Power meters are costly and we often can't afford one on every bike we own. AI Endurance calculates cycling power from activities without a power meter using heart rate, cadence and DFA alpha 1. The results are generally more accurate than speed based estimates such as Strava's estimated power. All you need is a heart rate monitor and ideally a cadence sensor on your bike and AI Endurance will estimate your power for every ride.

We need lots of bikes and we want more (N+1). A road bike for the road, an MTB for the trails, a TT bike for the triathlon races, a CX bike for cyclocross, a Gravel bike (what's the difference again) for dirt roads, a commuter bike, a winter bike, and so on and so forth - we get it!

Ideally you'd have a power meter on every bike since power is the best indicator of your fitness and training but there is a high cost involved. AI Endurance's training plans are based on power as it is the only metric that is truly predictive of cycling performance.

Setup

Our solution is to predict and calculate cycling power from heart rate, cadence and/or DFA alpha 1 (a₁). Heart rate monitors and cadence sensors are affordable and portable between bikes. All you need is the following:

• Have data with power, heart rate and ideally also cadence and a₁ in your history imported to AI Endurance. This could be from outside rides with a power meter or from indoor rides on a smart trainer. The more data the better. AI Endurance uses this data to train a machine learning model that predicts your power. So when you upload an activity that doesn't have power data, we use the model to infer your power values.
• Wear a heart rate monitor on rides without a power meter. Ideally have HRV logging enabled and have a cadence sensor installed. Cadence and a₁ significantly improve the accuracy of the predictions, see below. Some cadence sensors such as the Wahoo RPM can even be mounted on the shoe which makes them as portable as a heart rate monitor. The Polar H10 is the heart rate monitor of choice for high quality HRV data and accurate a₁ calculation.

That's it - now we'll calculate your cycling power for rides without a power meter and take them into account for your optimized training plan and our performance predictions.

To be clear, power measurements from an accurate and calibrated power meter are naturally superior over this method. Power meters exist for a reason, so if you can get measured power data on every ride that's what we recommend.

Predicting cycling power without a power meter

AI Endurance learns to predict power from your past activities that have power, heart rate and/or cadence and a₁. These include rides outdoors with a power meter or indoor rides on a smart trainer while wearing a heart rate monitor. For outdoor rides, gradient can provide an additional data input to improve the prediction accuracy. From these inputs, we train a machine learning model that predicts power from heart rate, gradient, cadence and a₁. Especially heart rate is highly individual, hence every user gets their personalized model (digital twin). Finally, the power to heart rate relationship may vary significantly over the months and years as fitness varies. Hence, time is another variable we take into account. For example, a year ago, a typical power output for 140 bpm may have been 180 W, while now being in a fitter state, the output may be 200 W.

To infer the power values in an activity without power data, we automatically use the model that has the lowest prediction error for every user. The model options are:

• heart rate + gradient (typically ~25% accuracy)
• heart rate + gradient + cadence (typically ~20% accuracy)
• heart rate + gradient + a₁ (typically ~20% accuracy)
• heart rate + gradient + cadence + a₁ (typically ~15% accuracy)

Generally speaking, the more data inputs there are, the more accurate the estimated power values. Let's discuss a few examples:

Calculate cycling power from heart rate and cadence

This is an example of predicting 20 minutes of activity time from heart rate and cadence. 'p_true' is the true, measured power from a Stages power meter. 'p_pred' is our machine learning model prediction. The prediction error is the cross validation error for time series. The model is trained on 300 hours of ride data of one individual.

Calculate cycling power from heart rate only

A different 20 minute of activity time. The power is predicted from heart rate only this time. As we can see, the predictions are much less accurate relative to the model with cadence. In particular, the model over-predicts when the true power output is zero and below 100 W.

Gradient provides similar information to cadence in the sense that it correlates strongly with zero power outputs. For example, the vast majority of steep descending at less than negative 10% gradient will happen at zero power output. Most steep uphill gradients will also correlate with relatively high power outputs.

Challenges

There are a few principal challenges that systematically bias the approach to calculate cycling power from heart rate (and gradient, cadence and a₁):

• Cardiac lag: Power is immediate while heart rate lags, i.e. there is a finite response time of the cardiovascular system. If we get out of the saddle to suddenly sprint for 3 seconds, this has no immediate effect on heart rate. Hence, instantaneous power surges are hard to predict from the input data. As a result, rides with a very 'spiky' power profile will have less accurate power estimates than e.g. time trials.
• Cardiac drift: Heart rate can be depressed or elevated, depending on recovery status, sleep, temperature, etc. a₁ can alleviate this situation as it represents a second somewhat independent marker of internal effort.
• Rides without cadence: Cadence tells us immediately when the pedalling stops, i.e. zero cadence equals zero power. This is why models including cadence data are more accurate. Heart rate does not display the same immediate response as cadence, i.e. it only slowly decreases after pedalling stops.

Strava estimated power

Strava calculates cycling power without a power meter as a rough approximation from weight, speed, and elevation change. This approach is limited due to the significant influences and variability of

• wind speed and direction
• drag coefficient (ride position, clothing, etc)
• air density (altitude, temperature, humidity)
• rolling resistance (trail vs gravel vs rough road vs smooth road, different tires/pressures)
• drivetrain efficiency (e.g. dirty chain)

on the power to speed relationship. For a more detailed discussion, see this article. Once again, power meters were invented for a reason after all.

Strava's estimated power approach is less computationally expensive as it boils down to evaluating a simple formula without having to train a personalized model for each user. Hence, the lack of accuracy is not surprising. It is worth mentioning though that Strava estimated power comes at no cost to the user.

With the power from heart rate, cadence and a₁ approach, we can bypass almost all the external influences that trouble Strava's estimated power listed above. Temperature, altitude and humidity however can influence heart rate and there are other biases such as cardiac lag and drift, as discussed above. In most real life situations, the above external influences cause significant biases in the speed based calculation and it is more accurate to calculate power without a power meter from heart rate, cadence and a₁ from a personalized model for each user.

Summary and outlook

• Our AI can now take into account your activities without power. It creates a power profile for each ride with heart rate data based on a personalized model trained on your past data with power, heart rate, gradient, cadence and a₁.
• For best results, we recommend wearing a Polar H10 heart rate monitor with HRV logging enabled and having a cadence sensor on your bike(s) without a power meter.
• If your heart rate data is highly inaccurate, e.g. from wrist based optical measurements, you can turn this feature off altogether on the Account page.
• For the future, we plan to extend this approach to detect your training loads for cross training activities such as cross country skiing, hockey, etc.
• Real-time power on your head unit. With growing hardware capabilities your model could be uploaded to your head unit to process the real time heart rate, gradient, cadence etc data to give you live power readings during your ride. Like a virtual power meter that you can use on any ride without a power meter.