FF&S and a sphere errata?

[atpollard]

FF&Sv1 claims to base its calculations and design system on 1 displacement ton being equal to 14 cubic meters, the geometric properties of a sphere and a 1 cm thick shell.

TNE-0304 Fire Fusion & Steel v1, pg 10:
First select a basic hull size from the Hull Size table(page 11). All hulls have a rate (or "tonnage") which is the displacement of the hull in tonnes of liquid hydrogen (the most common starship fuel). Therefore, a ship with a rate of 7 could hold 7 tonnes of liquid hydrogen (provided nothing else was put in the hull). Thus, Traveller uses the term "ton" as a unit of volume where 1 ton equals 14 cubic meters (m3) of internal volume (also measured as 14 kiloliters). The Hull Size table indicates the volume (in cubic meters), the material volume of the shell (assuming a uniform thickness of 1 centimeter) in cubic meters of hull material, and the length of the hull (actually its diameter, as all hull ratings are based on the characteristics of a sphere) in meters.

TNE-0304 Fire Fusion & Steel v1, pg 11:
Rate: The hull rating is a standard measure of the volume of the hull expressed in tonnes of liquid hydrogen. Each tonne of liquid hydrogen displaces 14 cubic meters of volume (and is referred to as a "displacement ton").
Vol: The enclosed volume of the hull in cubic meters (m3). Each cubic meter contains 1000 liters of volume, and so the term kiloliter is sometimes used interchangeably with cubic meter.
MV: Material volume, the volume (in cubic meters) of material required to enclose the hull in a shell 1 centimeter thick.
L: The length of the hull in meters. For spherical hulls, this is also the diameter.
Surface Area: Surface area in square meters is the hull material volume multiplied by 100.

From any geometry textbook, we get the following formula for a sphere
[Eq.1] Volume (V) = 4/3 * pi * r^3
[Eq.2] Surface (s) = 4 * pi * r^2
And rearrange equation [1] to solve for radius
[Eq.3] Radius (r) = (V * 3/4 * 1/pi)^1/3 = 0.620350490929 * (V)^1/3

From FF&Sv1 and basic geometry:
[Eq.4] Length (L) = Diameter = 2 * r

Let us examine the 200 dT hull from Fire Fusion & Steel v1, pg 11.:
Rate = 200 displacement tons (dT)
Volume (V) = 2800 cubic meters
Material Volume of 1 cm thick shell (MV) = 9 cubic meters
Length or Diameter (L) = 17 meters
Surface Area (s)= 100 * MV = 900 square meters
Check the math:
Volume (V) = 200 dT * 14 cu.m. per dT = 2800 cubic meters [OK]
Radius = 0.620350490929 * (2800)^1/3 = 8.7436
Length (L) = Diameter = 2 * 8.7436 = 17.4872 [-3% error]
Surface Area (s) = 4 * pi * 8.7436^2 = 960.7037 sq.m. [-6% error]
Material Volume (MV) = s/100 = 9.6070 cu.m. [-6% error]

Let us examine the 2 dT hull from Fire Fusion & Steel v1, pg 11.:
Rate = 2 displacement tons (dT)
Volume (V) = 28 cubic meters
Material Volume of 1 cm thick shell (MV) = 0.5 cubic meters
Length or Diameter (L) = 4 meters
Surface Area (s)= 100 * MV = 50 square meters
Check the math:
Volume (V) = 2 dT * 14 cu.m. per dT = 28 cubic meters [OK]
Radius = 0.620350490929 * (28)^1/3 = 1.8837
Length (L) = Diameter = 2 * 1.8837 = 3.7675 [+6% error]
Surface Area (s) = 4 * pi * 1.8837^2 = 44.5919 sq.m. [+12% error]
Material Volume (MV) = s/100 = 0.4459 cu.m. [+12% error]

There is no reason for a design system as detailed and math oriented as FF&S to improperly calculate the surface area and diameter of a sphere. Here is the corrected table for Fire Fusion & Steel v1, pg 11 (note that all values in a collumn have been rounded to the same number of significant figures)

[FONT="Courier New"]
      RATE         VOL   Surface     MV      L
        1          14    28.0911   0.2809  2.99
        2          28    44.5919   0.4459  3.77
        3          42    58.4319   0.5843  4.31
        4          56    70.7853   0.7079  4.75
        5          70    82.1390   0.8214  5.11
        6          84    92.7549   0.9275  5.43
        7          98    102.794   1.028   5.72
        8         112    112.365   1.124   5.98
        9         126    121.543   1.215   6.22
       10         140    130.388   1.304   6.44
       15         210    170.856   1.709   7.37
       20         280    206.977   2.070   8.12
       25         350    240.176   2.402   8.74
       30         420    271.217   2.712   9.29
       35         490    300.572   3.006   9.78
       40         560    328.556   3.286   10.2
       45         630    355.395   3.554   10.6
       50         700    381.256   3.813   11.0
       55         770    406.267   4.063   11.4
       60         840    430.530   4.305   11.7
       65         910    454.128   4.541   12.0
       70         980    477.128   4.771   12.3
       75       1,050    499.586   4.996   12.6
       80       1,120    521.550   5.216   12.9
       85       1,190    543.061   5.431   13.1
       90       1,260    564.154   5.642   13.4
       95       1,330    584.860   5.849   13.6
      100       1,400    605.205   6.052   13.9
      200       2,800    960.704   9.607   17.5
      300       4,200   1,258.88   12.59   20.0
      400       5,600   1,525.02   15.25   22.0
      500       7,000   1,769.63   17.70   23.7
      600       8,400   1,998.34   19.98   25.2
      700       9,800   2,214.63   22.15   26.6
      800      11,200   2,420.82   24.21   27.8
      900      12,600   2,618.57   26.19   28.9
    1,000      14,000   2,809.11   28.09   29.9
    2,000      28,000   4,459.19   44.59   37.7
    3,000      42,000   5,843.19   58.43   43.1
    4,000      56,000   7,078.53   70.79   47.5
    5,000      70,000   8,213.90   82.14   51.1
    6,000      84,000   9,275.49   92.75   54.3
    7,000      98,000   10,279.4   102.8   57.2
    8,000     112,000   11,236.5   112.4   59.8
    9,000     126,000   12,154.3   121.5   62.2
   10,000     140,000   13,038.8   130.4   64.4
   20,000     280,000   20,697.7   207.0   81.2
   30,000     420,000   27,121.7   271.2   92.9
   40,000     560,000   32,855.6   328.6   102
   50,000     700,000   38,125.6   381.3   110
   60,000     840,000   43,053.0   430.5   117
   70,000     980,000   47,712.8   477.1   123
   80,000   1,120,000   52,155.0   521.6   129
   90,000   1,260,000   56,415.4   564.2   134
  100,000   1,400,000   60,520.5   605.2   139
  200,000   2,800,000   96,070.4   960.7   175
  300,000   4,200,000   125,888    1,259   200
  400,000   5,600,000   152,502    1,525   220
  500,000   7,000,000   176,963    1,770   237
  600,000   8,400,000   199,834    1,998   252
  700,000   9,800,000   221,463    2,215   266
  800,000  11,200,000   242,082    2,421   278
  900,000  12,600,000   261,857    2,619   289
1,000,000  14,000,000   280,911    2,809   299
[/FONT]

I leave it to any other gearheads and FF&S fans to decide whether the errors are large enough to warrant inclusion as errata.

 

[far-trader]

I suspect nothing more sinister than simple rounding. They probably didn't even use more than two decimal places for Pi. These were the guys who rounded a standard G (9.8 N/kg) to 10 N/kg right?

 

[atpollard]

Agreed.
It just seems perverse to calculate starship costs in credits and mass in kg (thousandths of a percent precision) and let the initial values that drive the entire design be off by 12 percent.

 

[far-trader]

Definitely

FWIW, I only ever did my first FF&S design "by the book" with multiple decimal places. It proved that anything more than one decimal in the most significant unit was generally pointless. Having done it that once I never understood the reasoning for more detail.

 

[DonM]

So... errata?

 

[far-trader]

Maybe a note that the figures are rounded? Not precise? Suggested additions in red below:

TNE-0304 Fire Fusion & Steel v1, pg 10:
First select a basic hull size from the Hull Size table(page 11). All hulls have a rate (or "tonnage") which is the displacement of the hull in tonnes of liquid hydrogen (the most common starship fuel). Therefore, a ship with a rate of 7 could hold 7 tonnes of liquid hydrogen (provided nothing else was put in the hull). Thus, Traveller uses the term "ton" as a unit of volume where 1 ton equals 14 cubic meters (m3) of internal volume (also measured as 14 kiloliters). The Hull Size table indicates the volume (in cubic meters), the material volume of the shell (assuming a uniform thickness of 1 centimeter) in cubic meters of hull material, and the length of the hull (actually its approximate diameter, as all hull ratings are based on rounded calculations for the characteristics of a sphere) in meters.

TNE-0304 Fire Fusion & Steel v1, pg 11:
Rate: The hull rating is a standard measure of the volume of the hull expressed in tonnes of liquid hydrogen. Each tonne of liquid hydrogen displaces 14 cubic meters of volume (and is referred to as a "displacement ton").
Vol: The enclosed volume of the hull in cubic meters (m3). Each cubic meter contains 1000 liters of volume, and so the term kiloliter is sometimes used interchangeably with cubic meter.
MV: Material volume, the volume (in cubic meters) of material required to enclose the hull in a shell 1 centimeter thick.
L: The approximate length of the hull in meters. For spherical hulls, this is also the approximate diameter.
Surface Area: Approximate surface area in square meters is the hull material volume multiplied by 100.

 

[atpollard]

So... errata?

If you decide to include the rounding note as errata, the table should at least be rounded correctly. Rounding the actual values (from my calculations at the top) to 2-3 significant figures will give the following values that are within a 1% margin of error:

[FONT="Courier New"]
      RATE        VOL     MV     L
        1          14    [COLOR="Blue"]0.28   3.0[/COLOR]
        2          28    [COLOR="blue"]0.45   3.8[/COLOR]
        3          42    [COLOR="blue"]0.58   4.3[/COLOR]
        4          56    [COLOR="blue"]0.71   4.8[/COLOR]
        5          70    [COLOR="blue"]0.82   5.1[/COLOR]
        6          84    [COLOR="blue"]0.93   5.4[/COLOR]
        7          98    [COLOR="blue"]1.0    5.7[/COLOR]
        8         112    [COLOR="blue"]1.1    6.0[/COLOR]
        9         126    [COLOR="blue"]1.2    6.2[/COLOR]
       10         140    [COLOR="blue"]1.3    6.4[/COLOR]
       15         210    [COLOR="blue"]1.7    7.4[/COLOR]
       20         280    [COLOR="blue"]2.1    8.1[/COLOR]
       25         350    [COLOR="blue"]2.4    8.7[/COLOR]
       30         420    2.7    [COLOR="blue"]9.3[/COLOR]
       35         490    [COLOR="blue"]3.0[/COLOR]    9.8
       40         560    [COLOR="blue"]3.3   10.2[/COLOR]
       45         630    [COLOR="blue"]3.6   10.6[/COLOR]
       50         700    3.8   [COLOR="blue"]11.0[/COLOR]
       55         770    [COLOR="blue"]4.1[/COLOR]   11.4
       60         840    [COLOR="blue"]4.3   11.7[/COLOR]
       65         910    [COLOR="blue"]4.5   12.0[/COLOR]
       70         980    [COLOR="blue"]4.8   12.3[/COLOR]
       75       1,050    [COLOR="blue"]5.0   12.6[/COLOR]
       80       1,120    [COLOR="blue"]5.2   12.9[/COLOR]
       85       1,190    [COLOR="blue"]5.4   13.1[/COLOR]
       90       1,260    [COLOR="blue"]5.6   13.4[/COLOR]
       95       1,330    5.8   [COLOR="blue"]13.6[/COLOR]
      100       1,400    [COLOR="blue"]6.1   13.9[/COLOR]
      200       2,800    [COLOR="blue"]9.6     18[/COLOR]
      300       4,200     [COLOR="blue"]13[/COLOR]     20
      400       5,600     15     22
      500       7,000     [COLOR="blue"]18[/COLOR]     24
      600       8,400     20     25
      700       9,800     22     27
      800      11,200     24     28
      900      12,600     26     29
    1,000      14,000     28     30
    2,000      28,000     [COLOR="blue"]45     38[/COLOR]
    3,000      42,000     [COLOR="blue"]58     43[/COLOR]
    4,000      56,000     [COLOR="blue"]71     48[/COLOR]
    5,000      70,000     [COLOR="blue"]82[/COLOR]     51
    6,000      84,000     [COLOR="blue"]93     54[/COLOR]
    7,000      98,000     100    57
    8,000     112,000     110    60
    9,000     126,000     120    62
   10,000     140,000     130    64
   20,000     280,000     [COLOR="blue"]220    81[/COLOR]
   30,000     420,000     [COLOR="blue"]270    93[/COLOR]
   40,000     560,000     [COLOR="blue"]330   102[/COLOR]
   50,000     700,000     [COLOR="blue"]380   110[/COLOR]
   60,000     840,000     [COLOR="blue"]430   117[/COLOR]
   70,000     980,000     [COLOR="blue"]480   123[/COLOR]
   80,000   1,120,000     [COLOR="blue"]520   129[/COLOR]
   90,000   1,260,000     [COLOR="blue"]560   134[/COLOR]
  100,000   1,400,000     [COLOR="blue"]610   139[/COLOR]
  200,000   2,800,000     [COLOR="blue"]960   175[/COLOR]
  300,000   4,200,000   [COLOR="blue"]1,300[/COLOR]   200
  400,000   5,600,000   [COLOR="blue"]1,500[/COLOR]   220
  500,000   7,000,000   [COLOR="blue"]1,800   237[/COLOR]
  600,000   8,400,000   [COLOR="blue"]2,000   252[/COLOR]
  700,000   9,800,000   [COLOR="blue"]2,200   266[/COLOR]
  800,000  11,200,000   [COLOR="blue"]2,400   278[/COLOR]
  900,000  12,600,000   [COLOR="blue"]2,600   289[/COLOR]
1,000,000  14,000,000   [COLOR="blue"]2,800   299[/COLOR]
[/FONT]

One can calculate the actual values for the table (to better than 1% accuracy) using these simplified formula:

Volume (Vol) = Rate x 14
Material Volume (MV) = 0.281 x (Rate)^0.667
Length (L) = 2.99 x (Rate)^0.333

This could serve as an alternative to interpolating values as presented in the rules and errata.

 

[Antony]

Speaking as a gear head I do my designs to 4 decimal places but my players need never know.

Now could someone have a look at the surface areas of grapples per FF&S1
Grapples require area equal to the square of the final length of the craft carried by the grapple.

How do you attach that squadron of battleriders again?

 

[far-trader]

Can you rephrase your issue Antony? Do you see a specific problem?

FWIW, I always treated the whole surface area issue as one big approximation. The usable surface area being accessible area for features. And some features, like external grapples, being the amount of area lost/used not by the feature itself but by the whole of the area, such as the carried craft's shadow in the case of grapples.

Of course I also played free and loose with the interpretation of the grapple rules, permitting the grapple to be on the mother ship, the carried craft, or split between the two It helped make some design conversions possible.

 

[Antony]

OK the problem with grapples. Take a typical battle tender say a 300,000 dt Lurenti class Open USL configuration which FF&S1 would give a surface area of 244,000m^2 (using the tables in the book not above). Now strap on a 20,000 dt wedge configuration Nolikian class battlerider. FF&S1 would give this a length of 200m which would require a surface area of 200x200 = 40,000m^2 of grapples on the surface of the tender ie a little over 16% of the total surface area of the tender. A Lurenti is equipped with 7 Nolikians so approximately 112% of the surface area of the Tender is covered in grapples and so far no drives sensors etc have been fitted to the tender.

Now if the battleriders were of a needle instead of wedge configuration there length increases to 240m requiring 57,600m^2 of grapples or more than 23% of the tenders hull per battlerider. Hence the problems, surface area is at a premium in large ships anyway but linking grapple sizes to the length squared of a carried craft seems a little excessive to me.

 

[far-trader]

Yep, the Lurenti/Nolikians was the first one I "fixed" by splitting the grapples between the two. But that's not an official solution.

Neither is another idea I'd tossed around at the time, that being using half the surface area of the carried craft (i.e. the carried craft "shadow"). I seem to recall that didn't help though as the area was still too large to fit 7 Nolikians on the Lurenti.

I think there was a (semi?) official fix for the L/Ns where they dropped it to fewer Ns.

Come to think of it now, I have a vague recollection of there being another way around it. Docking rings instead?

Not sure it's so much errata as different though. In the TNE/FF&S verse you just can't do it the way it used to work. So you have to approach it as a different set of rules and accept that it can't be done that way. Sort of like how TNE/FF&S dropped the limitation of hardpoints per tons. So you can't put 7 Nolikians on a Lurenti, but you can probably put more firepower (weapons) into the same tonnage total. If you must have 7 riders then make them smaller and you can probably still fit the same weapons on each one.

 

[Starviking]

OK the problem with grapples. Take a typical battle tender say a 300,000 dt Lurenti class Open USL configuration which FF&S1 would give a surface area of 244,000m^2 (using the tables in the book not above). Now strap on a 20,000 dt wedge configuration Nolikian class battlerider. FF&S1 would give this a length of 200m which would require a surface area of 200x200 = 40,000m^2 of grapples on the surface of the tender ie a little over 16% of the total surface area of the tender. A Lurenti is equipped with 7 Nolikians so approximately 112% of the surface area of the Tender is covered in grapples and so far no drives sensors etc have been fitted to the tender.

Now if the battleriders were of a needle instead of wedge configuration there length increases to 240m requiring 57,600m^2 of grapples or more than 23% of the tenders hull per battlerider. Hence the problems, surface area is at a premium in large ships anyway but linking grapple sizes to the length squared of a carried craft seems a little excessive to me.

Could the grapples rule in FF&S be there to account for the clearance needed between craft if more than one are carried by grapples?

If that is the rationale, then seeing that Battletenders tend to be Open Frame, and thus have a dispersed structure, then perhaps a different rule is needed for such ships.

I guess maybe even a 'docking pylon' rule could be made - though like turret extenders I would guess any streamlining would be lost.

 

[Starviking]

FF&Sv1 claims to base its calculations and design system on 1 displacement ton being equal to 14 cubic meters, the geometric properties of a sphere and a 1 cm thick shell.

I did a check myself, and my figures are in general agreement with yours, though I didn't go into surface area.

I wonder if the table designer did some extrapolating and interpolating instead of crunching all the numbers?

I never noticed before, but I am a bit surprised that the hull material volume is on top of the hull rate - so the 200dT hull is a hares-breadth from being a 201dT hull. Personally I would have though that the MV should be on the inside of the hull - though you'd run up with volume difficulties if you try to design stuff on the scale of a few centimetres.

 

[far-trader]

I never noticed before, but I am a bit surprised that the hull material volume is on top of the hull rate...

I'm missing where you get that idea from. Never did it that way, and istr the examples all had hull MV subtracted from the total hull V. Else why even bother calculating it?

 

[Antony]

Using docking rings for the battleriders carried creates a worse problem. The volume of the docking ring has to be taken into account, so the 20,000 dt Nolikian class BRs then require a 20,000 dt docking ring. This is supposed to have a surface area but this does appear to be missing in FF&S1. This is given in the Brilliant Lances Technical Booklet as 2*L where L is the length of the hull unmodified by hull form of the largest craft that will use the ring.

So effectively a docking ring will use 10 times the volume of a grapple, assuming an unstreamlined type but will have a much lower surface area cost to the tender.

 

[far-trader]

The missing Surface Area for Docking Rings does sound like errata.

My take on the docking ring was that the volume was the carried craft and an empty docking ring would be empty volume, thus reducing the total volume of the mother ship by the missing carried craft volume when launched. Basically the docking ring is (the way I saw it) a conformal hanger* open to space, permitting no maintenance or repair. Launch and recovery is slower than externally carried being the trade-off.

* not even entirely enclosing the carried craft hull, more of a surface mated fixture

One CT example of (the way I saw) Docking Rings: 50ton Modular Cutter with a 30ton Docking Ring to carry a 30ton Module. With the Module detached you're left with a 20ton Cutter with 30ton open to space.

 

[Starviking]

I'm missing where you get that idea from. Never did it that way, and istr the examples all had hull MV subtracted from the total hull V. Else why even bother calculating it?

I was assuming that the quote on page 11:

MV: Material Volume, the volume (in cubic meters) of material required to enclose the hull in a shell 1 centimeter thick.

I took enclose to mean 'in addition to the hull volume', for MV to be subtracted from hull volume, 'line' would have been the word I would have used. That said, I've always subtracted MV from hull volume too - 'enclose' just leap out at me on a re-read.

As for examples of hull design - is there any in the FF&S book?

 

[Starviking]

Using docking rings for the battleriders carried creates a worse problem. The volume of the docking ring has to be taken into account, so the 20,000 dt Nolikian class BRs then require a 20,000 dt docking ring. This is supposed to have a surface area but this does appear to be missing in FF&S1. This is given in the Brilliant Lances Technical Booklet as 2*L where L is the length of the hull unmodified by hull form of the largest craft that will use the ring.

So effectively a docking ring will use 10 times the volume of a grapple, assuming an unstreamlined type but will have a much lower surface area cost to the tender.

I always thought that docking rings were more-or-less limited to one type of craft, and so the surface area required was the smallest cross-sectional area of the carried craft - so for a modular cutter in the Broadsword-class the docking ring area would be 2*pi*r2.

If you want a really sneaky way around the limitations of grapples, consider this:

A grapple fully rated for displacement is only needed if the ship that carries the grappled craft must manoeuvre with the craft grappled. If the craft is independent (as I assume Battle Riders are) then the only time the Battle Tender must be grappled to the Riders is just prior to, during, and just after jump. So you could definitely drop the tonnage rating of the grapples a magnitude or two. To account for the need to recover damaged riders you could have one or two fully rated grapples available for that eventuality.

 

[far-trader]

MV: Material Volume, the volume (in cubic meters) of material required to enclose the hull in a shell 1 centimeter thick.

Ah, whereas I can see the same interpretation for "line" without much difficulty But yeah, I can see how one can easily go with either way.

Perhaps something more like:

MV: Material Volume, the volume (in cubic meters) of material required for a shell 1 centimeter thick.

As for examples of hull design - is there any in the FF&S book?

Unfortunately no. There was a good one iirc in Brilliant Lances, and I think a magazine article at the time. I don't have either any longer though.

 

[atpollard]

Ugh. FF&S is becoming quite a pain. Here goes another question ...

From FF&Sv1 page 11:
"The price of a hull in Credits is its internal volume multiplied by the price shown on the Vehicle and Craft Construction Materials Table."

This would make the Hull Plating Cost (in MCr) = HPV x Price of hull material from the Vehicle and Craft Construction Materials Table, but FF&Sv1 page 10 throws in an extra "x Sm".

At first glance, the "x Sm" would appear to be an adjustment to the sphere to compensate for the difference between the surface area of a sphere and the surface area of the actual shape. Upon closer examination, the calculation for HPV already includes “x MVM” as an adjustment factor between the sphere shell and the actual shape shell and a “x 1.3” to adjust for the surface area of the airframe.

So why does the table for Hull Form and Configuration modify the HPV with an “MVM” and then generate a price based on this modified HPV and then modify the price again based on Hull Form?

Why is HPV modified by x 1.3 on page 10 for an airframe, then the Hull Plating price based upon this modified HPV and then the price modified for an airframe again on page 12?

Why are non sphere shapes and airframes being modified for shape and streamlining twice? Once when price is calculated based on hull plating volume, and a second time for “Sm” based on the Hull Form Table. This stands in direct contradiction to the definition of price listed on page 11.

Is it possible that the table on page 12 was intended to modify the hull volume of a sphere with the “MVM” and intended to modify the hull cost of a sphere with the “Sm”? Is the price definition on page 11 correct and the Modified HPV x the price shown on the Vehicle and Craft Construction Materials Table is the correct price?

Whatever their intent, I am confused.