During a discussion on start-and-stop vehicle technology some bloke began pushing the point that re-starting the car uses stored energy from the battery, which needs to be replenished by increased fuel usage once the engine is moving. Well, this is obvious, the question is that of significance of such additional usage, especially in comparison with savings from reduced idle. Common sense tells me that this is splitting hairs: if ICE efficiency outlays put all accessory usage at 2 to 3% of overall energy consumption, which includes AC, and all electricals, then it can’t be that much.
More over, this dissertation explores idle-reduction technologies for long-haul commercial trucks, and one of the systems exampled is battery-powered (p. 14) that stores enough energy to power AC or heater overnight, and takes about six hours of charge while driving. Author acknowledges increased fuel consumption due to necessity of higher-amperage alternator, although there are no specific numbers provided. However, the mere existence of such commercial application available on the market leads me to believe that such added load is still better than idling.
But, in the interest of science, I need some hard numbers (besides, the fellow just wouldn’t go away). I have some ideas on what to consider, but I’m not well versed in electrical and mechanical engineering, so I do not think I can account for most major factors.
Energy use of the starter motor can be calculated by using the amount of current used per start (which would be 2 to 3 seconds) by the motor itself and the solenoid that engages the starter gear onto the flywheel. Both current and power demand can be found in the starter’s specifications, but I am not sure as to how reliable those numbers would be in the real-world application.
Then there is fuel consumption of the start itself which is estimated at 10 to 15 seconds worth of idling (and Florida chapter of ASME even calculated six seconds for 6-cylinder engine (in a simple, non-rigorous field experiment), but the original link is broken).
Now, how to calculate the increased consumption due to the charging of depleted battery from the starter motor itself, and, additionally, to account for all the accessories that were running while the engine was stopped? Is it a simple matter of using the same number calculated for energy usage of starter motor, and arriving at it by calculating the amount of fuel needed to produce that much extra energy given the losses in the engine itself and in the charging circuit? And, ultimately, how significant are those considerations in the bigger picture?
Answer
First, consider the case with negligible auxiliary loads (no air conditioning).
For a Civic-sized engine (1.8 liters), this US DOE worksheet estimates about 0.3 US gallon/hour fuel consumption at idle.
Here is a conservative starter calculation:
- The Civic starter is rated at 1.0 kW (83A$\times$12V). A 3 second start therefore produces 3 kJ. Assume an additional 25% in battery internal dissipation that must be replaced.
- As you note, this energy must be replenished by the ICE (internal combustion engine). Max ICE efficiency is only 30%. The incremental efficiency, which is what matters for this small additional load, is no doubt higher, but I’ll use 25% as a conservative estimate.
Alternator efficiency is not great either; I’ll use a conservative 50%.
With these values, it requires 3.0 kJ$\times$(1.25 / 0.25 / 0.5) = 30 kJ worth of fuel to recharge the battery (Note the overall charging efficiency is only 10%!).
Now, the energy density of gasoline is 120 MJ per US gallon (42.4 MJ/kg), so the amount of fuel required to recharge the battery, including all the inefficiencies, is 30 kJ $\div$ 120 MJ/gal = 0.00025 US gallon.
So, the “crossover” idle time in this case, above which it is more efficient to stop and restart, is 0.00025 gal $\div$ 0.3 gal/hour $\approxeq$ 8.3 $\times10^{-4}$ hours, or about 3 seconds.
Now suppose an air conditioner (PDF) is consuming 1 kW of electrical power.
- With the engine running, the A/C requires (via the alternator) an additional engine fuel consumption equivalent to 1 kW / 0.5 / 0.25 = 8 kW, or 29 MJ/hour, or 0.24 gal/hour of gasoline. For a duration $t$, the total fuel consumption with the engine running is (0.3 + 0.24)$t$ = 0.54$t$ (with $t$ in hours).
- With the engine stopped, the A/C still consumes 1 kW, or 3.6 MJ per hour. With that low 10% charging efficiency, it requires 36 MJ worth of fuel (or 0.3 gal) to recharge an hour’s worth of A/C operation. Adding in the starter contribution, the total fuel requirement is 0.00025 + 0.3$t$ (with $t$ again in hours).
Equating these two new fuel requirements, the crossover time with the A/C on increases, but only to about 4 seconds.
Although the battery charging efficiency is low, the waste of the idling fuel consumption dominates the calculation.
Note that I don’t have a reference for the 25% battery re-charge inefficiency. Unfortunately, that’s an important number when running an A/C, since it reduces the advantage of shutting off the engine. At some high load level (in the neighborhood or 4 kW) that disadvantage outweighs the advantage of turning off the engine.
Further (experimental) data to confirm the above estimates can be found here: http://www.iwilltry.org/b/projects/how-many-seconds-of-idling-is-equivalent-to-starting-your-engine/
In my case it consumes about the same amount of fuel as 7 seconds of idling. However, the additional fuel consumption observed seems almost entirely due to a faster idle speed setting for the first 20 seconds after starting. Any good driver would start moving within 1-2 seconds after starting, which would effectively eliminate the fast idle losses. If you can begin extracting useful work from your engine within 1 second after starting the engine then it appears starting the engine consumes fuel equivalent to about 0.2 seconds of idling.
No comments:
Post a Comment