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.

Also remember that on an ebike, Pt savings go to less effort or greater speed or battery range for the same effort.

Example: When does bike weight really matter?
Set the sliders for you, your bike, and a familiar flat ride with gradient G = 0. Then watch total power loss Pt (blue profile) as you play with bike mass Mb. Note how little Mb affects Pt on the flat. Now repeat with the gradient upped to a steep G = 0.1 (10%). Pt's much more sensitive to Mb now.

So, if you ride only on the flat, improving handling is the only real reason to spend $$$ lightening your bike. However, different story if you ride a lot of steep terrain.

Example: Crossover speed
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 drag area Ad and bike mass Mb. How's your upgrade money best spent? Lowering Ad with more aero clothing or a less upright posture is generally much cheaper than shedding even 1 kg of bike mass.

 

[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.

 

[PCeBiker]

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

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.

OK, so riddle me this,..

I live on flat lands and all my routes are the same with the same rolling resistance and grabity
(unless the 's are warping the fields or sumthin??)

The only variable is wind for me.

So what if,.. the wind is blowing NE in the morning and switching to a NW later in the day?

And the wind is blowing 20 mph gusting to 40.
And the gusts are different from one moment to the next.

Your ammeter is bouncing continuously between 3 and 18 amps, but your throttle is Locked at a Constant 32 kph.


It takes two hours to top up both your batteries, and by then the wind has changed.

So,..to get the most range, do I head NE directly into the headwind, cuz it's still morning, and use the changing prevailing winds to blow me home?

Or do I head NW to make sure that I will be blown home, (perhaps with the help of a ️ or kite ?), once I get as far NW as my debilitating Range Anxiety and my Complete Lack of interest in pedaling take precedence?



It's kinda hard for me to plan my route when it's windy and there's 🌪's about. Lol

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.

 

[PCeBiker]

My current setup will go at least 88 kph, but that's with a tailwind.

I have 3000 watts available that I can crank up to 5000 watts if it's really windy.

My hub motor can only go 32 kph before the motor cuts out (or 43 kph with it turned up), so after that it's up to my mid-drive to take over with up to 25 amps to a top speed of 88 kph before my mid-drive reaches top speed (BBS02B with a 52t chainring on an 11t cog 28" diameter wheel)


What kind of tailwind will I need to go 88??
(keeping in mind that top speed drops as your running low on voltage)

You'll need to involve real-time satellite weather communication to actively prevent running outta ️️

 

[PCeBiker]

Dual battery dual motor rear wheel drive

 

[harryS]

Need to put in good value for Ad, the frontal area of bike and rider. Google sez a commuter bike and rider is around .43 -.50. Sliders start at .3, which is pretty small, I used 0.50 but I think I;m wider than that, plus I wear baggy shorts.

The tire resistance has a small effect, I use .006. Also 190 lb rider (80 kg) and 40 lb bike (20 kg).

15 mph is 6.7 m/sec. SImulator says I need 150 watts, I'll buy that. 25 mph is 11 m/sec, and over 500 watts, If I trust my ebike displays, it would mean I'm kicking in about 20% of the power at 15 mph. as the display says 100-120 watts at 15 mph.