Perhaps you might simplify the table a bit? Break it down to fewer categories? I know you'd lose some precision but you could make it easier to use and deal with the rounding troubles at the same time.

Maybe these categories:

Light fighters - 1 to 49 tons
Heavy fighters - 50 to 99 tons
Very Light ships - 100 to 499 tons
Light ships - 500 to 999 tons
Escorts - 1000 to 4999 tons
Destroyers - 5000 to 9999 tons
Light cruisers - 10000 to 49999 tons
Heavy cruisers - 50000 to 99999 tons
Battleships - 100000 to 499999 tons
Dreadnoughts - 500000 to 999999 tons
Leviathans - 1 million tons +

or some other set of ranges.
Click to expand...
Good idea. I had to add two categories and change your break points (the ranges vary significantly at the low end). Here's my version of your idea:

Base Armor Percentage (P)
1 to 29 tons -- 16%
30 to 59 tons -- 13%
60 to 99 tons -- 11%
100 to 199 -- 9%
200 to 299 -- 7.5%
300 to 499 -- 6%
500 to 999 -- 5%
1000 to 1999 -- 4%
2000 to 9,999 -- 3%
10,000 to 74,999 -- 2%
75000 to 149,999 -- 1%
150,000 to 449,000 -- 0.75%
450,000+ -- 0.5%

The indicated % is the tonnage of 1 point of armor at TL14-15. Armor of lower TLs is less efficient:

Armor Tech Level Adjustment (T)
7-9 -- x4
10-11 -- x3
12-13 -- x2
14-15 -- x1
16-17 -- x.75?

So, to determine the tonnage of armor, use this formula:

A x P x T x H

A - Points of Armor Desired
P - Armor Percentage
T - Armor Tech Level Adjustment
H - Hull Tonnage

Cost Per Ton:

Cost is MCr0.1 per ton for TL. Note that the indicated percentage is the total tonnage of the armor; there is no "up front" tonnage cost like in classic High Guard. Also, I ditched the MCr0.3 fixed cost for armor; this was probably a weak disincentive to armor smaller vessels.

Example -- TL12 50,000 ton fleet intruder. The designer wants it to have 5 points of armor.

5 x 2% x 2 x 50,000 = 10,000 tons

This armor belt will cost (0.1 x 10,000) = MCr1000.

--Ty
 
Originally posted by tbeard1999:
Originally posted by The Oz:
[qb] Perhaps you might simplify the table a bit? Break it down to fewer categories? I know you'd lose some precision but you could make it easier to use and deal with the rounding troubles at the same time.

Maybe these categories:

Light fighters - 1 to 49 tons
Heavy fighters - 50 to 99 tons
Very Light ships - 100 to 499 tons
Light ships - 500 to 999 tons
Escorts - 1000 to 4999 tons
Destroyers - 5000 to 9999 tons
Light cruisers - 10000 to 49999 tons
Heavy cruisers - 50000 to 99999 tons
Battleships - 100000 to 499999 tons
Dreadnoughts - 500000 to 999999 tons
Leviathans - 1 million tons +

or some other set of ranges.
Click to expand...
Good idea. I had to add two categories and change your break points (the ranges vary significantly at the low end). Here's my version of your idea:

Base Armor Percentage (P)
1 to 29 tons -- 16%
30 to 59 tons -- 13%
60 to 99 tons -- 11%
100 to 199 -- 9%
200 to 299 -- 7.5%
300 to 499 -- 6%
500 to 999 -- 5%
1000 to 1999 -- 4%
2000 to 9,999 -- 3%
10,000 to 74,999 -- 2%
75000 to 149,999 -- 1%
150,000 to 449,000 -- 0.75%
450,000+ -- 0.5%

The indicated % is the tonnage of 1 point of armor at TL14-15. Armor of lower TLs is less efficient:

Armor Tech Level Adjustment (T)
7-9 -- x4
10-11 -- x3
12-13 -- x2
14-15 -- x1
16-17 -- x.75?

So, to determine the tonnage of armor, use this formula:

A x P x T x H

A - Points of Armor Desired
P - Armor Percentage
T - Armor Tech Level Adjustment
H - Hull Tonnage

Cost Per Ton:

Cost is MCr0.1 per ton for TL. Note that the indicated percentage is the total tonnage of the armor; there is no "up front" tonnage cost like in classic High Guard. Also, I ditched the MCr0.3 fixed cost for armor; this was probably a weak disincentive to armor smaller vessels.

Example -- TL12 50,000 ton fleet intruder. The designer wants it to have 5 points of armor.

5 x 2% x 2 x 50,000 = 10,000 tons

This armor belt will cost (0.1 x 10,000) = MCr1000.

I've modified a nifty High Guard spreadsheet (created by someone whose name escapes me) to handle this armor system. If anyone wants it, email me and I'll forward it.

--Ty
Click to expand...
 
Originally posted by tbeard1999:
Originally posted by The Oz:
[qb] Perhaps you might simplify the table a bit? Break it down to fewer categories? I know you'd lose some precision but you could make it easier to use and deal with the rounding troubles at the same time.

Maybe these categories:

Light fighters - 1 to 49 tons
Heavy fighters - 50 to 99 tons
Very Light ships - 100 to 499 tons
Light ships - 500 to 999 tons
Escorts - 1000 to 4999 tons
Destroyers - 5000 to 9999 tons
Light cruisers - 10000 to 49999 tons
Heavy cruisers - 50000 to 99999 tons
Battleships - 100000 to 499999 tons
Dreadnoughts - 500000 to 999999 tons
Leviathans - 1 million tons +

or some other set of ranges.
Click to expand...
Good idea. I had to add two categories and change your break points (the ranges vary significantly at the low end). Here's my version of your idea:

Base Armor Percentage (P)
1 to 29 tons -- 16%
30 to 59 tons -- 13%
60 to 99 tons -- 11%
100 to 199 -- 9%
200 to 299 -- 7.5%
300 to 499 -- 6%
500 to 999 -- 5%
1000 to 1999 -- 4%
2000 to 9,999 -- 3%
10,000 to 74,999 -- 2%
75000 to 149,999 -- 1%
150,000 to 449,000 -- 0.75%
450,000+ -- 0.5%

The indicated % is the tonnage of 1 point of armor at TL14-15. Armor of lower TLs is less efficient:

Armor Tech Level Adjustment (T)
7-9 -- x4
10-11 -- x3
12-13 -- x2
14-15 -- x1
16-17 -- x.75?

So, to determine the tonnage of armor, use this formula:

A x P x T x H

A - Points of Armor Desired
P - Armor Percentage
T - Armor Tech Level Adjustment
H - Hull Tonnage

Cost Per Ton:

Cost is MCr0.1 per ton for TL. Note that the indicated percentage is the total tonnage of the armor; there is no "up front" tonnage cost like in classic High Guard. Also, I ditched the MCr0.3 fixed cost for armor; this was probably a weak disincentive to armor smaller vessels.

Example -- TL12 50,000 ton fleet intruder. The designer wants it to have 5 points of armor.

5 x 2% x 2 x 50,000 = 10,000 tons

This armor belt will cost (0.1 x 10,000) = MCr1000.

I've modified a nifty High Guard spreadsheet (created by someone whose name escapes me) to handle this armor system. If anyone wants it, email me and I'll forward it.

--Ty
Click to expand...
 
Ty,
Try this empirical equation to simulate your table:

A = T * F * 0.4467 * (D)^0.67

where:
T = TL modifier (TL 14-15=1, TL12-13=2, TL10-11=3, TL 7-9=4)
A = armor required (dTons)
F = Armor Factor (High Guard)
D = Ship Displacement (dTons)

A/D * 100 should equal the percentages in your table, although this equation calculates the required dTons of armor directly.

EXAMPLE: 100,000 dTon ship, TL 15, Armor 1
Given T=1; F=1; D=100,000
A = 1*1*0.4467*(100,000)^0.67 = 1000.0367 dTons
(1000.0367/100,000)*100 = 1.0 percent

EXAMPLE: 1,000 dTon ship, TL 15, Armor 1
Given T=1; F=1; D=1,000
A = 1*1*0.4467*(1,000)^0.67 = 45.7105 dTons
(45.7105/1,000)*100 = 4.57 percent

EXAMPLE: 50,000 dTon ship, TL 12, Armor 6
Given T=2; F=6; D=50,000
A = 2*6*0.4467*(50,000)^0.67 = 7,542.3573 dTons
(7,542.3573/50,000)*100 = 15.0847 percent


[The base equation is based on the relationship between the surface area and volume of a sphere and assumes that for any given thickness of armor, the required dTons of armor will be proportional to the surface area. The 0.4467 constant was calculated based upon your initial assumptions of TL 15, factor 1 armor on a 100,000 dTon ship should be 1% or 1000 dTons. If you wanted to change the initial assumptions, then just plug the assumed values into the equation and solve for the new constant.]

Hope this helps.
 
Ty,
Try this empirical equation to simulate your table:

A = T * F * 0.4467 * (D)^0.67

where:
T = TL modifier (TL 14-15=1, TL12-13=2, TL10-11=3, TL 7-9=4)
A = armor required (dTons)
F = Armor Factor (High Guard)
D = Ship Displacement (dTons)

A/D * 100 should equal the percentages in your table, although this equation calculates the required dTons of armor directly.

EXAMPLE: 100,000 dTon ship, TL 15, Armor 1
Given T=1; F=1; D=100,000
A = 1*1*0.4467*(100,000)^0.67 = 1000.0367 dTons
(1000.0367/100,000)*100 = 1.0 percent

EXAMPLE: 1,000 dTon ship, TL 15, Armor 1
Given T=1; F=1; D=1,000
A = 1*1*0.4467*(1,000)^0.67 = 45.7105 dTons
(45.7105/1,000)*100 = 4.57 percent

EXAMPLE: 50,000 dTon ship, TL 12, Armor 6
Given T=2; F=6; D=50,000
A = 2*6*0.4467*(50,000)^0.67 = 7,542.3573 dTons
(7,542.3573/50,000)*100 = 15.0847 percent


[The base equation is based on the relationship between the surface area and volume of a sphere and assumes that for any given thickness of armor, the required dTons of armor will be proportional to the surface area. The 0.4467 constant was calculated based upon your initial assumptions of TL 15, factor 1 armor on a 100,000 dTon ship should be 1% or 1000 dTons. If you wanted to change the initial assumptions, then just plug the assumed values into the equation and solve for the new constant.]

Hope this helps.
 
Originally posted by atpollard:
Ty,
Try this empirical equation to simulate your table:

A = T * F * 0.4467 * (D)^0.67

where:
T = TL modifier (TL 14-15=1, TL12-13=2, TL10-11=3, TL 7-9=4)
A = armor required (dTons)
F = Armor Factor (High Guard)
D = Ship Displacement (dTons)

A/D * 100 should equal the percentages in your table, although this equation calculates the required dTons of armor directly.

EXAMPLE: 100,000 dTon ship, TL 15, Armor 1
Given T=1; F=1; D=100,000
A = 1*1*0.4467*(100,000)^0.67 = 1000.0367 dTons
(1000.0367/100,000)*100 = 1.0 percent

EXAMPLE: 1,000 dTon ship, TL 15, Armor 1
Given T=1; F=1; D=1,000
A = 1*1*0.4467*(1,000)^0.67 = 45.7105 dTons
(45.7105/1,000)*100 = 4.57 percent

EXAMPLE: 50,000 dTon ship, TL 12, Armor 6
Given T=2; F=6; D=50,000
A = 2*6*0.4467*(50,000)^0.67 = 7,542.3573 dTons
(7,542.3573/50,000)*100 = 15.0847 percent


[The base equation is based on the relationship between the surface area and volume of a sphere and assumes that for any given thickness of armor, the required dTons of armor will be proportional to the surface area. The 0.4467 constant was calculated based upon your initial assumptions of TL 15, factor 1 armor on a 100,000 dTon ship should be 1% or 1000 dTons. If you wanted to change the initial assumptions, then just plug the assumed values into the equation and solve for the new constant.]

Hope this helps.
Click to expand...
Excellent! The results from your formula simulate my spreadsheet within +/-4%. In the 100 ton to 10,000 ton range, your formula matches +/- about 1.5%. And I really like the fact that it is most accurate in the "sweet spot" for RPG starships -- 100ton to 1000 ton range.

I'll use your formula, with all armor values rounded up to the nearest ton.

In fact, your formula probably does not distort the results as much as my "rounded off" chart did.

--Ty
 
Originally posted by atpollard:
Ty,
Try this empirical equation to simulate your table:

A = T * F * 0.4467 * (D)^0.67

where:
T = TL modifier (TL 14-15=1, TL12-13=2, TL10-11=3, TL 7-9=4)
A = armor required (dTons)
F = Armor Factor (High Guard)
D = Ship Displacement (dTons)

A/D * 100 should equal the percentages in your table, although this equation calculates the required dTons of armor directly.

EXAMPLE: 100,000 dTon ship, TL 15, Armor 1
Given T=1; F=1; D=100,000
A = 1*1*0.4467*(100,000)^0.67 = 1000.0367 dTons
(1000.0367/100,000)*100 = 1.0 percent

EXAMPLE: 1,000 dTon ship, TL 15, Armor 1
Given T=1; F=1; D=1,000
A = 1*1*0.4467*(1,000)^0.67 = 45.7105 dTons
(45.7105/1,000)*100 = 4.57 percent

EXAMPLE: 50,000 dTon ship, TL 12, Armor 6
Given T=2; F=6; D=50,000
A = 2*6*0.4467*(50,000)^0.67 = 7,542.3573 dTons
(7,542.3573/50,000)*100 = 15.0847 percent


[The base equation is based on the relationship between the surface area and volume of a sphere and assumes that for any given thickness of armor, the required dTons of armor will be proportional to the surface area. The 0.4467 constant was calculated based upon your initial assumptions of TL 15, factor 1 armor on a 100,000 dTon ship should be 1% or 1000 dTons. If you wanted to change the initial assumptions, then just plug the assumed values into the equation and solve for the new constant.]

Hope this helps.
Click to expand...
Excellent! The results from your formula simulate my spreadsheet within +/-4%. In the 100 ton to 10,000 ton range, your formula matches +/- about 1.5%. And I really like the fact that it is most accurate in the "sweet spot" for RPG starships -- 100ton to 1000 ton range.

I'll use your formula, with all armor values rounded up to the nearest ton.

In fact, your formula probably does not distort the results as much as my "rounded off" chart did.

--Ty
 
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