BU-1006: Cost of Mobile and Renewable Power

Compare battery energy with fossil fuel and other resources

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.
 

Since Type of power source Generated power
3000 BC Ox pulling a load 0.5hp 370W
350 BC Vertical waterwheel 3hp 2,230W
1800 Watt's steam engine 40hp 30kW
1837 Marine steam engine 750hp 560kW
1900 Rail steam engine 12,000hp 8,950kW
1936 Queen Mary ocean liner 160,000hp 120,000kW
1949 Cadillac car 160hp 120kW
1969 Boeing 747 jet airplane 100,000hp 74,600kW
1974 Nuclear power plant 1,520,000hp 1,133,000kW

Table 1: Ancient and modern power sources


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 cell AA cell C cell D cell 9 Volt
Capacity (alkaline) 1,150mAh 2,850mAh 7,800mAh 17,000mAh 570mAh
Energy (single cell) 1.725Wh 4.275Wh 11.7Wh 25.5Wh 5.13Wh
Cost per cell (US$) $1.00 $0.75 $2.00 $2.00 $3.00
Cost per kWh (US$) $580 $175 $170 $78 $585

Table 2: Capacity and cost comparison of primary alkaline cells. One-time use makes energy stored in primary batteries expensive; cost decreases with larger battery size.
 

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) 30–50 45–80 60–120 100–250
Cycle life Moderate High High High
Temperature performance Low when cold -50°C to 70°C Reduced  when cold Low when cold
Applications UPS with infrequent discharges Rugged, high/low temperature HEV, UPS with frequent discharges EV, UPS with frequent discharges
Cost per kWh ($US)
Load leveling, powertrain
$100-200 $300-600 $300-600 $300–1,000

Table 3: Energy and cost comparison of rechargeable batteries. Although Li-ion is more expensive than Lead acid, the cycle cost may be less. NiCd operates at extreme temperatures, has the best cycle life and accepts ultra-fast charge with little stress.

 

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 type Equipment
to generate 1kW
Life span Cost 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
$3,000–7,500 2,000h
4,000h
40,000h
$0.35
       ->
       ->
       ->

$1.85 – 4.10
$1.10 – 2.25
$0.45 – 0.55
Solar cell $12,000, 5kW system 25 years $0 ~$0.10*
Electricity
electric grid
All inclusive All inclusive $0.20
(average)
$0.20

Table 4: Cost of generating 1kW of energy. Estimations include the initial investment, fuel consumption, maintenance and replacement of the equipment. Grid electricity is lowest.

* 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.

  Calories Milliwatt-hour Joule
Food calorie 1 1.16 4,184
1 gram of protein 4 4.64 16,736
1 gram of carbohydrate 4 4.64 16,736
1 gram of body fat 9 10.46 37,656

Table 5: Relationship of calorie to watt-hours.
The body stores store energy in the form for fat containing high net calorific value.


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.

Function Boeing 747
jumbo jet
Ocean liner
Queen Mary
SUV
or large car
Bicycle
(Bike & rider)
On foot
Full weight 369 tons 81,000 tons 2.5 tons 100kg (220lb) 80kg (176lb)
Cruising speed 900km/h
(560 mph)
52km/h
(32mph)
100km/h
(62mph)
20km/h
(12.5mph)
5km/h
(3.1mph)
Maximum power 77,000kW
(100,000hp)
120,000kW
(160,000hp)
200kW
(275hp)
2,000W
(2.7hp)
2,000W
(2.7hp)
Power at cruising 65,000kW
(87,000hp)
90,000 kW
(120,000hp)
130 kW
(174hp)
80 W
(0.1hp)
280 W
(0.38hp)
Passengers 450 3,000 4 1 1
Power per passenger 140kW
580kJ*
40kW
2,800kJ*
50kW
1,800kJ*
80W
14.4kJ*
280W
200kJ*

Table 6: Power needs of different transportation modes. Air travel consumes the least per passenger-km in high-speed transportation; the boat is efficient for slow tonnage transport, but the absolute lowest energy consumption is the bicycle.
* 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).

Last updated 2017-05-19

 

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Comments

On July 21, 2016 at 2:55am
Austris wrote:

Interesting article.. I liked the idea from another article, that for lower speeds electrical power should be used.. also the next step would be to downsize cars and make cars more mobile (smaller) - 1 and 2 passanger capable cars.

On August 1, 2016 at 12:47pm
Tim Moore wrote:

I would suggest that battery, wind and solar price tables need to be DATED or else they are worthless because of the amazing reductions in price that these industries are undergoing.

For instance, Li-ion battery prices and solar are now one third what you cite in this article and there is no date in the byline (no byline whatsoever) and only an update date.

Please correct this because the article is effectively pro fossil fuel when showing such outdated prices presented as if they were current.

On February 5, 2017 at 12:42am
Tony Manning wrote:

I have to agree with Mr Moore above. It is now 6 months after his comment and no update on solar and Li-ion costs has been done. This is very deceptive.
Otherwise an interesting article.

On February 9, 2017 at 6:44pm
Anita wrote:

interesting comments to all
I am in engineering. I bought 2 “pre-owned” ebike last summer and the algebraic sum is awesome!
Where I live, it costs less than 7¢ of electricity per 100 Km and at a descent speed
As we say here, the pedal to the metal. I ride my bike at 30~32Km/h (25MPH) the legal speed limit. Beyond this point, one needs registration, drivers permit, insurances…

In your comments all of you are missing lots of details.
On my bike, I had the opportunity to try several chemistries. The result is Li-ion batteries would keep your car lights ON the longest, no if or buts.

When it comes to cranking the engine, you would find that the 100$ lead acid battery is quite mighty compared with any other chemistries (except nicad). Not to mention the cost.

Yes the Cadex table has not been updated, but I find it is quite adequate*. To start the car we would talk about 20 times the cost of lead acid batteries. But for light duty application, like keeping the lights ON, yes Li-ion can probably cost half the price of lead acid on the long run

E-cars cannot be what petrol cars are. E-cars cannot have heat like petrol cars.
Air conditioning, maybe

In the context of making the “car” smaller, I would like to change the description to “personal transporter”

This would include, roller skates, hover boards, bikes…and lots of other stuff (trailers)
like carrying a fridge (up a steep hill of course) or a large TV with my bike!

I have done about 1000 Km on my bike last summer, and have a good deal of technical information about batteries performance if interested

* just as an example, my bikes battery is 36V 9.6Ah costs 1300$
my lead acid batteries 3X 12V 18Ah are 50$ ea (but mighty heavy!) but climbs hills!
they climb at 27 KM/h, the LI-ion climbs the same hill at 6~7 KM/h

On July 16, 2017 at 11:57pm
John wrote:

@timmoore
The price reduction comes from heavily subsidizing, and thus falsification of true market prices.

On August 31, 2017 at 4:53pm
Sivadasan wrote:

Seems a pro-fossil fuel post. No problem. Table 1, the inventiveness is very useful. We can interpolate this into different fields. Innovations sure to come in course of time in every sector. None would have thought of a cheap source of power ‘solar’ 25 years back. It was $100/- per watt in 1977 and now it is 34 cents per watt and is falling. New materials are discovered for cheaper and more efficient harvesting. No one knows the final cost of solar power. 

Cost of battery (Li-ion) is falling. It was almost $500/- per kwh in 2014 and it declined to $300/- per kwh as of now. It is projected to decline to $50/- per kwh by 2030. Batteries with higher life cycles are available which would be attractive to the market. Rigorous research is going on to find cheaper materials and new technologies in the field of storage.

Cost of grid energy has an upward path whereas cost of solar power takes a downward path. In several regions solar cost gets cheaper. In a few years solar cost will be cheaper than grid energy in all countries.

Table 6 gives Power needs of different transportation modes. A column for passenger boat (20 Ton and 50 passengers) could have been included.

A battery powered car can run 5-7 km per kwh. Electric motor is 5 times more efficient than an Internal Combustion. Electric vehicles are 10 times cheaper to charge/Fuel. ICE vehicle has around 2000 moving parts and electric car has around 20 moving parts resulting in low maintenance cost and longer life.