The (probably) last post on regenerative braking

I've posted a couple of times on regenerative braking in my CT200h. This will, I expect, be the last. In the previous post I estimated that regenerative braking on a trip saved me about 5.9% of the gasoline I'd have used without it. I decided that a better test would be a full tank, so I monitored all of the regenerated watt hours for my most recent tank. Since it's kind of a pain in the rear, I'm not going to keep it up.

Calculating in a more efficient way than the very detailed way in the previous post, the results are as follows:

• The measured economy by miles divided by gallons at fill-up: 50.60
• The calculated economy without regenerative braking: 47.55
• Gallons per 100 miles: 1.976
• Gallons per 100 miles without regenerative braking: 2.103
• Per cent fuel savings: 6.04%

Not much different, so I think that it's safe to say that regenerative braking saves about 6% of the fuel I'd otherwise use.

I'm a bit surprised that the number is that low. In this post I discussed some of the factors that make hybrids so much more fuel efficient than their non-hybrid cousins and the regenerative braking was one of the factors I considered most important.

There is no non-hybrid CT with which to compare the fuel economy. I went to the DOE fuel economy site for the Camry (the four cylinder version)  and for the Camry hybrid. Using the combined highway and city estimates for each (28 m.p.g. and 41 m.p.g. respectively) it looks like the hybrid, per the government's test protocol, will use about 31.7% less fuel over any distance. It's reasonable to infer that, while the regenerative braking is a significant fuel saver, other factors (operating more frequently on more efficient areas of the engine map, capturing energy while coasting, automatic engine shut-off where appropriate, etc.) are at least as important.

More on fuel saved by regenerative braking

I published a post regarding how much energy is captured in the regenerative braking system in my Lexus CT200h hybrid. After some discussion with commenter Gabriel Grosskopf, I estimated that about 59% of the energy available (after subtracting the energy used to overcome aerodynamic drag, rolling resistance, and internal friction) was recaptured and used to charge the battery.

Since I (and others) have represented that the regenerative braking system is among the key reasons that hybrids achieve superior fuel economy, I decided to check the actual impact.

My round trip commute, generally downhill in the morning and uphill in the evening, is 62.46 miles and, for the last 10 fill ups, my average m.p.g. has been 52.47. So, to make my commute, I use, on average 62.46/52.47=1.190 gallons of gasoline. My display showed me today that my regenerative braking system added 700 watt hours or 2,520,000 joules to my battery that I could use for accelerating, hill climbing, etc. If I assume my electric motor is 90% efficient, I put 2,268,000 of these joules to work.

A gallon of gasoline (reformulated blend in this case) has an energy upon oxidation of 111,836 btu or 117,993,000 joules. I estimate that my internal combustion engine is about 25% efficient, so I put about 29,498,000 of these joules to work. My 1.19 gallons thus provide 35,103,000 joules that propel my vehicle (the remainder being lost as waste heat in myriad ways).

If I assume that I used all of the energy my brakes provided, then 35,103,000 + 2,268,000 = 37,371,000 joules of work were done to propel my car. Then, dividing by 0.25, I can estimate that 149,484,000 joules of oxidized gasoline would have been necessary to do this work. This is the energy in 1.267 gallons. Dividing this into 62.46, I find that the fuel economy without the regenerative braking would have been about 49.30 m.p.g. The regenerative braking thus upped my m.p.g. by 3.17.

As I've often said, it's much more intuitively informative to discuss gallons per mile, or gallons per 100 miles. So, the regenerative braking took me from 2.03 gallons per 100 miles to 1.91 gallons per 100 miles. So it takes me 5.9% less fuel to go a given distance, ceteris parabus.

There's no question that I'm carrying a lot more significant figures (apologies to John Denker) than are warranted by the precision of my data, but I think that the figure I've determined is probably in the ballpark.

Regenerative braking in the Lexus CT 200h

I've been driving my Lexus CT 200h for about two years and about 39,000 miles. In that time, I've learned a lot about driving techniques to minimize specific fuel consumption (g.p.m., gallons per mile). I've also given some thought to what it is about a hybrid that makes it more fuel efficient. One of those items is regenerative braking, where some of the kinetic energy in the moving vehicle is used to charge the battery rather than to heat the brake rotors. This is done by having the energy of the moving vehicle turn the electric motor backwards, thus making it a generator and thereby charging the battery. Of course, friction brakes are also used.

I've wondered just how much of the braking energy goes into the battery and have been hard pressed to find data for this. However, the CT 200h has a display option for "Consumption" (see photo at left). It's difficult to see (click to enlarge) but there are small boxes in the vertical bars that indicate mileage by the minute. Each complete box, according to the legend, represents 50 watt hours of energy (180,000 joules). At the top of a hill, I applied sufficient braking to keep my speed at approximately 35 m.p.h. At the bottom of the hill, a stoplight brought me to a stop.

I can calculate the energy difference from 35 m.p.h. at the top of the hill to 35 m.p.h. at the bottom of the hill by using Google Earth to find the elevation change. I determined it to be 103 meters. Because my speed didn't change, neither did my kinetic energy, therefore the reduction in my potential energy went to some combination of heating my brake rotors and charging my battery.

My best estimate of the mass of the vehicle with the 1/4 tank of gasoline and myself and my baggage is 1,600 kg. Therefore, the potential energy lost in the descent is ~E=mgh=1600kg*9.8\frac m{s^2}*103 m=1.62*10^6joules~. The display shows "E" boxes and fractions of "E" boxes and my best estimate, assuming that 3.5 "E" boxes are shown is that ~3.5*50Wh=175Wh~ or ~630,000joules~ were sent to the battery. I don't think it could be lower than ~585,000joules~ or higher than ~675,000 joules~.

Assuming that I'm interpreting the cryptic display correctly (and that Ed Davies doesn't haul me up short!), about ~630000/1620000=38.9\%~ of the potential energy went to charge the battery. The rest was dissipated as thermal energy in the disc brake rotors and, ultimately to the atmosphere. The battery pack in the CT 200h is a 1.3 kWh Ni metal hydride battery. The 630,000 joules equal 0.175 kWh or 13.5% of a full charge for the battery. Per the owners' manual, I'm able to drive in "EV mode" (battery only) for two miles, but I'd best accelerate slowly even by my standards, and not exceed about 20 m.p.h.

As an aside, this is the energy in about 18 cm^3 of gasoline. Figure I'd have to burn about four times that, or 72 cm^3 to charge the battery with the engine at 25% efficiency. And, of course, the regenerative braking isn't effective when the battery is fully charged, isn't used (much) in hard stops, etc. Still, it does increase overall fuel efficiency.

Finally all of these figures have large "error bars," the regenerated energy on the display, the elevations from Google Earth, the mass of the vehicle, and the ability to stay at precisely 35 m.p.h. (although really, all I need is to be going at the same speed when I stop logging as when I start so that the kinetic energy is unchanged). Still, it's enough for me to have a good idea of what the regenerative braking can give me.

Update: Based on a comment by Gabriel Grosskopf, I measured the distance over which I descended. It was 1,530 meters, thus the slope is 3.86 degrees (0.0673 rad). The typical instrument landing system glideslope is 3 degrees though a few, such as VNY - Van Nuys - at 3.9 degrees, are steeper. Assuming that I drove the 1530 meters at 35 m.p.h. or 15.6 m/s, it took me 98 seconds to put 630,000 joules into the battery. This is a charging rate of 6,440 watts or 6.4 kW. As mentioned in a previous post, when I put fuel in my gasoline tank, I'm adding energy at a minimum rate of 11 mW, about 1,700 times as fast. To be fair, we'll divide that by four since IC engines are much less efficient than electric motors. So we're adding useful energy at 2.75 Mw or 430 times as fast. Coincidentally, the Nissan Leaf touts a 6.6 kW charger to charge its 24 kWh battery.