## Wednesday, February 08, 2012

### Cycling vs. driving: which makes a faster commute?

My commute is roughly 4 miles each way, and although I don't own a car, I recently wondered which would make for a faster door-to-door commute: driving or cycling. Before I decide to rent a car or ask someone to do the drive for me, I want to estimate the difference.

My average "easy-commuting" speed (door-to-door) is about 10mph in the winter and 12mph in the summer, meaning that I get from my front door to the university in 24minutes and 20minutes, respectively. This is a total time that includes waiting for signals. My average moving speed is closer to 15mph during the winter and 18mph during the summer (meaning that if I didn't tire and I didn't have to stop, I would reach the university in 16 minutes and 13 minutes 20 seconds, respectively). However, since stop lights, stop signs, pedestrian flow, etc. exist, I will use the 24minute and 20minute figures for comparison.

Now, let's presume the fastest (legally) possible trip from my house to the University (i.e., no acceleration; one is immediately moving at the speed limit; no stops):
1. Cabin to the gate (0.4mi) can be driven at 20mph (1.2mins).
2. From the gate to Scio Ridge Road (0.9mi) is at 45mph (1.2mins).
3. From Scio Ridge to Virginia (1.3mi) is at 35mph (2.2mins)
4. From Virginia to First St (0.8mi) is at 30mph (1.6mins)
5. From First St to the Church St Parking Structure (1.0mi) is at 25mph (2.4mins)
• TOTAL: 4.4mi, 8.6minutes
However, we know that this is not a reasonable answer, since acceleration (and deceleration) occur, stop lights and stop signs exist, and we often cannot drive at the speed limit in the city due to traffic. Okay, so let's start to make this more realistic by adding in stop lights. If we assume that we will wait an average of 1 minute for each stop light, and 0.2 minute (12 seconds) for each stop sign, then we get:
1. Cabin to the gate: 1.2mins
2. Gate to Scio Ridge: 2.2mins
3. Scio Ridge to Virginia: 4.2mins
4. Virginia to First St: 2.8mins
5. First St to Church Street Parking: 9.2mins
• TOTAL: 19.6minutes
Already, the amount of time spent due to stop lights and stop signs brings this a lot closer to my summer travel time of 20 minutes! And we didn't even take acceleration into account. However, what is the average acceleration of a typical car? Well, according to hypertextbook.com, it's somewhere between 3m/s/s and 4m/s/s. Let's be generous and use the example with the higher acceleration (something like the 2000 Mitsubishi Eclipse GT). Now, we need an equation, something from elementary physics. Something like:

v = at + u
t = (v - u)/a

where t is the amount of time (in seconds), v is the final velocity (the speed limit, converted to meters/sec), u is the starting velocity (0m/s at stops, the previous speed at transitions), and a is the constant acceleration (4m/s/s). This will give us the time that it takes to reach the speed limit. Then we can find the distance it traveled over that acceleration time:

s = ((v + u)/2)t

where s is the distance traveled (in meters). The remaining distance will be traveled at the speed limit. (Stopping will be calculated in a similar fashion, and will assume 15fps (~4.6m/s/s). Now, running it through Excel (and adding all the stops), we get:
1. Cabin to the gate: 1.21min
2. Gate to Scio Ridge: 2.33min
3. Scio Ridge to Virginia: 4.25min
4. Virginia to First St: 2.73min
5. First St to Church St Parking Structure: 9.97min
• Total: 20.49minutes
Already it's on par with my average summer cycling commute time. And this is considering maximum acceleration and deceleration of a 2000 Mitsubishi Eclipse GT (i.e., stomps on the brake at each stop and floors it after each stop). If we assumed a more conservative driver, and take only 2/3 of the maximum acceleration and deceleration (still a bit of a lead foot, though), we get:
1. Cabin to the gate: 1.22min
2. Gate to Scio Ridge: 2.38min
3. Scio Ridge to Virginia: 4.30min
4. Virginia to First St: 2.79min
5. First St. to Church Street Parking Structure: 10.19min
• Total: 20.88minutes
Not much of a change in travel time (about 24seconds of difference if you don't have such a heavy foot). However, this doesn't take into account the additional time needed to find a parking spot (about 4 minutes) and to walk to the department building from the car (about 5 minutes), increasing the time to almost 30 minutes. If we add in things like waiting in traffic (the above calculations assume that you're the only car stopping at the stop lights and the only one stopping for the stop signs), and you can likely add another 2-5 minutes to the estimate.

In the end, using simple physics and reasoning, we can determine a few things:
1. It would take about 30 minutes to get from the cabin to my department using a car.
2. Driving at reckless acceleration and deceleration wouldn't really help reduce this figure.
3. Using a bike gives me 25 minutes of exercise in the morning (and about 30 minutes of exercise in the evening for my return trip), which I wouldn't get by driving, and would therefore need to spend at the gym as additional time.
Therefore, in addition to the points about cost that I mentioned earlier, riding a bike is, for me, a good way to travel for me. Still, I don't think that I'll be spending THIS much time on my bike:

THE MAN WHO LIVED ON HIS BIKE from Guillaume Blanchet on Vimeo.

UPDATE (4/11/2012): I took a quick drive to and from my house (via Zipcar), and on my way back, I actually clocked the driving time, which turned out to be 13 minutes (caught lots of green lights, and parked at a lot west of campus, meaning that I didn't have to drive through campus), followed by 10 minutes of walking from the parking lot back to my office. In contrast, my bike commute time that morning was 22 minutes.