How is take-off power defined?

Question

In a recent post it could be read that by definition, turbofans do not produce power in the static case (at velocity zero). The statement could be a bit confusing since turbofans and propeller engines are at their highest power setting just before the take-off roll commences.

What is the referenced definition that results in zero power for turbofans at zero speed, regardless of the throttle setting?

Answer 1

You're asking about this answer by Peter Kämpf, in which he writes (emphasis added):

Now for turbofans. Here we have thrust which needs to be converted into power first by multiplying it with flight speed. It would be nonsensical to compare the static case – here by definition turbofans do not produce power.

You ask, "What is the referenced definition that results in zero power for turbofans at zero speed, regardless of the throttle setting?" The referenced definition is the sentence in bold above. Peter is defining power as thrust multiplied by flight speed.

Now, let's back up a little bit. Why would Peter define power like that?

For propeller engines (and car engines), defining the "output power" of an engine is easy: it's the power being transmitted through the drive shaft (which is the product of the torque the engine is exerting on the drive shaft, and its rate of rotation). I'm going to call this definition "shaft power."

A jet engine, however, doesn't have a drive shaft, so we are unable to use this definition. We're forced to choose a different definition of power, and so Peter chooses to use the product of thrust and flight speed. I'm going to call this definition "ultimate power". (This generalizes to any vehicle; we can define "ultimate power" as the forward force on the vehicle produced by its engine, times the vehicle's forward speed. Equivalently, "ultimate power" is the rate at which the engine adds kinetic energy to the vehicle.)

However, Peter also points that power as defined this way (ultimate power) can't be directly compared with the other definition (shaft power), at least not when the vehicle is stationary. This is because the "ultimate power" for a stationary vehicle is always zero, whereas the "shaft power" for a stationary vehicle is generally much greater than zero.

It may seem counterintuitive that the "ultimate power" for a stationary vehicle is always zero, but it is. Kinetic energy is proportional to the square of speed, which means that if an object is traveling extremely slowly (as in the first few nanoseconds after it starts moving), it gains kinetic energy at an extremely slow rate (on the order of nanowatts).