# 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.

• Comments are not for extended discussion; this conversation has been moved to chat.
– L.Dutch
Commented 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. Commented 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? Commented 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. Commented Jan 9, 2019 at 21:44
• Suggest the distance from the emitter should scale effectiveness by inverse-square, not inverse-cube. Commented Jan 9, 2019 at 21:59

The key thing about a fighter is speed and agility, and fighters consequently need to be small and as light as possible. While you could build a small ship with large power generation capabilities, it would move and turn slowly compared with a more stripped-down fighter and would thus be vulnerable.

If, OTOH, the shield is a perfect defense, then you wouldn't build fighters, because their whole point is to deliver a punch with speed and agility. So if you want a class of ships that are analogous to fighters, the shield must have vulnerabilities that a fast-moving, agile craft can exploit.

• Yep. It is hard to put a nuclear engine on a rowboat. Commented Jan 8, 2019 at 0:57
• Looks like we're going back to broadsides... Commented Jan 8, 2019 at 1:00
• @Willk Not especially. The real problem with putting a nuclear engine on a rowboat is that the rowboat snaps in half and sinks ... well, and all the Navy guys shooting at you for stealing their nuclear engine, of course. Commented Jan 8, 2019 at 3:03
• some row boarts were quite big Commented Jan 8, 2019 at 3:19
• So you've got an high output light generator for your fighter. You have your guns and a nigh impenetrable shield. But, what if we syphon off some of that shield power to make the guns hit harder! We wouldn't have to take as many hits and could drop a larger target. The balance isn't size vs power, it is offense vs defense. You want more attack in an attack vessel. Commented Jan 9, 2019 at 17:12

Energy Dissipation across Surface Area

The shield operates by absorbing the energies of impacts and then radiating that energy away across its surface as heat/radiation, similar in principle to how a bulletproof vest catches the kinetic energy of a bullet and spreads it across the wearer's whole torso.

Consequently, the size of the shield itself has an effect on how efficient it is, a smaller shield might be easier to generate, but has far less surface-area to radiate much energy at a time. Continuing the analogy, a patch of kevlar a few inches across will not meaningfully protect you from a bullet, even if it's the same thickness as found on a vest. The surface-area matters as much as the thickness.

A powerful attack from a foe will therefore immediately saturate the smaller craft's shield and bleed through to strike the craft underneath, while a larger craft has significantly greater surface-area and can spread the force of the blow properly.

• This is often depicted in movie space battles. An energy beam/laser hits the shield and it glows in a radius around the hit as if the energy is being spread out and dissipated by the shield. Commented Jan 8, 2019 at 21:35
• Stargate is a prime example as all its shields are single planes or bubbles that glow across their surface emanating from the point of impact when struck, Star Trek features something cosmetically similar too. Commented Jan 9, 2019 at 8:59

A small generator in your backyard is enough to power your house, but that power plant is enough to power an entire city. The same can be applied to your ships. Your fighters aren't big enough to house proper full sized generators to supply your shield generators with the required power, while your capital ships can.

Another consideration is that there is a maximum limit a shield generator can obtain. Your fighter simple uses a small or medium sized shield generator, powered by a small or medium power generator. Your Capital ships use large or Extra Large Shield Generators linked to multiple large power generators. Simple put, your Capital ships can push its Shield generator to the limit, while your fighter is maintaining a minimum requirement.

So from a game perspective, your fighter can only install a small shield generator. Your capital ship can install 2 large shield generators. Your small fighter only has 2 guns. Your capital ship has 20. Your small fighter only has 100 hp. Your capital ship has 1000 hp. But your small fighter is cheaper and more maneuverable while a capital ship is a more costly investment.

• Only the reverse of this premise would need an explanation, unless for some reason we're still killing each other over oil. "Power is everything." – Apollo 13 Commented Jan 8, 2019 at 5:05
• The capital ship can also distribute the projection across multiple projectors (and would likely have to at that size), which can be used to add redundancy as well. Commented Jan 8, 2019 at 7:34
• +1 Square cube law indeed.
– NofP
Commented Jan 8, 2019 at 9:39

The capital ship doesn't have to have one big shield. It could have a lot of little ones, like bubble wrap. This would require some thinking about what happens when shields intersect each other or the ship itself.

Say each small shield is the same radius as a fighter's shield. Perhaps the capital ship has somewhat less power per unit volume than the fighter, but it also has much less surface area per unit volume. So power per unit surface area could be substantially larger.

• Hi, Dan. Welcome to the site. Can you explain that a bit more? It doesn't quite make sense to me.
– JBH
Commented Jan 8, 2019 at 6:47
• @JBH I'm pretty sure Dan is talking about multiple layers of shields in the first paragraph. The second seems clear enough to me; the ship can expend more power to shield a smaller area, which makes the shield stronger. Commented Jan 8, 2019 at 7:36
• Ancient memories here, forgive my forgetfulness. I saw this in... Macross maybe, where they lined the deck of the SDF1 with mecha each with their own shields. Pretty much the idea is lots of small hemispherical shields instead of a giant spherical one. Commented Jan 8, 2019 at 19:30
• +1 OP said that curvature is good. Bubble wrap has lots of curvature. Commented Jan 9, 2019 at 8:43
• I feel like there's an analogy to be found in scale-mail vs plate-mail, but I only just woke up and my brain is still very fuzzy. Commented Jan 9, 2019 at 9:04

The shield strength scales with the protected surface area (quadratically), while the power generation scales with the available volume (third power). So capital ships should have stronger shields.

• Of course, one thing that's commonly forgotten in space sci-fi is power dissipation, which also scales with the surface area rather than volume. This means small ships are extremely vulnerable to overheating (due to low heat capacity), then you have your sweet-spot ships, and finally ships that are way too big to dissipate heat efficiently. Each has their place - e.g. the fighters might be designed for strafing, so they have short periods of high intensity shooting, punctuated with long "idle" periods; mediums have endurance; oversized again the short-lived high concentration as fighters. Commented Jan 8, 2019 at 12:31
• @Luaan That is indeed correct, so stating that the power production scales cubically isn't really correct. However I think in case of something battle-related I think this can be handwaved as saying that the "normal" power consumption" is a lot lower and peak power is only needed in battle. Then either say the shields can only be maintained X minutes/hours because of heat - and add tricks like storing heat somewhere for later dissipation. Commented Jan 8, 2019 at 15:01

## Power generation is simple. But it generates heat. Heat dissipation, is not simple.

Heat can be vented to space through heat exchanger on the surface towards space, but fighters have to have a tiny cross section from as many angles as possible. Sure, you can try to make some cylon-baseship shaped objects, but remembering that curvature also increases power usage, probably not a good idea. Heat shielding demands mass and volume. Without shielding, just ramping up the power usage would cook a pilot in a light and nimble fighter quite quickly.

So, to summarize:

1. A small fighter cannot withstand high temperatures at the HX or the cockpit will overheat
2. A small fighter has a smaller surface where it can vent heat, AND the heat loss is approximately proportional to the temperature in Kelvins (space is 3K so about 1% wrong)

thus, to manage the heat flux, a fighter cannot accept a larger shield projector.

A capital ship, of course, has many layers of heat shielding between the hot parts and the soft fleshy parts. It can tolerate many thousands of kelvins in heat reservoirs and not worry about it until next week. They also have a large-ish surface (and can probably accomodate huge HXs and appropriate subsystems and processes to manage the heat).

The potential increase of shield efficiency with "power used" by far outweighs the effects of the two other factors.

The answer is actually simple. You listed 3 criteria for shield efficiency: Power used, distance, curvature. Well, you just have to adjust the numbers. Power used would be the major scaling factor for the shield efficiency, while the shield distance and curvature are mere modifiers.

Meaning, even if you could double the efficiency of the shields (relatively) by improving on shield distance and curvature, you couldn't multiply the total efficiency by any value possible (like 1000).

Example with simple numbers:

• A fighter with 25 shield capacity, great curvature (*2) and minimal distance (*2) may have an effective shield of 100.
• A cruiser with 1000 shield capacity, moderate curvature (*1) and moderate distance (*1) may have an effective shield of 1000.
• A carrier with 20000 shield capacity, bad curvature (*0.5) and maximized distance (*0.5) may have an effective shield of 5000.

I have to admit though, it's a nice idea to compensate low shield values for smaller ships besides just speed!

• Assuming this works like wear on rolling wheels(A not terrible approximation).The curvature of the sphere relative to a penetrating force drops off by the 4th power of their ratios, meaning that to a 1cm projectile a 1m sphere and a 1000M sphere are virtually identical. Commented Jan 8, 2019 at 19:38
• The Square/Cube 100' Ant problem applies as well. 10 M ship with 1M^3 reactor needs 400 M^2 shield. A 100M ship with 1000M^3 reactor (10x bigger all directions) only needs a 40000 M^2 shield, meaning that 10x as much power is available to be put into it. Commented Jan 8, 2019 at 19:44
• @MongoTheGeek Those are the kind of numbers I'm interested in seeing - I was unsure on the actual value of curvature, and that says that it's likely a lot smaller than what I was anticipating (though still not 0). Do you have additional data on that? (Perhaps spin it off into an answer of its own?) Commented Jan 8, 2019 at 20:11

# Two and a Half Reasons

## Curvature isn't all that.

While it makes sense to think of things which are more curved as being stronger, the more curved is a relative thing and it needs to be considered against an outside impulse.

In engineering there is a concept called dimensional analysis where there is an attempt to get a pure number that doesn't have units. One of the most common values is the mach number, the ratio between aircraft speed and the speed of sound.

The attack striking the shield work to distort it before penetrating it much like pressing two ball bearings together where all other things being equal, the larger one will tend to distort more than the smaller one. The distortion and peak force is related to the sum of the reciprocals of the radii. To convert the sums of the reciprocals m^-1 into a dimensionless number we divide by the attack radius. For full math behind this approach see(https://en.wikipedia.org/wiki/Contact_mechanics)

Efficiency = Attack Size / (1/Shield Size + 1/Attack Size)

This means that a 1 cm attack striking a 1m target would be 1/[(1 + 100)*0.01] or 99% efficient.
The same attack against a 10m target would be 1/[(0.1+100)*0.01] or .999 efficient.

A 1m sized blast from a capital ship is a different matter. A 1m target would experience 1/(1+1) = 50% efficiency A 10M target would experience 1/(1+10) = 90% efficiency

## 100' Ant Problem

100' ants can't exist because of square cube problem. Some things scale proportional to the square of size, others by the cube. Material strength for instance goes up by the square of a cross section, while weight goes up by the cube. A 100' ant would have an unbreakable exoskeleton but it would weigh so much it could never move.

Sometimes this works for you. Assume power generation goes up by the cube. A 100m ship has the same plan as a 10M ship, but the reactor is 10m on a side instead of 1m. That means your small corvette has 1000 times more power to run guns, shields, applied whimsium generators as the the 10m fighter.

A 10m fighter would have a 1m^3 reactor and would need to project a shield to cover ~315m^2 of area. A 100m corvette will have to cover 31,500m^2 of area, but it would be able to do it with 1000 times more power.

## All Together

Until you start burning out cables and running into not being able to apply enough power, where you start running into heat dissipation problems bigger ships will almost always have the advantage in terms of offense and defense, and possibly speed.

Small ships will have to aggressively optimize to compete.

## Side Effects can be nasty

Your shield generator has side effects, which can easily be ameliorated by a capital ship, but are harder to compensate for on a fighter. The Square Cube Law means that while the capital ship takes a lot more power to make a much bigger shield, the side effects are also less noticeable at a big enough remove from the generators.

Maybe the generator emits radiation and requires heavy shielding in close proximity... It would be technically feasible to put a capital shield on a fighter, but your pilots would be dead a couple days later from exposure whereas the radiation from a small shield generator isn't enough to get through the regular space suit pilots wear.

Alternatively maybe the side effect is contiguous artificial gravity generation/inertial compensation. Which is generally a good thing, except when the ship gets hit. On a capital ship this is fine, and even wanted... in emergency you can push the power up a bit, and the crew can (hopefully) withstand 2-3g during combat maneuvers. However when the shield is impacted the internal gravity field is affected. This is why in the early Star Trek documentaries sometimes when the ship is hit everyone is shaken in different directions. There have been continuous improvements in spreading the inertial perturbations of a shield hit throughout the gravity field, hence in later years everyone gets shaken much more consistently. However, on a fighter the same square-cube law that causes shields to be so much more effective, also means the gravity variance on a hit is much stronger ... A shield doesn't do much good if a hit that takes it down also pulverizes the fighter pilot.

The answer could be economics.

A capital ship is much more expensive than a fighter - and so has a larger budget. It is also very embarrassing/strategically damaging when a capital ship disintegrates. So the shielding gets a big chunk of the budget. Capital ships get the very best shielding technology on the market.

Fighters on the other hand get blown up sometimes. It's a hazard of the job. Shields are important, sure, but the important thing is taking the enemy out before they take you out. A 10% reduction in shield efficacy might be worth it if it saves money which can then be spent increasing the firing rate by 12% - allowing you to take down your opponent before your shield fails. This applies to the power budget during combat as well as to the budget for components during construction.

So it may not just come down to the dynamics of power generation and size effects on shielding. The capital ships' shields may just be objectively better.

• Yes! Design and budget constraints! This should be rated higher Commented Jan 10, 2019 at 15:38
• I created an account to upvote this. Commented Jan 11, 2019 at 13:24
• Following the path of money ultimately answers all! Commented Oct 4, 2019 at 13:36

## Power requirements not linear

You've listed things that affects the power requirements for your shield, but actually that is entirely up to you. The size and shape of the shield need not be linearily scaled with power draw. In less fancy terms: Who decides a bigger shield needs more power? You.

Intuitively, it makes sense, the bigger the shield, the bigger the power requirement, and inversely. But how Cartesian of you.

You might try to explain it with unconventional maths or physics, or it might just be best left unexplained, but somehow your shield emitter actually doesn't require more power as the shield scales up, or the increase is very manageable. Because linearity is overrated.

Practically, the amount of power to create a peanut-sized shield is already enormous, like you need a couple naval nuclear power plants. Good luck attaching that to a space-F-18. Even if you could spare the space, you can't spare the mass because, as other have already pointed, mass doesn't help your speed and maneuverability in the least.

This puts a hard limit to the size a shielded ship can be (it needs to be big enough for the power plant) and also a tonnage limit (it needs to be a big boy to negate the mass increase). So there you have your perfectly reasonable explaination.

But wait! You might think that there's a problem with this at the other end of the spectrum. If the power requirements don't scale up linearly, that means you could shield a planet with a single power plant, wouldn't it? Which is where the non-linearity saves the day, again. There may very well be a point after which the size of your shield does affect dramatically the power requirement.

That doesn't seem physically possible? Think of the graph for the function $$1/x$$. If $$x>1$$, then $$1/x$$ tends towards 0. If $$x<1$$ (and keeps a positive attitude), then $$1/x$$ tends towards infinity. Think of it as $$x=1$$ being the sweet spot where a capital ship-size shield requires a capital ship's worth of power, and everything else is out of whack. Except your power draw graph would be flipped horizontally, and $$y=0$$ would actually be a lot of power already. Hopefully that was more helpful than confusing.

Simply said, this puts a hard limit to the size a shielded thing can be. If it's too big, the power requirements suddenly become ludicrously unfeasible, which also probably means woefully unsafe and prohibitively expensive.

• To extend your concept, if you decide that it takes more energy to bend the field than it does to generate a flat plane, a small fighter has to wrap its shield all the way around itself in a tiny space, while a larger ship can operate with far less curvature in a given space and the shield is more efficient for it. Commented Jan 8, 2019 at 9:49

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)

## A BIG punch

People said this earlier. A fighter sacrifices protection and, IMO, power. Like Mark Olson said in his answer, the whole point of a fighter is dealing a good punch in a quick way. Capital ships, on the other hand, have to be durable - they house smaller ships, machinery and a ton of people! If you ask me, these ships should have a generator that compares to 50 fighters in size alone. They have to capitalize (ha!) big time in the point 1 of your three statements.

A fighter's generator will use points 2 and 3 in his favour in order not to need such an enormous generator. Think of this as two people going from point A to point B. Capital has a motorcycle while Figher has a bycicle. Instead of trying to motorize the bycicle, the Fighter will just find a street with a steep slope to go faster. It might not be as fast as a motorcycle, but it will definitely be faster and less tiresome.

They also need to deal high amounts of damage. In order to create a blast capable of piercing through equally or even stronger shields, these ships need a lot of power (IMO, most of the generator's power). So they save all that energy to the blasts (that might be as powerful as those of the big guns from capital ships) while using points 2 and 3 as engineering advantages, "perks", to ensure good shields with smaller amounts of power.

## Different kinds of projectiles

Since you like games, I'd recommend you play FTL: Faster Than Light. It's an amazing game and they use this concept perfectly.

Your shields are about protecting the ship from damage - but who's to say they're effective against EVERY kind of damage?

In FTL there are a few types of weapons but we can narrow them down to, basically, two kinds: Lasers and Missiles. Shields are only effective against lasers. They deal no damage whatsoever to a ship with shields up. A missile, however, will pass straight through the shields, damaging the hull instantly if it hits - and this is why maneuverability is important in this game.

## Smaller Lifespan

Alright. The Fighter's shields are, indeed, stronger than the capital ship's. But for how long?

Keeping the shields up while powering a Figher AND dealing a big punch might be too much for a small generator. With this in mind, maybe these shields could be completely situational.

Think of the X-Wings in Star Wars. Every pilot is in company of a droid that aids him in battle. Maybe this droid is able to make decisions in real time and selectively activate the shields when needed - although the pilot can have full autonomy to bring the shields up whenever he wants.

Maybe they can only be up for small amounts of time, in order not to affect the other systems of the fighter. After each use, they have a cooldown time while the generator stores enough energy for another use.

It's also a good mechanic for your game, since all you have to do is put in a cooldown counter.

I've been mulling this question over in my mind, and why on earth wouldn't a fighter have a weaker shield? Volume increases faster than surface area, which means the capitol ship will always have more power to dump into shields per area protected than the fighter. None of the other conditions scale to overcome this. No matter how you justify a stronger shield for the fighter, you can always take that shield and muliply it by the increased volume per area protected of the capitol ship.

Solution: inject a contrivance

The only way I can think of is to impose a contrived restriction, such as: a fighter only needs one shield emitter, but the emitted shield has a maximum radius of protection.

Unfortunately, when two or more shields interract, they weaken, forcing the emitters to be closer together so that you always need more emitters-per-area-protected as the area to be protected gets larger. As the number of interacting emitters increases, the interference also increases, forcing the emitters even closer together (and thereby compounding the problem, there's a minimum distance at which adding emitters has no beneficial effect).

Since this interference increases faster than the volume-vs-surface-area increase mentioned earlier, there comes a point where even a capitol ship can't dedicate enough energy to improve the shields.

Consequently, fighter shields are always stronger than those for capitol ships.

• I believe you're reinforcing the opposite of what Spitemaster is looking for, he already believes a smaller craft is logically stronger, but wants bigger ships to be more powerful and is looking for justifications for that. I like your alternative approach though! I imagine it being sorta like how individual grains of sand are literally rock-hard, but a handful of it will be crumbly and trivially broken apart. There are no bonds between shields, even though the shields themselves are individually strong, together they are weaker than the sum of their parts. Commented Jan 8, 2019 at 10:02
• @Ruadhan, that's half my problem. His question is unclear. But, life's not always clear.
– JBH
Commented Jan 8, 2019 at 15:24

It's not the power to set it up, it's the energy bound up in sustaining it.

Shields function on a stored energy system. Every time they repel an attack, some of that energy gets used up, and must be replaced. When a shield has had all of its energy bled away, it collapses. The capital ship has structures that project a larger shield, yes, but that larger shield contains significantly more shield energy, and the generators on it recover shield energy more quickly. The fighter's shield is probably more efficient, but the Capital ship's shields can handle much larger blows, and recover from them more quickly. They're also a little more subject to specialized shield-breaker attacks, where you try to overwhelm a very small part of the shield too fast to be recovered, but if you attack it with anything short of that, the energy in that very large shield will rebalance, and you're back to having to fight your way through all of it in order to get anywhere.

Bullet Impulse vs Ship Inertia

You said your shields main purpose is to stop attacks attacks from hitting the hull of the ship and acting as a barrier rather than solely a deflector. As well I am going to assume that your shields do not negate kinetic energy but partially disperse it based on what I've read.

Lets suppose that like you said fighters have more powerful relative shields than dreadnoughts. Lets also suppose that a dreadnought can withstand multiple waves of attacks from another dreadnoughts main gun and that fighter shields are on average 10x stronger than those of dreadnoughts. This makes our fighter shields, for all intents and purposes, indestructible during a battle.

As such fighter vs fighter combat would be nearly non-existent as they wouldn't be able to touch each other with anything but the strongest of miniaturized handwavium weaponry. (If fighter vs fighter combat is a core feature ignore this answer)

Now although the shields are unbreakable that doesn't mean its impossible to damage the things inside. Lets assume that dreadnoughts weapons hit targets with a massive impulse. The increase in momentum for dreadnoughts would produce a small increase in velocity due to their large mass whereas the small mass of a fighter means the resulting increase in velocity will be quite large.

Lets image a ship is hit by a dreadnought main gun. For a large and weighty dreadnought this may only amount to some dramatic creaking and flashing lights but otherwise not really affect the people inside. What happens to a fighter is far bloodier. Even assuming the shields absorb some kinetic energy a fighter hit by a dreadnought would experience a massive increase in velocity over a short period of time producing incredible G-Force, killing the pilot instantly.

From what I understand even one-minute at 10G is fatal so a force of a few hundred G over a even a single second will almost certainly turn our would be fighter pilot to mush. Even assuming they have advanced suits and other gadgets to help withstand G-Force the impact would still simply flatten humans into a pancake.

A dreadnought main gun is costly however so we don't want to waste them on fighters. Luckily its not necessary too. As long as our bullets have a large enough impulse the G-Force produced would be enough to leave the ship intact but knock our fighter pilots unconscious or heavily injured even if they don't instantly kill them. This would allow secondary or even tertiary guns on larger ships to remove fighters from battle even if the actual ships are left mostly intact. (A great way to increase the number of fighter ships you have and a necessary recycling plan!)

In relative terms, the fighter shield is better, it's more efficient.

But the capital ship has a generator which is 10,000x more powerful so of course it's shield is going to be better.

The shields in the fighters are limited because they operate on chemically stored energy, i.e. batteries and have to use the power sparingly as it is used for all functions.

Reaction-less thrusters, beam weapons and life support/controls all need some and the shields will drain it continuously. This means they are made as small as possible to gain advantage of curvature benefits but still have to enclose craft with batteries and so a optimisation problem leaves them weaker as a result (the SWAT units have option to operate shields at 100% but only for a short time while line craft only have about 35% shielding capacity maximum.

Square cube law

Suppose all spacecraft are cubes. A spacecraft with side length L has volume of L^3 and a surface area of 6 L^2. As you mentioned, available power scales with volume, we'll call that P=xL^3. The size of the shield scales with surface, we'll call that A=6yL^2. This gives us an expression for the power available for each square foot of shield:

P/A = (6y/x)L

so a constant times the length of your ship. Bigger ship means more power per square foot.

There's an easier way to prove this though, no math required. Suppose you had a huge capital ship with wimpy shields, and fighters with strong shields. To beef up the capital ship's shields, you could simply cover it with fighters. Bolt them onto every part of the surface of your ship, and switch on their shields. Tada! You've got a heavily shielded capital ship.

Obviously that's a bad design, but it proves the possibility.

The best approach to such shielding, in my recent reading experience, is expanded in great detail in Neal Asher's "Transformation" series. Massive spoiler alert, if you want to enjoy a really good read, get his books instead of mouse-overing.

At the beginning of his 3-book series, technology is such that shields must be perfectly planar; they transfer incoming energy or matter into heat, which is stored by some shield generator until that one is overloaded. At this point, the generator is forcefully ejected from the ship as a burning lump of mass.

In other words, the energy has to go somewhere (conservation of energy).

At this stage, it makes sense for a larger ship to have more shielding, simply because the storage mechanism can be physically larger (or more of them).

Eventually, one of the players develops an advancement where - hitherto unfathomable - perfect spherical shapes become possible, which is obviously a great benefit simply due to geometrics. You don't need to simulate semi-spherical shapes by plastering your surface with individual small planar shields anymore.

...

Finally, they are further advanced to subvert the incoming mass/energy into "subspace", and from there channel it back into the generator. At this point, shields get stronger when being attacked, and are thus absolutely unattackable. Generators will not fail anymore at all, and are utterly unassailable... until something in subspace fails, at which point all the energy is released back into real space in an instant, obliterating everything in the vincinity. This capacity is by orders of magnitude larger than the earlier "generators", but it is still limited to be used as a plot twist.

At this stage, massive, huge shields become possible, spanning entire cities, but also small, incredibly strong ones covering just a human-scale object; both quite invincible.

This series is quite hard sci-fi (as in very technology-based), and this approach works very well to give a sense of advancement over the time of the story; as well as pressure on the protagonists, etc. etc.

The takeaway: whatever you do, try to think a bit out of the box. Yes, starting hard-science'y is good, but try to think what happens when you losen some restrictions (like conservation of energy/mass or the number of dimensions, or the existance of local wormholes or "pockets" in space, storing energy in "quantum foam", and so on and so forth).

Actually you raise a good point - and in naval warfare, the small powerful ship with strong armor, which might be called a battleship.

You'll note that while battleships are smaller than, say, aircraft carriers. You would want a ship large enough to carry the type of battery and armament to make it a formidable weapon and well-protected, but small enough to be maneuverable - and lo, you would have a battleship (Or, if you want to go even smaller and more maneuverable, a Cruiser or Destroyer).

Capital ships would still have the capacity for very powerful shield systems - and due to their importance, would still have them too. But so would the more specialized battleships.

And the reason for small fighter-type spacecraft in such a scenario? Well, the same reason airplanes and carriers are so useful to the navy today. Small, fast, easy to maneuver, difficult to hit crafts that can still pack significant punch, and a large ship that can carry a lot of them.

In short - it's simply a matter of size, but they could easily get a mix of both in something like a battleship or a destroyer - however, they could just as easily get the same kind of punch out of a carrier with lots of smaller craft supporting it.

• Cruisers are smaller than battleships, but bigger than destroyers. Commented Jan 8, 2019 at 19:08
• @Acccumulation Good thing I never joined the Navy - I'll correct this. Commented Jan 8, 2019 at 19:23

Another thing to consider is that shields need somewhere to dump the energy they absorb. That somewhere is the structure of the ship itself, unless and until they can radiate it outward (and the laws of physics dictate that as much will go in as out, so your shield will radiate 50% of incoming energy in towards the ship itself, and the rest out).

As a result your small ship will get HOT much more rapidly than the large one, quickly becoming unlivable, at which point no matter how effective your shields are at blocking direct damage to the ship from incoming fire, the crew and systems are simply cooked to death.

A ship might have an option to dump that heat into a heatsink which can be ejected outside the shield, but again the small ship will not have the capability to carry as many of them or as large as a large vessel, plus the ejection port will leave a relatively much larger vulnerable area in the shield (as it needs to poke through the shield when ejecting). So again, it won't last as long under fire, no matter how efficient its shields are.

In Elite Dangerous this is simulated in part, in the way that if you scoop fuel from a star with your shields up your ships internal heat goes up faster than if you do it with your shields down.

Shields in every Sci-Fi setting that I am aware of demonstrably do not in any way rely on shield generators (even though canon may say otherwise) but on shield capacitators.

You keep shooting at a starship to wear down its shields. That doesn't make any sense at all. A shield generator with a constant output doesn't work that way. It isn't getting tired!
No matter how often you hit it, unless either a hit exceeds its total "absorb" capacity or the generator encounters sudden failure, or several hits strike simultaneously, it will still maintain the shield.

That is however not what happens (well, for drama, in some novels, exceptionally, a shield generator actually does explode). What normally happens is that shields gradually lose "energy", whatever that means exactly. It is often even predictable how many hits the shield will be able to sustain further.
Also, shields are usually not up instantly (very, very few exceptions), they take a few moments to come up, and often several seconds to reach their full power. You hit your enemy before their shields are fully up. Classic.

So what shields really look like, demonstrably, is a small-ish shield generator of some more or less obscure, magical kind, and a large shield capacitator being constantly charged by the generator. Which, when sufficiently charged, obcurely and magically, via some emitter thingie, stops stuff and absorbs energy at a distance.

Capacitators or batteries (of any serious, no-joke capacity) are huge and heavy, so the amount of shield capacitator that you can fit into a fighter is limited. There's your explanation.

• I actually had that in a space shooter game I developed once. The player was able to upgrade their shield capacitor in order to improve their maximum shield points and their shield generator in order to improve the rate at which shield points were replenished. Commented Jan 10, 2019 at 11:52

One Shield is not Enough

Shields you say - no problem, we've got what you need - step right this way!

So this is your regular shield generator. It's the standard 'washing machine' size, so fits in all the standard mounting. It's got 1E of protection, so that'll take care of all the space dust and small asteroids floating about while you're flying through space.

Oh! You'd like protection against space pirates using lasers and projectile weapons, eh? No problem, we've got the double-pack for you. Again, standard sized units, but you'll need two slots available to put them in. Together 3E of protection and they'll easily repel that kind of stuff, and you'll be able to push through some pretty tough rocks and planet rings with these babies on board.

Still not enough, eh? So long as you're not running around in some sort of pea-shooter, well, how about our quad pack then? You'll need a quad slot for them to go in, but our service teams can help you out with enlarging your bays for it. These bad boys have 7E of protection and will stop pretty much everything except the Carillion Armoured Invasion, and well, if you're anywhere near that, you'll be dead already.

Oh, I see - Well, we can certainly help with your rather heavy requirements. We offer complete discretion of course, and our service teams can fit, test and maintain the system for you too. We can offer a fully bespoke solution with redundant backups, extra wide 'feelers' that can offer warning shots to anyone getting too close trying look into your windows. Everyone hates a tourist, right!? How much bay space have you got for us to work with?

I think your general approach may be wrong; I don't think you need to compensate for the fact that your smaller shields are technically stronger for unit of power you can pump into them, I think you need to consider the possibility that;

That is; what makes a capital ship a capital ship is that it can fit the smallest "Anti-matter reactor" (or whatever it is) that can be made. The big ships are big because they need to carry that large, energy spewing, piece of equipment; they can afford to pump ridiculous amounts of energy into inefficient shield arrays to make them strong; fighters and corvettes have to make due with low-power fusion/fission and batteries.

What has better armour, an aircraft carrier or a frigate?

The aircraft carrier always has the better armour because it's thicker.

The capital ship has better armour because it has the energy to produce much thicker shields than a fighter.

Sure the curvature might make a difference if the shields were the same but it doesn't compensate for shields 100 times thicker.

• Would be interested to see your numbers to back up the assertion that aircraft carriers have thicker armour than frigates, assuming you are talking contemporary real-world wet navies. Commented Jan 8, 2019 at 4:32
• I just went and looked it up, it seems that modern wet-navies pretty much abandoned the concept of armour. There is no armour that can protect them against the kinds of weaponry that are commonplace, so they don't bother. The Arleigh-Burke destroyer for example has a double-hull of roughly cm thick steel with a kevlar liner between it. Enough to withstand hand grenades and resist small-arms fire, but essentially nonexistent to any actual ship-to-ship weaponry. Commented Jan 8, 2019 at 10:10
• @Ruadhan Indeed. There's a nice post about it on the History SE site Commented Jan 8, 2019 at 16:32

Point of Impact Defence - a couple of thoughts

The shield 'bubble' is only a boundary in space and not an actual physical obstruction until it is required, more of a sensor screen. Once a point on the boundary is impacted then only that local point of the shield is activated to defend against the intrusion. A larger ship could either carry or provide power for more 'point defence' devices therefore defending against more simultaneous attacks. Each device could have a certain maximum rating for defence but several could work together providing a higher point defence value. The addition of devices is not 100% efficient so to get really strong shields require many devices and therefore power and space requirements. Larger ships can therefore afford to have many devices to give really strong point shields or defend against many smaller attacks. Smaller ships can only carry a limited number of devices and consequently have weaker shields.

Energy Usage

In place of expending energy to generate an impenetrable shield the defence shield could absorb the energy of the incoming attack. This could be easy with energy weapons not so easy with kinetic weapons to give an interesting tech race for weapon design, point to point energy weapons easy to aim at fast moving space ships over long distances but maybe less effective due to shielding verses slow kinetic weapons harder to land on target but also harder to defend against. The absorbed energy has to be stored and go somewhere. Large capital ships have plenty of volume for this storage and many systems that could be used to bleed it off again to release the storage for more capacity. Engines, weapons, life support and other systems will all require a large energy cost. A small fighter will have limited capacity for storage and energy bleed off. Hit a capital ship with a large energy weapon and the shield capacity can absorb it, a fighter doesn't have that capacity. It's up to you what happens when shield are overloaded, either they stop working or fail and release the stored energy etc.

Non-linear returns of field strength and shield capacitors.

Assuming a shield using 100 Power Units over an area of 100 area units is 90% effective, a shield using 200 power units over same area is 95% effective. 50 power units would be 85% effective and so on.

Thus higher energy consumption doesn't mean shields are that much better

Second is capacitors. Those are bulky. Now while your shield is effective at stopping stuff, if it tries stopping too much, it will fail because energy will run out. Pew pew has x amount of energy and you need a similar amount to counteract it.

Large ships have a lot of space inside. They can fit a lot of capacitors to have a much higher staying power.

Small ships are manueverable and fast to get hit with grazing hits (much less energy used to deflect than to stop) and rarely. this allows the internal reactor to recharge the shields between hits.

Large ships have lots of capacitors to stay in battle for a long time and hit the enemy hard and provide cover, support, sensors, jamming, supply and refuel for smaller craft.

Different roles, different configurations.

Who says that a tighter curve is better at stopping the weapons in question? Maybe a flatter surface works better for some reason. That would put the fighter at a disadvantage on two fronts.

But, as others have pointed out, if a fighter's shield were actually stronger than a capital ship's, then the simple solution would be to cover the outside of the capital ship in fighter shield generators, and, if necessary, arrange them in a manner which stacks two (or more) layers of those bubbles over the hull. (Think two layers of stacked marbles, with stalks going out through the gaps in the first layer to project the second layer.)

I would go with a simple power law argument.

To generate a shield, you need a shield generator. The amount of shielding the generator can generate depends on its volume. A generator that occupies twice the volume can generate twice as much shielding.

To shield something, you to need to shield all of its exposed surfaces. To shield something with twice as much surface area equally well, you need to generate twice as much shielding.

So, our shield strength is roughly how much shield we can generate divided by how much surface area we have to cover with shielding.

Now, let's consider a fighter. We'll use a cube shape for simplicity. Say its 100 wide, 30 tall, and 80 long. It has a volume of 100x30x80 or 240,000 cubic units. It has a surface area of 26,800 square units. So the shield strength of a fighter would be 240,000/26,800 or about 8. (Assuming 100% of the fighter's interior were devoted to shield generators.)

Now, let's consider a capital ship. Again, we'll use a cube shape for simplicity. Say it's 12,000 wide, 250 tall, and 5,000 long. It has a volume of 15 billion units and a surface area of about 130 million units. So the shield strength of this capital ship would be 116. (Again, assuming 100% of its interior were devoted to shield generators.)

So that gives this capital ship shields that are more than 14 times stronger. And, of course, you can't devote all of a fighter's space to shield generators while you could devote most of a capital ship's space to shield generators.

A much larger ship would almost certainly have much more powerful shields. You could argue that the shields are less efficient and that pound for pound, the light fighter has much better shields. But in a straight up fight, the big ship should win in terms of shielding. Almost without exception. (Of course the strength of science fiction is you can bullshit your way through almost anything and make it sound plausible. So go for it if you like lol.)

Were you to try to justify stronger shields for your smaller fighter, maybe you can tell yourself/your players that it is just a fact of the technology. That b/c of the nature of force fields bigger fields are naturally less stable, thus easier to penetrate... apart from explaining why a fighter might have stronger shields, it could add an interesting dimension to your game design, strategy wise.

• No; I stated in the post that I don't (didn't) believe that you're correct, and I justified my position. I don't want the fighters to have stronger shields, and I think it would be a problem in terms of game balance for them to be that way. The question was why that wouldn't be the case, and this does not address the question for that reason. Commented Jan 9, 2019 at 2:19