Fuel Consumption: Newton's Second Law

As oil is depleting, the price of vehicle's fuel is likely to shoot up. In reality, fuel price will not be dropped although the value of global crude oil is falling. Hence, it is very important to pick a car that has good fuel consumption or fuel economy in order to reduce financial burden.

Without sophisticated understanding about the technology and mechanism behind a vehicle, Newton's Second Law is the simplest way to identify a car with fuel economy since Newton is the OG of classical mechanic such that we still apply Newton's Law today. Just to refresh the memory,

F = ma

The Statement:
"The resultant force (F) acted on an object is directly proportional to the mass (m) of the object and the acceleration (a) of the object where the direction of the resultant force acted on the same direction as the accelaration"

However, a more fundamental version of Newton's Second Law is 

F = kma

where k is the proportionality constant.

Extra Fact: 

With the rise of quantum mechanic, modern physicist concluded that k is Lorentz Factor in order to apply Newton's Second Law in the quantum world so k is unnecessary equal to 1.

Experimentally, scientist discovered that k is approximately to 1 hence if you rearrange the fundamental form of Newton's Second Law as shown below.

k = F / ma

The significance of k is it defined the physical quantity, Newton (N).

What does 1N of  force means?

With definition of k,
In order to accelerate an object with 1 kg of mass such that there is an increment of 1m/s for each second, it need 1 N of force.

Some engineer and physicist consider Newton's Second Law as the Conservation of Mechanical Energy.

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Automotive Example:

Mass of a vehicle: 1100 kg

Acceleration from 10km/h to 20km/h within 5 sec.

Acceleration (m/s/s): 0.556 m/s/s

Amount of force required to accelerate 1100kg of car from 10km/h to 20km/h within 5 sec require 611.6 N.

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As mentioned Newton's Second Law is Conservation of Mechanical Energy hence there is a relationship between force and energy.

The moment the car accelerate, it has apply work. In physic, Work Done (W) is defined as

W = Fs

where s is the distance travelled.

Combining the definition of F and W, we get

W = m x a x s

In short, the car will apply more work (or more fuel would be consumed) when the car is heavier, rapid change in acceleration and the longer the distance travelled.

Of course, distance travelled and acceleration are essential, there is no way we could change our driving habit to minimize the accelerating behaviour and the distance travelled. However, the MASS of the vehicle is something we can decide.

In short, the lighter the car, less fuel would be consumed.

Therefore, smart consumer will not fill in their oil tank in 100%, optimum around 80%  because they want to reduce the loading on the vehicle.

In fact, I wrote this topic dedicated to fellow Malaysians who need to drive in order to earn a living therefore it is very common that a family of 4 members would have 4 cars in Malaysia.

Since it is likely that only the driver alone in the car so it is smarter to pick a car that is 1000kg - 1200kg in order to save fuel.

Of course, engine efficiency and power transmission efficiency are major factors that affect the fuel consumption however I will assure you that even an high efficiency 2000kg cars would consume more fuel than a low efficiency 1000kg cars. Because Newton had taught us that the amount of work done require to move a massive object under 100% efficiency.

However, there is one factor to be considered, the maximum engine output of the vehicle. A simple way to identify the maximum engine output is determine its engine capacity/engine size.

Ever wonder what does 1300cc means?

Just a reminder, we called it Internal Combustion Engine because there is a combustion process require both fuel and air.

1300cc means the amount of air required to start the combustion.

In order to have a good combustion efficiency, the greater the engine capacity would require more fuel to be consumed.
In short, more air in, more fuel would be consumed.

Therefore, typical sport cars like Ferrari and Lamborghini were unlikely to have good fuel economy. It has a relative lower mass but its engine capacity was at least 3800cc. In another words, it consumed more fuel then it needed to travel a specific distance. Another good example would be Aerial Motor's Atom that used Honda Civic's K20A engine. Its mass was about 700kg only but it used a 2000cc engine hence it burned more fuel than it needed because Newton told us that it didn't really need that much of energy to accelerate respective to its mass.

Ideally, mass of car from 1000-1200kg just require 1300cc to 1500cc based on my experience in vehicular exhaust emission industry.

Considered that Japan placed very high priority in environment protection, each year they would update the fuel economy of each vehicle according to its mass. [1] Similarly, Macau Government offered tax exemption to eco-friendly vehicle. [2]

In fact I did plot a graph to combined both Japan and Macau Vehicular Exhaust Emission Standard as shown below:

Fuel Economy Target vs Average Mass of Vehicle

By showing real example on two different policies, we could see that policy makers expected heavier vehicle would have lower fuel economy.

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Automotive Example 2:

Based on the manufacturer website[3], they claimed that Lamborghini Huracan LP610-4 has a fuel consumption of 8km/l (12.5 l/100km)
The dry weight =  1422 kg

According to Japan's Fuel Economy target, Lamborghini Huracan failed to meet the Fuel Economy Target as it required at least 13km/l.

Similarly, it also failed to get tax exemption from Macau Government as Macau Government expect its fuel consumption to be at least 17km/l.
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With this guidance and two real example from Japan and Macau, I hope my friends has a simple understanding on fuel consumption.

One more example dedicated to Malaysian drivers.
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Automotive Example 3:

Based on the manufacturer website[4], they claimed that Perodua Axia 1.0 Standard E - Manual has a fuel consumption of 21.6km/l
The kerb weight =  820 kg

According to Japan's Fuel Economy target, Perodua Axia achieved the standard as it expect to be above 18.8km/l.

However, it also failed to get tax exemption from Macau Government as Macau Government expect its fuel consumption to be at least 23.8 km/l.
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Two important lessons I expected my fellow readers realized them;

Lesson#1:"Lighter the car, less fuel will be consumed provided the engine capacity is optimum"

Lesson#2:
"Fuel Consumption alone does not define the magnitude of eco-friendliness, it depend on its mass and which country's policy"

Reference:

1. http://delphi.com/docs/default-source/catalogs/delphi-worldwide-emissions-standards-pc-ldv-15-16.pdf?sfvrsn=2
2. http://bo.io.gov.mo/bo/i/2015/14/despce_cn.asp#59
3. http://www.lamborghini.com/en/models/huracan-lp-610-4/technical-specifications/ 
4. http://www.perodua.com.my/specification/axia



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Fuel Consumption: Newton's First Law

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