TBP: Well it's "out of my field" as well! I was talking COLD ground water (48F)in an OPEN LOOP (once thru);whereas your talking a HOT water CLOSED LOOP.. but your explanation makes sense: What's the difference (except time) if the tank takes 5 mos to waterlog (cold) at "reasonable" pump cycle rates... or if the pump cycles with cold water as many times (in a short time due to small volume and high drawdown) as in an entire season at lower flows?? Answer: No difference!! And the bangin' on and off agitates the water, which is favorable for air absorbtion. Right? (No?)
Due to the relatively large flow-to-tank-volume (75% run time = 10 gpm @ 45min/hr) , the analogy in the EXTREME "LIMIT" would be to have a P tank the size of an 8oz glass ( I could choose a thimble;-)) for a normal residence. Do you see my point?
I was going to see if in your eqn (still no time to look at)there is as relationship between volume and flow. IE: with a flow of 10 gpm and a desired cycle rate of say every 10 minutes, you'd need a 100 gal storage volume: 100 gallons would have to exit the tank before the CI pressure is reached. Since most residences have a 40 to 50 gal capacity (TOTAL that is!) and the draw down until CI is much less less: (~25% of 50 gal =~ 12 gals); one gets a cycle rate (at 10 gpm) of almost 1x per minute!! (1.2500?000????.. to be "exact'... no one can be exact!)
If there were a bladder that could expand way down until almost all of that 50 gal capacity were drawn... say 10 gals left at CI, then the time from CO until CI would be longer. "Ballpark" would be: 40 gals / 10gpm = 4 mins ... BUT: as the pressure decayed to CI, the 10 gpm WOULD DECAY TOO! ... due to the fixed flow resistance. Perhaps to an unacceptable level (?) depending on the load's (WSHP) requirements. To "solve" that problem, one would have to increase the CI pressure... and .. and... and ... and...
OH "My Buddaha"!!! You'd be back to short cycles... water logging (air cushion case)...... and burned contactors!!:_(
BUT:...... (Oh no!!.. here I go again!!.... DAMN!!!!!!) CONSTANT RUNNING is BETTER than short cycling( RIGHT??.. EVERYONE "KNOWS that!!!?)); so it'd be good if the pump "never caught up"! (RIGHT? ... right!!

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I guess I was kinda doing the right thing by putting in a larger tank!! Due to my concern about short cycles ......BUT!.. DANG... here I go AGAIn (Jim CAREY!); the problem COULD be solved (for more money!!:-() by using a DEDICATED pump WITHOUT a tank!! Damn!!! ... but that costs more $$$$!!
EUREKA!!! .......I got it: a pressure tank BYPASS.... so that the pump RUNS CONTINUOUSLY!!!... when the WSHP kicks in, solenoids bypass the pressure tank. That'll work.. Right???
THANKS!!!!, TBP, for making me THINK and BRAINSTORM with you...(my brain can be lazy... except when someone keeps it going for me!!)
But before I rush off to the patent office: what do you think of my ideas???
Hey if you think it'll work, just let me know and I'll let YOU "rush to the patent office" ... and go thru all the paperwork hassle!
Me?..... I'm moving on to the NEXT interesting problem... they're "fun"
I know: this is all "obvious" to all you pumping "experts". Please excuse me while I have fun "reinventing the wheel"!!

But is there a "high motion" bladder or diaphragm P tank available?? Maybe I'll check with manufaturers... NAH... no time... too "boring"!:_) Buddha's advice 2,500 yrs ago (I'm Christian!!???!!): "After deep, careful observation/analysis; and it agrees with reason, is conducive to the common good: accept it and live up to it."