66shelby, what may help you understand things better is that the engine has it's own inherent efficiencies. I'll ramble on a bit and maybe some of it may make sense.
When I asked you for the max torque and peak hp rpm, I was looking for two points of reference to include with the idle rpm. I then use the torque vector to work a theoretical efficiency curve. I know that the peak torque rpm is a little past the peak VE rpm and I know from various ECU tunes the typical VE at idle and max power for a single cam wheezer like your engine.
What we know about VE in the engine is the higher the volumetric efficiency the more power per stroke. With the turbo we know that the higher the pumping efficiency the less work is transformed into heat that reduces air density and thus reduces oxygen per volume.
In selecting the compressor we are selecting something that fits as snuggly as possible in our desirable boost range. It has nothing to do with the turbine at this stage, we just want to make sure the compressor can provide the mass air over the range with the smallest rotating mass.
In our example we could say we want the engine to pull like a train from idle up. Generally that means we want the conturs left of centre, but not left of the surge line to match up with the displacment of the engine at off idle revs. So for 2PR our 250 needs something like 8lbs/min at 1000 rpm = so you find a compressor that has the surge line sitting at 8 lbs/min where it intersects 2PR and the surge line, like the T3/45 you posted. Then you say to yourself I would like to have engine peak torque stay where it is, so you try to get the 24lbs at 2200 rpm into the peak efficiency island of the compressor like your TD48.
The problem now is that you effectively have a compressor that operates over (2200rpm - 1000rpm) x 2 = 2400 rpm , which means you don't get maximum benefit at peak power rpm of 4200 because the compressor is in choke condition; pumping relatively low density hot air that has a nasty habit of contributing to det. You could work back the other way and have the peak power rpm vectored to the choke line and the peak torque rpm vectored to the compressor peak efficiency island, but that would probably push the the low end revs into the surge region, like your TD48 where pumping tends to cease.
Now you asked how do you know where the sweet spot is, well that is highly subjective to the individual, but lets consider it's somewhere around peak torque. A simplistic way to estimate is to use some rubbery arithmetc:
So let's say your peak VE occurs at peak torque rpm and for the sake of the argument that figure is 80%, while the peak power is 60% VE. The turbocharger compressor meanwhile also has it's own efficiencies between, say 75% and 50%. Because engines operate on absolute pressures we need to work in absolutes. The 2PR means two atmospheres pressure. The efficiencies are therefore referencing two atmospheres.
If we take the peak compressor efficiency of 75% and add it to the phantom engine peak VE of 80% and average we would get (100 + 75 + 80)/2 = 127.5%. This is nothing to do with actual cylinder fill efficiency in respect to atmospheric pressure, it's just a way to make comparison.
But lets say you have chosen a compressor that sits the peak compressor efficiency island over the peak power rpm, leaving the 60% terrain sitting over the peak torque rpm. Now at peak torque rpm we have (100 +60 + 80)/2 = 120%. Because the peak efficiency island has moved over to the peak power rpm, the compressor 70% terrain is now sitting over rpms that equate to something like 75% VE, so applying the maths (100 +70 +75)/2 = 122.5%, this is higher than the 120% at engine peak VE rpm and therefore the comined compressor and engine efficiencies have moved the peak torque rpms higher. The highest result at the same PR will yeild something in the region of the peak torque rpm.
Of course you can manipulate the map by changing the turbine and it's housing, but that's another story.
)
