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 225W to go 10 m/s (22 mph) in the TdF case and 320W in mine. About 80% of the 95W 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.

A rider wishing to move at speed Vg without assist, with the sliders set as they are, will have to supply all of the corresponding Pt and a few watts more to offset drivetrain losses. With assist, 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.

 

[stompandgo]

I raced with three different brands of power meters, Quarq, Stages, and SRM. The SRM was by far the most reliable and accurate. The other two had constant problems with water incursion and strain gauge delamination, which caused inaccuracies and data dropouts. Drove my coach nuts. On the other hand, the SRM had no user serviceable parts inside, and had to go back to SRM in the offseason for a new battery and recalibration. In between, it worked flawlessly in all conditions.

From everything that I've seen from TQ users that have a left side power meter installed, the TQ torque sensor reads about 10% low. That's perfectly fine for what the motor needs to calculate assist. For rider power measurement, that's about an order of magnitude of inaccuracy, which is OK for an individual user that's only concerned about their own riding, but can be problematic for training, ride planning, etc.

I've been looking at adding a Tempo pod to the Pinarello, but right now I have other priorities.

 

[fooferdoggie]

I don't need perfect but I just want an idea on what I am doing. here is my regular bike. looking at the data it would look like I should burn more calories on the trek.

and the trek.

 

[Jeremy McCreary]

I don't need perfect but I just want an idea on what I am doing. here is my regular bike. looking at the data it would look like I should burn more calories on the trek.

View attachment 213993


and the trek.
View attachment 213994

If both data sets were from the same route ridden the same way, comparing the 2 bike's kcal per mile figures would be a good start.

But one route is 8.6 mi, and the other is 8.15 mi. And I don't see any climbing info on the 2nd route.

So I don't see a basis for a valid comparison based on the data shown.

The model above doesn't help here as it only deals in power (energy per unit time), not energy per unit distance. These are 2 different rates with no fixed relationship. The latter is more pertinent to your question.

 

[fooferdoggie]

If both data sets were from the same route ridden the same way, comparing the 2 bike's kcal per mile figures would be a good start.

But one route is 8.6 mi, and the other is 8.15 mi. And I don't see any climbing info on the 2nd route.

So I don't see a basis for a valid comparison based on the data shown.

The model above doesn't help here as it only deals in piwer vs. speed, not energy per mile. These are 2 different rates with no fixed relationship.

in this case yes but it's pretty close to this when they are exact. yes I don't get much info from bosch. its more energy on my regular bike without trying. I have to work on the e-bike to get even close to the workout I get on my regular bike. I think the norm power rating I get from the power meter arm is closer to what I am doing.

 

[Jeremy McCreary]

I have to work on the e-bike to get even close to the workout I get on my regular bike. I think the norm power rating I get from the power meter arm is closer to what I am doing.

If your rider power changes a lot over the course of a typical ride, or you're doing a lot of accelerations — say, due to traffic — normalized average power's a better metric than simple average power.

Guessing that riding your regular bike is significantly easier than riding your ebike in OFF — especially if there's climbing involved. Can you reprogram your lowest assist mode to make the efforts more comparable?

 

[fooferdoggie]

If your rider power changes a lot over the course of a typical ride, or you're doing a lot of accelerations — say, due to traffic — normalized average power's a better metric than simple average power.

Guessing that riding your regular bike is significantly easier than riding your ebike in OFF — especially if there's climbing involved. Can you reprogram your lowest assist mode to make the efforts more comparable?

it is my commute that I know exactly all the details of it after so many years. Lots of ups and downs and stops and starts. when I first started riding my regular bike I tried adjusting the level on my e-bike so it was close and got it a bit harder than the regular bike. It was a good workout too good. but I really had to work at it. I dont work hard on my regular bike but its more work.