I was just wondering if anyone at there could help me figure out mathematically why it's advantageous to run even pace versus fluctuating pace. Does it have to do with total energy consumed. Does it cost more to accelerate than going at a constant speed. I seem to remember somewhere in my Calc class why back when something about the integral of power being energy or was it work?
Any help would be greatly appreciated thanks.
It's not really a calculus thing. Integrals are just sums.
It has more to do with your body's ability to generate speed/power. When you're going fast, it puts more than a 10% bigger strain on your body to go 10% faster.
It does cost more to accelerate than to maintain a constant speed; however, the biggest factor is that energy expenditure increases exponentially with velocity. Therefore, it costs you more energy to run fast than you save by running slowly.
One important consideration is that the faster you run, the more elastic return you get from your feet, tendons and muscles. This is why it is possible for the best distance runners to run as fast as they do, they are more economical.
This doesn't answer the OP's question though, but one poster has pointed out that his heart rate actually goes down in races when he speeds up at the end.
Here is the post. The poster, not me, shows that his heart rate is actually GOING DOWN as he accelerates at the end of races. How? it must be improved economy.
I often wear the HRM in races and record the data after the fact. I will often see somewhere close to HRmax as the highest observed reading near the end of a good 5k race. As a general rule, HR rises through most races, so I see the highest numbers in the final mile/km split.
What I hadn't looked at until recently, however, was what the numbers do in more detail during the latter stages of a race. My last two longer track races (3000 and 5000), I took splits every lap, but then I also took 200m splits for the final two laps. The results surprised me. What I saw was that in the final 200, when I was kicking as furiously as I could manage, HR actually dropped.
In both races I started to press from 800 out, and closed as best I could with ~ 66-68s final laps (this is fast for me - no need to snicker). Here are the lap splits and HR data for the last 4 laps of each race:
5000:
78.3 @ 160/160
78.4 @ 159/160
38.3 @ 160/161
37.4 @ 161/161
35.2 @ 160/158
33.7 @ 157/155
3000:
75.8 @ 154 avg/156 end
75.1 @ 156/157
36.1 @ 158/159
35.7 @ 157/157
33.9 @ 158/159
32.2 @ 155/153
I thought it was just an error during the 5000, but when the same thing happened in the 3000, it got me wondering why HR would drop during the finishing kick when you're laying everything (in relative terms) on the line.
Anyway, just some data that maybe someone can make something of.
wellnow wrote:
Here is the post. The poster, not me, shows that his heart rate is actually GOING DOWN as he accelerates at the end of races. How? it must be improved economy.
I often wear the HRM in races and record the data after the fact. I will often see somewhere close to HRmax as the highest observed reading near the end of a good 5k race. As a general rule, HR rises through most races, so I see the highest numbers in the final mile/km split.
What I hadn't looked at until recently, however, was what the numbers do in more detail during the latter stages of a race. My last two longer track races (3000 and 5000), I took splits every lap, but then I also took 200m splits for the final two laps. The results surprised me. What I saw was that in the final 200, when I was kicking as furiously as I could manage, HR actually dropped.
In both races I started to press from 800 out, and closed as best I could with ~ 66-68s final laps (this is fast for me - no need to snicker). Here are the lap splits and HR data for the last 4 laps of each race:
5000:
78.3 @ 160/160
78.4 @ 159/160
38.3 @ 160/161
37.4 @ 161/161
35.2 @ 160/158
33.7 @ 157/155
3000:
75.8 @ 154 avg/156 end
75.1 @ 156/157
36.1 @ 158/159
35.7 @ 157/157
33.9 @ 158/159
32.2 @ 155/153
I thought it was just an error during the 5000, but when the same thing happened in the 3000, it got me wondering why HR would drop during the finishing kick when you're laying everything (in relative terms) on the line.
Anyway, just some data that maybe someone can make something of.
That is really interesting. By the way, I would certainly not snicker b/c I couldn't come close to running those times anymore. I know from personal experience that when I run slowly sometimes I am very inefficient and feel much better when I pick up the pace. Good to see your data. I wonder if anyone has really studied this phenomena?
tunkcart wrote:
It does cost more to accelerate than to maintain a constant speed; however, the biggest factor is that energy expenditure increases exponentially with velocity. Therefore, it costs you more energy to run fast than you save by running slowly.
That makes sense. It would be interesting to see graphs showing how energy ependiture goes up. I wonder where I might find something like that. I may have to do some more internet hunting.
The best graphs you're going to find deal with cyclists--but the same principle would apply to runners. The graph I derived from one study I saw plotting percent of maximal speed on the x-axis and wattage on the y-axis had a line of best fit of:
y = 27.415*e^3.04x
My calc is terribly rusty, but you can play around with that graph how you wish.
Interestingly, it takes "aerobic" energy contributions about 40 seconds to max out, and then they essentially flatline, no matter the velocity. Your increase all comes from anaerobic contributions. There was also a set store of anaerobic energy that could be used, no matter the racing distance.