# Estimate Your Heart Rate for a Given Running Power.

Oct 25, 2021

Power Tool now includes a heart rate calculator from the running power. It allows to visualize the heart rate of a power maintained during 4 minutes. 4 minutes corresponds to a prolonged effort and can be extrapolated over much longer period.

For shorter times, the heart rate for a certain power is difficult to represent. Indeed, a short acceleration creates a non-immediate variation (partly also caused by the sensor) and it depends in principle on:

• Power before acceleration
• The latency time of the organism
• The duration of the acceleration
• Of its intensity

All this complicates things…

The calculation is made from a model whose parameters are determined during the running session.

The model1 used is:

$$HR = a + b \times Power + c \times \log( Power + 1 ) + d \times Var( Power )$$

a, b, c and d are calculated in such a way as to minimize the difference with the set of measurements made during the races. Power is the power held for 4 minutes and Var (Power) is its variance.

In principle, if the pace is very regular Var (Power) can be considered as nul.

# Usage

## Setup

The first thing to do is to feed the algorithm with data. To do this, it is not necessary to follow a specific calibrarion procedure. Following a classic training plan is sufficient. We can consider that the analysis begins to give sufficiently precise results after a mix of two or three easy runs, two or three intervals and two or three fartlek. Basically after two weeks of a workout plan the computation should be reliable.

The first 10 minutes are not taken into account because during the warm-up, the heart rate is generally not very significant. The algorithm weight the newest data to ignore progressively the oldest one. This permits to stay accurate with the current fitness.

Do not forget to think about the quality of the measurements made. The wrist heart rate monitor is unreliable at due to its high latency, and in my case, it tends to produce spikes when not placed correctly. In this case, it is better to use a cardio belt to avoid erroneous measurements.
For the power, it is less critical but I still recommend to deactivate the algorithm in trail runs. During a trail run, the effort is sometime very irregular. I have the impression that in this situation the Stryd sensor is not really delivering accurate data. And also when walking, I’m not sure if the power is as precise as when running.

That said, you should not be paranoid, few measurement errors have no impact on the final result, you just have to avoid systematic and excessive errors.

## Interface

Once the running application (with the Power Tool data field) has started, a notification with link to the analysis is popup on the phone.

The dotted curve corresponds to the situation of a race where the power is maintained in a constant manner. The other curve is the one with an average power variation (here 23 watts).

In general, for a session at constant speed, we can assume power variation is close to zero. For the 30/30 interval, we can consider that the variation in power is the half of the difference between the intense phase and the recovery phase. (So for 180w recovery and 250w sprints we would have a variation of (250-180) / 2 = 35w)

Here an example of the result.

# Determination the vVO2max

The vVO2max, velocity at maximal oxygen uptake, is nothing more than the speed that can be maintained at its maximum oxygen consumption (VO2max). Generally speaking, oxygen consumption during a race is correlated with heart rate. The more you ventilate, the more the heart rate increases to bring oxygen to the muscles. Determining your vVO2max then consists in finding your speed at the maximum frequency that you can run. This is in general, the maximum heart rate. Thanks to the power/heart rate curve, it is easy to determine its maximum aerobic power, then deduce the pace on for it and convert it into a speed. This speed is precisely the vVO2max.

It turns out that I had done a Conconi test 6 months ago and I got a pace of 4:30min/km or 13.3km/h. My maximum heart rate is 179 pulses, using the calculator I find that it corresponds to a power of 231w maintained for 4 minutes. 231w corresponds to a track speed of 4:29min/km.
We see that the two results are consistent.

The advantage is that you can determine your vVO2max without having to do a Conconi or Couper test. Just follow your training plan and watch after a few sessions find the power at the maximum heart.

# Power Zones

Another possible application of heart rate knowledge for a given power is in the definition of the power zones.

Stryd defines his power zones from the critical power. The limits are only a fixed percentage of it.

Zone Range
Easy 65%-80% CP
Moderate 80%-90% CP
Threshold 90%-100% CP
Interval 100%-115% CP
Repetition >115% CP

This definition of zones is purely arbitrary and I find it difficult to to interpret. To be clear, if I run with friends and we start a long 4 km climb at 115% CP, what conclusion can I made? I will hold on without collapsing? This situation is a classic in trail running.

If now, we decide to replace the limit of this zone by the power at maximum frequency maintained for at least 4 minutes, I have an information much more relevant. I know then that if I’m over this limit, I won’t be able to maintain the pace only for for one or two minutes. And exactly at this limit, I am be able to do run approximately ten minutes.
Also, since that the critical power is the power that can be hold over one hour, we have then a second threshold which corresponds to an effort that we manage to hold at least ten minutes. I think it simplifies analysis during the effort.

We are then left with the following areas:

Zone Range
Easy 65%-80% CP
Moderate 80%-90% CP
Effort less than one hour 90%-100% CP
Effort less than ten minutes 100% CP - 100% HR
Intense effort >100% HR

1. For add ional information: Heart Rate Estimation From Running Power. ↩︎

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