# A Posteriori

## Attempts to grapple with and elucidate empirical knowledge

### Heating and Car MileageNovember 17, 2009

Filed under: General Physics — Rāhul @ 23:51
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We are all aware of the mileage hit we unwillingly take when we decide to run the AC on a hot day in the car. But, what about the reverse? What effect does running the heater have on petrol mileage? One of my friends recently brought up this topic and it made for some interesting discussion.

I don’t usually use heating in my car in the winter because I am usually dressed warm and my car rides are pretty short anyway. So, I haven’t had the opportunity to try out my hypothesis (to follow) by trying to mimic other conditions and see if I can get more or less miles for a full tank of Petrol if I have heating on. But, I do manage a pretty high mileage for my ’93 Corolla (nearly 30 miles to the gallon in cold weather with 50%ish highway miles), which could be related to my heating preference.

In my analysis below, the key fact to remember is that the mileage achieved by a car is a function of the ambient temperature. At normal ambient temperatures, a controlled quantity of fuel is injected into the cylinder during each cycle, which is then lit up to produce power. But, when temperature is very low, the car lets in a higher quantity of fuel every cycle in an effort to compensate for the lower temperature by having a higher fuel to air ratio. As temperature decreases, the air in the chamber needs to be more rich in fuel for the fuel to burn at the same rate (in terms of power produced per cycle) as at a higher temperature.  So, we see that when ambient temperature goes down, fuel efficiency reduces too. This is the reason why we see a large drop in petrol mileage in cold weather.

Fuel efficiency decreases also when the temperature is very high. But, this has mostly to do with the enhanced cooling needs of the engine and the passengers rather than the the internal combustion engine itself. Cooling requires energy which saps into the fuel efficiency. So, we see that there is a range of optimum ambient temperature when petrol mileage is the highest, on either side of which it tapers off. This is a feature of many systems when it comes to efficiency.

Coming back to the original question, let us look at the effect of heating on mileage is to see how it affects the temperature in the engine. Car heating systems usually work by siphoning off a part of the heat generated in the engine to warm the passenger area. In winter, especially right after the car is started, the temperature in the engine is much below the optimum range. If at this time, some of the heat being generated is diverted to heat up the passenger cabin, it will reduce the fuel mileage. But, if the car had been running for a while and the engine already above the optimum heat range (unlikely in harsh winters and short drives), then the fuel mileage will increase if the engine is cooled by letting some of its heat out. Of course, when the heat is on, there will be a fan which channels the heat as required. This fan is a drain on the engine whatever the temperature. At sufficiently high temperatures, the mileage gain from losing some engine heat is higher than the mileage loss from the fan. But then I am not sure why I would use the heater on such a hot day!

This post goes awry from the stated purpose of the blog. Rather than trying to form scientific conclusions from observed facts, this post tries to use a priori knowledge to predict what will happen. I hope to gather data and a make an a posteriori post on this matter sometime soon. Till then, my hypothesis is that using the heater in winter does reduce fuel mileage although the effect is likely much less than the effect of A/C in summer.