My oversized furnace runs 1/4th the time on probably the 95th percentile day.
My AC, maybe 50% of the time once the setpoint is reached.
And with the owner messing with the controls, it could be. . .
"Hunting is a self-exciting oscillation of a system, and is common in systems which incorporate feedback. It is an important phenomenon in many fields, including engineering, economics and biology.
en.wikipedia.org/wiki/Hunting_(engineering)"
Sounds like your furnace is at least 3-4x oversized, and your AC 1.5-2x oversized. (On design day your heating system only sees the full load for a handful of hours, but the daily average load on design-day will typically be well over half the full-load.)
Short cycling is about more than
duty cycle. There's a fixed amount of loss that occurs on every cycle, so maintaining a reasonably long minimum cycle is as important for efficiency as increased duty cycle. For a typical hot-air furnace it won't hit it's full steady state thermal-efficiency until it's been burning for at least a coupla minutes, and the first 30 seconds are about half it's full-rating. (For cast-iron boilers it's more like 6-10 minutes, due to the higher thermal mass.) On AC compressors it's a similar issue.
Minimum cycles can be stretched by the amount of hysteresis in the controls (thermostat, humidistat, other), or by adding thermal mass to the system (hard to do when air is the heat-transfer fluid.)
An ~80% AFUE- type hot air furnace running a 25% duty cycle on design day is really only hitting about 60% actual as-operated AFUE efficiency, even if it's not short-cycling (meaning all burns are at least 8-10 minutes or 4-5x the ramp rate to steady-state.) See:
http://simulationresearch.lbl.gov/dirpubs/42175.pdf
Look at figure 5 for derating your AC. If you're at 50% duty cycle on design day, you're running between 90-95% of steady-state efficiency, on THAT day, but most of the season you're much further to the left on the curve, something like the 10% of full-load zone.
For the furnace, see fFigure 6. Unless it's something special (sealed-combustion & forced draft condensing, etc.) , assume it's part-load performance is more like the SDL-C111 curve. If on design day you're at the 25% of full load mark, you're efficiency will be about 85% of full steady state thermal-efficiency rating. AFUE is typically 3-5% below steady-state efficiency assume steady state is 83-85%. 85% of 85% is 72%. But over the season most of the fuel is going to be burned during 5-15% of full-load region, so figure ~55% as-used AFUE if you have a standing pilot, ~60% if you have electronic ignition. If it's a fully sealed-combustion system (condensing or otherwise) with electronic ignition & automatic flue dampers, etc, it'll look more like the Bonn 85 Induced Draft curve, which isn't bad.
FWIW: Bonne was the guy who did the best most-accurated baseline measurements of this stuff back in the '80s while studying short-cycling issues, which is why the DOE regression analysis models try to fit his measured data. But if the equipment is actually short cycling a lot of the time you can toss those curves out the window- assume it'll be at least 10% worse, possibly much more.
Matching the equipment output to the load is the first most-important piece of designing for efficiency. The tendency in the trades over the years has been to always err to the overcapacity side to avoid the mid-winter morning call from the irate & freezing customer, but it's almost never the right thing to do. That's changing slowly, but there's still a wealth of ignorance out there- 3x oversized heating systems are almost the NORM in my neighborhood. AFUE presumes a 1.7x oversizing factor. By right-sizing it you can beat the AFUE numbers in a well designed system. But at 3x oversized and up you're slipping over an efficiency-cliff. (AFUE has many arbitrary and usually wrong assumptions- don't get me started!
)
Even if undersized slightly, most of the design-day heating hours occur while the occupants are in bed, and they never actually get cold even if the output lags the load for a few hours between 3-6AM. Similarly, if the AC is slightly undersized, even if it doesn't keep up with the full sensible-load on design day the fact that it's running at 100% duty cycle dries the air sufficiently that it's rarely a comfort issue, even if the temps run a few degrees high for an hour or three.