Assume that Handwavium is a gas many times lighter than Hydrogen. Is it realistic to use this gas to make relatively heavy full-body armor (say, brass) lighter and/or more maneuverable? This seems like a physics and momentum issue but I must admit my physics knowledge is pretty fuzzy.
Instead of superlight gas, imagine you had vacuum: no gas. Real things containing vacuum must be structurally augmented to avoid being crushed by atmospheric pressure which is why gas fill is nice. To sidestep this we will state that your light gas has the same mass as vacuum which is 0; vacuum gas.
How much would that reduce the weight of the armor? For each volume of vacuum gas in the armor you can subtract the weight of the same volume of air.
Imagine a cubic meter of vacuum gas. This would displace a cubic meter of air which weighs 1.29 kg. https://hypertextbook.com/facts/2000/RachelChu.shtml So a balloon containing a cubic meter of vacuum gas could lift up to a weight of 1.29 kg.
Here is an image demonstrating how large a cubic meter is. from http://year5rc.edublogs.org/files/2011/06/Kira-1luvv32.JPG
It would hard to make big enough pockets of vacuum gas in the armor to reduce its weight in any meaningful way.
However much lighter the gas is, to have any noticeable effects the gas pockets would still need to be huge to have any impact, which of course isn't practical for your purpose. Even if you have gas that's orders of magnitude lighter than hydrogen, it won't make much of a difference when having to stick to gas pockets that aren't overly large and thus remain maneuverability. The upwards force generated by this gas is minimal compared to the gravity working on the armor as a whole.
As an added bonus these gas pockets form weaknesses in the armor which make the entire idea even more impractical. If I personally had the choice between living, and my armor weight being reduced by a grand 500 grams or so, I'd choose living any day of the week. I think the only "realistic" way to realize light-weight but tough armor is either magic or fictitious metal akin to mithral.
Yes, this is called metal foam.
Foams are commonly made by injecting a gas or mixing a foaming agent into molten metal. Melts can be foamed by creating gas bubbles in the material. Normally, bubbles in molten metal are highly buoyant in the high-density liquid and rise quickly to the surface. This rise can be slowed by increasing the viscosity of the molten metal by adding ceramic powders or alloying elements to form stabilizing particles in the melt, or by other means
Composite metal foam (CMF) is formed from hollow beads of one metal within a solid matrix of another, such as steel within aluminium, show 5 to 6 times greater strength to density ratio and more than 7 times greater energy absorption than previous metal foams.
A less than one inch thick plate has enough resistance to turn a 7.62 x 63 mm standard-issue M2 armor piercing bullet to dust. The test plate outperformed a solid metal plate of similar thickness, while weighing far less. Other potential applications include nuclear waste (shielding X-rays, gamma rays and neutron radiation) transfer and thermal insulation for space vehicle atmospheric re-entry, with twice the resistance to fire and heat as the plain metals.
Lighter than air gases such as Hydrogen and Handwavium are lighter than air just because they have a lower density. Buoyancy states that the buoyant force is equal to the weight of the fluid displaced. This works exactly the same for gases. So because handwavium is less dense than air the same volume will have a lesser weight than the volume of air displaced.
So what does this mean? It means that the only way handwavyium can make an object apparently lighter is to increase the buoyant forces and to do this it has to increase the volume of an object while reducing its overall density. The problem is that the armour will still weigh the same overall. For ease of calculations lets assume handwavium is actually entirely massless(!). This way we know that a pocket of handwavium will increase the buoyant force by (density of air)*(volume of handwavium). The density of air is ~1.225kg/m^3. So to reduce the weight of our armour by 1 kilogram we need to increase the volume by 1 m^3. That is quite a lot of volume.
Assuming a person is a 2m tall cylinder of radius 1m (after the current heavy armour) and that we are not armouring the top or bottom. An increase of 5cm thickness will increase the volume of the armour by about 0.644m^3. That is just under 800g of eight reduction. Assuming the heavy armour is very heavy this is almost certainly pretty insignificant compared to the weight of your armour. Also you have added 5cm thickness onto everything which is a not insignificant amount for personal armour.
Alternatively you could consider armour plating. Steel has a density of ~8000kg/m^3. If we have a 10cm thick armour plate that is one metre squared then we now it will weight 800kg. Lets say we want to reduce that by 1% then we need to know what the equivalent volume of 8kg of air is. From our above density measurement we know that it is about 6.5m^3. That means our one meter squared armour plate has gone from being 0.1m thick to 6.6m thick for the loss of just 1% of its weight.
This of course is not going to help the strength of your armour. It is hard to quantify the effect it will have on its strength in the same way - it obviously won't make it stronger and we can imagine that giant gas pockets is not going to do it any favours. You are likely to either have a lot of very small air pockets though (which will likely make it less durable because it is then a series of easier to break thinner pieces of armour) or one big air pocket (in which case you'll need a lot of structural reinforcement to stop it just collapsing easily and that probably costs all the weight you've saved).
Just addressing the question of whether adding lighter-than-air would gas make your armor easier to move around in, the answer is no. It would have to be significantly bulkier to contain all of that gas, making it harder to move through the air--like wearing balloons to run faster.
Well, sort of. While the other answers are correct in saying these ultra-light gasses, or even gaseous vacuum would have a minimal effect, I felt there was something overlooked.
The pockets of gas could certainly add a slight lifting element, reducing weight marginally, barely noticeably infact. But what about the atmosphere itself? The buoyancy of the gas (and armor) would be significantly increased relative to the heaviness of the surrounding atmosphere. Take Handwavium-X, its a super dense gas; about 1/4th the density of water! Your planet's atmosphere is made of a great deal of Handwavium-X, your armor-wearing beings could even process it in a similar way to how we breath oxygen, or at the very least have it be non-consequential similar to the nitrogen and various other gasses in our system.
Combine this with Handwavium-Y (or Vacuum Gas) filling the gaps in your armor, and your armor becomes relatively light. Of course the other given concerns of extra bulk, armor weakpoints, compromised integrity, reliance on it being sealed, etc. might cause issues. Those aside, it is theoretically doable given the constraints (or lack-thereof) you provided.
No. Atomic weight of air is 29. Hydrogen has 1. So, raising effect of Hydrogen will be (29-1)/29 =28/29. Even if you have vacuum, the effect is 29/29. So, relatively you raise the effectiveness by 1/29. About 3%.
Find some gas with negative density. It will really help. But better use metal with negative density. Heavy armor in which you can fly... Or jump as on the Moon, by huge leaps. Imagine the tactics!
Maybe, but in the end it wouldn't help. Another answer already commented on using a vacuum and how little that would reduce the weight. But then consider the extra weight that would be added to produce the vacuum/maintain the seal on the armor. Keeping a seal on a system is kind of hard, especially one with joints that need to move. Your system would probably end up having more weight due to the extra equipment/sealing/whatever needed.
However, not all is lost! A quick thought: try using a system with some motors in the joints and a couple of pressure sensors. When enough force is applied against to the sensor in a limb by the human inside the armor, the motors kick in to assist with moving the limb. You could do that for all limbs.
Another option - use something like an AT-AT, but on a smaller scale. A small moving robot, with a cockpit with some bullet-proof glass, radar, etc, for the controller would protect it well. Now, of course, I'm just describing a smaller tank - soup it up a bit and you've got what you want.
Even better - if this is a sufficiently advanced society, construct some robots/drones and keep the human operators at home to control them. The U.S. is already doing something similar with some drones.
Maybe you can make this gas highly electromagnetic. Now the armor filled with this gas will be lighter around particular areas where electric charge of the surface on the planet is positive.
Have a look at bird bones. They have hollow bones. As the metalfoam answer suggests, having a lot of tiny pouches reduces weight. If you have a look at modern strut designs for stages, you can see the principle behind the bones enlarged.
I dont know your scenario but here are some ideas,
a special bird, like the emu, could have very hard bones (metal, maybe some handwavium bio compound). Warriors have to slay a bird to get to the ribcage.
special tree that incorporates a metal inside of its wood. if you burn the wood, it results in a metal object of the shape of the wooden object. The wood inside the metal pockets become gaseous.
3d printed metal objects, but to give the printer head something to support the printed mesh, small ice crystals are deposited. During the baking process, these turn to your special gas
That way, you still can have your special gas allthough it wont have that big of an impact. Perhaps, it becomes rigid if a certain pressure threshold is reached?
If your handwavium gas is a compount of gravity-negatium (say for the sake of chemistry handwavium gas is gravity-negatium pentahydride) and gravity-negatium has a nucleus that really massively is repelled by normal mass... and ignoring the fact that all the handwavium would have scooted up out of the atmosphere just as fast as it could... you could make a suit of armour that had no weight at all.
But as others have pointed out, it would still have mass. You could stand up in your brass/handwavium armour that masses 1 tonne, but the amount of power needed to get a single leg moving would be akin to towing sacks of sand. And once it was moving, it wouldn't readily stop. So if my some miracle you got your leg moving, you'd have to expend the same amount of energy to stop it when you put your foot down for the next pace. And if my some miracle you got yourself running at full charge towards the enemy, you'd be like an oil tanker with a five mile stopping distance.
Effectively, you would be about as mobile as if you were standing inside a pill-box, great for getting in the way of things but useless for fighting.
You haven't specified the "hardness" of the setting. In a hard setting , the lightest gas is vacuum and it doesn't have enough lifting power. If on the other hand this is a fantasy setting like Discworld, where materials can have negative weight(or a sci-fi setting with a Handwavium gas that experiences gravitational repulsion), then yes it would help. Your armor would be very difficult to get moving and stop moving, since the reduced grip of your feet would be totally out of proportion to the momentum of the armor.
Material strength comes from its molecular and/or microscopic structure. Metals are malleable crystals with a strong yet flexible structure that can withstand significant impact forces partially due to the structure's ability to diffuse the impact's energy mechanically, so they're well-suited for armor applications. Of course the density of this structure and the weight of the atoms themselves make the material quite heavy.
If you can replace heavier atoms/molecules with lighter ones, it will make the material lighter, but those atoms/molecules most likely won't fit into the metal's crystal lattice as nicely as the ones being replaced, or if they do they probably don't offer the same flexibility - making the structure more rigid and the material harder and/or more brittle. The structure has been compromised, so the effectiveness of the armor is reduced.
If you can make that exchange without losing the benefits of that crystalline structure, or if you can reorganize the material into an entirely new structure with similar properties, then you'll manage a lighter material without losing strength. One example of this, fresh in my mind as I just answered another unrelated question with the same example, is aerogel.
Aerogel starts as a semi-liquid gel. By "drying" it (i.e. chemically removing the liquid from it so only the solid components remain) through a meticulous process, the resulting material is usually far stronger than the original and only retains a tiny fraction of the original mass. This strength is due entirely to the structure that the solids form as the liquids are removed. In fact, it doesn't benefit or suffer much at all from whatever gas or vacuum may fill the voids within these structures.
Aerogels can be made from a variety of materials, including some metals (or rather their oxides). There are also some similar materials, e.g. made of vapor-deposited carbon nanotubes, which are sometimes incorrectly called aerogels but still provide the kind low-mass/high-strength ratio you're looking for.
Handwavium could enable this or analagous processes (probably also hand-waved to some extent) to produce similar materials suitable for armor plating.
Note that aerogels form extremely effective thermal insulation, so covering a tank in it for example would require special considerations for keeping its internals and personnel cool enough to function.