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Original title: "how to drive scientifically?" "

Photo Source: picjumbo_com / Pixabay for motorists, the cost of gas is undoubtedly one of the most important expenses of daily driving. Fluctuations in oil prices always involve the nerves of old drivers. Therefore, "how to save fuel" is always a topic that drivers like to talk about when communicating.

There are many factors affecting the fuel consumption of driving. For example, reducing the unnecessary load on the car, avoiding the aggressive driving behavior of frequent acceleration and deceleration, and turning off while waiting for a long time can all save fuel consumption.

Compared with these trivial factors, it seems easier to talk about "how fast is the most fuel efficient", especially at a constant speed. So is there a so-called "optimal speed" or the most economical speed that can minimize fuel consumption?

There is a simple answer to this question: neither fast nor slow is the best, too fast or too slow will increase fuel consumption, and there is a U-shaped relationship between fuel consumption and speed. However, specific to how much speed to drive is the most fuel-efficient, different cars will have some differences.

It is best for the most common fuel cars, where the chemical energy released by burning fuel in the engine provides all the power. After passing through layers of transmission systems, the energy is finally transferred to the wheels and converted into the kinetic energy of the vehicle.

Image source: in the process of driving, the efficiency loss in the vehicle transmission system, the rolling friction between the wheel and the ground, and the air resistance (wind resistance) of the vehicle will continue to consume energy. this is why the car still consumes fuel even at a constant speed. If the complex model is simplified, the road load (road load, that is, the resistance of the vehicle) can be expressed by a quadratic function under the condition of constant speed and no slope.

F corresponds to the resistance of the car, as well as the traction needed to drive at a uniform speed. Among them, coefficients A, B and C are all characteristic attributes of vehicles, and there are differences among different vehicles. A corresponds to the wheel rolling friction, braking system and wheel bearing friction, B corresponds to the wheel rolling friction and various pump devices, and C corresponds to the wind resistance that we are most familiar with.

Obviously, due to the existence of wind resistance, there is a quadratic function relationship between road load and vehicle speed. When the speed is fast, the driving resistance will increase sharply. Therefore, driving at high speed itself is very fuel-consuming. Studies have conducted experiments on 15 different cars and found that the fuel economy (the distance per unit volume of fuel) is reduced by 15% to 44% at a speed of 120 km / h compared to a speed of 90 km / h; in other words, driving the same distance, 120 km / h costs 18% more fuel than 90 km / h. The U.S. Department of Energy's recommendation also points out that driving at high speed reduces fuel economy by 15% to 30%.

On the other hand, why is it more expensive to drive too slowly? This is related to the energy transfer efficiency of the mechanical system. In fact, only a small portion of the chemical energy stored in the fuel can actually be transferred to the wheels to maintain the kinetic energy of the car. Some studies have found that at low speed, the efficiency of engine, gearbox and clutch is significantly lower than that of medium and high speed, because the gear (that is, gear ratio) affects the efficiency of the mechanical system.

Among them, the engine is the component with the greatest loss of efficiency, which is only about 10% at low speed and only about 30% at high speed. On the other hand, the efficiency of the gearbox and clutch in the transmission system is more affected by the gear, especially the efficiency of the gearbox changes step by step with the shift. In some models, the efficiency of the gearbox in the low gear is less than 50%. And the efficiency of the high-end position is close to 100%.

The curve of the efficiency (%) of the Ford focus mechanical system with the speed (km / h). (photo source: https://dspace.mit.edu/ handle / 1721.1ax 58392) therefore, although the external resistance of the car is small at low speed, the decrease in internal efficiency not only offsets this difference, but also leads to a surge in fuel consumption. When the speed increases, the resistance increases slightly, the efficiency increases significantly, and the overall fuel consumption decreases. At this time, the car is in the range of economic speed. Once the speed is too high, the wind resistance will increase sharply, and the efficiency will reach the bottleneck or even decrease slightly, so the fuel consumption will also increase.

How fast is the most fuel efficient? As mentioned earlier, the most fuel-efficient speeds of different models are not the same. A 1988 study tested 15 different cars and found that their optimal speeds were between 28km / h and 78km / h, with the lowest speed being the Toyota Corolla produced in 1982 and the highest Chevrolet Citation in 1982. Generally speaking, the optimal speed of 10 cars is between 40km / h and 70km / h.

More recent studies have yielded more or less the same results. In 2008, a study by Tsinghua University tested 10 different cars and found that the optimal speed was between 50km / h and 70km / h. These cars cover some of the more common models, including Volkswagen Santana, Jetta, Passat and so on, and the results are more referential for ordinary people. For example, the optimal speed of the 2001 Volkswagen Jetta is 65 km / h.

However, in actual driving, it is almost impossible to keep the speed at a certain value. Fortunately, when the relative optimal speed fluctuates up and down within a certain range, the loss of fuel economy will not be very great. The 1988 study found that, on average, if the range of fluctuation was less than 8 km / h, the loss of fuel economy would not exceed 5%; if the range of fluctuation was less than 19 km / h, the loss of fuel economy would not exceed 15%.

Honda Accord (square), Honda Civic (triangle), Ford Explorer (diamond) and Ford focus (round) 100km fuel consumption (liter) versus speed (km / h). (photo source: https://dspace.mit.edu/ handle / 1721.1Accord 58392) A 2010 study simulated Honda Civic, Ford focus, Honda Accord and Ford explorers and found that in a certain speed range, the fuel consumption of 100km can be controlled at less than 5% higher than the fuel consumption at the optimal speed-for the Ford focus, the narrowest range is 63-70 km / h. For Honda Accord, this range is the widest, at 48-63 km / h.

The general rule is that due to the different models, test methods, conditions and other factors in different studies, the results obtained in these studies are also quite different, but on the whole, the optimal speed is generally in the range of 40-50 to 70-80 km / h, which is about the same as the usual speed on urban trunk roads, outer ring roads, secondary roads and other roads with smooth road conditions.

In addition, the study also found some general rules related to the optimal speed. For example, the optimal speed of a large car seems to be higher than that of a small car, with an average speed of 44 km / h, 59 km / h and 68 km / h for cars with 4-cylinder, 6-cylinder and 8-cylinder engines, respectively. When going downhill, for every 1% increase in slope, the optimal speed will increase by about 5 km / h. The 2010 study summarized the effects of wind resistance, power-to-weight ratio and gear on fuel consumption (see table below).

As the metric of the corresponding column increases, ↑ indicates that the metric of the corresponding row increases, while ↓ indicates that it decreases. (source: https://dspace.mit.edu/ handle / 1721.1Accord 58392) you may think that many of the previous results are sporadic data that seem neither universal nor easy to remember. It is indeed very difficult to establish a purely theoretical model of the relationship between fuel consumption and speed, but some studies have made approximate estimates through a large number of tests. In a study published in 2013 by Oak Ridge National Laboratory, researchers used 74 cars and tested them at a constant speed of 50 miles per hour (80 miles per hour). Several models are built to fit the fuel economy of the vehicle.

Among them, the simplest model uses only two variables: in addition to the speed, there is also the nominal MPG value of the vehicle, which is a fuel efficiency index evaluated according to the regulations of the United States Environmental Protection Agency (EPA). Its value is not equal to the true fuel efficiency of the vehicle, but reflects the fuel efficiency of the vehicle to a certain extent. The formula for this model is also relatively simple:

The MPG on the left of the equal sign is the actual fuel efficiency in miles per gallon, while the X on the right is the nominal MPG,v and the speed is in miles per hour. If the variables are expressed in common metric units, the formula is approximately as follows:

Take the latest Toyota Corolla as an example, its nominal MPG is 40 under highway conditions. After being substituted into the formula, the variable is converted into metric units, and the result is

In other words, within the speed range considered in the study, the higher the speed per hour, the worse the fuel economy. Considering that the speed range of the study has exceeded the usual optimal range we mentioned earlier, it is also normal to have such a monotonous trend. It can be seen from the formula that for every 1 km / h increase in speed, the mileage of 1 liter of fuel can be reduced by more than 200 m; compared with the fuel consumption of 100 km / h (3.88 liters), the fuel consumption of 100 km / h (4.65 liters) is 20% higher than that of 120 km / h (5.81 liters) is 50% higher.

Photo Source: Taras Makarenko / Pexels suppose you live in a big city with a daily commute of 50 kilometers. According to the legal working day of 250 days a year and the oil price of 9 yuan / liter, compared with the speed of 120km / h, driving the Toyota Corolla at 80km / h can save nearly 2200 yuan a year, enough to buy a phone with good performance.

Time is money? Some readers may think that driving fast consumes fuel, but it can save their precious time, which can be spent on working to earn money, and may eventually offset the extra gas money, or even make a profit. Rhett Allain, an associate professor at the University of Louisiana in southeastern America, also expected this. So he suggested that taking into account the oil price and personal income, it is the most economical to calculate how fast the car is going.

Assuming that the time saved on the vehicle can be fully converted into income from normal work, the total cost of driving to and from the commute can be expressed as:

In other words, the total cost per commuter distance is:

Where Δ x is the driving distance, G is the oil price, and R is the income per unit time. After derivation, it can be concluded that the larger the ratio of G to R, that is, the higher the oil price and the lower the income level, the slower the most economical speed.

Professor Allain also provides a simple Python code that can easily calculate the most economical speed (accurate to 1 km / h). For example, if the oil price is 9 yuan / liter, if the hourly wage is 30 yuan, the most economical speed will be 90 km / h; if the hourly wage is 60 yuan, the most economical speed will reach 107 km / h; if the hourly wage is 150 yuan, the most economical speed will reach 128 km / h.

Of course, it should be emphasized that, after all, such a model is oversimplified, and many of the assumptions in this paper are not valid in real life. No matter what the result, the most important thing is to obey the traffic laws and regulations and not to exceed the speed limit. If you really want to save fuel, change some personal driving habits, or, where feasible, take public transport, ride a bike or commute on foot, or live closer to work.

Or change to a high-paying job and don't have to think about it.

Reference link:

Https://www.wired.com/story/is-there-an-optimal-driving-speed-that-saves-gas-and-money/

Https://www.fueleconomy.gov/feg/driveHabits.jsp

Https://doi.org/10.4271/2013-01-1113

Https://doi.org/10.1016/0191-2607(88)90036-2

Https://doi.org/10.1016/j.trd.2008.09.002

Https://dspace.mit.edu/handle/1721.1/58392

Https://www.fueleconomy.gov/feg/Find.do?action=sbs&id=44074

This article comes from the official account of Wechat: global Science (ID:huanqiukexue), written by Li Shiyuan, revised by Wang Yu

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