Kansas: Temperature and Horsepower

There were a lot of engine problems at the Kansas race last Sunday — and a lot of theories as to why there were a lot of engine problems.  Let’s start with the cooler-than-expected temperatures on Sunday.

When the air temperature changes, so does the number of air molecules heading into the engine.  Colder temperatures make air more dense.  Since density is the ratio of mass per unit volume, a volume of air at a lower temperature contains more molecules than the same volume of air at a higher temperature.  The plot below shows how air density changes between 0 and 100 °Fahrenheit.

Before EFI, changes in temperature during a race posed a problem.  Fuel and air prefer to combust with a very particular ratio that is determined by stoichiometry.  Remember all the balancing equations you did in chemistry?  It’s the same thing.

Combusting two octane (a component of gasoline) molecules require 25 oxygen molecules.   The ideal air:fuel ratio is 14.7:1.  If you have one ounce of gasoline, you would need 14.7 ounces of air.  NASCAR engines run slightly richer (meaning a smaller air:fuel ratio).

Engines introduce a fixed volume of air, which means that the number of air molecules changes depending on the density of the air.  You would like a system that introduces exactly the right number of gasoline molecules for the amount of air being introduced.  A carburetor cannot automatically adjust itself to maintain that ratio, but the NASCAR EFI system can.  When the temperature at Kansas turned out to be 20 °F cooler than expected, engine tuners weren’t worried because the EFI automatically compensates for the changing in temperature.

In fact, cooler is better in terms of horsepower production.  The more oxygen molecules in the cylinder, the more gasoline you can inject and the more power you can make.  That’s the idea behind turbochargers – compress the air so that you have more oxygen molecules in a volume of air.

The change in horsepower depends on the square root of the absolute temperature.  You may remember absolute temperature from chemistry and/or physics class.  When you use the ideal gas law, for example, you can’t just plug in the temperature you read from the thermometer.

The Fahrenheit and Celsius scales were developed around things we experience every day.  Water freezing is 0°C or 32 °F.  Water boiling in 212°F or 100°C.  As we discovered more about the molecular nature of temperature, we learned that physics places limits on how cold something can be.  The coldest possible temperature corresponds to -459.67 degrees Fahrenheit.  Rounding that to -460 °F for simplicity, 0 °F is 460 on the absolute temperature scale.  You get the absolute temperature by adding 460 °F to the temperature from the thermometer.  A temperature of 57 degrees F would be (460+57=)  517 F on an absolute temperature scale.  A temperature of 77 F would be 537 F.

The change in horsepower is proportional to the inverse square root of the ratio of the two temperatures.

If I go from 77 °F (537 °F in absolute scale) to 57 °F (517 °F in absolute scale), the horsepower would be:

This represents a 1.9% increase in horsepower.  If the engine was producing 850 hp at 77 °F, it would produce 866 hp at 57 °F.  In a sport where engine builders working really hard to get 1 or 2 hp, this is a huge change!

Some people have suggested that the engine failures at Kansas were due to the increased horsepower produced by the colder temperatures.  My favorite engine technical director Andy Randolph (of ECR engines) tells me this isn’t the likely cause for the engine failures.

What IS the cause will be my next post. (And it’s not EFI!)

3 Comments

  1. I believe some teams said they got less mileage. When you said “…the EFI automatically compensates for the changing in temperature” does that mean that because the air:fuel ratio changed due to temperature, did the ECU give MORE fuel to get closer to the ideal ~14.7:1? And, can you calculate how much less mileage the teams would get with a 20 degree drop in temperature? Great post once again. Can’t wait for the 2nd part.

  2. Hi Gary: Each team has its own EFI map that tells the engine how to behave. I think of it like a flowchart: If this happens, do that. The details of that map determine fuel mileage, so it’s hard to make a blanket statement.

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