You pay dearly for your fuel (or electricity, in case of an EV) but where does all the energy go?

Motoring is all about an energy balance. Without energy, a vehicle is just a static display and not the mode of transport (or fun driving machine) it was designed to be. It takes energy from the battery in the key fob to send a signal to open the doors; more energy from the vehicle’s auxiliary battery to light the cabin lights and instrument cluster; and another surge of power to crank the engine. This is all before the car has moved a single metre. We look at the energy-sapping components in a vehicle and investigate which portion of the energy realistically reaches the wheels.

Background on energy

The international system of units (SI) for energy is the joule, named for English physicist and mathematician James Prescott Joule, born in 1818. He discovered the relationship between mechanical work and heat which led to the law of conservation of energy. This law states the total energy of an isolated system remains constant and, although energy can be transformed, it cannot be created or destroyed. One joule is equal to a force of one newton applied to an object over one metre (N.m). In an electrical sense, one joule is equal to the work required to move one coulomb (electrical charge) through an electrical potential difference of one volt (CV). When talking about work, a watt is the unit describing one joule per second.

Investigation

For this exercise, we will consider a Volkswagen Golf 7 GTI travelling on a level road at 120 km/h. We will start with the external forces acting on the vehicle first, then the auxiliary loads on the engine before considering powertrain efficiency.

Electric GTI?

If we converted the Golf to an EV with an electric motor (and power electronics) efficiency of 90%, then only 36,4 kW (32,75 kW/90% = 36,39 kW) electric power would be required from the battery at 120 km/h. Therefore, 30,32 kWh will be needed in 100 km. At an electricity cost of R1,50/kWh, the cost would be R45,49 compared to R121,67 for petrol.

1. Drag force [16 kW]

At speed on a level road, one of the main forces opposing vehicle motion is aerodynamic drag force (Fdrag). The formula of the drag force which is measured in Newton is:

Fdrag = ½ρV2 ACd

where

ρ = air density [kg/m3]

V = vehicle speed [m/s]

A = frontal area [m2]

Cd = coefficient of drag

If we calculate the drag force of the Golf GTI (frontal area 2,59 m2, Cd = 0,27, ρ = 1,2 kg/m3) for a vehicle speed of 120 km/h, we have 466 N. To calculate the work done involves multiplying this drag force by the vehicle speed in metres per second (33,33 m/s). This equals 16 kW just to overcome aerodynamic drag at 120 km/h and this figure increases to 141 kW at the top speed of 250 km.

2. Rolling resistance [7 kW]

The flexing and recovery of the rubber at the contact patch of a tyre to the road surface creates a resistance force to motion that needs to be overcome by the powertrain. Although tyre manufacturers are continuously striving to lower the rolling-resistance coefficient of new tyres, there is a conflict between low rolling resistance and tyre performance (as performance tyres tend to use softer compounds). The average value for rolling resistance is around 0,015, with the basic formula:

Frolling= Crr mg

where

Crr = coefficient of rolling resistance [m/s2]

m = vehicle mass [kg]

g = gravitational constant [9,81 m/s2]

Therefore, the (simplified) rolling resistance force is independent of speed and equal to 221 N. The power consumption is calculated by multiplying the drag force by the vehicle speed in metres per second, which rounds to 7 kW.

3. Electrical energy [1 kW]

In a vehicle with an internal-combustion engine without electric recuperation capability, it is easy to forget the electrical energy needed also comes indirectly from the fuel consumed. It is difficult to determine the average electrical load on a vehicle because it depends on the driving conditions (day/night/rain) and user profile (infotainment system and heated seats status, for example). The minimum power needed for a petrol vehicle to run is around 200 W (ECU, fuel pump, ignition, etc.). The table below depicts general electrical loads and we will use an average of 1 000 W (1 kW) for this example.

Electrical loads Consumption
Running of ICE (ignition, fuel pump, ECU, etc.) 200 W
Cranking during start of engine 2 400 W
External lights 300 W
Wipers 130 W
Electric window 150 W
Heated rear window 120 W
Horn 40 W
Heating and ventilation (blower) 80 W
Cigarette lighter 100 W
Seat movement (electrical) 150 W
Seat heater 200 W
Sunroof motor 150 W
Infotainment system 50 W

4. Air-conditioning [3 kW]

A major auxiliary power consumer is an air-conditioning system. To produce cold air, a compressor is employed which is usually powered by the engine’s auxiliary belt. In the case of heating the cabin, the normally wasted engine heat (in the coolant) is used to heat the incoming air as it passes through a heater matrix (or radiator). In this case, little extra power is consumed.

Another significant parasitic loss used to be the hydraulic steering pump. However, as most vehicles employ electric power steering these days, energy is consumed only when the steering wheel is turned.

Engine and drivetrain efficiency

The potential chemical energy in fuel (around 34 MJ/L for petrol and 37 MJ/L for diesel) is converted to (crank) shaft power in an internal-combustion engine. Although around 99% of the fuel’s chemical energy is extracted, roughly only a third produces useful work while a third is lost to the cooling system and the final third escapes down the exhaust pipe. As the direct-injection turbopetrol engine in the GTI employs advanced technologies, we can assume a 38% efficiency in converting the energy in petrol to crankshaft power while cruising.

The torque moment (and power) at the crankshaft still needs to make its way to the driven wheels. This means it has to pass through the transmission, differential and drive shafts (each with an efficiency loss) before it reaches the wheels. Then, there are additional losses such as brake-pad drag and bearing friction that must be taken into account. For a front-wheel-drive vehicle like the GTI, a total power loss between the crankshaft and driven wheels is estimated at 20% (this brings total powertrain efficiency down to 30%). Therefore, the power to overcome aerodynamic drag and rolling resistance needs to be adjusted upwards to reflect the figures required at the engine’s crankshaft (the electrical and air-con loads are already present at the crankshaft). The aerodynamic drag is now 20 kW and rolling resistance 8,75 kW at the crankshaft.

Theoretical fuel consumption

For the Golf to drive in equilibrium on a level road at 120 km/h, the engine needs to produce power equal to all the opposing forces and auxiliary losses. If we sum up all the aforementioned required power figures (aero and rolling resistance now adjusted to crankshaft), we get 32,75 kW. Because the total engine efficiency is only around 38%, the total fuel energy needed is about 86 kW (32,75/38%) or 86 kJ/s.

To cover 100 km driving at 120 km/h takes 50 minutes, which equals 3 000 seconds. Therefore, the total energy needed in fuel is around 259 MJ (86 kJ x 3 000 seconds). As petrol contains roughly 34 MJ/L, the total fuel needed per 100 km is 259/34, which equals 7,6 litres. The GTI would require roughly 7,60 L/100 km when driving on a flat road at 120 km/h. The table below shows what you are paying for per 100 km.  

Energy cost breakdown per 100 km at 120 km/h
Fuel consumption predicted 7,60 L
Petrol cost
(@ R16,00/L)
R 121,67
Wasted energy (exhaust and cooling) R 75,44
Aerodynamic drag R 28,24
Rolling resistance R 12,35
Electrical loads R 1,41
Air-con R 4,23