This is a tough question to categorize because it involves fitness, physics, math, physiology, and probably more disciplines. But, it's being asked in the context of Fitness so I believe this is the best place to ask.
I began viewing watts back when I did cardio exercise on indoor cardio machines. For example, I used the Cybex Arc Trainer and would average around 250 watts, with short (30 second) spikes of up to 450 watts.
I also used the Schwinn Airdyne Pro trainer before, which is essentially a bike and 2 handles attached to a large fan which exponentially increases the resistance the faster a user pedals and pushes the handles. It is often used for High Intensity Interval Training (HIIT) for this reason. On this bike, I would average around 200 watts of output, with 20-30 second spikes up to the 700-900 watt range with what I would describe as "absolute, all out exhaustion." I would have to wait 2-4 minutes after these efforts before I could try for another major effort.
After these max efforts, my watts would dip to like 115 during the recovery period between intervals.
Fast forward a while, now I am a bicylist (road and gravel) and I have some questions that have arisen from my learning about power output applied to the bicycle.
Sadly, I do not have a power meter yet, but the Strava app based on speed, grade of the terrain, heart rate (I do have a HR monitor), and a few other metrics, will estimate my power output on an all-out sprint to be 450-480 watts. My perception of effort during these sprints is equal to the high intensity intervals that I used to do on the Airdyne bike; I can only sustain them for 20-30 seconds and I am near absolute exhaustion after. I absolutely cannot pedal any harder and many times the bike's gear is in the highest position (I have a "2 by" 34-50 crankset with 10 sprockets in the rear cassette, 11-34).
So I have a few questions related to this:
In the real world, do watts on a bicycle outdoors accurately measure "level of effort?" For example, will my watt output be lower when I am up against wind resistance, rough road surface, etc...? If so, how would I measure the actual effort that my legs/body are having to output?
Why is my max effort on a bicycle seemingly generating so much less power? Is it by nature of the bike that is such that it doesn't allow a human to as easily generate higher watts compared with a machine such as the Airdyne (perhaps because there is no upper body levers involved?)?
Is it possible to be exerting less power on a given machine, but expending more calories than on another machine which I am exerting more power?
I noticed that some "calorie calculators" such as the one on WebMD, use average speed as an estimation of calories burned during a given exercise. However, I noticed that it's entirely possible for me to ride my bicycle at a slow speed, but do so up a very steep hill which shoots my heart rate up and seems to be extremely taxing on my body. Is it generally possible on a bicycle to achieve high power output and calorie expenditure at slow speeds (say 6-7mph) if up against heavy wind resistance, hills, etc...?