curaqion

Issue #002 — November 2012

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If you replaced 2 train tracks with a dedicated 2 lane road and ran passenger buses would it be more efficient?

Amar Prabhu

A bus based rapid transit system is more efficient short term. A metro rail system will be more efficient and eco friendly long term (after 3-4 years), if its electricity is supplied from environment friendly sources.

Before explaining how the answer was arrived at, let me get the assumptions and the scope of this question out of the way. When considering the term "efficiency" for transporting people using different modes, the following factors have to be considered:

  • Efficiency at transporting passengers: Number of passengers transported per dedicated lane, per unit time
  • Energy efficiency: Carbon footprint of the transportation mode and setting up of infrastructure
  • Economical efficiency: Cost of infrastructure, energy source and maintenance that affects the cost of travel

To model this scenario faster, I am making the assumption that transportation of people is same as a computer network or a series of pipes. People are analogous to packets in a network or fluid through pipes. This eliminates lot of other calculations (at least 15-20 variables that I can think of) required to perform an analysis of real world traffic, while still maintaining accuracy to a reasonable degree. I am also comparing the carbon footprint of the different mediums so that a fossil fuel vehicle can be compared to a electric vehicle. Finally, all scenarios are the "cruise stage" of a vehicle where it is most efficient in terms of fuel efficiency, aerodynamic drag etc. Since the calculations are redundant and this is a matter of debate in many forums, I have included a motorcycle, a gasoline fuel car, a hybrid, an electric and an SUV as well, for comparison. I will try keeping this as simple as I can using the charts alone, the spreadsheet is below for those interested in the full details. Other than the initial data like length, width, motor rating, mileage to the gallon and passenger capacity (sourced from manufacturer website or Wikipedia), all calculations are done from scratch to maintain accuracy. I have compared the efficiency of all the transportation modes over a length of 100 kilometers, so extrapolate the base results as required.

Efficiency at transporting passengers / Passenger throughput:

Passenger throughput is the number of passengers transported per lane per unit time. In simple words, how many passengers can the system move? Factors that affect this are:

  • Passenger density (no of passengers per unit area)
  • Cruise speed (speed at which fuel efficiency is maximum)
  • Traffic density (degree of utilization of the lane)

Passenger density:

Passenger density is the number of people that can be transported per square meter of space available. It can be calculated by comparing the floor plans. For a bus, I am considering the ubiquitous Volvo chassis, used all over the world:

As an equivalent to the Volvo in a metro system, I am considering the R143 built by Kawasaki, used in NYC Subway:

The results for passenger density (higher is better) are as below:

Trains have the highest passenger density of 2.9 passengers per square meter

Cruise speed:

Though any vehicle is capable of high speeds, efficiency is maximum at the cruise speed where the factors like engine efficiency, drag, etc come together. The cruise speed (higher is better) of the different vehicles are:

Traffic Density:

Traffic does not denote conventional traffic here. It refers to how efficiently a lane is used. For example, there might be a train every 2 minutes or a train every hour. Distribution of traffic affects how many passengers can use the network. So traffic density is also a factor to be considered. If traffic density is 100%, that means that the lanes are utilised fully - maximum passengers are boarding an unlimited number of vehicles and moving at the cruise speed.

Though any vehicle is capable of high speeds, efficiency is maximum at the cruise speed where the factors like engine efficiency, drag, etc come together. The cruise speed (higher is better) of the different vehicles are:

Passenger throughput:

As assumed earlier, consider a 100 km stretch of lane(s) for each of the transport medium. Only other vehicles of the same type and speed are allowed, so that there is no hindrance in their movement.

To calculate the throughput, the number of passengers in the lane at any given point of time and the number of passengers who reach their destination are to be calculated. This is similar to volumetric flow rate of fluids, which is given by:

(change in volume and change in time are parameters)

The passengers mid way in the lane are eliminated for consideration. The size comparison of all the transportation modes are:

The passenger throughput for each of the transportation medium, is a pretty big dataset, so I am considering one particular case- passenger occupancy 60%, traffic density 30%. The lane width is 3.5 meters for vehicles and 4 meters for metro trains. So the passenger throughput (higher is better) is:

Trains are more more efficient at transporting people per lane - 153000 passengers an hour.

Energy Efficiency:

Energy efficiency of a particular transportation mode depends on two main factors:

  1. the vehicle/ engine efficiency
  2. the support infrastructure

Most studies I have come across neglect factor 2, which introduces a huge bias. For instance, when comparing an aircraft and a train for green credits, tail pipe emissions alone are considered. This method is flawed as trains require laying of tracks and maintenance activities performed on them, whereas aircraft need only the runway and the aircraft to be maintained. This becomes more significant when the plane is making a trans Atlantic flight. So applying the same to a bus/train comparison, a bus needs a road to run efficiently whereas a metro train usually runs underground with reinforced concrete floors and steel columns. Since green credits and energy efficiency are dependent on these too, I have included these as well for fair comparison.

Carbon foot print of the vehicle:

Carbon foot print is considered because the vehicles use different types of fuel. Motorcycles and cars use gasoline, whereas a bus uses diesel. Trains and electric cars use electricity. So the carbon emitted due to the use of the vehicle can be used to compare all these different transportation modes. Electricity comes from different sources with different carbon footprints, so for every 1Watt consumed at the socket, the power comes from different sources.

The world wide distribution of these sources are:

Considering these parameters and the miles to a gallon, the carbon emission per passenger (lower is better) for these different modes over a 100KM stretch is:

Few surprises here - Prius is the most economical personal vehicle, whereas trains and buses are close in terms of mass transport. Trains however have a edge of 250 grams of CO2 for every 100 KM.

Infrastructure related Carbon Footprint:

Infrastructure carbon footprint includes CO2 generated in the manufacture of the raw materials, construction of the infrastructure, transport of materials to the construction site etc. In several studies, this crucial and large contributor to efficiency is not included. Roads, bridges and every structure in the road use concrete. CO2 per ton of Concrete is in a ratio of 0.9:1 in many cases, and concrete manufacturing contributes to about 7% of world CO2 emissions. By this criteria, roads win hands down by a factor of 1300% initially. Trains catch up with the 250 grams of CO2 per 100 KM I had mentioned earlier for every passenger transported. After transporting a million passengers a day for 2 years in the case of overhead tracks or 10 million passengers a day for 3 years in the case of underground metro (by my estimates) they start being carbon footprint negative compared to buses. Consider the cross section of a underground metro system:

For an over head metro system, the cross section is as below:

Considering these three cases, the carbon footprint for these infrastructures (lower is better) are as below:

When including the infrastructure, Buses are the most efficient transportation medium.

Economical efficiency:

Economically, the cost for transporting a passenger is lowest for a train car. The Prius comes second. So the results for economical efficiency is:

For a metro train system, it saves 0.28$ per passenger. So if the system transports 10 million passengers a day, it will be recovering/paying for the initial investment after a period of 3.61 years to justify the extra investment.

So to summarize, comparing all the statistics together, we get:

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A bus based transit system is efficient for a period of 3-4 years, after which a light metro system starts yielding more returns (and efficiency) in terms of carbon emissions, cost per passenger and transporting people. This comparison is for a 100 KM length of a lane, factors like cost of infrastructure are to be extrapolated based on the distance of travel.

Trivia: The scenario described in the question actually exists in real life. In Sao Paolo (Brazil), buses have dedicated lanes (250 kms of them) and nearly 10 million people (the equivalent of everyone in Cuba) use it everyday, so my statement that buses are more efficient has some real world backing to it. Here is a picture of buses using dedicated lanes in Sao Paolo:

Disclaimer - This is a question with lots of assumptions, and I have tried to answer it to closely match real world problems. It is however just that - a simple analysis for fun and information, calculated over a few hours. Recheck the numbers yourself if you are using it for any REAL study. The values of infrastructure calculations are assumptions using concrete alone, so I expect the values to be off (smaller) by a large margin. The passenger density is dependent on many other factors like commuter preference, country etc. I do not accept any responsibility for errors in the calculations or gotchas which may arise(they usually do). You can find all calculations, and methods used here:

https://docs.google.com/spreadsh...

I would be happy to add/update anything that improves this answer, so comment away.

References:

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