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Power Curve

hamidsoltani

power curve graph

Many people buy a bike trainer to simulate an outdoor ride indoors. The Kinetic Road Machine is the only trainer specifically calibrated to replicate the resistance encountered on an outdoor ride (illustrated above). We have worked with Tom Compton at www.analyticcycling.com (perhaps the most knowledgeable person on the planet regarding the forces a cyclist encounters and produces) to create a mathematical relationship between power and speed while riding our trainers. These relationships are graphed in this PDF (2.59 MB).

As you might imagine, many variables affect a rider’s speed. The most obvious is the weight of the rider and bike. Tom specializes in the less obvious factors like frontal area and air density. With extensive use of differential equations and advanced numerical methods, Tom has created proprietary software to accurately estimate the cumulative effect of 16 different interactive forces that determine a rider’s speed. Visit the following site for more information: www.analyticcycling.com

With Tom’s help, we have been able to create an “average” rider assumed to be 165 lbs, riding a 23 lb bike with 170mm crank arms up a 1% grade, at sea level with no wind on rough asphalt... etc. The “outdoor ride” that we reference in the PDF is based on this “average” rider. Tom was then able to calculate how much power it would take for our average rider to maintain a given speed.

We then used our robot cyclist, Crank Armstrong, to measure the power needed to maintain a given speed while riding the Kinetic Road Machine. By altering the viscosity and the amount of silicon solution in the fluid chamber, we were able to match the data from our “average” rider to the data produced by Crank. The end result is a very accurate power curve and the most realistic indoor simulation.

It should be noted that the power curves in the PDF are not raw data. Because so many measurements are taken and the patterns within each experimental trial can be erratic, the raw data is often unintelligible. Tom relies on Mathematica (a computer program) to fish out a mathematical model from the raw data. This model is an average of the collected data. Surprisingly, the power curves are based on a simple formula.

Remember algebra? Good. The formula for the Road Machine turns out to be a cubic function. If we let S stand for “speed” in miles per hour, and P stand for “power” in watts, the formulas are as follows:

 Kinetic Road Machine:
P = (5.244820) * S + (0.019168) * S3

For example, to calculate how much power is produced at a speed of 16.1mph while riding the Kinetic Road Machine, plug 16.1 in for “S.”

P = (5.244820) * (16.1) + (0.019168) * (16.1)3

P = (5.244820) * (16.1) + (0.019168) * (16.1) * (16.1) * (16.1)

P = 84.4416 + 79.9935

Power = 164.435 watts

The Kinetic Road Machine power formula is accurate for all riders because the variables experience on an outdoor ride are controlled indoors. We are so confident in the accuracy of the Kinetic Trainer; we encourage you to try this test. Complete a 20 minute time trial on the trainer using a rear mount bike computer or Kinetic PC (Power Computer) Complete a similar ride on a flat course with a neutral wind. The distance covered will be within a range of + /- 3%.