I’ve thought about this for a while to try figure out why there is a difference between high vs. low inertia riding. I believe it comes down to the variation in angular velocity over the course of the pedal stroke, and how that’s different between high vs. low inertia riding.
I’d love to see the angular velocity data that maps to the torque data from the screenshots you took from Shane’s video, but since I don’t have that data, in good scientific practice, I’ll propose a theory, and hopefully somewhere I’ll be able to dig up the data to prove or disprove the theory
So here goes (warning, this ended up being pretty long):
Riding uphill (low inertia):
When riding uphill, the bike accelerates during the max power portion of the pedal stroke (~3-4pm), and decelerates during the min power portion of the pedal stroke (~noon). This acceleration/deceleration of the bike in turn means the angular velocity of the pedal stroke varies over the course of the revolution, being the slowest at noon, and fastest at ~3-4pm.
The reason the bike accelerates/decelerates (and the angular velocity subsequently varies over the course of the pedal stroke) is due to the nature of the loading on the bike - when riding uphill, the majority of the force is to overcome gravity, which does not vary with speed, hence its possible to accelerate the bike relatively easily during the power stroke of the pedal. Also the baseline speed is pretty low, so a given mph increase in speed will be a higher % increase vs. if speed is higher.
Riding on the flats (high inertia):
When riding on the flats, the bike does not accelerate much during the max power portion of the pedal stroke (~3-4pm), and does not decelerate much during the min power portion of the pedal stroke (~noon). This means the angular velocity of the pedal stroke does not vary much over the course of the revolution.
The reason the bike does not accelerate/decelerate much (and the angular velocity subsequently does not vary much over the course of the pedal stroke) is due to the nature of the loading on the bike - when riding fast on the flats, the majority of the force is to overcome aerodynamic drag, which varies with the square of the speed (power varying to the cube) - hence when riding at an already fast speed, its difficult to further accelerate the bike during the power stroke of the pedal.
Uphill vs. flats riding:
So the difference between the two is that the angular velocity of the chain ring fluctuates over the pedal stroke when riding uphill, but remains pretty constant when riding on the flats (despite the same average cadence in both situations). This means that different muscle groups are being employed for different durations over the course of the pedal stroke - in the case of riding uphill, the pedal takes a longer duration to rotate through the 12-3pm position than when riding on the flats. And a shorter duration to go through the 3-5pm position. And vice versa for riding flats vs. uphill.
Different muscle groups are used in the 12-3pm position vs. the 3-5pm position, so depending on the rider, and which muscle groups are relatively more developed, some riders will put our power better going uphill, and some riders may put out power better on the flats.
For less experience riders, they typically can put out more power going uphill, as the relatively slower rotation of the chain ring at the ~noon point in the cycle gives them more time to activate and deploy the glute muscles to get power out in in the earlier part of the pedal power stroke.
Big ring vs. small ring on the trainer.
The effect is the same here, but instead of gravity vs. aerodynamic drag causing the difference in loading, its the inertia of the flywheel. When riding in the small chain ring, the power stroke of the pedal may accelerate the flywheel by, say, 0.5mph which might be a 5% acceleration, whereas when riding in the big ring, the same power stroke will accelerate the flywheel by the same 0.5mph, but this might be only a 2% acceleration due to the faster baseline speed. This results in the same outcome vs. riding uphill/flats: In the small ring, the angular velocity of the chain ring varies over the course of the pedal stroke; In the big chain ring the angular velocity is relatively constant.
Round vs. oval chain rings
Oval chain rings by their design will have a different angular velocity over the course of the pedal stroke, even if the bike speed is fully fixed. Typically, these are placed on the bike where the angular velocity will be higher at the ~noon position, and slower at the ~3pm position. The goal with this is that it gives the rider more time activate muscles and deploy power at the ~3pm position - which is the max power point during the pedal stroke.
Compared to a round chain ring, using oval chain rings will have the effect of reducing the variation in angular velocity of the chain ring when riding uphill (or small ring on the trainer), and increasing the variation when riding on the flats (or big ring on the trainer).
This is the opposite to what happens when riding with a round chain ring - so riding an oval chain ring uphill (or in the small ring on the trainer) feels more like riding the flats on a round chain ring! i.e. low variation in angular velocity of the chain ring.
Riding the flats in an oval chain ring results in higher variation in the chain ring angular velocity - but this variation is “opposite” to that when riding uphill in a round chain ring. With oval on the flats, the chain ring is rotating faster at the noon position than the 3pm position.
Whether or not you’ll ride faster with oval vs. round is another issue - I know there’s been attempts to evaluate this, but I’ve not seen any study yet that has revealed a conclusive answer.
If anyone knows of any data to support or refute this theory, I’d be interested to see it!