# Kansas: Temperature and Horsepower

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

## Air Density Changes with Temperature

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.

## Denser Air = More Air Molecules

Before EFI, there was no way to compensate for temperature changes. 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 molecules, for example, requires 25 oxygen molecules. That’s where the ideal air:fuel ratio of 14.7:1 comes from.  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 receive a fixed volume of air. That means the number of air molecules changes depending on the air density. A carburetor cannot automatically compensate for changing air density, but the NASCAR EFI system can.  When the temperature at Kansas was 20 °F cooler than expected, engine tuners knew the EFI would handle it.

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.

## More Air Molecules Mean More Horsepower

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.

\frac{HP(at \hspace{0.1cm}T_1)}{HP (at \hspace{0.1cm}T_2)}=\sqrt{ \frac{T_1}{T_2}}

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

\frac{HP(57^{\circ} F)}{HP (77^{\circ} F)}=\sqrt{ \frac{537^{\circ}F}{517 ^{\circ}F}}=1.019

This represents a 1.9% increase in horsepower.

NOTE ADDED 2021-10-06: The numbers I picked for this example are unfortunate. The 1.9% change isn’t rounding off the 1.019. See the comments below. My readers gave a better explanation than the one I’m trying to give here.)

If the engine was producing 850 hp at 77 °F, it would produce 867 hp at 57 °F.  In a sport where engine builders work really hard to get 1 or 2 hp, this is a huge change!

Some people suggested increased horsepower due to the colder temperatures were responsible for the Kansas engine failures. 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!)

1. Gary says:

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. Dennis says:

Always enjoy how you connect the theory of science with it’s application Diandra. Keep it coming!

3. 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.

with all due respect, 1.019 is not rounded to 1.9 but 1.02

• Diandra says:

You are 100% (102%?) correct and thank you finding this after all this time! I did write the number wrong; however, I did the horsepower calculation in the following sentence correctly, so those numbers still hold.

I think. I’m so much better with x and y than actual, real numbers.

Thank you again!

5. Scottish Friend says:

The output of the calculation is is a ratio of change so it is actually 1.9% change when rounded.

If the temperatures were the other way around, say root of 517/537 = 0.9812. This represents a change of 0.9812 minus 1 x 100 = – 1.9% change in HP as you move to the higher temperature.

Almost double the 1.02% answer so significant that you verify this.

• You are right. I didn’t look closely enough at the first comment to realize what you just said.

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