This is something that was just offhandedly mentioned in a Sci-Fi book I read once and as I am now writing one myself I thought I might use it.

The scenario is that I have a ship approaching a warp gate and am describing the appearance and mechanics of the gate. The idea is that warp drive research on Earth ended in a dead end because we were never able to effectively produce enough energy to power a warp field larger than the ship and generator itself.

Jump to 400 hundred years in the future and humanity has colonized a few other star systems by means of sub-light, generation ships. They then develop a functioning warp bridge, rather than a ship drive, by building massive warp field generators on each end.

The generator stations, basically warp gates for simplicity, generate the necessary energy over several days, and then expend it all in a single day or a few hours (undecided) to power the warp field.

Would massive flywheels be a valid form of energy storage? If not, what other ideas of energy storage might be more reasonable?

I would like to clarify that this is the heaviest handwavium in my entire story. Besides the completion of warp theory, functioning cryogenics, fusion drive technology, and some advances in material science, the story is supposed to be as reasonably realistic as I can get. Real physics. No artificial gravity. Space travel takes days and weeks between planets in-system. The warp gates are posted at the far edge of a solar system, allowing instantaneous travel between systems, but once exiting the gate traveling in-system is much slower again.

Yes, but...

Flywheels are being used to store energy today, only not in any great amounts, and not as means of transporting energy from one place to another.

That big circle is a flywheel, acting as a sort of energy buffer between the strokes of the single cylinder of the locomotive.

In general, storing energy as momentum is a bad idea. You cannot store a lot of it before the flywheel is spinning so fast it tears itself apart, and unless you solve friction issues, you will quickly lose it as heat.

Also you get another problem: gyroscopic forces. Conservation of moment of inertia means that means you must mount these flywheels on some kind of gimbal, or you will never be able to turn your ship.

Finally, I must point out the inherent danger of having a huge rotating object inside your ship. Unlike chemical or nuclear fuel, you cannot just dump the energy and be rid of it. Also it means that your transport medium is extremely volatile. One thing that goes wrong with this... and you are in for a very bad time.

It is possible, but maybe not the best idea

Modern flywheels can accumulate a good amount of energy Energy densities, and they are relatively safe (meaning, they won't explosively disintegrate like solid flywheels can do), but they trail other means of energy storage in terms of energy density. Flywheel's specific energy, in MJ/kg, goes to 0.5, which is on par with regular Li-ion batteries, worse than Lithium metal batteries (1.8), and way, way worse than Hydrogen fuel cells (142). Actually, Wiki's figure for hydrogen assumes Earth conditions, where oxygen is plentiful. In spaceships, oxygen storage is also required. This would make the whole system several times less efficient per unit of mass, but still much better than a flywheel.

Flywheels are good when energy comes and goes in mechanical form. If you need the energy in a different form (to power the warp field) there will be extra overhead that would further negate their advantages.

But for creating a "streampunk universe", why not, go with flywheels!

Flywheels are not ideal for your application in the 25th century.

Due to materials advances, flywheels would have a larger capacity than today, but there are 2 reasonable tech advances that would likely be much nicer.

Super-capacitors have already been proposed that have energy densities equal to fuel cells. They also have power densities that are orders of magnitudes better. It is hard to predict just how powerful these could become with an additional 400 years of advances.

Room temperature superconductors may lead to high capacity storage as well.

Both of these technologies are inherently electrical instead of mechanical, and potentially more usable for directly powering a warp field.

You specify powering a warp gate for hours or more, these technologies would be suitable for this, or for powering warp gates for minutes or even seconds.

Flywheels are rarely used as a power source for hours, they are more commonly used as a power source for minutes or seconds until a secondary power source can respond (such as a diesel generator). This is because the storage densities of flywheels is relatively low.

But spinning metal is very good at averaging power fluctuations. In fact, spinning metal in the generators themselves is a large component in power averaging the current electric grid.

If you want another solution, consider the possibility of using hafnium, specifically 178m2Hf. You need technical advances to figure out how to release the stored energy when desired, but the storage potential is huge. This adds complication in radio-activity and how to convert the gamma energy-release into something for powering your warp-generators, but this could be woven into an interesting plot-line.

The answer is almost certainly no, but here's your state of the art:

This flywheel built around superconducting magnetic bearings is about 2m wide and 4 tons. It holds 100kW-h and can output it at 300kW, which means it can dump all of its energy in somewhere around 20-30 minutes.

You mentioned that warp drive tech failed to be developed on Earth because they couldn't get the power. Well that means we can draw meaningful comparisons to Earth power plants, like Kashiwazaki-Kariwa Nuclear Power Station in Japan. That mighty force can generate 8,212,000kW of power. This means you need 27,000 of those superconducting flywheels to match her output.

One of the major limits to effectiveness of modern flywheels is tensile strength. As you store more power, you put more stress on the material. At some point, the flywheel tears itself apart. (By the way, you want to make sure these flywheels are well insulated from one another... a chain reaction of exploding flywheels is a horrible sight to see. Here's what a small one can do).

Also consider that we can generate higher power discharges. Power plants are designed for generating continous power. If you just need a discrete shock, you may want to look at the Z-pinch machines like the Z-Machine at Sandia labs

Besides looking freaking awesome in pictures, the Z-machine is capable of generating pulses as strong as 350 TW (That's 350,000,000,000 kW, if we keep the kW units we used for flywheels), and there are plans on the drawing board for a new device that can hit 1PW (1,000,000,000,000 kW).

If you need all your energy to be released in one go (is in the case of generator stations) you have significantly fewer options than normal. Any thermal method of energy generation will likely be too hot for most materials and batteries are simply too slow to release your energy. This leaves you with just capacitors, flywheels and maybe handwavium if you've got it. Though in all honesty this explanation requires the bulk your energy to be released very quickly for batteries to be non-competitive.

(in space) Flywheels are very very cheap. This is because they are incredibly simple. if you find a significantly massive asteroid (of which there will probably be millions in any given solar system) you can simply smelt it into steel (quite cheap given the awsome source of energy that is fusion) and then BAMN flywheel, much more processing would be required for a given energy of capacitor bank.) The flywheel in question would be massive though.

With good barings your flywheel will basically lose no energy to the outside would

Lets say you have a 100 MW reactor given a energy density of 32 Watt-hours per kilogram storing energy over a week then that's going to be 500000 tons of steel. That's about 70 effiel towers. This is definitely doable just make sure to have your flywheels by BIG.