Can any of you clever people tell me why you shouldn’t do this?
For example, if I knew that to be in contention for a podium In a flat 10 mile TT I needed to ride at 350 watts for 25 minutes. Why is it a bad idea to start off at say 5 minutes at 350 watts and slowly increase the duration at the same power over a number of months until you reach 25 minutes?
I just listened to the AACC podcast that covered this exact question! They cover it in episode #144 at 48:45. I recommend you go listen there, but if you want to hear my regurgitation of it, here you go:
The short answer appears to be that holding a very high power for a short period of time won’t provide the type of physiological adaption that will allow you to hold that power for a long time; it will just make you able to hold a very high power for a very short time.
If you want to hold a high power for a long time the best way to train that adaptation is to hold incrementally increasing levels of power for incrementally longer periods of time.
They use the example of weight training. If you want to bench press 500 pounds you don’t go into the gym and try to lift 500 pounds over and over again until you’re strong enough to move it. You start with a weight you can lift and incrementally increase it until you reach 500 pounds.
But the best bet is to just listen to them explain it…
The original question seems to be different than the example of the weight lifter.
I think he’s talking about increasing reps not so much about reaching max weight in a single rep. It’s about increasing the number of reps you can do with a particular weight.
It’s more like pushups. At first you can do 10-20 reps in a minute with little to no repeatability but after days, months, years of training at the exact same weight you can do 50 pushups in a minute over and over again. So 350 watts for 3 minutes, then 5 minutes, then 10 minutes… seems like it would work.
I’ll check out the podcast. Sounds good.
You are describing time to exhaustion. 25 min is a little above ftp so you need to raise your ftp first to a level close to your target watts.
I have often wondered the same thing. If your goal was a 20 min power of 350 watts why not hold 350 watts as long as you can… and repeat a couple times a week until you reach your goal… effectively “pulling” your 20 min power up?
The energy systems in your body don’t work in the way that makes this achievable.
Awesome, I’ll give it a listen 
For a simpleton like me it seems like it would work, I think that the push up analogy is what I was thinking.
Kenyan style 
In a recent talk on training, famed Italian coach Renato Canova asks a question, “I am a crazy coach and I have two athletes. One is African and one is European or American. I tell them your training tomorrow is running 20km in 1-hour. Averaging 3minutes per km. Both of them are unable to do (this)…What are they to do?”
With both athletes set up to fail, as they are unable to complete the workout, what do they do? In this hypothetical scenario, Canova details that the American would look at the workout and say, okay I have to get in 20km, So I’m going to run 20km at the hardest effort that he can. So he completes 20km at 3:20 per kilometer pace.
The African, on the other hand, focuses on the pace. The intensity of the effort is of paramount importance. He runs the correct (3:00 per kilometer) pace until he no longer can. Maybe he makes it 14km or 16km. It doesn’t matter. As Canova states, the African thinks “when I finish the fuel, I stop.”
What this hypothetical scenario does is illustrate the difference in mindsets between the two runners. For one, volume or distance is paramount. For the other, the intensity is what matters. And these two different mindsets shape how each group sees training.
The African is about extending the quality. If he or she can last a little bit longer at the desired quality, then it is progress. From talking with athletes who I’ve had train over in Kenya and Ethiopia, you see this quite frequently. A group of runners might jump in the workout with a world-class runner. The “no-name” athlete will try to run with the Pro for as long as he can that day.
Source: The East African vs. American Mindset to Running: Volume or Quality – Science of Running
Depending on your current fitness relative to your potential, it might work. What’s more likely is that you hit a plateau somewhere short of the goal duration.
@sryke Wish TR forums had double thumbs up! One will have to suffice.
(edit/addendum: I’m assuming the OP is referring to a power output that is not unrealistically high. For example, I’m not going to ride 450W and then just hope I eventually get 30min @ 450W out of myself. Not going to happen).
I think a large part of this isn’t ‘is it possible to train this way’ but rather ‘is it the most efficient way to get to your goal’. There are multiple physiological system at play and just attacking one at a time like that isn’t necessarily the best way to get you to your goal.