## Monday, February 27, 2017

### Actionable Intelligence for Running Part 5 : Mapping Treadmill Power Against Speed, Weight and Incline

In part 4 of this series, I made baby steps with a commercially available footpod called Stryd and ran with it in in what is billed the 'fastest half marathon in the world'. I measured only power and made some indirect assessments of what would be a safe threshold power level to run that distance with current fitness level. I also looked at running effectiveness.

Today, I kept the Stryd aside and turned to a neat powermeter treadmill at the home gym called the Cybex 770T with Intelligent Suspension. In Part 2, I explained how this treadmill uses an AC motor with a variable frequency inverter drive. Treadmill belt speed is based on output frequency to the motor and according to the OEM, it would need no calibration. Infact, I measured the belt speed and even measured the time it would take for 10 revolutions. Comparing this to the treadmill speed readout gave a 1:1 match.

The objective of today's short test was to study how the treadmill maps power output to speed, mass and grade.

Objective : Curiosity, mostly. How does machine power vary with pace and mass? Perhaps mapping this would help in comparisons when doing the same with Stryd powermeter (to be tried later).

Test Protocol : Enter my correct weight of 64.5kg into the machine. Keep speed constant at 8kph (7:30 min/km) pace and get power readouts at 0%, 1%, 2%, 3%, 4%, 5% and 10% incline settings. Repeat this sequence with 10 kmph (6:00 min/km) and 12 kmph (4:36 min/km) speeds. I repeated the same experiment by entering weights of 70kg (+5 kg mass increase) and 80 kg (+10 kg). The total number of readings taken were 63.

Results :

Power output readings to corresponding mass and grouped by pace are shown below.

Fig.1 : Power table for 3 speeds and 3 weights for 7 different grades as measured on Cybex 770T.

For a given running pace, the power reading was linearly related to grade. Below, I show example of linear power lines for my weight 64.5kg and 70kg and 80kg for running pace 13kph (4:36 min/km). Also, both the y intercept (power at 0 grade) and slope of the line increase with mass.

Fig.2 : Power vs Treadmill incline for weight input of 64.5kg (yellow line), 70kg (orange line) and 80kg (green line).

To understand how power is mapped to speed, pace and mass, I performed a linear regression on the response Power with predictors speed, pace and weight input to the machine.

The regression equation I obtained was :

TREADMILL POWER (W) = - 225 + (7.46 x GRADE) + (3.00 x MASS)
+ (18.8 x Speed)   [tested for running speeds only > 8kph]

where grade is expressed in % , Mass in kg, and Speed in kph.

An equation is derived to map treadmill belt power to running speed, grade setting and pace for the Cybex 770T treadmill. The key takeaway is that maintaining the same power on an incline as on level ground running is impossible unless running pace is slowed down. For perspective, if a 64kg person ran on this treadmill at 8kph with a 10% incline setting, he'd have to slow speed by 1 min/km or more to match the same power reading obtained with a 0% incline.

My finding is that for a given weight, the power reading increases by 1.4 times between 0% and 10% grade. My finding is also that for a given grade, power increases by 1.24 times between 64.5 kg and 80 kg.

The equation tends to slightly overpredict at lower speeds and underpredict at higher speeds for a given weight. It also tends to slightly overpredict at lower weights and underpredict at higher weights for a given speed. The sweetspot of the prediction seems to be at a pace of around 10 kph where errors are less than 2%.

In the next post, I'll compare running uphill and power numbers using the Stryd to see if these same general takeaways are maintained. Ciao!