Hi, for a given level of effort is there any good data defining the dropoff in overall efficiency as cadence drops?

I ask because I recently wore out my 11-36 cassette and threw on the 11-28 the bike originally came with. I then went on my usual routes which have some pretty serious climbs, 10%-15% for sections, which require me to go pretty slow, sometimes under 4mph. (I'm 63-yo and a recreational cyclist, not a racer, so I'm not one to push myself to redline on hills - I just like getting up them without blowing a gasket.) At 3.5 mph, I was surprised that my perceived effort grinding away on a 34t front, 28t rear at 40 rpm didn't seem much different than doing the same with the 36t rear at 50 rpm. In some ways, I kinda prefer the slower cadence.

If my knees are Okay with the strain and I can pedal smoothly at these low cadences, I'm tempted just to continue using my 11-28 rather than getting a new 11-36.

- Mark