Bicycle operation cost versus car operation cost: fuel costs

It's said that bicycling is the new golf. I'm unsure whether this means that it's the new Saturday morning bonding thing-to-do or rather that it's expensive and the people who do it wear flamboyant clothes and cleated shoes. Both are applicable.

The cost of bicycling can be surprising. Of course the Saturday morning enthusiasts who listen to the salesmen in the bike shops and buy those soulless carbon-fiber-everything bikes are laying out a fat wad, but what about the commuter who wants only a good, dependable ride? The cost of operating a bicycle is an interesting topic to me for obvious reasons, and I will occasionally examine some of its many facets in future posts.

It's regularly assumed that a bicycle is cheaper to operate than a car, but is this true? and if so by how much? In this post I will explore one specific part: fuel costs. Fuel prices have increased in recent years both for cars and bicycles. We notice these increases whenever we pass those bright gas station signs boldly proclaiming their incessant faith in the one-tenth penny, and we notice these increases in the grocery store when that one pound brick of cheap cheddar costs more than five dollars.

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Case study

Subject: Craig
Description: Doesn't own car, wears a lot of Lycra, bikes everywhere around Phoenix.
Guess: Must be saving enough money not buying gas to buy an Italian racer.

I average about 126 miles of utilitarian bicycling each week. The amount sounds very specific, but it's a guess; I'm confident it's close to the actual amount, and I'm using it to simply calculations later. Most of the miles -- about 85 -- are for commuting to and from work. The remainder are for errands, social things, sports leagues, etc.

The first step is to calculate my fuel costs if I drove these miles rather than biked them.

My Mazda averaged a fuel efficiency of about 35 miles per gallon, so:

126 miles / 35 miles per gallon = 3.6 gallons
3.6 gallons * $3.50 per gallon = $12.60

Thus, my average fuel costs in a car would be about $12.60 per week.

Step two is to calculate bicycle fuel cost. How exactly does one go about calculating bicycle fuel cost? The key is determining one's energy expenditure when bicycling. This website provides a simple way of estimating one's power output to the bicycle. Only a subset of the input fields matter for calculating the power output field. These input fields are: speed, mechanical loss, air resistance coefficient, and rolling resistance. If one calculates for gradients, then the weight (both of the rider and of the bicycle) and grade fields are important, too. Gradient percentages can be tricky to calculate, and my utility bicycling is mostly flattish with the uphill generally canceling out the downhill, so in this exercise I ignore gradients. These are my inputs, as recommended by the website:

Speed: 18 mph
Mechanical loss: 3%
Air resistance coefficient: 0.0036
Rolling resistance coefficient: 0.004

These are conservative estimates. 18 Mph is a casual pace for me on the flats, and the three friction fields are on the low end according to the website.

The calculated power output with these inputs is 120W (watts), or one-sixth of a horsepower^[1]. This 120W figure is my power output to the bike. Of course, some of my effort is lost as waste, just as some energy in a tank of gasoline is wasted as heat when powering a car. I estimate my efficiency rating at 20%, meaning that for every one unit of energy I output to my bicycle, I must consume an additional five units of energy. This 20% figure is a guess; the experts say that riders' efficiency rates range from the high teens to the mid-twenties, and I'm pegging myself in the middle of that range.

So how much total energy do I use for utility bicycling?

126 miles / 18 mph = 7.0 hours

(Here is the reason for the 126 miles guess: it assumes that at my average speed of 18 mph I spend a simple, round 7 hours on the bike.)

To continue:

120W output / 0.20 efficiency = 600W input
600W input * 60 seconds * 60 minutes * 7.0 hours = 15,120,000Ws (watt-seconds)
15,120,000Ws = 15,120,000J (joules)
15,120,000J * 0.0002390kcal (kilocalories) per J = 3614kcal

Thus, I must consume about an extra 3600 kilocalories each week to meet the demand of utilitarian bicycling. For simplicity I will assume that I obtain all of these extra kcal by eating quinoa, which is a cheap, complete-protein grain. One ounce of quinoa contains about 105kcal, so:

3600kcal / 105kcal per ounce of quinoa = 34 ounces of quinoa
34 ounces of quinoa / 16 ounces per pound = 2.1 pounds of quinoa

One pound of quinoa goes for about $2.50 these days, so:

2.1 pounds of quinoa * $2.50 per pound of quinoa = $5.25

Thus, my average utilitarian bicycling fuel cost is about $5.25 per week. Remember that this figure is low due to conservative estimates. Even so, my total savings on the bike are:

$12.60 car fuel cost per week - $5.25 bicycle fuel cost per week = $7.35 savings per week.

So I save about one dollar per day on fuel costs. This is if I ride at a moderate pace. And if I get my extra calories by eating only quinoa as opposed to eating something pricier, and at about 675kcal (1 meal) per dollar, quinoa is a far from average cost.

Conclusion: I'll have saved enough for that Italian racer at about the same time I'll need it just to keep up my pace.

Questions? Comments?

¹ The most powerful cyclists in the world are track sprinters, some of whom can reach peak output levels of more than three horsepower!