How much wood would a woodchuck chuck, and other problems of estimation

I recently read a report in the newspaper. A company claimed to charge an Electric Vehicle in 15 minutes. Typical charging times are overnight or around eight hours. This was obviously a newsworthy claim, and it set me thinking. I know a thing or two about basic science and maths, and I asked myself the equivalent of the proverbial question “How much wood would a woodchuck chuck?”

I checked out that the batteries of today’s cars allow a journey of 400 – 500 km as a specification. I would take half of this figure to make the estimate. So how much energy is required to move a car with, let’s say, two passengers, a distance of 250 km in 4 hours. I know that my petrol-driven car gives me an average of 15 Km/litre on the highway and hence one would end up consuming 16.67 litres of petrol for the trip. If one computes the amount of energy in the 16.67 litres of petrol and accounts for the conversion efficiency, one would arrive at the energy used up during the trip.

The conversion efficiency could be determined by determining the energy losses, and subtracting them from the energy content of the fuel. The losses could be estimated by finding out how much fuel is consumed when the engine is merely idling. One could also estimate the losses in the heat of the exhaust, the heat lost in the engines through the radiator, the general heat loss through the body, the heat lost in the brake pads. Energy lost as the vehicle moves through the air (viscous losses) and friction losses in the moving parts. This is how my engineering brain buzzed.

A small voice in my head suggested a simple way of doing it. The published figures for the efficiency of a petrol engine is 30%. Also the calorific value of petrol is 47000 KJ/kg, and the density of petrol is 0.74.

Since one consumed 16.67 litres of petrol for a trip of 250 Km, it would allow us to estimate the energy used as = 16.67 * 0.74 * 47000 = 579510 KJ (Kilo Joules). Knowing the efficiency of the petrol engine to be 30%, the effective energy used for the trip would be = 0.30 * 579510 KJ = 173853 KJ. (This figure matches very well with the 318.2 Wh/Km of the MOBILE6 adjusted AC electricity consumption – Reference 1).

If the trip was undertaken by an electric car then after the trip was over, this much of energy would be needed to put back into the car battery, if the car was an electric car.

Hey, wait. The electric car is much more efficient that the petrol car. When the brake is applied in the electric car, the kinetic energy of the car is fed back to the battery and very little power is lost. It turns out that electric cars have an efficiency rating of 80 to 90%. So would the energy required to complete the trip still be 173,853 KJ? The answer after some thought was yes. The energy for the trip is still the same as it is the energy required to move a vehicle with passengers a distance of 250 Km, traveling at a speed of 60 Km/hour in a viscous fluid called air.

The time required for pumping 173853 KJ at the rate of 4 KJ/second (which is what 4 KW charger capacity represents) = 173853/4 = 43463 seconds or roughly 12 hours, 4 minutes. Typical car chargers deliver around 4 to 5 KW of charging power, and rarely are batteries fully discharged, which explains why it would take six to eight hours or an overnight charge to completely charge the battery.

On the other hand, if it was indeed required to charge the battery in say one hour, then the power required to be delivered by the charger = 173853/3600=48 KW.

Now that’s going to be a brute of a charger.

Multiple chargers of ratings of the order of 4 to 16 KW, working in parallel would be able to charge a car in a good fraction of the hour. This is where the current modern day Electric Vehicle charging systems seem to be headed.

I was able to estimate a claim that seemed outlandish to me at first glance with some basic pieces of information. There was a time when this information was available in textbooks and tables and only engineers and scientists might have copies of them on their bookshelves. Today this information is available at our fingertips on the internet. So with access to this information, and by practicing the techniques of estimation, a young person (or any person) may assess claims before investing their time and money into a technology. Similar techniques are also used to establish early feasibility of an idea.

In real life we may come across many statements where the full information is not provided. You can use estimation methods to determine the correctness of these statements with some degree of confidence. This is a scientific approach. With this story I hope to be able to pass on the technique of making estimates using incomplete input.

There are many formal courses where weighty terms like simulation, specifications gathering and other such abstract terms are used. They have a place in formal discourse, and my daughter, with all the training from her advanced degrees, loves to use them. I find them to be both too boring and too abstract to teach to any young apprentice. What I believe to be the central concept to teach is this: in addition to subject matter expertise, what goes into making a machine? With this central concept I return to my blog after a few months break. I hope to hear from those who read the blog about what caught their interest in current news, or what they might like to hear about next.

Bibliography:

1. Tammy Thompson et al 2009 Environ. Res. Lett. 4 014002 Air Quality Impacts of using Overnight Electricity generation to charge plug-in hybrid electric vehicles for day time use.