Rocket Propulsive efficiency at lift off

[jonquark]

According to Wikipedia:
http://en.wikipedia.org/wiki/Propulsive_efficiency
the propulsive efficiency of a rocket is at its peak when the rocket is traveling at the same speed as it is ejecting its exhaust. I understand that, but the graph (and equation) on that Wikipedia page (and elsewhere on the internet) show the efficiency to be 0 when the rocket is as rest.

I don't understand - how can the rocket ever take off without infinite energy if the efficiency is 0? It doesn't intuitively feel right either - if I'm stood on a skateboard at rest and I throw a rock off the skateboard, I'd expect the skateboard to move (assuming the rock was heavy enough and I threw it hard enough).

I'd really appreciate any help that explained what I'm misunderstanding.

 

[russ_watters]

Welcome to PF!

If the rocket is not moving, then it has no kinetic energy. In other words, there is no output energy, only input energy (power). That does not in any way imply that it can't accelerate: that intput energy is still able to generate a force that accelerates the rocket.

 

[Lsos]

The power gained by the rocket = Force* Velocity. Since velocity is 0, the power is 0, and therefore the efficiency is 0.

However, there is still a force and an acceleration, which means that the efficiency will not stay at 0 for long.