Perhaps I’m a linear thinker and this is why I focus on torque and force production:
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The self selected cadence thing always make me scratch my head. I’m a low cadence guy but still able to finish my workouts. Just did lion rock -2 averaging 63rpm and tried to hit the chad-suggested 85rpm only to see my HR spike.
if your naturally selected low cadence is low are you leaving power out there or more musclular energy? In the end it said it was a largely tempo ride with my HR tempo at 40% of the ride and power tempo was 42%, Ugg idk
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The lower left panel shows a relatively high negative relationship between rpm and crank torque. That’s why exogenous changes to cadence don’t always have a clear effect on power: if you increase cadence by 1% but crank torque drops by more than 1%, power will decrease. The lower right panel makes that clear: power is superimposed on the same data as the lower left panel so you can see that increasing cadence decreased power.
Primarily because shorter cranks allow for a more open hip angle at pedal stroke top, which, in some people more than others, seems to have a meaningful effect on muscle oxygenation and performance, in part by putting less compression on the iliac artery. Some people don’t appear to be affected much. Probably those lucky riders who don’t lose much power moving into a TT position. Yes, it can be trained to some extent.
Second, shorter cranks tend to shift freely chosen cadence higher to achieve the same pedal speed (which is a proxy for fibre contraction velocity) which suggests a shift in the metabolic efficiency curve to be higher at higher cadence. But chatting with @RChung has been useful, I’m thinking a bit differently whether/how this would provide a meaningful benefit to performance. 40% confidence.
Shorter crank length ⇒ 
cadence * 
torque = same power output
Freely chosen cadence is theoretically at minimum RPE for any given power output on the schematic below, as the optimum our brain arrives at between mechanosensory feedback from joint torque/intramuscular tensions and metabosensory feedback from metabolic costs.
FCC indicates optimum between efficiency & torques may have shifted (black dot to red dot, all exaggerated of course). What I don’t know is by how much FCC increases from from e.g. 175 to 170 cranks, vs the change in torque required to meet a given power output. The change in metabolic efficiency from crank length per se seems to be negligible, but I don’t know how to quantify the interaction with the increased FCC. 
@RChung want to check my thinking on all this?
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I suspect, but don’t know, that the main benefit of shorter cranks is that it can improve one’s aerofit rather than improving metabolic output, though I suppose that might be testable.
From the perspective of FCC, I think of the bicycle drivetrain from foot to rear wheel as being a series of levers, so a change anywhere along that sequence from changing crank length to chain rings to cogs to wheel diameter ought to have an effect on FCC – and looking at changing gear ratios is a lot easier than looking at changing the crank length.
So many years ago I tried looking at “when do cyclists change gear ratio?” They obviously change because they’re looking to optimize something but to analyze this fully, we need to know if at that moment they’re trying to optimze RPE or speed or acceleration or something else. Nonetheless, we might be able to tell from race situation what was in their mind, at least sometimes. Anyway, if we know wheel speed and wheel circumference and cadence, you can back calculate what gear they’re in. If you also know power, you can calculate crank torque, so I was looking at cadence, crank torque, and gear ratio. (BTW, a side effect of this is that since on a derailleur bike there are only a discrete number of gear ratios, when you calculate the imputed gear ratios you can figure out how reliable the reported cadence is, which gives you a way to figure out how reliable the crank torque or pedal force is. This is when I discovered that acceleromter-based cadence is less reliable than old-fashioned reed switch cadence sensors.) At the time I was doing this I didn’t have a way to measure anything other than what I got from a power meter, cadence sensor, speedometer, and HRM but nowadays I suppose you could measure resp rate and HRV and some other markers even if you don’t easily have a way to measure actual VO2 or blood lactate or a-vO2 diff or stroke volume or other clues.
Anyway, I haven’t seen much work on when and why riders change gear ratios so that could be something you might be interested in doing. Most studies look at cadence as if it were static and in equilibrium; but if it’s dependent (and I think the evidence is that it is) then looking at its dynamics might tell you something deeper about the physics, physiology, and behavior.
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If we are talking about fixed gear bikes then all the foot speed, pedal arc diameter (circles) etc…are as you write. With a geared bike IMHO it all goes out the window as we compensate with shifting.
I’ve run 165’s on all bikes now for many years from 172.5’s. Everyone talks about open hip angle (change in TDC and BDC) pedal height which is real but, for me not very noticeable in any way. The real benefit for me was the shorter crank brought the pedal under my foot more at the 3 o’clock position (and 6 I reckon but, didn’t notice that). No one seems to talk about that which I find interesting.
There’s no magic just biomechanics. Honestly I don’t really know if 165’s are better than 172.5’s for me. They feel better. I think the only way to know is to track the HR/power relationship. Too much noise for me to determine so I just go by what feels best.
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Going off that chart it would appear the lower RPM efforts were easier based on heart rate given that it doesn’t appear temperature really played a part. But I have two questions first was your RPE lower on those two efforts versus the others and how did you feel for the rest of the ride after those two efforts. I would assume that the efforts themselves felt easier but am wondering if maybe relying on muscular strength at lower rpm left you feeling more tired as the ride went on?
Post-workout Notes:
May 7, 2021 71F 264W 249W 258W 0.98 145bpm 75rpm 33.1Nm 34:37
First climb up Prefumo Canyon, a 2 mile 7.7% grade. Averaged 251W for 22:09 in 70F temps and strong winds along the ridge. Was feeling strong at this point. Really strong.
- 15 minute warmup on the 1st of 2 climbs, second climb below
May 7, 2021 64F 264W 273W 274W 1.04 149bpm 67rpm 39.2Nm 17:37
Dropped down See Canyon which I thought was about the same length as Prefumo but its shorter at 1.45 mile. At the bottom of the steep part I thought it was a 20+ minute climb for me so I turned around for an impromptu field test on the 9.8% grade.
First time actually trying a field test on an incline. Liked it. Ran out of uphill after 17:30 of hard pushing. Legs felt just fine, could have kept going and finished even stronger. Heart rate never even hit my LTHR at 160bpm (big surprise). Breathing was huffing and puffing but absolutely in control just deep breathing. At the 17:30 mark I felt ‘no problem’ on a 3 minute strong finish pushing even harder than up to that point. It was disappointing to be looking at a -7% descent when I ran out of road about 2.5 minutes before the 20 minute mark.
- 75 minute ‘warmup’ which was the climb above, and started the 2nd climb after 850kJ work
Felt fine…
Ended up doing some hike a bike at the end, because around 2 hour mark I went from road to mountain bike trail on a gravel bike. Got in over my head and walked some of the trail.
Post workout notes from two others:
Jan 22, 2022 52F 272W 276W 276W 1.01 157bpm 79rpm 33.8Nm 32:10
Ended up doing a 32 minute field test. Felt really good, could feel the breathing/HR tipping point every time I spent 10-ish seconds above 285-ish. Could have easily extended this past 32 minute, to at least 40 or 48 minutes. Based on this, and a quick look at WKO I’d eyeball my FTP at 275W.
- 38 minute warmup / 350kJ
Jan 24, 2023 52F 272W 287W 288W 1.06 158bpm 79rpm 34.8Nm 20:34
After 10-minutes of pacing a 20-30min TT something snapped and I kept going for 20+ minutes. Two brief traffic interruptions. A lot more confident now about 20-30min TT pacing. This was not all-out but pretty close.
- 82 minute ‘warmup’ / 905kJ
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How are others with low (60 - 70 cadence on say 2 hour efforts)?
Maybe low cadence works for shorter efforts in the <30 minute range?
I self select around 78 cadence for a 50 mile TT
On the trainer if I go to 60 I can put out a lot more power but for much shorter time
If I do 100+ I can crush VO2 Max TR workouts but think I am cheating the system maybe?