How many linked computers are enough?
I have a desktop computer that I bought back in January with 20 cores, Intel Core i7-14000KFat 3.40 GHz. It currently has 32GB RAM and an NVIDIA GeForce RTX 4070 SUPER graphics card with 12 GB RAM. Yesterday a render I attemped would have taken about five hours to complete, and I'm trying to figure out how much better of a system I actually need. How many machines like this would I need to network to handle this kind of render? 100? 200? 100,000? I assume I need to get up into the category of gigaflop supercomputers, but I don't think most users actually have supercomputer access. What's the level of hardware requirement?

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Before you start investing in a personal render farm, if you're rendering in Iray, the most important consideration is the GPU. Iray will only render with a GPU if the scene fits into the GPU's VRAM, so the more VRAM you have (on a single card), the larger and more complex scenes you can render. Cards with more VRAM will also have more CUDA cores, and thus will also render the same scene faster (note: CUDA cores can't be compared across generations of cards, so a 50x0 with the same number of CUDA cores as the 4070 Super will still generally render faster). First things first, download GPU-Z to measure your GPU use more accurately than task manager, render a scene with your 4070 and make sure the render is actually using the 4070 at all. If not, then the scene is too large and the GPU is not being used at all. If the scene is using your GPU to render, adding a second 4070 Super would also speed up your render quite a bit; if not, you either need to optimize the scene better, or get a GPU with more VRAM.
Actually, the 12 GB is good, but is far from "SUPER", and indeed for textures, the more VRAM the better, as Gordig pointed out.
At the same time, Gordig comment is true (different generations are not the same), but only in part, so much that NVIDA itself does compare the generations - though the comparisons in their ads often based on design theory and not reality. To check the reality, you have to check the databases like the techGPU with the performances, though even that, may not always be 100 accurate, because it depends also on the usage you make.
It is actually possible for a card of older generation to have better performances than a newer one in certain situations, some of which can apply also to the use with Daz e.g. larger memory bandwidth between VRAM and GPU in the older card (yes, it can happen), or as I observed bettter dForce simulation performances.
Anyway, a suggestion would be, unless you really want to do a huge (or even small) render farm, instead of n computers and then having to deal with the complexity and cost of that, get more graphic cards in the same computer (or a different computer that can host more than one GPU) - if there is more than on GPU in the computer, Iray with daz will use all of them, insofar as they are all compatible iwith the same graphic driver, I have three cards in my computer, and it it goes very nicely.
Also, increase the RAM in ther computer (I see you have 32GB, for many uses is a lot, for graphics, not really), and make sure in DAZ you have deselected the CPU fallback, so if the scene is really too big to fit in the VRAM, DAZ will give you an error.
About the RAM, yes I know that many people think only VRAM matters, but before and after moving stuff to the VRAM, the computer still uses RAM, so does DAZ for a number of things, and so do the OS and CUDA.
You need :
a) Be more picky about the types of hair in your scenes. The amount of glass, water, reflections, translucency, number of polygons all make for a lot of memory usage.
b) A complex scene at 4K even on an 4070 12GB Super will take a long time.
c) A 5090 with 32GB will only cut that time be 30% to 50% so still a couple of hours.
d) Try rendering a FHD or 2K instead of 4K and upscaling.
e) Set convegence at 95% instead of the defauilt 99% (which is often just generating unresolvable noise being generated by the shader materials. Set maximum iterations to 5000.