Walking fast in Manhattan

Today I attempted to solve a walking related question that has been bugging me for a while. 

Let me give a bit of background and then I will get to the question: 

For those of you, who haven't been to NYC before, one of the prominent features of the city is the long North-South avenues. These start in Harlem and go all the way downtown. Numbered streets cross the avenues at constant intervals.

Traffic on most North-South avenues flows in one direction, uptown-bound (North) or downtown-bound (South). Traffic lights on these avenues are set to switch in a wave rather than synchronously to minimize interruptions. Once you catch a green light, you ride the wave and as long as you can keep a certain speed, you travel a good number of blocks before seeing a red light (it is a whole different story if someone hails a cab in front of you, but we are not dealing with that here).

Of course the lag between the lights is optimized for car speed. If you are a slow-moving pedestrian, riding the wave is not a realistic option. You will unavoidably hit the red lights more often, because the wave will be long gone by the time you get to the next light. Unless you are slow enough that the next wave comes and catches you. As a pedestrian you also have the option to walk against the traffic (on the sidewalk, of course) and there might actually be a case where this is the best option.

So, here is the question that formed in my mind during a 40 block walk: Assuming the red light is on for X seconds, the green light is on for Y seconds, there is a Z second lag between traffic lights and you are walking at P pace which direction should you walk in, with the traffic or against the traffic?

To be able to change variables and get a list of ETAs for different paces, I wrote a simulator using PHP. It basically advances from light to light, calculates the time, determines if the light is red or green and calculates how long the total trip will take. I tested the numbers it turned up to see if there are any bugs. I couldn't find any, but if you think there is a mistake, let me know.

In this first blog post I will keep the light variables constant. I am not patient enough to wait at the corner with a stopwatch and measure how long it takes for the light to switch, so in order to get a rough idea, I counted seconds in my head while walking. Based on this highly unscientific measure, red and green lights each are about 45 seconds. There is a 5 second blinking red light period, which I lumped with the green, because the NYers treat it so. The lag between two lights is about 5 seconds. 20 Manhattan blocks make up 1 mile and that is my assumed trip distance.

The numbers can be seen on this table below. You have your speed, your pace on the left and total trip time, red lights hit and total wait time if you go with the traffic or against the traffic on the right.

As you see, for car-like speeds going with the traffic is much faster than against (and safer, if I may add). The slowest speed where going against the traffic becomes advantageous is 6 min/mile. However, the window there is pretty small. You have to hit a 6-6.5 min/mile pace consistently. The 11-18 min/mile pace range, which most regular human beings fall into, is divided into two. If you are on the faster end of the spectrum (ehem!), walking against the traffic saves about 20 percent; if not, it can be disastrous.  

Whichever way you are traveling, one interesting outcome is that there are vast speed ranges, where walking faster doesn't get you to your destination quicker. In fact, if you attempt such a North-South walk in Manhattan you will end up passing some people only to see them again at the next traffic light. It is very uncomfortable until one of you turns to a side street. (a little note here. These numbers are equal, because you come to a red light at the end of the last segment and you wait to cross it. If you ignore that red light, there are very small differences, because you traveled the distance between the last two lights faster.)

If I can get a chance, I would like to test different light lags to see what value would be the best to speed up pedestrian traffic. That will be the next post. Until then, walk carefully and let me know about your results if you give this a try.

Traffic light photo from Fotopedia.