Is there a relationship between heart-rate over time and calories burned, or is it just duration? What about a non-cardio workout?
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Both, and here's why.
The answer here is pretty obvious. The longer you workout the more calories you burn.
Of course, if you're trying to maximize the amount of calories burned you need to look at more than just the calories burned during exercise.
If you consider that exercise alone only accounts for up to 30% of overall calorie consumption then how are you supposed to achieve greater results.
The answer is simple, increase your RMR (Resting Metabolic Rate) and burn a lot of calories through exercise. Which leads me to talk about intensity.
And... don't forget about EPOC (Excess Post-Exercise Oxygen Consumption).
Last but not least, don't forget that lean muscle mass requires energy. The more you have, the more you burn.
Intensity means everything in when it comes to burning fat mass. Duration definitely also plays a big part, but only when it comes to how you fine tune your workouts to your personal ability (ex. out of shape = shorter workout duration).
I know it goes against the conventional wisdom taught by most personal trainers today (being that aerobic workouts are supposedly the best types of workouts to burn fat) but the results have been proven and backed by scientific fact.
Plus, take a look around at the typical gym. How many people do you see who are overweight or out of shape putting in their 40 minutes on the treadmill 2-3 times a week vs the few who are doing weight or resistance training?
I always thought it was insanity that there were so many people at my local gym who would be there before I arrived and leave after me who had so little to show for how much time/effort they put into exercising. Whereas, I would do my little 30-45 minutes of a high intensity sprint (2-4 miles) with some focused bodyweight and resistance/weight exercises twice a week at most and have great results to show.
Of course, higher intensity means you need to be strict about taking rest days but the best part is, recovery takes an excess amount of energy too (say hello to elevated RMR).
The better way to understand it is the load you are putting your body under. If you exercise long enough (duration) you can get to the same place as you would working harder (intensity) for a shorter period of time.
You can find that for your current ability you can find the sweet spot once you know how long you can maintain any given intensity. But it also shows that if you only have so much time available, you can increase the load by increasing the intensity.
Lower intensity (i.e. lower heart rate) burns more fat percentage wise, and higher intensity (i.e. higher heart rate) burns more sugar percentage wise. The volume of calories burned can outweigh the benefits of a low heart rate workout assuming you only have so much time.
The above is a simplification of everything, because our bodies don't linearly progress in the number of calories burned as you increase your intensity. You get to a certain threshold and the number of calories burned jumps way higher.
The higher your heart rate, the more calories you will burn. However, a person is not able to maintain a high effort/ high burn rate for as long as a lower effort /lower burn rate.
However, depending on the effort, the calories will be burned from different fuel sources. For more information on this specific topic check out the "Aerobic versus anaerobic exercise" section at http://en.wikipedia.org/wiki/Aerobic_exercise