Engine Physics 101: Power Curves

 

 

This article is the final posting in our short series about the physics of diesel engines. Today, we discuss power output and power curves. Whenever you purchase an engine, you are given a data sheet that shows a curve with the power output of the engine, the torque produced, and, normally, the fuel consumption of the engine at specific speeds. These curves are not derived out of thin air, there are formulas used to determine the shape of the curve and the power produced by the engine at different speeds. All engine manufacturers adhere to strict ISO standards when testing the engines and producing these graphic depictions of power.

So, how is the power output of an engine determined? Here’s the science:

 

power output

where:

P = engine power [W]

ρa = air density [kg/m3 ]

Vs = engine swept volume [m3 ]

S = engine speed [revs/sec]

formula1= fuel:air ratio [no units]

Qlhv = lower heating value of fuel [J/kg]

η = efficiency [expressed as a decimal]

Thus, this formula is repeated along the entire power curve at each speed and the results plotted along the curve. But what about turbochargers and their impact on air density? Simple. The change in air pressure is adjusted according to the amount of pressure produced by the turbocharger.

For torque, the formula is also relatively simple:

torque for

where:

Ti = engine indicated torque [Nm]

imep = indicated mean effective pressure [N/m2]

Ac = cylinder area [m2]

                L = stroke length [m]

z = 1 (for 2 stroke engines), 2 (for 4 stroke engines)

           n = number of cylinders

           θ = crank shaft angle [1/s]