by C.R. Kline
I have always thought the spaceship design rules in the Knight Hawks campaign book had a fundamental flaw in assigning the number of engines to a given hull size ship. For example, why are the same ADF/MR values used when the ship hull-size increases from 3 to 4, or from 6 to 7, yet the number of engines decreases in these cases? Why would a hull-size 4 yacht have the same number and size engines as a hull size 1 fighter? Even as a teenager in the 1980’s I recognized that discrepancy, and my old copy of the rules has handwritten corrections in the tables from the campaign book.
Assuming editing for consistency to mathematical formulae was not a focus of the original rule books, then it may be that some of these tables are typographical errors or design oversight. In that case, what should the tables actually reflect?
In answer to that question, I have established a redesigned set of ship hull-size to engine size values which follows a basic correlation of total engine thrust to ship size. In reality, the thrust requirements would be correlated to the ship’s mass, but this gets incredibly fiddly very quickly once one adds equipment, armor, and life-support to the ship, not to mention weapons, luggage, and etc. Therefore, several basic assumptions are required to simplify the calculations to provide a realistic yet playable set of rules. Now of course, I could just give you my redesigned table, but remember, this is SCIENCE fiction so it is a little more meaningful if we go into the science behind the fiction.
I had originally intended to use a correlation to the volume of the ships, assuming they were solid cylinders of uniform density defined by their length and diameter. In that case, ship thrust would correlate to volume, where volume = length * π * diameter squared / 4. But this equation did not lead to a useful linear correlation between engine requirements and small hull sizes0F[1]. Essentially I would have had different engine sizes for each of the first 6 or 7 hull-sizes to come close to matching the original material, but I felt that strayed too far from the flavor provided in the Knight Hawks rules and artwork.
However, on thinking through the problem of how to represent the ships as geometric objects; it occurred to me that what we are really dealing with are not solid cylinders of uniform density, but something much more like hollow tubes. The hollow-tube design is evidenced in almost every deck plan ever published: there is a lot of open space in these ships. We then make the following two assumptions: that the super-structure is the primary source of mass for the ship (more so than any equipment added later1F[2]); and that the outer surface of the cylinder has a finite thickness that is small in comparison to the tube’s diameter. These assumptions allow us to consider the spaceships as very large tubes, where the overall mass is directly related to the surface area of the tube.
Using the above relationship of mass to surface area provides for a much more steady increase in the thrust needs for the ship’s engines, and this in turn allows one to create several groupings of engine size across multiple hull-sizes. Refer to the table of ship dimensions, which includes the surface areas and volumes of each hull size (Table 1).
hull size |
length |
diameter |
engines |
type |
base ADF/MR |
surface area |
Thrust = SA/ENG*ADF |
volume |
1 |
10 |
2 |
1 |
A |
5 |
38 |
188 |
31 |
2 |
30 |
5 |
1 |
A |
4 |
275 |
1,100 |
589 |
3 |
50 |
8 |
2 |
A |
4 |
729 |
1,458 |
2,513 |
4 |
75 |
12 |
1 |
A |
4 |
1,640 |
6,560 |
8,482 |
5 |
100 |
15 |
3 |
B |
3 |
2,710 |
2,710 |
17,671 |
6 |
130 |
20 |
3 |
B |
3 |
4,712 |
4,712 |
40,841 |
7 |
150 |
25 |
2 |
B |
3 |
6,872 |
10,308 |
73,631 |
8 |
180 |
30 |
2 |
B |
3 |
9,896 |
14,844 |
127,235 |
9 |
210 |
35 |
2 |
B |
3 |
13,470 |
20,204 |
202,044 |
10 |
240 |
40 |
3 |
B |
3 |
17,593 |
17,593 |
301,593 |
11 |
270 |
45 |
3 |
B |
3 |
22,266 |
22,266 |
429,416 |
12 |
300 |
50 |
4 |
B |
3 |
27,489 |
20,617 |
589,049 |
13 |
340 |
55 |
4 |
B |
3 |
34,126 |
25,594 |
807,782 |
14 |
380 |
60 |
6 |
B |
3 |
41,469 |
20,735 |
1,074,425 |
15 |
420 |
70 |
4 |
C |
2 |
53,878 |
26,939 |
1,616,349 |
16 |
450 |
75 |
6 |
C |
2 |
61,850 |
20,617 |
1,988,039 |
17 |
475 |
80 |
6 |
C |
2 |
69,743 |
23,248 |
2,387,610 |
18 |
500 |
85 |
6 |
C |
2 |
78,108 |
26,036 |
2,837,251 |
19 |
540 |
90 |
4 |
C |
2 |
89,064 |
44,532 |
3,435,332 |
20 |
600 |
100 |
8 |
C |
2 |
109,956 |
27,489 |
4,712,389 |
Looking at Table 1, with an eye towards keeping to the original design flair where possible, one can devise several logical break points in the numbers. Additionally, several new break points occur, especially for the small ships. This requires the creation of two new engine types, which I have termed AA and AAA (using a similar nomenclature as US standard alkaline battery sizes). Addition of these two new break points allows one to put a reasonable number of engines in the smaller ships, from HS 1 to 4. Also, it allows one to maintain certain traditions in ship design from the Knight Hawks artwork, such as fighters with one engine, and assault scouts with two engines. These new break points counter the bizarre possibilities which arise from using a single engine size across this range of hull sizes, such as a HS1 ship with an ADF of >100 when using even a single HS4-sized engine, or a HS4 ship with 32 of the engines used on a HS1 ship.
Another advantage of this paradigm is that GM’s could provide a wider variety of designs for the small engines (AAA, AA, possibly even A), to account for the fact that multiple races/companies could economically produce small engines, whereas only a small number of companies could (or would bother) to produce the largest engine sizes (B, C)2F[3]. This creates a situation which allows easy incorporation of the multi-engine fighter designs provided in past fan publications (e.g. Star Frontiersman issues 5, 7, 11).
Once the cut-off values are determined, then one can look at how many engines are needed for various speeds. The equations for this are the following:
Number of Engines = ADF * Surface Area / Thrust
ADF is the desired ADF for the ship, up to the maximum from the original Knight Hawks tables. Surface area is based on the dimensions given for the HS of the ship3F[4]. Thrust is a constant for various sizes of engines:
AAA = 180, AA = 1450, A = 7200, B = 17,000, C = 28,000 (units: m^{2} per engine per ADF)
The results are found in Table 2. Of course, using an equation results in a non-integral number of engines required at some steps, so then one must round up or down to get the actual number of engines required (second to last column in Table 2). Finally, one can recalculate the ADF now that the number of engines is fixed (last column in Table 2), or one could ignore this step, sticking with the suggested ADF values. Other than a difference in numbers of engines for many of the ships, the only other real difference created by this method is that HS2 ships are slightly faster than they used to be. But given they are intended as heavy fighters, making them fast should not be too much of a problem and will match very well with prior fan publications.
hull size |
length |
diameter |
surface area |
calc engines |
Type |
base ADF/MR |
Engines (rounded) |
calc ADF |
1 |
10 |
2 |
38 |
1.0 |
AAA |
5 |
1.0 |
4.8 |
2 |
30 |
5 |
275 |
0.8 |
AA |
4 |
1.0 |
5.3 |
3 |
50 |
8 |
729 |
2.0 |
AA |
4 |
2.0 |
4.0 |
4 |
75 |
12 |
1,640 |
0.9 |
A |
4 |
1.0 |
4.4 |
5 |
100 |
15 |
2,710 |
1.1 |
A |
3 |
1.0 |
2.7 |
6 |
130 |
20 |
4,712 |
2.0 |
A |
3 |
2.0 |
3.1 |
7 |
150 |
25 |
6,872 |
1.2 |
B |
3 |
1.0 |
2.5 |
8 |
180 |
30 |
9,896 |
1.7 |
B |
3 |
2.0 |
3.4 |
9 |
210 |
35 |
13,470 |
2.4 |
B |
3 |
2.0 |
2.5 |
10 |
240 |
40 |
17,593 |
3.1 |
B |
3 |
3.0 |
2.9 |
11 |
270 |
45 |
22,266 |
3.9 |
B |
3 |
4.0 |
3.1 |
12 |
300 |
50 |
27,489 |
4.9 |
B |
3 |
5.0 |
3.1 |
13 |
340 |
55 |
34,126 |
6.0 |
B |
3 |
6.0 |
3.0 |
14 |
380 |
60 |
41,469 |
7.3 |
B |
3 |
7.0 |
2.9 |
15 |
420 |
70 |
53,878 |
3.8 |
C |
2 |
4.0 |
2.1 |
16 |
450 |
75 |
61,850 |
4.4 |
C |
2 |
4.0 |
1.8 |
17 |
475 |
80 |
69,743 |
5.0 |
C |
2 |
5.0 |
2.0 |
18 |
500 |
85 |
78,108 |
5.6 |
C |
2 |
6.0 |
2.2 |
19 |
540 |
90 |
89,064 |
6.4 |
C |
2 |
6.0 |
1.9 |
20 |
600 |
100 |
109,956 |
7.9 |
C |
2 |
8.0 |
2.0 |
As noted, a certain amount of flexibility in the Thrust values for the AAA and AA engines can be incorporated into the model, to allow differentiation in capability of engines from different races or organizations. For instance, it is clear the UPF must have tinkered with the engines on the assault scouts to make them more powerful, because civilian ships could not achieve their ADF rating and still carry any payload. If a GM intends to modify the constants in these equations, I do not recommend changing the Thrust values by more than 1/3 the recommendations above for Frontier designed ships, but that is only out of deference to artwork in the Knight Hawks campaign book. Star-faring races outside the known frontier could use whatever thrust values the GM pleases. The only strict recommendation I make is to limit a ship design to ADF of 5 for most races (6 for Sathar), as explained in the “Beyond the Frontier” published modules.
In order to design and pay for their ships, players and GM’s will want to know the costs of these engines. The costs of the A, B, C engines can be used as found in the original rules, with AA engines costing 50% of A-size, and AAA costing 25% of A-size engines. This means the cost of small engines is proportionally much higher per unit of thrust. Consider this as the price of miniaturization for small engines, while the large engines benefit from economies of scale. The new tables and costs will change the price of constructing certain size ships, reducing the cost of smaller ships and increasing the cost of some larger ships.
[1] A mathematician would have quickly pointed this out, as ship diameter is linearly related to HS, but the volume equation contains the square of diameter, so a linear correlation to HS is not going to happen.
[2] There are already several excellent articles on the subject of minimum hull sizes, equipment limitations, and their effects on reducing ADF for a given ship. This treatise does not imply one method or another is more valid for calculating the effect of adding weapons, defenses and other equipment.
[3] Think about it – how many automobile companies and designs are out there today vs how many companies produce aircraft carriers? How many more cars are sold than aircraft carriers?
[4] I have calculated the surface area considering the ships as closed cylindrical tubes, considering the two ‘end caps’ as circles. Surface area = Length * pi * diameter/2 + 2 * pi * diameter^{2} / 4. Simplifying terms yields surface area = pi*diameter/2*(length + diameter).