Theory: Speed-Density


If you do not have a strong background in physics and chemistry, be prepared to do a lot of reading in the numerous side links on this page.  This isn’t intended to be a brutal presentation of the topic, but theoretical concepts are necessary in order to be able to understand what is going on behind the scenes.

Speed-Density is a method of estimating airflow into an engine in order to supply an appropriate amount of fuel and adequate spark timing.  First, vocabulary:

  • ECM, ECU, Engine computer : used interchangeably to mean the computer operating the fuel injectors and running the engine
  • RPM : Revolutions Per Minute – how fast the motor is spinning
  • MAP : Manifold Absolute Pressure – (usually) the pressure of air entering the motor
  • ECT : Engine Coolant Temperature sensor – sensor used to measure the temperature of coolant circulating through a motor.  Sometimes called different things by different manufacturers.  I will use ECT here
  • IAT : Intake Air Temperature sensor – sensor used to measure the temperature of air entering the motor.  Sometimes called different things by different manufacturers.  I will use IAT here.
  • Displacement : the volume swept by a piston descending from the top to the bottom of the cylinder bore.  More here.
  • AFR : Air Fuel Ratio – the ratio of air to fuel present in a combustible mixture.  Usually stated as a ratio, i.e. 14.7:1 for the stoichiometric AFR for gasoline.  Stoichiometric AFR varies from fuel to fuel.
  • Lambda : similar to AFR, except usually expressed as a number where 1.0 represents a stoichiometric mixture for all fuels.  Lambda and AFR are the same concept expressed in different units.
  • Stoichiometric : a mixture containing the precise amount of oxidants required for complete combustion of all fuel present.  See here or here for more information on chemistry involved.
  • Ideal Gas Law : PV= nRT (Pressure times Volume equals moles of gas times ideal gas constant times temperature)  More to be read about this here.
  • Moles : a measure of how many atoms are present.  See here.
  • Induction stoke :  the part of a 4-stroke engine’s cycle in which air is drawn into the cylinder by the piston.  See here for more information if you are not familiar with a 4 stroke engine’s operation.

Basic Goals and Method

The goal of Speed-Density is to accurately predict the amount of air ingested by an engine during the induction stroke. This information is then used to calculate how much fuel needs to be provided and may also be used for determining an appropriate amount of ignition advance.

The theoretical basis for this is the Ideal Gaw Law (more here.) rearranged to solve for “n” (the number of moles of gas present :

  • n = PV / RT

In order to use n = PV / RT to calculate the amount of air a motor ingests during the induction stroke we would need:

  • P is pressure in the cylinder immediately after the intake valves close.
  • V is volume, which we know from engine displacement.
  • R we know (it’s the Ideal Gas Constant see here for more)
  • T is the temperature of the gas in the cylinder immediately after the intake valves close.

Many of the things required to calculate the amount of air the engine ingests using the ideal gas law are missing, unavailable or at least incomplete.  Some notable points where reality is less than ideal:

  1. Our MAP sensor measures the pressure differential caused by the downward stroke of the piston in the intake manifold, not pressure in the cylinder as the intake valves initially close.
  2. We are assuming that there is no residual exhaust left in the chamber to contribute to “poisoning” of the intake charge.
  3. Camshaft overlap (i.e. when both intake an exhaust valve are open simultaneously – see here) makes fluid flow modeling considerably more complicated.
  4. T that we need is the temperature of the gas in the cylinder.  This is not usually MEASURED – instead it is ESTIMATED from the temperature of air in the manifold (IAT), the temperature of the cylinder heads (ECT) and other factors.  “RT” is often referred to as the “density correction term” as it tries to account for how air density varies with temperature.  Density correction is arguably one of the biggest problems with speed-density. (more on this later)

Speed-Density introduces the concept of Volumetric Efficiency (VE) to account for the differences between what it can observe and what is really going on.  (mostly problems 1-3 above)  Roughly speaking, VE is the ratio between the amount of air actually present in the cylinder and the amount of air we predict would be in the cylinder using MANIFOLD pressure (MAP) instead of cylinder pressure for our “P” Pressure term, REVOLUTIONS Per Minute (RPM) times Displacement (Volume / REVOLUTION) for our “V” term and an air temperature value estimated from some combination of ECT and IAT for our “T” term.

A motor said to be operating with 100% VE has the same amount of air actually in the cylinder as predicted by n = PV / RT.  Most engines operate at considerably less than 100% VE in most operating conditions.  The difference between actual airflow and theoretical maximum airflow is termed “pumping loss.”  Some engines (most notably Honda engines 🙂 ) can achieve slightly greater than 100% VE in certain conditions.  Most engines operating under forced induction can be thought of to have a VE greater than 100% in some conditions.

Speed Density ECMs generally have one or more VOLUMETRIC EFFICIENCY (VE) tables that are a critical item to be adjusted.  These tables allow predicted airflow values to be more closely adjusted to observed reality.

Strengths of Speed-Density

Speed-Density has many things going for it:

  1. Pressure sensors do not pose any restriction to the flow of air into the engine, unlike a MAF sensor.
  2. MAP sensors respond to changing conditions very quickly, enabling it to have fairly good transient response especially compared to Mass-Air-Flow
  3. Compared to a carburetor, it allows much more control over the mixture at different engine loads
  4. Simplicity: all the sensors required are extremely reliable.

Weaknesses of Speed-Density

Speed-Density is known for having several notable issues:

  1. Density correction, density correction, density correction.  You might not think that temperature is that big of a deal, but trust me it is!  Seasonal changes can wreak havoc on speed-density systems.  Superchargers or turbochargers that compress air and raise its temperature from adiabatic heating cause significant changes in density that must be accounted for.  Altitude can also be really problematic.  Many systems incorporate Barometric Pressure sensors to try to address this, but it’s an imperfect correction.
  2. Large camshafts with extremely low vacuum due to high overlap close to idle.  Camshafts that have low or pulsing vacuum close to idle present a challenge for Speed-Density.  MAP sensor averaging can help.  Alpha-N blending can help.  It is still very tricky to use speed density to predict airflow with a pressure sensor with camshafts that do not build an appreciable amount of vacuum.
  3. Volumetric Efficiency tables can be very time consuming to tune.
  4. Engine modifications generally produce volumetric efficiency changes requiring re-tuning.
  5. Quite a lot of math is required to do Speed-Density “by the book.”  Because of this, most manufacturers implement something kind of like theoretical speed-density and cut corners or combine math operations in order to allow faster execution on puny computing hardware.  (Remember, most ECUs made prior to 2000 have a slower processor than the average inexpensive cellphone circa 2010)

Sanity Checking a Speed-Density Tune

There are a few rules that transcend particular manufacturer implementations:

  1. Volumetric efficiency rarely changes suddenly.  VE tables should almost always have very gradual changes.
  2. VE usually DECREASES as pressure DECREASES (i.e. more vacuum = less VE)
  3. VE usually maxes out at an RPM close to peak engine torque at maximum observed load, which is usually where peak cylinder filling occurs.
  4. Remember that VE tables are not the only thing that controls fueling.  Temperature correction tables (ECT, IAT) are often implemented as multiplier/divider tables.  Don’t forget about injector battery tables either! (see the separate article on Injector Tuning for more on this)