Stump the Scientist: Force spinning a large generator
We’ve got another one for you! A Stump the Scientist question for you comes from reader Chris, posted way back in December. Sorry to keep you waiting Chris! Hopefully your curiosity is finally quenched with this answer. Feel free to submit more questions to @EdisonsDesk!
Question posted by Edison’s Desk reader Chris:
I would like to know, exactly, or at least very closely, how much force is required to spin a large generator. Something in the range of 50Mw. By force, I mean Newton’s, or horsepower, or foot pounds…something I can relate to!
If I wrapped a rope around the pulley or shaft and pulled on it, what would it take to make the generator turn? For the sake of argument, let’s say the gen is on its side and I wrap a wire rope around the pulley or shaft, then I hang weights on the rope to produce torque. How much weight to turn it? How much torque is required?
I got an answer of 154,000 Hp from someone else. I think 1,500 Hp would be closer, and maybe as little as 500Hp, but I’d really like to know for sure! I realize the pulley size, if it has one, changes things a little, as does the production of electricity.
The closer you get to operating at 100%, the harder it is to turn. I’d just like to be in the ballpark! Help a guy out will ya?
The way to solve this problem is first to think about the power you want to generate (and, for general information, power is the time rate of production of energy). You have picked 50 MW (50 million watts). If I tell you that small utility generators are about 98% efficient (as they are, and 50 MW is fairly small), then you know you have to supply 50/0.98 = 51 MW of power to the generator to get the required output. You would like to know the force you have to apply, and there are several ways you might apply a force to produce this power.
You specifically mention wrapping a rope around a shaft. Power (P) equals force (F) times velocity/speed (V) that the force is acting (P=FV). If the shaft were a meter in diameter and the rope is wrapped around it, we must say how fast we want to pull the rope in order to find the force. Most utility generators run at 3600 rpm, or 60 revolutions per second. For a 1 meter diameter shaft, the surface speed is therefore π*(1 meter)*60/sec = 188 m/s approximately. If we divide this into the input power, we find that the needed force on the rope is 2.71×105 Newtons, approximately. (By the way, horsepower (Hp) is a power unit, and foot-pound is an energy unit, so neither one measures force.)