Thermodynamics of modes of transport: Cycling vs EV's

[cvrcv]

Cycling without question viewed as "good for the planet" versus any other mode of transport. I've tried to actually confirm this with a physics approach, and I always get answers that are very upsetting to cycling crowd. If all cities are planning for future in which bicycles solve the energy and environmental issues, this would be a huge problem. I understand that there is a space problem to be addressed, but I am not doing so here. I would like to see if anyone can either bolster or poke holes in this calculation.



I've approached this calculation is several ways in the past, but I think I found the simplest approach, via using the calorie estimator here: Calorie Calculator - MapMyRide

Using inputs for an average male 200lbs 5'8" 35 years. Riding 1 mile in 10 minutes:
71 calories burned, per mile.

Of course food calories are actually kcal's, and 1 kcal = 1.16222 Wh
71*1000*1.16222 = 82.5178 Wh/mi

So this is already at 1/3rd what a Model 3 achieves (~230 Wh/mi), a very large number!

Now, let's take into account thermodynamic conversion losses:

For the Model 3 powered with solar/wind, I roughly estimate "well-to-wheel" efficiency as 70%
For a human powered with food, I roughly estimate the "well-to-wheel" efficiency as 15%. Now obviously this is a difficult estimate, but any research into this area I've found has come up with a similar number.

So applying efficiencies:

Model 3: 230/.70 = 328.57 Wh/mi (1 passenger)
Cyclist: 82.5178/.15 = 550 Wh/mi


Cycling seems significantly worse just from a thermodynamics perspective, especially considering the Model 3 can take up to 5 people, which brings the per person consumption to 65.7 Wh/mi. Almost any way you slice that, 5 passengers in Model 3 beats 5 cyclists, but it doesn't even seem necessary to have passengers.

Of course, I didn't estimate production costs for the Model 3, but I also don't have a good way to estimate the food production cost, not just thermodynamically but holistically for the cyclist. There's water and arable land usage, as well as methane production, both at the animal as well as the human. Also, people that commute to work on a bike will often take a shower after their morning (please, don't stop) and evening commute, which increases their water consumption even more.

 

[SageBrush]

Using inputs for an average male 200lbs 5'8" 35 years. Riding 1 mile in 10 minutes:
71 calories burned, per mile.

This 71 Kcal per mile is way too high, but it has another important error: it includes the calories the person will burn unrelated to being on a bicycle.

Look at this article
Net Heart Rate to Prescribe Physical Activity in Middle-Aged to Older Active Adults

And try it out on yourself during casual bicycle riding. I doubt you will reach 3 METS, so 2 METS net from the riding which is
~ 120 Kcal per hour,
~ 20 Kcal per mile

The other way to approach this number is to figure that human efficiency is ~ 20%.
Find the decline that keeps your bicycle moving at 6 mph, calculate the potential energy change per 10 minutes and multiply by five.

 

[SageBrush]

Here is a really good article on the energetics of bicycling:

Bicycle Drag Force Formulas

It takes ~ 2 N to bicycle at 12 kph on level ground without extra wind.
Since Work = Force*distance,
One km = 2000 Joules ---- close to nothin

 

[SageBrush]

And here is a calculator that gives results in the same ballpark as the graph above
Science of Cycling: Aerodynamics & Wind Resistance | Exploratorium

You got me thinking about this ...
a few moments thought tells us that rolling losses can be ignored since the (person + bicycle) mass is so much less per wheel than a car and a bike tyre rolls much easier than a car tyre. If you want a number though, it is about one Newton or about 0.3 Wh a km.

So lets focus on air drag, calculated as
0.5 * Rho * V * V * CdA
V ~ 2.5 meters a second
Take the worse case of a human Cd being 1.0, standing and facing forward. In practice it is probably half that amount.
Frontal area is around 1.8 * 0.5 meters squared
So the air drag is Rho * 0.5 * 2.5 * 2.5 * 1.8 * 0.5 Newtons
At sea level then where Rho = 1.225 Kg/meter^3,
drag is 3.37 Newtons.
This number is obviously an over estimate and it is still peanuts.

 

[abasile]

Yesterday, I did a 36km round trip bicycle ride involving 685m of climbing and strong winds. It took me almost 1.5 hours (longer than usual). Strava estimates that I burned roughly 980kcal, which is probably on the low side because it didn't account for all of the wind. 980kcal * 1.16Wh/kcal / 1000Wh/kWh = 1.14kWh. But let's call it 1kWh to be conservative. If we assume food production thermodynamic efficiency of about 20% (a wild guess), then that's 5kWh of source energy needed.

For the Model 3, figure 150Wh/km, or 150Wh/km / 0.70 efficiency = 214Wh/km = 0.214kWh/km "well to wheels". 36km * 0.214kWh/km = 7.7kWh. Considering all of the wind, maybe it would have actually been 9kWh.

Now, Strava doesn't say whether its Calorie estimate includes "baseline" human consumption. But a sedentary human will most likely burn fewer than 80 Calories per hour, so at lowest, my additional kcal burned would be 980kcal - 1.5hours * 80kcal/hour = 860kcal. Significant, but not game changing.

Clearly, this comparison is highly dependent on the thermodynamic efficiency of food production and delivery, which is going to vary a great deal. If I grew my own food in a local garden using only rainfall and no fertilizer, then biking clearly has a lower footprint than driving. If I fueled myself with beef burgers, then driving the Model 3 would have had less impact on the environment than biking.

I suspect that a Model 3 with multiple passengers will usually have less environmental impact per mile than all of those passengers using bicycles instead. A Model 3 powered by renewable energy will come out ahead in most cases.

All of that said, the purpose of my bike ride yesterday was exercise and mental renewal. The natural scenery was beautiful, and fighting the wind provided an added challenge that was good for me. Biking for transportation obviously has physical and mental benefits. I would do it for those benefits, not for the environment. If it's a pain to bike to work, and it's easier to get exercise elsewhere, then I would just drive and not worry about it.

 

[SageBrush]

Yesterday, I did a 36km round trip bicycle ride involving 685m of climbing and strong winds.

Your example is quite different than OPs due to your bicycling speed and opposing wind.
Aero forces are proportional to the square of speed.

You had ~ 9x more Aero work than a casual ride at 6 mph. Of course a car would have proportionally that much more Aero work as well.

 

[abasile]

Your example is quite different than OPs due to your bicycling speed and opposing wind.
Aero forces are proportional to the square of speed.

You had ~ 9x more Aero work than a casual ride at 6 mph. Of course a car would have proportionally that much more Aero work as well.

I'm pretty sure that Strava's energy consumption estimate did not account for the wind, as the Calorie estimate was similar to past rides without wind. That said, you have a very good point - my example is quite different than the OP's. As a lifelong avid cyclist, I travel faster and burn significantly more Calories compared with casual cyclists. However, when I do bicycle for transportation, I ride just as fast as always. I'm not the only one - a substantial fraction of bicycle commuters in the US seem to be "serious" cyclists, at least among those who ride far enough to justify showering upon arrival at work.

In my opinion, the most important takeaways of this exercise are:

1. Our food consumption choices are an extremely important component of our overall environmental impact, and this is magnified for those of us who are physically active. I'm far from perfect overall, but avoiding red meat and most dairy does make a real difference. It's also worth trying to avoid wasting any food.

2. Our transportation choices are very significant. We drive a lot, so we're thankful to be able to mitigate much of that impact by using EVs, while offsetting a significant portion of our EV charging with solar energy.

 

[roblab]

First, the plural of EV is EVs, not EV's. I know. Ex-school teacher mode.

Second, I have never felt inclined to ride a bike anywhere, though I did it a couple times in college. Those that did ride did it because it was all they could afford, not because they got an extra serving of endorphins saving the planet, etc., etc.

Third, I live in the mountains. Though that could be fun going to town, coming back is "all uphill" as the saying goes. Bikes are a pain. Bikes are slow. Bikes are hot in summer and cold and wet in winter. I find I can stay fit by eating less and taking the stairs. Riding a bike in Colorado raises serious questions in my mind.

AND, fourth, the people who ride in Napa Valley seem to be doing it for their health, while drunk tourists zip by three feet away (legal minimum) doing 65 in a 55. Unless you're riding on a dedicated bike trail, you're taking your life in your hands.

 

[SageBrush]

I'm pretty sure that Strava's energy consumption estimate did not account for the wind, as the Calorie estimate was similar to past rides without wind.

Good point. FWIW though, I am quite skeptical of calorie meters. They routinely way over-estimate.

When I am not playing around with joules and watts, I put on my MD hat and think of METs and exertion. Prolonged 10 MET activity is really, really hard and only seen in fit people. The average American views 2-3 METs as casual exercise of the type OP described. One MET is about 60 kCal an hour, or about 70 Wh. The MET includes the body (in)efficiency.

 

[SageBrush]

I suspect that a Model 3 with multiple passengers will usually have less environmental impact per mile than all of those passengers using bicycles instead. A Model 3 powered by renewable energy will come out ahead in most cases.

Not even close for casual riding.
Look at the energy calcs posted above. Around 2 Newtons. About 0.5 Wh per km

 

[cvrcv]

This 71 Kcal per mile is way too high, but it has another important error: it includes the calories the person will burn unrelated to being on a bicycle.

Using 1800 calories a day basal metabolic level (for the example rider) BMR Calculator, Basal Metabolic Rate Calculator | MyFitnessPal.com, for the 10 minute bike ride above this only comes out to ~14Wh. Does not change the calculation significantly enough. That's assuming basal rate is included in the rate above, which is not clear in the first place.

 

[Rashomon]

Another way of looking at this is how much energy does an ebike use? I use about 20wh/mile on my commute, at an average speed of about 18mph. Alternatively, simulations I've run of a moped/L1e class motorcycle put its usage at roughly 30wh/mile on the low-speed urban leg of the WMTC (World Motorcycle Test Cycle). In either case, an order of magnitude or more better than an M3. The ebike will be faster than an M3 in a purely urban environment as well; only motorcycles have a chance to get around cities quicker than an ebike.

On a mpg-e basis, the simulated ultra-light-motorcycle was projected to do 1000 mpg-e; low-speed e-bicycles are around 2000 mpg-e, and s-pedelecs (class 3 ebikes in California, top speed 28 mph) get somewhere in between.

 

[SageBrush]

Another way of looking at this is how much energy does an ebike use? I use about 20wh/mile on my commute, at an average speed of about 18mph.

1+++
At the 6 mph posited in the OP the aero forces will be 1/9th, and since they account for the lion's share of energy we end up at the same very low figures I posted earlier.

 

[cvrcv]

Another way of looking at this is how much energy does an ebike use? I use about 20wh/mile on my commute, at an average speed of about 18mph.

I haven't seen data on real-world consumption for a full ebike. Seems most units are pedal assist, which makes this more difficult. There's much more data on calories burned.

Alternatively, simulations I've run of a moped/L1e class motorcycle put its usage at roughly 30wh/mile on the low-speed urban leg of the WMTC (World Motorcycle Test Cycle).

Zero motorcycles seems to be about around 100Wh/mi based on their website, and you know *everyone* exaggerates their range and consumption claims. Of course, real world consumption data is appreciated.

In either case, an order of magnitude or more better than an M3. The ebike will be faster than an M3 in a purely urban environment as well; only motorcycles have a chance to get around cities quicker than an ebike.

My argument follows that it is better to let electric drive work no matter the mode of transport, human labor is too costly for the environment. However, keep in mind that small devices usually have many compromises like incredibly inefficient power supplies, I wouldn't be surprised if the charging efficiency for an ebike came out at 50%, vs 90+% for Tesla. You lose your order of magnitude very quickly.

On a mpg-e basis, the simulated ultra-light-motorcycle was projected to do 1000 mpg-e; low-speed e-bicycles are around 2000 mpg-e, and s-pedelecs (class 3 ebikes in California, top speed 28 mph) get somewhere in between.

I'd prefer to stick with real units of energy rather than contrived ones. Too many fudge factors in there already. Real-world consumption figures from the outlet would be best.

 

[cvrcv]

1+++
At the 6 mph posited in the OP the aero forces will be 1/9th, and since they account for the lion's share of energy we end up at the same very low figures I posted earlier.

6 mph is just too slow, that is jogging speed. Commuters on bicycles go much faster than this. According to this article, commuters range from 15.5 mph to 18.6 mph. I would suspect as well with electric assist these speeds increase. What is a reasonable speed for long distances on a bike?

 

[SageBrush]

6 mph is just too slow, that is jogging speed. Commuters on bicycles go much faster than this. According to this article, commuters range from 15.5 mph to 18.6 mph. I would suspect as well with electric assist these speeds increase. What is a reasonable speed for long distances on a bike?

I don't tell people how fast to ride. I was responding to the OP's question, and then pointing out that the Ebike data gives similar results when corrected for the speed difference.

I'll guess that commuters ride at 20 kph (5.5 m/s)
RR remains 1 N
Aero is about 0.6*5.5*5.5*0.8 = 14.5 N
Which gives 15.5k Joules per Km = 4.3 Wh/km

 

[abasile]

Another way of looking at this is how much energy does an ebike use? I use about 20wh/mile on my commute, at an average speed of about 18mph.

This is easy to measure, but it remains tricky to estimate how efficiently a human being converts food-based energy into work (i.e., pedaling a bicycle). If I am to believe the Calorie consumption estimates generated by the Strava fitness app, the human body is not terribly "energy efficient" in this sense. This seems to be borne out by my years of personal experience, as I tend to eat significantly more food when I'm very active compared to periods when I'm forced to be relatively sedentary, and I'm not overweight. In addition, most modern food production has a fairly high energy footprint.

My argument follows that it is better to let electric drive work no matter the mode of transport, human labor is too costly for the environment.

Human labor is great to the extent that it supports physical fitness and well being, and we'd rather see people mitigate the environmental impact of their exercise by making better food choices as opposed to not exercising. With increasing levels of physical activity, though, there seems to be a law of diminishing returns, and too much activity may be detrimental to one's health. I'm grateful that we live in an age where electric motors can replace day-long physical labor!

Today, e-bikes are a great option for commuters because they are extremely energy efficient and they generally enable some exercise as well. You can choose to arrive at work without breaking a sweat, then pedal home under your own power for a workout. (I used to achieve virtually the same thing with a regular bicycle by living mostly uphill from the office.) Being able to turn some commute time into exercise time can be a real benefit.

 

[SageBrush]

This is easy to measure, but it remains tricky to estimate how efficiently a human being converts food-based energy into work

20-22% is a good estimate.

If you want to inflate the field to pedal numbers you could consider farm energy inputs, processing, transport, waste, and absorption.

 

[abasile]

20-22% is a good estimate. If you want to inflate the field to pedal numbers you could consider farm energy inputs, processing, transport, waste, and absorption.

Okay. If I rightly recall from past years of reading cycling magazines, your Cd estimate of 1.0 for a human cyclist is actually about right. Let's go with your estimate of 4.3 Wh/km to propel the bicycle and rider at a very moderate 20 kph. Let's say 20% efficiency from "dining table to pedals", and let's say 20% efficiency from "farm to dining table". That's 20% times 20% equals 4% overall energy efficiency. 4.3 Wh/km divided by 4% equals roughly 108 Wh/km.

Now, let's go with 30 kph (about 18 mph, or 8.3 m/s), a very typical speed for a reasonably fit cyclist. Plugging in the numbers as before (0.6 * 8.3^2 * 0.8, we end up with 32.9 N aero. Going with 1 N rolling resistance for 33.9 N total, that translates to 9.4 Wh/km at the pedals, or very roughly 235 Wh/km from "farm to pedals". Note that this is actually higher than my above, Strava-based consumption estimate (which also assumed 20% "farm to dining table" efficiency).

If the Model 3 uses about 140 Wh/km, or about 200 Wh/km from "well to wheels", and if our "farm to dining table" efficiency is at all close to reality, then a human cyclist doing at least 20 kph and the Model 3 do indeed appear to be within the same ballpark in terms of net energy use. Also, it's worth noting that the Model 3's efficiency would be better than "rated" if it were driven at a constant 20 kph or 30 kph to match the speed of the cyclist.

Does anyone have a better "farm to dining table" estimate than 20% efficiency? One could pick a basic, vegetable-based food item like whole wheat bread and come up with an estimate using a series of assumptions. Or find some good, published data. I'm going to stop here for now!

 

[cvrcv]

Okay. If I rightly recall from past years of reading cycling magazines, your Cd estimate of 1.0 for a human cyclist is actually about right. Let's go with your estimate of 4.3 Wh/km to propel the bicycle and rider at a very moderate 20 kph. Let's say 20% efficiency from "dining table to pedals", and let's say 20% efficiency from "farm to dining table". That's 20% times 20% equals 4% overall energy efficiency. 4.3 Wh/km divided by 4% equals roughly 108 Wh/km.

Now, let's go with 30 kph (about 18 mph, or 8.3 m/s), a very typical speed for a reasonably fit cyclist. Plugging in the numbers as before (0.6 * 8.3^2 * 0.8, we end up with 32.9 N aero. Going with 1 N rolling resistance for 33.9 N total, that translates to 9.4 Wh/km at the pedals, or very roughly 235 Wh/km from "farm to pedals". Note that this is actually higher than my above, Strava-based consumption estimate (which also assumed 20% "farm to dining table" efficiency).

If the Model 3 uses about 140 Wh/km, or about 200 Wh/km from "well to wheels", and if our "farm to dining table" efficiency is at all close to reality, then a human cyclist doing at least 20 kph and the Model 3 do indeed appear to be within the same ballpark in terms of net energy use. Also, it's worth noting that the Model 3's efficiency would be better than "rated" if it were driven at a constant 20 kph or 30 kph to match the speed of the cyclist.

Does anyone have a better "farm to dining table" estimate than 20% efficiency? One could pick a basic, vegetable-based food item like whole wheat bread and come up with an estimate using a series of assumptions. Or find some good, published data. I'm going to stop here for now!

Actually thank you for pointing this out. While my calculation was using Model 3 and car speeds and bicycles at bicycle speeds, this gives a huge unfair advantage to the bicycle. We know from published data that Model S maxes out at ~22 mph at ~170Wh/mi, down from a rated ~300Wh/mi. Given the PMAC motors in the Model 3 expect even better scaling, meaning that the 230Wh/mi I used above is realistically less than 130Wh/mi. If we're talking about city commutes, we know Model 3 will be limited in it's top speed anyway so it's a fair comparison.

Seems no contest at this point.