How big could a Mecha be?

Question

We've established that you can't simply scale up animals because as the creature gets bigger the square-cube law (if you double the size of your animal the weight increases eight times). This quickly becomes unsustainable and limits the size your creature can be...

However, metal (and other high tech materials) is significantly stronger than organic tissue.

Is there a similar upper limit for artifically constructed vehicles (for the sake of clarity I'm talking about walking robots or Mechas rather than ships like tankers).

Please assume a modern or near future level of materials technology and gravity at earth-normal.

Answer 1

Strength does not matter

You say...

However, metal (and other high tech materials) is significantly stronger than organic tissue.

Well that does not matter. Once we reach the max size about what is tenable for a machine, the square-cube law is just as valid. And even if metals are stronger than some/most organic materials (not all of them, nota bene) they are also more dense and — as such — heavier. When it comes to strength per unit of weight, metals rarely offers a significant advantage over organic materials. And when we throw price into the equation as well, then we quickly find that materials that has a good strength-to-weight ratio rarely comes cheap.

Also the real showstopper is not strength, but bulky energy storage and locomotion. Why are humanoid mechs — even in just the Puny Human size-category — coming into existence only now and not before? Because we have had no way of creating locomotive elements and energy storage small enough to fit these things. Such elements were all too heavy and too large, and they still are. A human can keep going for a lot longer than a humanoid mech, and our muscles are a lot leaner and compact than ditto for mechs.

We are always are at the limit of how big we can make machines, even out of metal. And looking at where we are today, we still have a long way to go before we make mechs that are as fast as cheetas; that are as tall as giraffes; that fly as good as birds(*); that have the strength, versitility and size of elephants. So organic materials are — still — well in the lead over human metal mechs.

However...

...technology marches on. And it does so at a pace that always leaves the human mind coming running after it, desperately trying to keep up, with breath in throat and flabbergasted at what technology has achieved.

What is the upper size limit for a mech? No-one knows. No-one can know. I am sorry but your question has no answer because it would require the forseeing of technology and concepts that do not exist yet. If we could say "Here is where the upper limit for future mechs will be", then we would be magic fortune tellers.

_{(*) Actually we are becoming quite good at flying. Drones have made some amazing progress the last few years. But there we use plastics and composites, not metals chiefly}

Answer 2

Is it more important that this mecha move or just be?

The largest static structures that humans build are buildings, skyscrapers specifically. These structures never need to move so the structure can be optimized to resist wind, earthquake and gravity loads. A giant mecha has to be built to deal with gravity and all the dynamic loading from moving around as well as the mission requirements. That's a really hard problem.

On the continuum between absolutely huge and absolutely tiny, there is an inverse relationship with power required to move the object. For example, the largest machine in the world, the Bagger 293 move at a stately pace of 1km/hour (I couldn't find any information on the power requirements). The somewhat smaller Crawler-Transporter used at Cape Canaveral moves at 1.6Km/hr and requires ~6KW to operate, very slowly.

Large, very high speed machines such as the Space Shuttle or Saturn V rocket are very fast but devote practically all of their weight to propulsion and fuel.

On the other end of the scale, tiny batteries can be used to move very light loads very quickly.

Power Density is the Main Problem

In my opinion, the reason we don't have soldiers in powered armor right now is the lack of sufficiently strong/long lasting power supplies. Building a self-contained power armor isn't too hard since we already have space suits, pressure suits and a host of other protective gear. The energy density of batteries just isn't high enough. Fusion doesn't work. Who would want a fission power supply strapped to theirback? Internal Combustion engines are too bulky/loud.

Conclusion

As the author, you'll have to choose your priorities: physical size, power output/speed, mission payload size. You'll have to pick some ratio of those.

Answer 3

You can only give an estimate of maximum size for a given technology. It could be that in the future part of the weight could be conveyed by electromagnetic field, similar to levitation. If this is possible it is not even the strength of material that restricts the size.

Answer 4

Bipedisum and the square cube law get you again.

Yes there are compounds that have better strength to weight ratios than bone https://en.wikipedia.org/wiki/Specific_strength

Yes robots can have higher power to weight ratios a Honda Accord for several hours outputs 124 W/kg and Olympic cyclist outputs 20 W/kg as a 5-second maximum

But the square cube law will still get you. A leg bone whether made of steel or bone has strength proportional to lxw and weight proportional to lxwxh so if you double the size of the bone you square the strength and cube the force guess which one wins out.

Being a biped is very hard. It means you have to have enough structural strength in either leg to hold your entire body, and enough force in either leg to move you whole body. The costs a great deal of added weight. Where a wheel mounted robot can get away with only having enough force to roll you weight not lift it.

It is also very easy to fall over as a biped as the DARPA completion robots discovered.