# Is consumption of car (engine+gearbox) monotonic with (steady) speed?

I try to understand the interaction of (real) engine + gearbox on the consumption. So I purposely don't want to account for friction on air and floor for now.

For the engine alone, the optimal efficiency is obtained for some given rotation speed ( about 2000 RPM, I guess ), then the consumption per turn increases above as well as below this optimal.

Now if we couple a gear box, as the wheels velocity slowly increase (slowly for quasi-stationarity) we have to change gear. During this slow process the engine thus cycles between under-rev, optimal, over-rev several times.

→ at the end, might it be that the consumption per km/h varies non monotonically with the wheels velocity ? (again, not accounting for air and floor friction. Could be tested on rolls.)

## 1 Answer

A guy on youtube named "guns cars and digits" explained this indirectly with his camshaft design video and his electric vehicle range video. You need his drag force and power equations and you can find them on wiki.

You can close the intake valve after bottom dead center. When you do that, there are certain circumstances where the air goes back into the intake plenum. Every cylinder head and camshaft combo has its own "Air slew" function to define this. Airflowresearch or Brodix describe their cylinder head flow, and the conditions for which it's possible. This will tell you when the cylinder fills up completely and makes the proportionate amount of torque.

Take those results and plug them into the horsepower equation. If your engine is making more power than drag and uphill force require, you accelerate. If you don't, you slow down. You burn the fuel no matter what, depending on throttle position and load.