This article is part one of a series about turbochargers. In this article, we’ll introduce the equations you need to calculate how much air a turbocharger is flowing. We’ll also see how to calculate the pressure ratio, outlet air temperature, and density ratio. Once we’ve gotten the raw numbers, you’ll learn how to plot them on a compressor flow map and how to read the results.

Don’t worry about getting drowned in math, we’ll take you through it step by step. At the end of the article, we’ll provide an easy to use calculator you can download and use to make all of these calculations yourself without having to step through all of the equations.

What is all of this information good for, anyway? Lots of things actually; in this issue we’ll use it to see how turbo/engine performance is affected by altitude. In future issues, we’ll show you how it relates to surging, choke flow (the maximum amount of air your turbo can move), selecting an upgrade turbo, and the basics of compound turbocharging.

Let’s start out by looking at the numbers for a stock truck running at sea level. We’ll calculate the maximum flow rate required from the turbo. Most stock trucks max out around 18psi of boost, and wind out at around 3200 rpm.

The first thing we need to calculate is the pressure ratio (PR). The pressure ratio of the turbocharger is determined by the difference in input pressure and output pressure. The input pressure (Pin) is the atmospheric pressure, which is 14.7psi at sea level. What we think of as boost pressure is actually the amount the air has been compressed over atmospheric pressure. That means that the output pressure (Pout) is the sum of the atmospheric pressure and the boost pressure. Given that, the pressure ratio (PR) is easy to calculate:

As air is compressed, it is is heated. This is important to consider because heating the air causes it to expand. The outlet temperature (Tout) of the turbo is a function of the pressure ratio (PR) and inlet temperature (Tin). If we assume the ambient temperature to be 70 degrees F,

The temperature rise (Trise) is the outlet temperature (Tout) minus the inlet temperature (Tin):

Trise = Tout – Tin

Trise = 204.531 – 70 = 134.531

This is assuming ideal conditions; in reality, a factor called adiabatic efficiency (AE) comes into play. This is also referred to as the compressor efficiency. Turbocharger compressors have a certain AE based on pressure ratio and flow rate. The AE tells how much higher than ideal the temperature rise will be. Most turbos have an AE of 65 – 75% in their normal operating range. To find the actual temperature rise (Trise), the ideal temperature rise is divided by the AE: