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I've created a character for my world that has the ability to manipulate water with her magic. She applied this ability by using it with a katana hilt. I will try to explain how she uses this ability first before I ask the question.

  1. She wears a special plastic/rubber gauntlet that stretches from her hands/palms to her elbow. This special "gauntlet" contains some amount of water. Essentially she's wearing a water gauntlet that covers her forelimbs, from fingers to elbow with water.

  2. In the event that she has to use her katana, she draws out the hilt which always hangs on her right thigh.

  3. She takes a stance, says her magic words, then the water starts moving out from the Gauntlet through pores of the Gauntlet. The water then forms the sword/sharp part of the Katana. I'm yet to decide in what state the water would be to be able to deal physical damage. For now, I'd like to go with "frozen sharp ice". (If there any other ways water can be made sharp, I'd be glad to know)

  4. She can cut flesh, bones and wood with it. The Gauntlet is on her left arm and it's the only one that provides water.

My question is, how much water would be needed to forge such a sword?

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Instead of ice, you could make it a "sword" that uses a jet of extremely high-pressure water to make the cut. From Wikipedia:

In the nozzle, the water is focused into a thin beam by a jewel orifice. This beam of water is ejected from the nozzle, cutting through the material by spraying it with the jet of speed on the order of Mach 3, around 2,500 ft/s (760 m/s).

Waterjets use between one half and five gallons (2 to 19 liters) of water per minute when cutting. If you're only making a single cut (about a few seconds of operation), then the water requirements become much smaller. Depending on the magic system, you could continually pull in water from the atmosphere or have a portable tank of water available.

Industrial water jet cutters are used regularly to cut steel into precise shapes without destroying the integrity of the structure (since there's a lot less heat going into the metal). There's often an abrasive mixed in the water for extra cutting potential.

This would require some special construction, especially when it comes to the nozzle. Granted, you could handwave that with the fantasy setting. You could make the "hilt" portion the nozzle that the character holds to channel the water through.

While this doesn't really resemble a "sword", it can still cut like one. Bonus: it has multiple uses, not only as a sword, but a way to cut/puncture doors, locks, and small spaces.

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    $\begingroup$ Depending on the amount of magical control, it could essentially be a water chainsaw, where the water sprays out on the cutting edge, and then loops back toward the handle on the back edge, continuously recycling, and removes the need for pulling it out of the atmosphere or something. Also, possible that you could have a percentage of the water become ice crystals to give it a little extra abrasiveness. $\endgroup$ – AndyD273 May 31 '19 at 16:40
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    $\begingroup$ @AndyD273 - Ice crystals would form around the "contaminants" that make up the abrasives added to water for a waterjet cutter that make it more effective, so I suspect this would be the opposite of helpful. $\endgroup$ – William May 31 '19 at 20:44
  • $\begingroup$ It would have to be wielded one-handed together with a shield though, because while it can cut steel, it can't cut it fast enough to stop the opponents (mundane) blade (in contrast to katana, which is wielded two-handed). $\endgroup$ – Jan Hudec Jun 1 '19 at 9:05
  • $\begingroup$ Water jets used for cutting have an extremely short range. Most of these cutters are placed practically on top of the material as the water will quickly lose cohesion and velocity. The structure is also important, something that gives way is more resiliant than something as solid as steel, meaning that flesh would warp and move but wouldnt immediately be cut (depending on the force). So you'd need the water to be continuously accelerated and kept in place around the sword's edge. Also most steel cutting this way takes time, the nozzle moves slowly to properly cut through. $\endgroup$ – Demigan Jun 3 '19 at 11:24
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Something that might help you is that there are at least 17 forms of ice, depending on pressure and temperature where it is formed.

enter image description here

So you may be able to use some of the properties of these exotic types of ice to do what you want. For instance, ice that forms at super high pressure is much more dense, and ice that is colder is much harder.

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    $\begingroup$ As far as I can see here (www1.lsbu.ac.uk/water/ice_phases.html), the densities of various forms of ice are still significantly less then those of steel. The only exception is 'metallic ice', but as far as I see, it's a theoretic form and hadn't been laboratory tested. Am I right? $\endgroup$ – Cumehtar May 31 '19 at 14:50
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    $\begingroup$ @Cumehtar It wouldn't have the density of steel, but that affects weight more than anything else. I did find one source that said that at ultra low temperatures ice can get very hard, with a MOHs hardness rivaling steel/granite. It would still be more brittle, where steel can be flexible, but at those temperatures a steel blade (and everything else) would be very brittle too, so depending on how the magic works it could ultra cool what it's being swung at before cutting/shattering it. $\endgroup$ – AndyD273 May 31 '19 at 16:49
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    $\begingroup$ Yeah (+1), but it's a question of how much; aka: volume. And water (being basically incompressible, and using the type of ice that we're all familiar with) when frozen increases in volume by about 11%. So, @OP : 11% less than the volume of water that would fill a mold for the sword. My question for you, Andy, is what that '11%' is for all 17 forms of ice. $\endgroup$ – Mazura Jun 1 '19 at 1:13
  • $\begingroup$ @Mazura I'm not an exotic ice expert, but according to the entry on ice phases, ices beyond ice-III are denser than water, meaning that you'd need more water, not less. I'm not sure how much for most of them, but ice-XII is "approximately 1.3 times more dense than water". This is still some crazy pressure/temperature control magic. $\endgroup$ – AndyD273 Jun 3 '19 at 14:12
  • $\begingroup$ Actually, according to the link posted by @Cumehtar, ice-X appears to be the densest (other than metallic ice), at 2.51 times denser than water. Interesting stuff. $\endgroup$ – AndyD273 Jun 3 '19 at 14:19
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That depends on the size of the sword. If your intention is simply to create a water replica of a katana, you would simply need the volume of the katana as the amount of water. Assuming the blade is about 1,50m long, about 3 cm wide and on average 0.5 cm thick, you would need 15*0.3*0.05 = 0.225l of water.

E: Also, a katana isn't really the best weapon from for cutting solid things like bones and wood. Katanas are only viable because of their layered crafting. But with magic involved, one could argue that the ice is strengthened and sharpened by the magic, making the form irrelevant.

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    $\begingroup$ 1.5 meters is too long for a katana ) A normal katana blade is significantly below 1 meter in length. 60-70 cm is much more usual. $\endgroup$ – Cumehtar May 31 '19 at 12:10
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That's a tricky question, because a lot of problems can be circumvented by saying 'because magic'.

First problem is that ice is much more brittle then steel, so a cutting sword made of ice with be shattered easily. But it seems that our protagonist can prevent it by magic.

Second problem is the density. The average density of steel is around 8 gram/cm3. The density of ice is 0.9 gram/cm3, which is almost 10 times lighter. So if you go just by replicating the shape of a katana blade in ice, it will weigh around 90-110 grams (katana blade without hilt and fittings is supposed to weight from 800 to 1000 grams, as far as I remember).

Using katana hilt with the blade as light as 100 grams will be a problem of its own, if you want to use it as a sword, especially against other people with swords. A weapon that light will have problems cutting because of the lack of the mass in the blade, it's easy to block or batter aside with a heavier weapon. Generally, cutting swords rarely went down below 600 grams in overall weight, and specialized cutting swords (ones able to do damage to bones and wood) very rarely weighed less then 800 grams (Here is some data on the weights of different variants of British 1796 light cavalry sabers, one of the lightest effective cutters I know of). But calculating the weight of a cutting sword mathematically is a very tricky proposition - it's more of an engineering task, not purely mathematical. A lot of nuance lays in the physical properties of materials, their flexibility and strength. If we assume a material with infinite tensile strength, infinite sharpness and infinite slickness (zero friction), then we may go lighter then 600 grams for a sword.

As far as I see, your character can circumvent the problem in two ways, both of which will be decidedly magical. First, we can assume she can also vary the density of ice at will - then your ice blade would weight just as much as a steel one, and for all effects and purposes it will behave as a metal weapon, as far as handling and balance is concerned. So upwards from 800 grams if it's a katana blade, less (around 600-700) if it's a thinner and broader one, like tulwar or 1796.

Second variant is treating 'water' as an advanced nanomaterial. Here, again, we don't care that it's water before magic starts acting on it. In effect, what you want is a mono-molecular blade - one molecule in thickness, but of the length and breadth of a sword blade. The amount of water for this task will be trivial, less then 10 grams, I think.

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  • $\begingroup$ Thanks for your answer. I appreciate it. I have one major question though. If the sword is made as you proposed in the final line, will it be able to parry other sword attacks? I thought about it and came up with an idea but I don't think it works very well. I assumed this character will be capable of a sort of "parry-less" sword style. In this style she can attack faster and turn her sword back to water right before it makes contact with the opponent's sword. So basically, her katana goes through the opponent's sword, "hardens" again and slashes his head off. $\endgroup$ – Nass King May 31 '19 at 11:36
  • $\begingroup$ @NassKing I do not think you will be able to parry effectively with a sword that light. As for fighting without blade contact - yes, it's possible, but it's hard. You need to be a very good judge of distance and have very good footwork. Having extremely light blade with help, but she will have problems, especially if pressed into corner without much room to maneuver. Rapidly shortening distance into grappling will also work good against her, since in the close distance the opponent will be able to just grab her wrist, effectively preventing her from cutting. $\endgroup$ – Cumehtar May 31 '19 at 11:46
  • $\begingroup$ Makes sense. Thanks $\endgroup$ – Nass King May 31 '19 at 13:07
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    $\begingroup$ If it's a mono-molecular blade, would it be able to just cut through the opponent's weapon? $\endgroup$ – Admiral Jota May 31 '19 at 17:15
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Not quite a katana

You need about half a liter or less of water, so it comfortably fits an arm bracer. What you need next is energy.

Water by itself cuts very little, and ice is too weak and brittle to form a blade (you can still stab with it though).

Your water-mage must follow a different approach: the "katana" is actually two laminar sheets of water and ice crystals, one twentieth of a millimeter thick, held together by a pressure in excess of 600 MPa, and flowing one into the other at three times the speed of sound. Under these conditions, ordinary water will cut through hardened steel, though slowly. You do not have a katana, but a water chainsaw plus drill.

Used to stab, this katana will go through a 1mm thick steel armour plate in about two seconds, and the body behind in not much more.

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A monomolecular blade

This would use a tiny amount of water and be sharp enough to cut through most substances.

Have your magic user put her energy into aligning and strengthening the intermolecular bonds. Water molecules are chevron shaped. Align them head to tail.

An individual molecule is ~2.75 angstrom, 10 -10 m. Allow ~30% overlap. So 2 A per molecule.

You need 5 billion molecules, 5 x 109 for a 1 m blade. 1 molecule weighs 18.02 amu.

1 amu = 1.661 x 10-27 kg.

5 x109 x 1.661x10 -27 x 18.02 = 150x10-18 kg.

0.15 femtograms!

It will be completely invisible.

Magic user draws what looks like a sword handle from her belt and adopts a stance. Bad guys fall about laughing. She swings a cut. Nearest bad guy slides in two invisibly sliced from shoulder to hip. Bad guys stop laughing.

There could also be an element where she can vary the length. A very scary weapon.

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  • $\begingroup$ A very stiff molecular whip! $\endgroup$ – Muuski Jun 3 '19 at 20:24
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You could also consider adding impurities to the water (there is some precedent for this in fantasy stories, see Avatar: The Last Airbender where certain water benders are capable of "bending" blood due to its high water content, and metal benders are earth benders who can manipulate metal by the "impurities" in it).

As a practical example, there is a real world material known as pykrete (a mixture of water ice and sawdust) which has properties similar to concrete. 

Mechanical properties   | Ice   | Concrete | Pykrete
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Crushing strength [MPa] | 3.447 | 17.240   | 7.584
Tensile strength [MPa]  | 1.103 | 1.724    | 4.826
Density [kg/m³]         | 910   | 2500     | 980

There are also variants which use hemp or newspaper to increase the tensile strength. Its not a stretch to envision that this user might have some specific recipe which creates a stronger pysteel composite for instance (the alchemy of their specific water mixture could also be a source of on going experimentation or the gauntlet might have different compartments of suspensions which can be swapped out to provide different physical properties of the final sword).

Returning to the actual question assuming the user is creating a standard size katana you would effectively just need to use the formula

Volume(blade) = Volume(water) * .91

where we assume the standard expansion of 9% volume increase during freezing (I'm not a materials expert so I'm not sure if the expansion of pure water during freezing would be identical to that of an impure mixture but I assume relative parity here).

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