# Two Hydrogen Cars

## Stephen Hibbs October 23, 2010

### Submitted as coursework for Physics 240, Stanford University, Fall 2010

In this article I will discuss the two forms of hydrogen-fueled vehicle propulsion that are being implemented commercially: hydrogen combustion and hydrogen fuel cells. By looking at the stated mileages of each vehicle, I will compare the efficiencies of each technology, and discuss what these results mean for the feasibility of each technology.

For ease of calculation and citation, I will lay out some constants that will be used later:

Quantity Value
Energy Density of Gasoline 31 MJ/liter (44 MJ/kg) [1]
Mass density of Gasoline 0.7 kg/liter
Energy Density of Liquid Hydrogen 8.5 MJ/liter (120 MJ/kg) [1]
Specific Gravity of Liquid Hydrogen 0.071 [2]
Specific Gravity Of Petroleum 0.71 - 0.77 (I shall use 0.75) [3]
Table 1: Physical parameters of gasoline and hydrogen fuels.

A useful fact is that 1kg of hydrogen has the same energy content as 1 gallon of gasoline. The energy density of Hydrogen is 120MJ/kg. The energy density of gasoline is

31 MJ/liter × 3.8 liter/gallon = 117 MJ/gallon

The method that I will use for evaluating performance will be to compare each hydrogen car to its petroleum-burning equivalent, and so a quick note on comparing hydrogen to petroleum is in order. It is important to note, from looking at our constants above, that the energy-density by volume of petroleum is 31MJ/liter, and that of liquid hydrogen is 8.5MJ/liter, giving us an energy density of petroleum that is is 31/8.5 = 3.6 times as large as that of liquid hydrogen; this means that 1 gallon of petroleum contains an equivalent amount of energy as 3.6 gallons of liquid hydrogen. However, if we look at the mass density of petroleum (.75 kg/liter) relative to the mass density of hydrogen (.071 kg/liter) we see that the mass density of gasoline is roughly 10 times that of liquid hydrogen. Using that ratio, 3.6 gallons of hydrogen still weighs less than half as much as 1 gallon of gasoline. When I make reference to "equivalent amounts" of hydrogen and petroleum, I will be referring to equivalent amounts of stored chemical energy, and using 3.6 times as large a volume of liquid hydrogen as of petroleum. The way I will be using it later on, it is important to remember that gallons are a measure of volume, so to convert from hydrogen to petroleum, we use the following conversion:

1 mpg with hydrogen = 1 mile / gallon Hydrogen × 1 gallon hydrogen/ 3.6gallons petrol = 3.6 mpg with gasoline

So if we get 3.6 mpg with hydrogen, we have the equivalent of 1 mpg gasoline.

This article will look at two hydrogen-powered vehicles, the BMW Hydrogen 7 and Honda FCX Clarity, that use two different hydrogen-propulsion technologies. Because of the obvious performance and design differences between the high-performance BMW Hydrogen 7 and the high-efficiency Honda Clarity FCX, it would be unfair to use the cars' fuel efficiencies directly against one another in order to compare the two forms of hydrogen propulsion. Instead, we will look at the efficiency of each hydrogen propulsion technology relative to its petroleum counterpart, and then compare those values.

The first method of hydrogen propulsion that we'll look at is hydrogen combustion as it is currently used in the BMW Hydrogen 7. This car stores hydrogen as a liquid in cryogenic, high pressure tanks, and then burns it in a combustion engine very similar to a regular petroleum engine. The BMW Hydrogen 7 is a good place to start our analysis as well, because it can run on both hydrogen and petroleum, giving us an easy way to compare the efficiency of each fuel source as combustible material since everything else about the vehicle remains constant.

Interestingly, BMW has omitted to list any of the official specifications for the Hydrogen 7 on the BMW website, but a quick google search provides us with an array of blogs and news reports providing consistent data. Looking at a Wired.com article, we see that the the car carries ~8kg of liquid hydrogen, and gets a rated range of 200Km (124 miles) burning hydrogen. [4] Using the density of hydrogen, we can we can easily compute that there are about

8kg /(.071Kg/liter) × 0.264 gallons/liter = 30 gallons

of hydrogen being carried in the tank, giving us 124/30 = 4.13 mpg with Hydrogen. Remembering that an equivalent amount of energy from hydrogen is 3.6 times as large as the equivalent amount of petroleum, we see that we are effectively getting 4.13 × 3.6 = 14.9 miles of transportation from the equivalent amount of energy as a gallon of petroleum. Similarly, we can compute the mpg for gasoline; the same Wired.com article lists the Hydrogen 7 as getting 300 miles of range on a 19.5 gallon gasoline tank, giving it 15.4 mpg with gasoline. From this, we can see that the method of hydrogen combustion used in the BMW Hydrogen 7 is roughly as efficient as standard petroleum combustion, with each method getting about 15 miles of range for the equivalent amount of stored chemical energy as one gallon of gasoline. This shouldn't be too surprising since combustion engine efficiencies are largely limited by heat loss, an unavoidable side effect of igniting the fuel, regardless of its composition.

Next we will look at hydrogen fuel cell technology as it is currently used in the Honda FCX Clarity, with data coming from the U.S. Department of Energy.[5] Honda's technology stores hydrogen as a compressed gas, and mixes it with oxygen from the atmosphere to generate electricity (useful) and water (a waste byproduct). This system has the advantage that the energy produced is initially stored in a battery as electricity, allowing the vehicle to take advantage of many of the energy-saving methods, such as regenerative braking, that petroleum hybrids like the Prius do.

Working out the energy equivalency for the Honda FCX Clarity is a bit different than with the Hydrogen 7 since compressed gaseous hydrogen and liquid hydrogen have different volumetric densities. Further, while I could find the density of liquid hydrogen, I could not find it for compressed, gaseous hydrogen. We can get around this problem however, by looking at energy density by mass instead of by volume. It is claimed that the Honda FCX gets 240 miles of range, and 60 miles per kilogram of hydrogen. Using this value we get 240 miles / 60 miles/kG = 4 kg of Hydrogen, the energy equivalent of roughly 4 gallons of petroleum, as already shown. And while I don't know the exact density of gaseous hydrogen, it will be less dense that liquid hydrogen (since liquids are generally more dense than gasses at the same pressure). So now we have a volume ratio for hydrogen:gasoline of at least 3.6:1. So even without the Honda listing the tank size, we can see that we're still using at least a 4 gallons × 3.6 = ~15 gallon hydrogen tank to carry the energy equivalent of 4 gallons of gasoline.

The Honda FCX Clarity has an EPA-specified range of 60miles/Kg Hydrogen, which is roughly equivalent to 60 mpg with gasoline. Comparing this to the 40 miles per gallon of gasoline achieved by Honda's most efficient petroleum hybrid, the Honda Civic Hybrid, we see that an efficiency gain of 150% is made by moving to hydrogen fuel cells from petroleum combustion, assuming the Civic and FCX Clarity are otherwise equivalent vehicles.

Now that we have found the performance of each hydrogen technology, relative to its petroleum equivalent, we can compare the two. Looking back at the results we found above, the hydrogen combustion engine in the BMW had roughly the same efficiency as its petroleum counterpart, while the Honda achieved roughly 150% efficiency relative to its petroleum-based equivalent.

This would suggest that if our goal was to use the highest-efficiency method of hydrogen-propulsion, we would be smart to further push hydrogen fuel cell technology. This is not terribly surprising since one of the main advantages of hydrogen fuel cells comes in their lack of waste heat- a problem that hydrogen and petroleum combustion still share. However, it is important to keep in mind the cost associated with using fuel cell technology. Because rare metal electrodes are, at this time at least, necessary to avoid rapid fuel cell degradation, the cost of producing the Honda FCX is quite high:

"Honda engineers estimated three years ago that its previous fuel-cell cars cost more than \$1 million to build. Duleep [managing director of Arlington, Virginia-based Energy & Environmental Analysis Inc], who completed a fuel-cell vehicle study this year for the U.S. Department of Energy, believes Honda has cut its production costs to between \$120,000 and \$140,000 per vehicle." [6]

There is also no easy way to check the market cost of the Honda FCX since it is only being leased for limited terms. Similarly, the BMW Hydrogen 7 can only be leased by the rich and famous, so there is no price tag for it either. However, general logic suggests that moving to hydrogen combustion technology may be a cheaper short-term transition to make, since car companies are already good at making combustion engines.

Unfortunately, it is still difficult to determine an obvious winner at this fairly early point in both technologies' lifecycles, especially just by looking at the specifications of just two vehicles. However, we have shown here that hydrogen fuel cell technology does have distinct energy efficiency advantages over traditional petroleum combustion, and that hydrogen combustion technology can at least break roughly even with the tried-and-true petroleum combustion engine. It is even more significant that this has been demonstrated in working cars that will be leased to the public by established companies in the near future.

© Stephen Hibbs. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.

## References

[1] G. Thomas, "Overview of Storage Development DOE Hydrogen Program, Sandia National Laboratories, 9 May 00.

[2] "Hydrogen Properties," College of the Desert, December 2001.

[3] "Lead Free Gasoline Material Safety Data," Bell Fuels, 21 Oct 94.

[4] B. Gain, "Road Testing BMW's Hydrogen 7," Wired News, 13 Nov 06.

[5] "Fuel Economy Guide: Model Year 2011," U.S. Department of Energy, DOE/EE-0333.

[6] A. Ohnsman, "Honda to Deliver 200 Fuel-Cell Autos Through 2011," Bloomberg, 21 May 08.