BU-1006: Cost of Mobile and Renewable Power (2022)

Lifting off in a large airplane is exhilarating. At a full weight of almost 400 tons, the Boeing 747 requires 90 megawatts of power to get airborne. Take-off is the most demanding part of a flight and when reaching cruising altitude the power consumption decreases to roughly half.

Powerful engines were also used to propel the mighty Queen Mary that was launched in 1934. The 81,000-ton ocean liner measuring 300 meters (1,000ft) in length was powered by four steam turbines producing a total power of 160,000hp (120 megawatts). The ship carried 3,000 people and traveled at a speed of 28.5 knots (52km/h). Queen Mary is now a museum in Long Beach, California.

Table 1 illustrates man’s inventiveness in the quest for power by comparing an ox of prehistoric times with newer energy sources made available during the Industrial Revolution to today’s super engines, with seemingly unlimited power.

SinceType of power source

Generated power

3000 BCOx pulling a load0.5hp370W
350 BCVertical waterwheel3hp2,230W
1800Watt's steam engine40hp30kW
1837Marine steam engine750hp560kW
1900Rail steam engine12,000hp8,950kW
1936Queen Mary ocean liner160,000hp120,000kW
1949Cadillac car160hp120kW
1969Boeing 747 jet airplane100,000hp74,600kW
1974Nuclear power plant1,520,000hp1,133,000kW

Large propulsion systems are only feasible with the internal combustion engines (ICE), and fossil fuel serves as a cheap and plentiful energy resource. Low energy-to-weight ratio in terms of net calorific value (NCV) puts the battery against the mighty ICE like David and Goliath. The battery is the weaker vessel and is sensitive to extreme heat and cold; it also has a relatively short life span.

While fossil fuel delivers an NCV of 12,000Wh/kg, Li-ion provides only between 70Wh/kg and 260Wh/kg depending on chemistry; less with most other systems. Even at a low efficiency of about 30 percent, the ICE outperforms the best battery in terms of energy-to-weight ratio. The battery capacity would need to increase 20-fold before it could compete head-to-head with fossil fuel.

Another limitation of battery propulsion over fossil fuel is fuel by weight. While the weight diminishes when being consumed, the battery carries the same deadweight whether fully charged or empty. This puts limitations on EV driving distance and would make the electric airplane impractical. Furthermore, the ICE delivers full power at freezing temperatures, runs in hot climates, and continues to perform well with advancing age. This is not the case with a battery as each subsequent discharge delivers slightly less energy than the previous cycle.

Power from Primary Batteries

Energy from a non-rechargeable battery is one of the most expensive forms of electrical supply in terms of cost per kilowatt-hours (kWh). Primary batteries are used for low-power applications such as wristwatches, remote controls, electric keys and children’s toys. Military in combat, light beacons and remote repeater stations also use primaries because charging is not practical. Table 2 estimates the capability and cost per kWh of primary batteries.

AAA cellAA cellC cellD cell9 Volt
Capacity (alkaline)1,150mAh2,850mAh7,800mAh17,000mAh570mAh
Energy (single cell)1.725Wh4.275Wh11.7Wh25.5Wh5.13Wh
Cost per cell (US$)$1.00$0.75$2.00$2.00$3.00
Cost per kWh (US$)$580$175$170$78$585

Power from Secondary Batteries

Electric energy from rechargeable batteries is more economical than with primaries, however, the cost per kWh is not complete without examining the total cost of ownership. This includes cost per cycle, longevity, eventual replacement and disposal. Table 3 compares Lead acid, NiCd, NiMH and Li-ion.

Lead acid

NiCd

NiMH

Li ion

Specific energy (Wh/kg)30–5045–8060–120100–250
Cycle lifeModerateHighHighHigh
Temperature performanceLow when cold-50°C to 70°CReduced when coldLow when cold
ApplicationsUPS with infrequent dischargesRugged, high/low temperatureHEV, UPS with frequent dischargesEV, UPS with frequent discharges
Cost per kWh ($US)
Load leveling, powertrain
$100-200$300-600$300-600$300–1,000

~$100 (2021)

Power from Other Sources

To reduce the fossil fuel consumption and to lower emissions, governments and the private sector are studying alternate energy sources. Table 4 compares the cost to generate 1kW of power that includes initial investment, fuel consumption, maintenance and eventual replacement.

Fuel typeEquipment
to generate 1kW
Life spanCost of fuel
per kWh
Total cost
per kWh
Li-ion
Powertrain
$500/kW (20kW battery
costing $10,000)
2,500h (repl. cost $0.40/kW)$0.20$0.60
($0.40 + $0.20)
ICE in vehicle$30/kW
($3,000/100kW)
4,000h (repl. cost $0.01/kW)$0.33$0.34
($0.33 + $0.01)
Fuel cell
- portable
- mobile
- stationary
$3,000–7,5002,000h
4,000h
40,000h
$0.35
->
->
->

$1.85 – 4.10
$1.10 – 2.25
$0.45 – 0.55
Solar cell$12,000, 5kW system25 years$0~$0.10*
Electricity
electric grid
All inclusiveAll inclusive$0.20
(average)
$0.20

* Amortization of investment yielding 200 days of 5h/day sun; declining output with age not included.

Power from the electrical utility grid is most cost-effective. Consumers pay between $0.06 and $0.40US per kWh, delivered with no added maintenance cost or the need to replace aging power-generating machinery; the supply is continuous. (The typical daily energy consumption per household in the West is 25kW.)

The supply of cheap electricity changes when energy must be stored in a battery, as is the case with a solar system that is backed up by a battery and in the electric powertrain. High battery cost and a relatively short life can double the electrical cost if supplied by a battery. Gasoline (and equivalent) is the most economical solution for mobility.

The fuel cell is most effective in converting fuel to electricity, but high equipment costs make this power source expensive in terms of cost per kWh. In virtually all applications, power from the fuel cell is considerably more expensive than from conventional methods.

Our bodies also consume energy, and an active man requires 3,500 calories per day to stay fit. This relates to roughly 4,000 watts in a 24-hour day (1 food Calorie* = 1.16 watt-hour). Walking propels a person about 40km (25 miles) per day, and a bicycle increases the distance by a factor of four to 160km (100 miles). Eating two potatoes and a sausage for lunch propels a bicyclist for the afternoon, covering 60km (37 miles, a past-time activity I often do. Not all energy goes to the muscles alone; the brain consumes about 20 percent of our intake. The human body is amazingly efficient in converting food to energy; one would think that the potato and sausage lunch could hardly keep a laptop going for that long. Table 5 provides the stored energies of calories, proteins and fat in watt-hours and joules.

* A calorie specifies the energy level food provides to the body. Kilocalories on food packages and related nutrition are normally published in “Calories with capital “C”. Example: 800 Calories on the food label are in essence 800 kilocalories. Table 5 below uses the official standard of 1.16mWh/cal.

CaloriesMilliwatt-hourJoule
Food calorie11.164,184
1 gram of protein44.6416,736
1 gram of carbohydrate44.6416,736
1 gram of body fat910.4637,656

Table 6 compares the estimated power and energy per passenger/kilometer for a loaded Boeing 747, the retired Queen Mary ocean liner, a gas-guzzling SUV, a fit person on a bicycle, and walking on foot.

FunctionBoeing 747
jumbo jet
Ocean liner
Queen Mary
SUV
or large car
Bicycle
(Bike & rider)
On foot
Full weight369 tons81,000 tons2.5 tons100kg (220lb)80kg (176lb)
Cruising speed900km/h
(560 mph)
52km/h
(32mph)
100km/h
(62mph)
20km/h
(12.5mph)
5km/h
(3.1mph)
Maximum power77,000kW
(100,000hp)
120,000kW
(160,000hp)
200kW
(275hp)
2,000W
(2.7hp)
2,000W
(2.7hp)
Power at cruising65,000kW
(87,000hp)
90,000 kW
(120,000hp)
130 kW
(174hp)
80 W
(0.1hp)
280 W
(0.38hp)
Passengers4503,000411
Power per passenger140kW
580kJ*
40kW
2,800kJ*
50kW
1,800kJ*
80W
14.4kJ*
280W
200kJ*

* 1 joule is the energy of 1A at 1V for 1 second, or 1 watt times second.
4.186 joules raise the temperature of 1g of water by 1 Celsius; 1,000 joules are 0.277Wh.

The bicycle is by far the most effective form of transportation. Comparing a bicycle to a car, a cyclist would only consume 0.4 liter of fuel per 100km (630mpg). Walking is also efficient; it uses about 1 liter per 100km (228mpg). The problem with self-powered propulsion is the limited travel range before fatigue sets in.

In terms of energy usage, cars are one of the least efficient modes of transportation. Most ICEs utilize only 25 percent of the net calorific value from the fuel for propulsion. The math looks even worse when including vehicle weight and a single passenger, the driver. The ratio of machine to man is about ten-to-one, higher on a large vehicle. When accelerating a 1.5-ton vehicle, less than 2 percent of the energy moves the 75kg (165 lb) driver, his briefcase and his lunch bag; 98 percent goes to heat and friction. Even a modern jet plane has better fuel efficiency than a car. A loaded Airbus 340 gets 3.4l/100km (70mpg), cruising at 950km/h (594mph).

Trains are one of the most efficient modes of transportation. The 36km Yamanote circle line, connecting major urban centers in Tokyo carries 3.5 million passengers per day. During rush hour, the 11-car train runs every 150 seconds. Such a passenger volume would be unthinkable by private cars on city streets.

Modern trains are less intrusive than freeways to move people and goods. Building efficient public transportation systems would give cities back to the people who are the rightful owners. The most desirable cities were built before the arrival of the car as designers had the well-being of people in mind. Trains are also economical to move freight. Transporting one ton of freight consumes only 0.65 liters of fuel per 100km (362mpg).

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