Don't worry, Training Zones don't need to be too complicated. Training Peaks enables you to create and measure all kinds of different training zones, but you can keep things simple if you prefer.
Training Zones are just a way of breaking up your training into a few broad intensity groups. We use a system of five different training zones. They are defined in fairly broad ranges because:
1) It's hard to maintain an exact pace, power or heart rate.
2) There is no magic heart rate or power output for success.
3) Heart rate, pace and power can fluctuate on a daily basis anyway.
Most of the sessions in your training plan are done in Zone 2 and Zone 4. Zone 2 is easy/steady and feels like an effort level that requires some focus but you should be able to chat during it.
Zone 4 is your 1 hour race pace for bike and run, which is also the hardest sustainable effort you can do before you start laboured heavy breathing.
Pick one method for measuring your intensity, like % Max HR and stick with it for now. Then once you complete and log a certain number of workouts, Training Peaks will have enough information to start suggesting changes to your thresholds.
Alternatively you can use the columns "RPE" and "Hellemens" in this table that came with your plan. These will help give you a better idea of the right feel for each zone.
One of the most successful coaches in the world, Brett Sutton, bases all his training on feel and doesn't ask his athletes to use power, pace or heart rate. The most important things for continued improvement are consistency and varied training. You don't need to get obsessed about the zones.
That said, training zones are a useful aid. If you start off with a working set of zones, Training Peaks will help you refine them over time.
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