How fuel temp can affect your tune accuracy, a copy and paste not written by me "In last month’s TechnoRant, I discussed the difference between injector volume flow, and mass flow, and described how mass flow is dependent on fuel density. I also hinted at the fact that fuel density is dependent on temperature. This month, I will detail that dependence, describe how it affects your tune, and give you a tool to compensate for it. Let’s start with what really matters, which is how it affects your tune. Have you noticed that even a well-tuned engine runs leaner when the fuel is hot? There’s a reason for that… The reason is that the density of the fuel changes with temperature, which changes the injector mass flow rate. Predictably, your air fuel ratio changes because your fuel injector is now effectively smaller. (Remember, air fuel ratio is mass based.) This change in density can be predicted with a parameter called the “Coefficient of Thermal Expansion” (CTE) which is a description of how much the fuel expands with temperature. It sounds complicated, but like many things related to performance, most of us already have an intuitive feel for it. For instance, we all know that our pistons expand when they get hot, which is why we specify a cold clearance. And we all know that the fluid in the radiator expands when it gets hot, which is why we need an overflow tank. It should come as no surprise then that our fuel also expands when it gets hot, and in fact it expands at a greater rate than either water or aluminum. So let’s consider how this expansion changes the fuel density. Let’s start by filling a cylinder to the very top with ethanol. Ignoring evaporation, if we heat the ethanol, it will expand and overflow just like the fluid in our radiator. The cylinder contains the same volume of ethanol, but because a portion has spilled out, the mass of ethanol in the cylinder has changed. Referring to last month’s TechnoRant, we know that density is defined as mass divided by volume. As we divide our unchanged cylinder volume into a lesser mass, we get a lesser density, which we already know will reduce our injector mass flow rate. The situation is the same on a running engine. The fuel injector delivers a specific volume of fuel to the cylinder, but as the temperature of that fuel changes, so does the mass, and so does our mass based air fuel ratio. The hotter the fuel gets, the smaller the fuel mass delivered to the cylinder, and the leaner the air fuel ratio becomes. Let’s move beyond generalizations, and be more specific. Gasoline, ethanol, methanol, toluene, etc all have a similar CTE value of approximately .001 per degree Celsius. This means that for every change in temperature of 1 degree C, our volume will change by a factor of .001, which you math geeks will recognize as 1/10 of one percent per degree Celsius. Let’s apply this to a sample 1000 cc/min injector, and calculate the mass flow rate at a few different temperatures. We start by looking up the density of ethanol, and we find that the density of .789 is stated at a temperature of 20 degrees C. Multiplying our 1000cc/min by ethanol’s specific gravity of .789, we get a mass flow rate of 789 grams per minute at a fuel temperature of 20 degrees C. Now let’s consider what happens after a half hour of driving in stop and go traffic when the fuel temperature climbs to 70C, using the following formula: (((Reference Temp – New Temp) * CTE) + 1) * Reference Density = New Density Using the values from our example: (((20 – 70) * .0011) + 1) * 0.789 = 0.746 As a result of the density changing from 0.789, to 0.746, our injector mass flow rate has now gone from 789 g/min (13.2 g/sec, or 104.4 lbs/hr) to 746 g/min (12.4 g/sec, or 98.7 lbs/hr) Putting that to numbers that we can more easily relate to, our air fuel ratio of 11.5 to 1 has just become 12.2 to 1 and would need a trim of approximately 6% to bring it back in line. Not the end of the world as long as our tune is conservative, but potentially ugly if we are cutting it close. And I think most would agree that a 6% trim is unnecessary if we can compensate for it in the tune right? While half of you are nodding your heads in agreement, and planning to perform the calculations to account for this density change, the rest of you are shaking your heads violently, thinking “There is NFW I am going to struggle with a bunch of math just to fix a 6% trim!”