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

Very interesting thread... I'm more of a "mile" guy than a "km" guy, but the logic holds true through the conversion.

I just spend a few minutes going through some of my workouts and especially on my varying speed runs, the beats per miles are relatively consistent.

5 mile run

AVGHR: 147 = 1,232 bp mile
PeakHR: 171

M1 @ 122 @ 8:36 = 1,049 bp mile (warming up)
M2 @ 147 @ 8:30 = 1,249 bp mile
M3 @ 152 @ 8:26 = 1,282 bp mile
M4 @ 156 @ 8:20 = 1,299 bp mile
M5 @ 161 @ 8:03 = 1,296 bp mile

I'm kind of a numbers junkie, and I don't know that I could consume this data before a run or during a run (or after the run through any type of analysis.)

(I'm not a coach, and I don't know much about what I talk about )

Seems to me that if your goal is to improve your feel at the end of the marathon ("feel good, rested, and well prepared"), then a more simple approach would hold true.  It seems to me that you could just follow the HR alone (maintaining it within a relatively conservative range), and then run the pace that it is.

By way of example (and looking at my data for miles 3 & 5 above), if the faster pace leads to increased HR, but the resulting beats per mile is constant, then why burden your body with an additional 9 beats per minute to save 23 seconds per mile.  Or, you could ask the inverse of the same... Why wouldn't I run the faster pace if the increase in BP minute leads to a consistent beats per mile?  Seems like the answer might be that there would be 26 of them in a row within a marathon, and I couldn't maintain it..... There are too many factors.

It seems to me that a goal might be to reduce the beats per minute for a specific pace at a certain phase of a run (reduce M3's AVGHR from 152 to 145 while holding a 8:26 pace).

But, to reduce the beats per mile seems messy within the data.

Am I missing something?

Cheers,

2017 Goals:

#1: Do what I can do (200+ training days, 200+ aerobic hours).

#2: Race shape (1/2 marathon, 2 half Ironmans, marathon)

#3: Prepare for 2018

Then you can get an oval sticker that reads “<550!” and slap it on your HP12C.

Good morning, RA nation!

2017 Goals:

#1: Do what I can do (200+ training days, 200+ aerobic hours).

#2: Race shape (1/2 marathon, 2 half Ironmans, marathon)

#3: Prepare for 2018

Oh, by the way here are some formulas for doing the distance correction calculations:

Take the distance of a training run (e.g. 10 km), your measured average heart rate (e.g. 140) and your speed (e.g. 11 km/h) and put them into the following equation.

Distance corrected heart beats per km = mean heart rate * (1-0.005*distance)*60 / speed

With my numbers above that gives 140*(1-0.005*10)*60/11 which is 725 distance corrected heart beats per km. The distance correction here is 0.5% rise in mean heart rate per km covered (equal to a rise of 1% in the heart rate per km).

(make sure you stick to either miles and miles per hour or km and km per hour).

If you want to make a race prediction based on the distance corrected heart beats per km you may find the following formula useful...

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

So, using that formula with the above 725 heart beats per km gives a predicted marathon (42km) time for a 45 year old of:

Time  =725*42/((220-45)*0.92*(1-0.005*42))

which amounts to ~239 mins or ~4 hours.

And, it predicts a 5Km time of 23 mins.

This formula uses a fraction (0.92) of the predicted mean maximum heart rate (220-age). I suspect the formula is not quite ideal since the maximum mean heart rate that can be achieved will decline with distance. It is easy to put in a correction for that.

I would be interested if anyone thinks this fits with their datasets. My feeling is that these predictions only work from training runs and will only predict performance if the race course profile and characteristics broadly match those of the training environment.

Have fun!

Christof

“Now, all I need to do is get to ~550 BPKM and a sub-18 min 5K should be possible.”

Actually, all you need to do is run a sub 18 min 5k and 550 bpkm should be possible. Then you can get an oval sticker that reads “<550!” and slap it on your HP12C.

Yes, you are right that if I did a sub 18 min 5K then I should be able to run at 550 beats per km. But, I train at longer distances and use data (distance corrected beats per min) from those runs to calculate the pace to use for other races. The whole issue arose because I had no idea how fast to run my first marathon. My 5K times suggested I might be able to do it in 3:15 (using the equivalent run time calculators) - yet my longer training run seemed to suggest that 3:45 was closer to the truth. In the end I went for 3:30 pace (flat) and made it with a few seconds in hand.

The problem I have is that I don't have enough experience to know what pace I can maintain for 42km. I hate starting too fast and then fading, and there is nothing as frustrating as running negative splits because I set off too slow. So, I wondered if there might be a physiological metric that would allow me to make a better pace prediction.

I never had a HP12C - but, I was in love with my fx-81 and still use it when I get annoyed with the silly graphical calculators!

"The problem I have is that I don't have enough experience to know what pace I can maintain for 42km."

The obvious solution to that problem isn't more minitab, it's more experience. Clearly, you enjoy the exercise (the sitting down kind), so I suspect you'll keep at that as well. But, like Nobby wrote above, adherence to data can lead to suboptimal results if you don't ALSO listen to what your body is telling you. You may feel fast on race day, it may be perfect outside, you may have fast runners with you to pace, wind, sun, no sun, ad infinitium.

My 2 cents. Also, well done on not letting my snarky comment derail the thread.

`Come all you no-hopers, you jokers and roguesWe're on the road to nowhere, let's find out where it goes`
JimR

Oh, by the way here are some formulas for doing the distance correction calculations:

Take the distance of a training run (e.g. 10 km), your measured average heart rate (e.g. 140) and your speed (e.g. 11 km/h) and put them into the following equation.

Distance corrected heart beats per km = mean heart rate * (1-0.005*distance)*60 / speed

With my numbers above that gives 140*(1-0.005*10)*60/11 which is 725 distance corrected heart beats per km. The distance correction here is 0.5% rise in mean heart rate per km covered (equal to a rise of 1% in the heart rate per km).

(make sure you stick to either miles and miles per hour or km and km per hour).

If you want to make a race prediction based on the distance corrected heart beats per km you may find the following formula useful...

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

So, using that formula with the above 725 heart beats per km gives a predicted marathon (42km) time for a 45 year old of:

Time  =725*42/((220-45)*0.92*(1-0.005*42))

which amounts to ~239 mins or ~4 hours.

And, it predicts a 5Km time of 23 mins.

This formula uses a fraction (0.92) of the predicted mean maximum heart rate (220-age). I suspect the formula is not quite ideal since the maximum mean heart rate that can be achieved will decline with distance. It is easy to put in a correction for that.

I would be interested if anyone thinks this fits with their datasets. My feeling is that these predictions only work from training runs and will only predict performance if the race course profile and characteristics broadly match those of the training environment.

Have fun!

Christof

An observation: you're using part of the formula to calculate the beats per km:

----> Distance corrected heart beats per km = mean heart rate * (1-0.005*distance)*60 / speed

and reusing these values to perdict pace for a different distance:

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

I think these parts essentially negate each others which makes the beats per km rather superfluous and the formula ends up really no different than a pace calculator based on paces/distance only.  At least that's the way it appears to me without going through the exercise of factoring out like values in the formula.

"The problem I have is that I don't have enough experience to know what pace I can maintain for 42km."

The obvious solution to that problem isn't more minitab, it's more experience. Clearly, you enjoy the exercise (the sitting down kind), so I suspect you'll keep at that as well. But, like Nobby wrote above, adherence to data can lead to suboptimal results if you don't ALSO listen to what your body is telling you. You may feel fast on race day, it may be perfect outside, you may have fast runners with you to pace, wind, sun, no sun, ad infinitium.

Absolutely, more experience is definitely the solution. The playing with Excel is just something I like doing! When I started my marathon training many (?all?) of my runs felt terrible. I was getting back exhausted, with the feeling that I would never be able to make a whole marathon. If I had had a coach he would have said; "Relax, you are doing just fine! You are getting fitter, your training is working." Instead I had that little devil inside my head who kept going on about how slow I was and how the long runs were just making me slower still. So, I spent some time developing a metric that told me - no matter how bad the run felt - that I was getting more efficient. Most importantly the devil in my head found the maths too difficult and decided to shut up!

An observation: you're using part of the formula to calculate the beats per km:

----> Distance corrected heart beats per km = mean heart rate * (1-0.005*distance)*60 / speed

and reusing these values to perdict pace for a different distance:

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

I think these parts essentially negate each others which makes the beats per km rather superfluous and the formula ends up really no different than a pace calculator based on paces/distance only.  At least that's the way it appears to me without going through the exercise of factoring out like values in the formula.

Hi Jim,

I think I took too many short cuts in explaining what I have done.

On each training run I do (from a cold start and taking no breaks) I calculate (afterwards) the distance corrected heart beats per km. So, each run produces a single number that reflects my fitness level. It produces a single number from a run - no matter what the distance or pace that I can use to track my fitness. Occasionally, I also do a race (5km) to prove that I am getting fitter.

Then, I use that number (or rather the lowest recent number) in the second formula to predict a likely possible finish time.

So, the number in the first formula is the training run distance (between 5 and 32km) with mean heart rate and speed. The second formula I use to predict times and set the speed for my pre-race trials.

I think this sort of analysis will probably work for others too. Of course, if you use data from half way through a run, from runs on hilly terrain, from interval sessions then I doubt it will work very well.

Greetings,

Christof

Scout7

CPT Curmudgeon

If you want to make a race prediction based on the distance corrected heart beats per km you may find the following formula useful...

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

So, using that formula with the above 725 heart beats per km gives a predicted marathon (42km) time for a 45 year old of:

Time  =725*42/((220-45)*0.92*(1-0.005*42))

which amounts to ~239 mins or ~4 hours.

And, it predicts a 5Km time of 23 mins.

This formula uses a fraction (0.92) of the predicted mean maximum heart rate (220-age). I suspect the formula is not quite ideal since the maximum mean heart rate that can be achieved will decline with distance. It is easy to put in a correction for that.

I have an issue with the bolded part (220-Age).

Formulas for determining heart rate are appropriate for populations, but not for individuals, and especially not for determining a value that you would use for racing/training.  The reason is that there is a significant amount of variation between individuals, and the formula won't take any of that into account.

If using heart rate for training purposes, I would recommend a field test to determine Lactate Threshold, and use that bpm value rather than a generic (and generally debunked) formula.

(I have spent waaaay too much time talking to triathletes recently...)

For reference:

History of the 220-Age Equation

Setting HR Zones

JimR

Hi Jim,

I think I took too many short cuts in explaining what I have done.

On each training run I do (from a cold start and taking no breaks) I calculate (afterwards) the distance corrected heart beats per km. So, each run produces a single number that reflects my fitness level. It produces a single number from a run - no matter what the distance or pace that I can use to track my fitness. Occasionally, I also do a race (5km) to prove that I am getting fitter.

Then, I use that number (or rather the lowest recent number) in the second formula to predict a likely possible finish time.

So, the number in the first formula is the training run distance (between 5 and 32km) with mean heart rate and speed. The second formula I use to predict times and set the speed for my pre-race trials.

I think this sort of analysis will probably work for others too. Of course, if you use data from half way through a run, from runs on hilly terrain, from interval sessions then I doubt it will work very well.

Greetings,

Christof

I got that part.  I'm looking at it mathematically and it seems the beats/km are basically irrelevent in the formula and it's more of a theoretical age-graded performance calculator.

I have an issue with the bolded part (220-Age).

Yes, (220-age) is not going to be perfect - no doubt about that (and I have read the JEP paper you cite). I agree that (in general) no formula can predict with accuracy a race performance - there are too many variables. Nevertheless, if it works on average then - by definition - it may well be useful to some!

Of course you can replace 220-age with either a measured maximum or some other calculation. The main point - I think - I was trying to make is that by calculating a 'distance corrected heart beat per km' you can track changes in fitness. The accuracy of the predicted race time is something each individual will need to test and tweak. I have a theoretical 92% of maximum heart rate in the formula too - that is just what works for me. I know my daughter would tolerate something rather higher and my wife certainly wouldn't get to 85% of her maximum in a normal race.

I got that part.  I'm looking at it mathematically and it seems the beats/km are basically irrelevent in the formula and it's more of a theoretical age-graded performance calculator.

OK, I see what you are getting at. Yes, you can substitute the beat/km calculated from a training run into the prediction equation. That will give you a predicted time equation from mean heart rate and pace data over one distance extrapolated to another. Yes, that is true. The heart beats per km is just an encoding of pace and heart rate over a given distance (it cannot be more than that).

The value of calculating the heart beats per km is that it gives you a single metric from different distance/pace training runs. So, one short fast run can be plotted as a single datapoint along side a slower long run to reveal a change in fitness over time. Or, that is how it seems to me.

JimR

OK, I see what you are getting at. Yes, you can substitute the beat/km calculated from a training run into the prediction equation. That will give you a predicted time equation from mean heart rate and pace data over one distance extrapolated to another. Yes, that is true. The heart beats per km is just an encoding of pace and heart rate over a given distance (it cannot be more than that).

The value of calculating the heart beats per km is that it gives you a single metric from different distance/pace training runs. So, one short fast run can be plotted as a single datapoint along side a slower long run to reveal a change in fitness over time. Or, that is how it seems to me.

I'd say the value of the beats / km metric is diminished because it has to be adjusted for pace and distance and I'd consider such adjustments to not necessarily be globally applicable.  Great for your own custom tracking methodology but not really something that could be considered universal enough to have here as it's own entity.

As for the pace/time predictor, time to play math-head

This:

mean heart rate * (1-0.005*distance)*60 / speed

Can be rewritten as:

t*HR(1-.005d) / d

where t -is time for given distance in minutes, d is distance in km, and HR is the mean heart rate for that run...justreplace speed with distance/time and using km and minutes means dropping the no longer needed *60 min/hour adjustment

and this:

Distance/((220-Age)*0.92*(1-0.005*Distance))

is fine, just substitute D for Distance for simplicity

D / (0.92*(220-Age)*(1-0.005D))

thus

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

can be rewritten as:

Time = (D*t*HR(1-0.005d)) / (0.92*d*(220-Age)*(1-0.005D))

or:

D*t*HR(1-0.005d)

--------------------------------------

0.92*d*(220-Age)*(1-0.005D)

D-desired prediction distance

d - distance for given run

t - time for given run

HR - mean/avg HR for given run

Age is age

Most of it makes sense...increased age reduces Max HR and thus should increase the predicted time, while a reduced HR for a run for a given distance reduces the predicted time so in theory it takes into account age and fitness.  You don't need the beats/km metrics.

The results are the same as you indicated in your calcs for 5k or 42k based on 140HR, 11km/h (54.5 minute) 10k run, 45 y/o, just reformulating the equation to just use distance, time, age and HR.

Interesting formula.  I think it has merit.

Jim

Hi Christof,

Take the distance of a training run (e.g. 10 km), your measured average heart rate (e.g. 140) and your speed (e.g. 11 km/h) and put them into the following equation.

Distance corrected heart beats per km = mean heart rate * (1-0.005*distance)*60 / speed

The idea behind your equation is transparent and nice, and I would like to give few remarks. The factor 0.005 depends on aerobic conditioning, for a poor trained runner it is probably more than 0.005. And it depends perhaps on weather and course relief.  But it is not a big deal. During the training before marathon on the similar relief and temperature\humidity one can assess this factor from his long-distance runs. If not, one can make a suggestion about.

What does look for me more important is that the HRBKM  is not so simple during a long distance run. I can highlight  the following parts:

(1) Warming up for the first 3-5 km, HRBKM increases fast to an aerobic plateau.

(2) The aerobic plateau. The duration of the plateau depends on the starting HR. The closer HR to the up aerobic limit, the plateau is of less duration.

(3) Regress of the HRBKM due to fatique - this regress is described by your equation.

(4) The getting lower HRBKM if you still have forces to run faster at  the finish.

Unfortunately, I have got this knowledge about HRBKM after my first marathon. Based on my HM (half-marathon) results, 1:43, an online calculator predicted my marathon  time 3:37, but I failed. I payed no attention to the HR and starting pace. I based solely on my feeling. So the first 30 km were in 2:35, I was so happy, then 35 km - 3:05, still happy, and the last 7 km I was completely dead and invested more than 50 min, it was a disaster. Able to finish in 3:57. According to LHR gurus, my aerobic conditioning is poor, because I run 5 km in 21 min, and unable to run M in 3:30 as predicted from 5K pace. I agree with the gurus.

But I think that HRBKM is a more flexible metric than those from the MAF test. It is rigidly linked neither with MAF heart rate nor 5 miles running in the same conditions. It is easily to trace the HRBKM, if you run always on the same courses and weather at your aerobic heart rate. This is a reason why I would like to have this metric in my workouts, although it can be easily calculated manually. For instance, my  aerobic range is for HR 120-144, where my current pace changes respectively 6:30-5:24/km, but the HRBKM is approximately the same 750-800, and getting better in proper workouts.

I'd say the value of the beats / km metric is diminished because it has to be adjusted for pace and distance and I'd consider such adjustments to not necessarily be globally applicable.  Great for your own custom tracking methodology but not really something that could be considered universal enough to have here as it's own entity.

I am not so sure about this. I don't see what adjustment for pace and distance have to be made. Each training run (sub-maximal) will yield a number (distance corrected heart beats per km or mile). That number, for a given persons age will indicate their aerobic capacity in a fashion that is (at least for me) comparable with other runs over time. I suspect that it is also comparable between people - but, I haven't had the time to investigate this. If one expresses the number as a scaled for maximum heart rate (or age....) then it may allow comparison between individuals. What we need is some more data analysis!

What is important here is that we have a metric from a non-maximal, non-competitive run that *may* help inform about aerobic capacity. Whilst there are other 'equivalent performance' calculators out there, they tend to work from race times. It would be great to be able to offer a plot of heart beats per km over time, from just training runs, that shows a gradual improvement with on-going training. It would - at the very least - be motivational!

The fact that on some runs the data will produce rather high heart beats per km isn't a big problem - what one needs to focus on is the lower envelope of the dataset. The only way you will get values that are lower than would normally be possible (I think) is if you are doing the whole run down hill or with a tail wind (neither tend to occur on circular runs). Otherwise I think most of the errors are in the upwards direction. Running on hilly terrain will produce a rather high number of heart beats per km since going up hill takes far more energy than one gets back. If an upward slope costs me an addition 20W of external power output, that equates to (on a first approximation) to about 100W of metabolic energy and the associated increase in cardiac output and therefore heart rate. Running down the slope will return the 20W to me leaving an 80W deficit. A simplistic analysis, but it does highlight where the metric is bound to go wrong.

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