# Why would a fighter have a weaker shield than a capital ship?

I enjoy designing games, and in one that I'm working on the ships have shields, similar to the shields in Star Trek. They are created via some kind of force field projection mechanism and are spheroidical (that is, they take the shape of a spheroid). I would expect that those shields have strength relative to:

• The power used (more is better)
• The distance from the emitter (less is better)
• The curvature of the shield (more is better - which implies smaller)

Now, on a small fighter or shuttlecraft, the second and third criteria imply that the shield would be stronger. I would naïvely expect both power and distance to scale the strength of the shield with the third power - but power generation capabilities also scale with the cube of size, so those two things are about a wash. But the fighter, being smaller, would have a more curved shield, so it would be stronger.

Moreover, with less space dedicated to other things (like hydroponics or living space) and more justification for having as much power as possible, a fighter would likely have more power per cubic metre, and thus an even stronger shield.

Why wouldn't this be the case? The justification doesn't need to be short and pithy; I need the explanation so I can feel good about the system more than I need to have players understand why it works the way it does.

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– L.Dutch
Jan 8, 2019 at 16:51
• Can you fire your weapons while the shield is at full power? Could be that the shields have to be lower, if not off completely, in order to make full use of offensive capabilities. Think back to early aviation warfare, it could be that you have to fire "inbetween the propeller blades" ie the shield has to have some sort of oscilatting on/off feature which allows firing without damage to fighter but results in weakening of overall shield strength. Jan 9, 2019 at 18:34
• Why is curvature better? I would think that if a shield gets hit, it is hit. The only advantage of a smaller shield is a smaller chance of getting hit. But if it is hit, what is the advantage of greater curvature? Jan 9, 2019 at 21:28
• @TylerS.Loeper As mentioned by MongoTheGeek, it's not as great an effect as I had expected. But see that answer for a better explanation. Jan 9, 2019 at 21:44
• Suggest the distance from the emitter should scale effectiveness by inverse-square, not inverse-cube. Jan 9, 2019 at 21:59

Just make the dependence on curvature less sensitive than on the surface area of the shield and you should be fine.

Suppose the power of the shield emitter is proportional to the volume of the reactor powering it, and the strength of the shield inversely proportional to its surface area. Then if the radius of your ship is $$R$$, the strength of the shield is proportional to

$$S\propto V/A \propto R^3/R^2 \propto R$$

That is, without a curvature effect, scaling everything in your ship up will increase its shield strength. But, mathematically, curvature $$C$$ is proportional to $$1/R$$. So now if, say,

$$S\propto \frac{V\sqrt{C}}{A}$$, or maybe the logarithm of $$C$$, or something else slower than linear, you will still get an increase in shield strength with increasing ship size.

Another small trick you could exploit is to demand that there be a gap of a minimum size between shield and hull. For the sake of argument, let's say it's ten meters. Then a spherical fighter with hull radius 5m would need a shield radius 15m, but a 10m fighter would only need 20m of shield. Thus, doubling the size of the fighter increases the shield surface area by a factor of only about 1.8, instead of 4. Even a destroyer with radius 100m would get a benefit of 3.6 v 4 when you double everything except for that mandatory 10m gap. That would be another way to make big ships naturally have stronger shields, though the benefit diminishes for very large ships.

I would like to point out that distance from the generator doesn't have to go up if the ship is bigger. Having multiple shield projection points that make a local shield would be good enough to keep the shield close to its point of projection. So no inverse square rule law here.

It's simple math.

1. Power. For simplicity's sake let's assume the bigger the engine, the more power you can generate (for example, a nuclear power plant can generate much more power than a nuclear submarine and stupendously more than a family car). So, engine size grow by volume, as you make the ship bigger both the volume of the ship and the volume of the engine increase by x^3 (cubed).

2. Distance. Distance grows linearly by x.

3. Surface area (what you imply by "curvature"). Surface area of a sphere grows by x^2 (squared).

It's easy to see that engine size trumps the other two factor. If it's not obvious it's easy to plug in some numbers to see it. For simplicity the following are just factors rather than any real units:

x           : 1, 2,  3,  4,   5,   6,   7,   8,   9
power       : 1, 8, 27, 64, 125, 216, 343, 512, 729
distance    : 1, 2,  3,  4,   5,   6,   7,   8,   9
shield area : 1, 4,  9, 16,  25,  36,  49,  64,  81


So a ship that is 9 times larger will need 81 times more energy to generate similar strength shield but can potentially install an engine that is 729 times more powerful.

another game developer here.

I believe the gameplay secret lies elsewhere, to the armament of the capital vessel, but:

If you mean the fighter shields to be stronger than the capital vessel ones in absolute numbers I believe this is a gravely wrong choice as I see no reason at all to build a capital vessel for combat purposes.

If you mean proportionally stronger, this is a choice you can make. If for example the capital vessel is 100 times the mass and all of the fighter, and have a shield value of 1000, the proportional fighter shield value is 10. If you want to make this value 15 or 20 then yes I see your point. And you can excuse it with the reasons you provide yourself. Getting too much disproportionally high though makes things unbalanced - 100 or even 50 is a lot I believe. I talk for base values, not modified by research and stuff.

Think again the armament issue. A capital vessel may be a capital vessel destroyer, armed with just 2 huge weapons to destroy other capital vessels. This vessel however is ineffective against 100 fighters as destroying just 2 each time, the fighters will have plenty of time to bring it down. If the capital vessel is armed with 200 fighter class weapons (since the previous capital do had 2 capital class weapons, fighters also have 2 fighter class weapons thus proportionally speaking you can replace the 2 capital size class weapons with 200 fighter class weapons - capital vessel is 100x the fighter) as you can imagine the fighters will face a tremendous and analogous firing distribution thus this capital vessel will make a short work of them, as their firepower will diminish at each capital vessel firing. 2 capital vessels, 2 opposite results.