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# Heart beats per kilometer (mile) (Read 3101 times)

[snip] ....and the last 7 km I was completely dead and invested more than 50 min, it was a disaster.....[snip]

Sounds like you ran into a fuel availability issue! Have you looked at Rapoports modelling?

http://endurancecalculator.com/

His calculations don't work terribly well for me since I have a dreadful running technique - however, the general analysis and principles are good. As you work harder the proportion of energy that come from carbohydrates rises. If this proportion is too great you will be left with insufficient carbohydrates to fuel the same pace towards the end of the run.....

Have you looked at Rapoports modelling?

No, I did not know about this modelling.  What I heard was just a wording about the marathon wall, what I finally faced. Now I have an experience, and should pay attention to HR during the marathon in order to avoid it. Hope, Rapoport gives me an detailed explanation about the starting HR and pace.

Thank you, Christof !

No, I did not know about this modelling.  What I heard was just a wording about the marathon wall, what I finally faced. Now I have an experience, and should pay attention to HR during the marathon in order to avoid it. Hope, Rapoport gives me an detailed explanation about the starting HR and pace.

Thank you, Christof !

By the way, be a bit careful about using heart rate to set your pace during a race. My understanding, and personal finding, is that heart rates are elevated in race situations for a given pace. This elevation is well tolerated, so whilst you might run at ~140 bpm in a training run the same pace might give you ~150 bpm in a race. So, if you just stick to your training heart rates in a race your times will be slower than you might be expecting. My advice is to run at a pace you have worked out in advance (either by experience, calculation or desire to hit a particular time). If your heart rate goes higher than you were expecting don't necessarily worry. It could well be your normal race response - or, it could be a sign of impending doom!

For anyone with enough energy to go further with this, I have a re-arrangement of the general idea which might be better for age-independent comparisons. I have redefined the age and distance corrected heart rate per kilometer - which is a bit of a mouthful - as simply heart rate score. It is calculated from a training run using mean heart rate over the run, distance covered and average speed.

Heart rate score = mean heart rate * (1-0.005*distance)*60 / speed / (220-age)

*****I know 220-age isn't a good individual predictor, but this idea is for a general purpose metric****

So, if I (aged 45) did a training run (e.g. 10 km) with an average heart rate of 130 and an average speed of 11 km/h that would give me a heart rate score of:

Heart rate score = 130*(1-0.005*10)*60/11/(220-45)  or 3.85.

Now, I should be able to compare that directly with another persons score. The lower the score the faster I would predict you should be able to run (in an endurance type of event).

To get a rough estimate of the time it would take me to race a particular distance I could then use this equation:

Race time = heart rate score / (1/distance-0.005)

So, for 5km I should be able to do: 3.85/(1/5-0.005) or 19.74 mins (19 mins 45s) and putting in 42 km I should be able to do a marathon in: 204.7 mins or about 3 hours 25 mins.

It seems to work for me. Is there anyone else younger or older than me (and still reading) with a heart rate score of 3.85? Want to compare times?

Greetings,

Christof

You guys are all too smart for your own good, Methinks.

You guys are all too smart for your own good, Methinks.

I hope Karaul doesn't mind, but I have just analyzed a bit of his data.....(it was the first I came across with both heart rates and pace without being multisport).

The last four runs are listed below (I didn't do anymore than that....)

 Date Distance (km) Heart Rate Score 14/9 22.56 3.96 13/9 8.7 4.17 11/9 32 4.06 10/9 5 4.04

So, I would say Karaul has a heart rate score of about 4.05 on average.

Putting that into my prediction equation suggests he might be able to do a 5km in about 20:46 and a marathon in perhaps 3:37.

It so happens that he ran a 5K - race - on the 10/9 and finished in a splendid 20:44.

So, it certainly seems to me that a heart rate score analysis can allow comparison of different length and paced runs (32km run produced 4.06 and a 5km run 4.04) - and, in this case the time predicition wasn't too shabby for the 5K race. I doubt it will always work quite as well - but, is anyone convinced yet?

Greetings,

Christof

Christof,

I am proud that you used my data to validate your theory and am ready to supply to you more data. But there is something fighting  with the logic of the theory, what I could not understand so far, I am 45 too, and as I see, you used for generality my HR_max equal 220-45=175, since 220-age included into your equation. But my HR_max, if you look for instance to my two 5K races, on different courses, on June 4 (21:18,  it was very hot), and September 10 (20:44), my HR_max is 189.  Though during my regular workouts I seldom have HR more than 175, and it is normally in the workouts in the range 120-165.

Moreover, if you look to the graphs: HR as a function of distance on these two races

June  4

and Sept.10

you find that the second half of the races was at HR higher than 180.

That means that your data must be corrected with the factor 175/189, if one takes my proper HR_max. That is, my average heart rate score is 4.05*175/189=3.75. Then, I should run 5K faster than  20 min, the same as you, but I could not.

What is wrong?

Christof,

I am proud that you used my data to validate your theory and am ready to supply to you more data. But there is something fighting  with the logic of the theory, what I could not understand so far, I am 45 too, and as I see, you used for generality my HR_max equal 220-45=175, since 220-age included into your equation. But my HR_max, if you look for instance to my two 5K races, on different courses, on June 4 (21:18,  it was very hot), and September 10 (20:44), my HR_max is 189.  Though during my regular workouts I seldom have HR more than 175, and it is normally in the workouts in the range 120-165.

Moreover, if you look to the graphs: HR as a function of distance on these two races

June  4

and Sept.10

you find that the second half of the races was at HR higher than 180.

That means that your data must be corrected with the factor 175/189, if one takes my proper HR_max. That is, my average heart rate score is 4.05*175/189=3.75. Then, I should run 5K faster than  20 min, the same as you, but I could not.

What is wrong?

Good question! I think I need more data from other people before I can be sure. I have recorded my heart rate data in races - including a cross country race on Hampstead Heath in London. It was the South of England Championships with around 1,500 runners. I was at the start line chatting to one of our clubs superheros. He was predicting a top 100 finish for himself - I was just hoping to finish the race. Mid conversation the starting gun went off and in the heat of the moment I forgot that I was slow! By the time the adrenaline surge had passed I was heading, next to Mike, into a progressively narrowing path, up hill, with about 900 runners who were all faster than me behind. Elbows were flying (I am quite small) and it was very frightening. There was no room to stop and the thought of being trampled by all those spikes...the result was a heart rate of just over 180 for about 7 mins (peaking at 191). There was no other option.

So, I suspect that my constants are set for individuals who can achieve above the 220-age prediction. The 220-age correction is just there to provide an age correction.

I am a bit ambivalent about the whole idea of 'maximum heart rate'. The ability to push heart rate up to some extreme value is not necessarily linked tightly to aerobic performance. Rather, the ability to hold heart rate for prolonged periods at a high value will be more important. So, at the moment - whilst I tune the parameters - I would rather think of the 220-age as a simple age normalization. I wouldn't take it too seriously. It would be interesting to look at a functional endurance maximum heart rate - i.e. have runners try and run for 5 mins as hard as possible. That kind of value would be of more use. Perhaps there are some exercise physiologists out there who know of such data in the literature?

Or, it is because I have made a mistake in my time prediction formula ....I forgot the 0.92 scaling.....

I originally was using this equation for time prediction:

Time (in mins) = distance corrected heart beats*Distance/((220-Age)*0.92*(1-0.005*Distance))

which if you express the 'distance correct heart beats' scaled for age (what I now call Heart Rate Score) it should become:

Race time prediction = Heart Rate Score * Distance / (0.92*(1-0.005*Distance))

OR in its simplified form (dividing top and bottom by Distance) becomes:

Race time prediction = Heart Rate Score / (0.92*(1/Distance-0.005))

And, Heart Rate Score from a training run is (as before):

Heart Rate Score = mean heart rate * (1-0.005*distance)*60 / speed / (220-age)

where (220-age) is the age scaling factor....

Now, (and hopefully my maths is right) your Heart Rate Score of 4.05 (using 220-age) predicts a 5km time of 22:34 and using your estimate of max heart rate your heart rate score become 3.75 with a 5km estimate of 20:54.

I don't believe that this equation is yet the best one - or indeed that any such simple equation can predict race performance - but, it might give an indication of what might be possible if the limiting factor is aerobic performance. I really need data from more people to test it. Also, the data needs to be from flat runs, from rest with the occasional bit of flat race data . Ideally, I would like some data from an elite athlete (<16 min 5Km) and some from a casual runner with a >30 min 5km time.

For anyone who wants a spreadsheet to do a race prediction or 'heart rate score' from a training run, there is a spreadsheet here:

Christof's training-based race performance predictor v0.1

First select the units you want to use (km or miles, speed or pace). Then enter your age and, if you have it, your maximum heart rate.

Finally, take some data from a training run. You will need the distance of the run, your average measured pace and your average measure heart rate. All of that will produce some values of heart beats per km and a heart rate score. That score has been scaled to sit somewhere in the range of 1-10. If you are a 1, you are probably having a very, very rough time. If you are a 10 then, can I have your autograph?

From that single heart rate score the sheet then predicts some race performance times. You can enter your own numbers.

This sheet is based on some fun ideas (possibly this has been done before?) and has not been tested very rigorously. Let me have any comments. Whilst this is based on some sound bits of physiology, albeit simple physiology, don't take it too seriously or get cross with the results.

Have fun!

Christof

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