Playing what-ifs with an interactive power vs. speed model

[Jeremy McCreary]

Resistance to forward motion is an ever-present foe in cycling. In the spirit of know thine enemy, here's an interactive visualization of the 3 main power losses due to air, gravitational, and rolling resistance. It's made in the Desmos online graphing calculator.

power vs. speed

www.desmos.com

The visualizer lets you manipulate the key rider, bike, and external factors with 7 independent sliders. The effect on the power-speed profile shows on the graph in real time.

Great for visualizing what-ifs bearing on things like how best to spend your bike money, your battery range, or your own effort.

The interactive power-speed profile

Power-speed profile for a typical TdF scenario.

The model graph plots ground speed Vg in m/s on the horizontal x-axis and the associated mechanical power loss in W on the vertical y-axis. The orange curve is the aerodynamic power loss Pa as a function of Vg. I think of this kind of plot a power-speed profile.

The red profile shows the weight-dependent power loss Pw due to gravity and rolling resistance combined. This profile rises as speed, system weight, and especially gradient increase.

The blue profile shows total power loss Pt = Pa + Pw. Blue is the mechanical power needed to hold speed Vg with the parameter sliders as you left them. The few watts of drivetrain losses are ignored.

Sliders and other stuff below the graph

The headwind, drag area, and air density sliders determining air resistance.

Below the graph are text lines for symbol explanations and slider lines for playing around with key parameters like bike mass Mb and system drag area Ad. Don't worry, the sliders are the only things you need to pay attention to here.

The default slider settings describe a best-case Tour de France scenario on smooth, flat pavement in still air. These result in the power-speed profile above.

Power-speed profile with my own bike and rider parameters.

The sliders are there to be played with. My own bike and rider parameters produce a power-speed profile significantly taller and steeper than the TdF profile above. For example, on flat pavement in still air, it takes 220W to go 10 m/s (22 mph) in the TdF case and 300W in mine. Most of the 80W difference is aerodynamic.

Other lines set constants or do the actual math and graphing. Diddle with the sliders all you want, but messing with anything else will likely break your local copy of the model.

Applies to ebikes, too
The model's power-speed profiles apply to all bicycles. You just need to set the sliders appropriately.

On an unmotorized bike, a rider wishing to move at speed Vg with the sliders set as they are will need to supply all of the corresponding Pt and a few watts more to offset drivetrain losses. On an ebike, the rider and motor will have to share that load somehow.

Playing what-ifs
The finished power-speed model's pretty easy to use. Many different practical and theoretical questions can be explored.

Remember, garbage slider settings in, garbage profiles out.

For example, the intersection of the orange and red curves shows the "crossover speed" at which the aerodynamic loss equals all other losses combined. It may be lower than you think.

Now watch how crossover speed changes as you vary the air resistance parameters and bike mass. Where's your bike money best spent? Lowering drag area with more aero clothing can bring a lot of bang for the buck. And on an ebike, that goes to greater speed or battery range for effort.

 

[fooferdoggie]

My god make biking hard Me trying to compare my trek to my regular bike is hard enough. I dont know if the bosch power meter is something the same accuracy as my power meter crank arm. I know I have age a higher wattage on the e bike but A lower HR average and less tired. but my regular bike is slower so its a longer ride. I really need a power meter crank arm on the bosch to really see.

 

[PedalUma]

Fluffy things fly. Here is what a butterfly wing looks like under a microscope:

here are eagle feathers under a microscope:

When I want to fly on a bike I have on Cashmere or Moreno wool. The little micro-vortices create a layer of aero smoothness that one can feel, regardless of the math of it. This is also why sharks have sandpaper-like skin. Micro-vortices lay down opositinal wind/fluid resistance making it slick. It is also why Frisbees that work best always have ridges on top. Try roughining the top of a Frisbee to see how much farther it goes; you will find something like 15 a further meters of travel.

 

[Jeremy McCreary]

My god make biking hard

I don't see it making the doing of cycling any harder. But it can make thinking about certain aspects of cycling easier. And that's the whole point.

Guess it's a matter of personal taste. As with all my other hobbies, I enjoy thinking about my riding as a process sometimes. Only makes riding more interesting — and sometimes better — without taking away any of the enjoyment.

Me trying to compare my trek to my regular bike is hard enough. I dont know if the bosch power meter is something the same accuracy as my power meter crank arm. I know I have age a higher wattage on the e bike but A lower HR average and less tired. but my regular bike is slower so its a longer ride. I really need a power meter crank arm on the bosch to really see.

Interesting HR and perceived exertion observations. Is there a consistent cadence difference between the 2 bikes?

The power meter built into my Specialized ebike is my first. Not the most accurate by all accounts, but it's been a very interesting lens on my riding. Don't do any kind of formal training, but I wouldn't be without one now.

@mschwett has years of power meter experience, and he feels that the same meter in a previous bike of his generally read about 5% too high. No basis for comparison, but that sounds plausible to me. Mine's certainly not reading low.

Don't really need any more accuracy than that for my purposes. But I do hope it's as consistent as I think it is, as I'm more interested in real-time variations and trends than in absolute numbers.