# Physical characteristics

Generally speaking these are lumped into two categories, the power needed to overcome rolling friction and overcome aerodynamic drag. All things being equal, the vehicles that are the most efficient are the ones that do the best job minimizing the magnitude of these characteristics. Aerodynamic drag is minimized by reducing both the referece area, which is generally defined as the vehicle’s silhouette when looking at it from the front, and the drag coefficient, a decimal that represents how well different vehicle shapes behave in this context. Rolling friction is minimized by reducing a vehicle’s mass and the coefficient of friction betweens it’s tires/wheels and the road surface.

$P = M g(v C_{R0} + v^2 C_{R1}) + (M g C_{R2} + \frac{A_f C_D \rho_{air}}{2}) v^3 + M v (a + g sin\theta )$

The rolling resistance coefficients $C_{R0,R1,R2}$ tend to be generated from actual data via interpolation, although single decimal approximations $C_R$ are used where accuracy is not a large concern, in which case the equation tends to take the form

$P = M g C_{R} v + (\frac{A_f C_D \rho_{air}}{2}) v^3 + M v (a + g sin\theta )$

Vehicle efficiency can also depend on operating conditions. For instance a small scooter can require as much energy per mile as a very aerodynamic compact car at highways speeds due to a relatively poor drag coefficient, but can also require much less energy in stop and go city traffic due to relatively low mass. The most efficient vehicles tend to be purpose built for specific competitions like velomobiles or solar cars.

# Energy efficiency

In this page we will look at three components of vehicle energy efficiency. The production efficiency of fuels that are used to power vehicles, the efficiency of the storage media for those fuels, and the efficiency of the powertrains those fuels are used with.

## Fuel production efficiency and qualities

Different fuels are used in different forms of motive power and can have good to relatively poor energy efficiency, along with other characteristics that such as energy density, depending on how they are created as well as how they are used.

### Petroleum based fuels

These are the most commonly used due to their availability, which makes them relatively affordable, and their energy density, which makes it possible to travel farther between fuel stops and refuel quicker than other energy sources. That said, when it is used in heat engines it’s efficiency is at most near fifty percent in heavy duty engines and a bit over thirty percent in light duty engines like those used in automobiles. Very small engines like those used on a motorized bicycle have even worse efficiency.

Petroleum is also fairly energy intensive to produce, transport and refine into fuels. In California, the energy used to produce and refine a gallon of gasoline that can propel a conventional car about thirty miles is enough to power an EV most of that distance. Roughly forty percent of all oceanic tonnage is petroleum and it’s refined products, so even in areas that don’t require as much energy for production, the net result for fuels refined from petroleum may be the same.

### Electricity

Electricity comes from a variety of sources. It can be generated through the combustion of fossil fuels, through natural events like the flow of air, water, or energy, or through nuclear fission. The efficiency of electricity as a transportation fuel is quite high, however depending on how it was generated the well to wheels carbon emissions can be as high as other fuel sources depending on how they are used. It’s storage media, batteries, also have relatively poor energy density as well as other limitations, that restrict the useful range and increase refueling times.

### Biofuels

Biofuels are primarily ethanol and biodiesel, but can also be biogas, and tend to be used like the refined products of petroleum. Because of this their efficiency during use is roughly comparable to other fuels like gasoline and diesel. Some biofuels like ethanol can also be used in fuel cells but this is limited due to the high cost of fuels cells.

### Compressed or liquefied gases

These tend to be compressed natural gas and liquid propane gas, although gas from landfills and other sources can be used. When compressed or liquefied their energy density approaches that of gasoline and diesel, and can be used in either type of engine.

### Hydrogen

Like petroleum, hydrogen can be used in heat engines with roughly the same limits on efficiency. In fuel cells, it has the potential to be used more efficiently, however fuel cells are currently much more expensive than the alternative, batteries. Unlike other forms of energy, hydrogen has to be produced from an existing source of energy like electricity or natural gas. The NREL puts production from electricity at roughly 75% efficiency, and production from natural gas at about 90% efficiency. There are other ways to produce hydrogen, but the most common are from electrolysis and steam reforming of natural gas.

## Storage efficiency

Outside of vehicles that are permanently connected to an energy source, like subway cars connected to a third rail, all vehicles require some form of energy storage. This can be by storing the energy source as a gas, like compressed natural gas, as a liquid like gasoline, or in batteries.

Generally the efficiency of storage is fairly high, but there are exceptions like hydrogen gas, because it tends to leak out of storage tanks, or NiMH batteries, which can exhibit relatively high self discharge rates.

## Powertrain efficiency

### Transmission efficiency

A transmission can be as simple as one gear reduction as seen on a single speed bicycle or as complex as a ten speed automatic transmission in a modern automobile. Transmission efficiency varies depending on the type, and even the driving cycle.

Remarking on transmission efficiency in a paper on advanced technology vehicle modeling, Edward Nam of the U.S. EPA states

Manual transmissions range in efficiency from 87-99%. Automatic transmissions range 85 – 95% when locked, but can drop to 60 - 85% unlocked. An overall 1.5% improvement in transmission efficiency could correspond to a 0.1 km/L increase in fuel economy [Greenbaum, et al., 1994; Kluger, et al., 1995; Bishop, et al., 1996]. Manual transmissions have similar efficiencies to continuously variable transmissions (CVT), so can be seen as equivalent to advanced transmissions.

Vehicles whose drivetrains run off of motors do not require complex transmissions employing gear shifts. These motor driven vehicles usually only require a single gear due to the large operating range of motors. Single gear transmissions naturally tend to be very efficient and are assumed to be 95% efficient in this report.

### Engine and motor efficiency

The efficiency of the motive source, be it an electric motor or internal combustion engine also varies depending on the driving cycle, conditions, and even vehicle size. Internal combustion engines exhibit greater efficiency with greater load due to pumping losses at lower loads, as show by this PV diagram, and at about a third to a half of their maximum speed due to friction losses. Maps of engine efficiency indicate the best loads and speeds to operate an engine at, however since the most efficient operation tends to occur at high loads, taller gearing is required, which reduces the rate of acceleration in a given gear and may make it change gears more frequently. Hybrid vehicles like the Prius get around this by designing the transmission such that the engine is only operating at high loads, and include an electric motor to provide additional power for acceleration. Due to emissions regulations gasoline and diesel engines tend to have a minimum fuel consumption of ~200-220 g/kWh, while heavy duty diesel engines that don’t have to comply with the same emissions regulations can be as low as 165g/kWh.

Electric motor efficiency also depends on load and speed. Unlike an engine, higher loads lead to higher currents that increases losses, and like an engine, higher speeds lead to greater friction losses. The efficiency of human power is a bit harder to quantify than the efficiency of an electric motor or heat engine, and is estimated to be ~20% to 25%.

# References

Edward Nam, U.S. Environmental Protection Agency, Advanced Technology Vehicle Modeling in PERE, EPA420-D-04-002, March 2004

AC-150 Gen-2 EV Power System specifications, AC Propulsion

Ecomodder.com, List of Specific or Brake Specific Fuel Consumption (BSFC/SFC) maps

Margaret Sheridan, California crude oil production and imports, California Energy Commission, CEC-600-2006-006, April 2006

In the above equations, $M$ is mass, $g$ is gravity, $v$ is velocity, $C_{Rn}$ is the coefficient of rolling resistance, $A_F$ is the reference area, $C_d$ is the coefficient of drag, $a$ is the “stray” force, and $\theta$ is the angle of ascent or descent.