The sloth with which large jet engines transition from idle to full thrust is being cited by theorists as a factor in Saturday’s crash of Asiana 214. The claim is that the big engines of a Boeing 777 require something like 5-7 seconds to transition from idle to full thrust.
A couple of questions:
-Is the spin-up rate of a jet engine exponential in nature? That is, if we call idle “0%” and full power “100%,” does it take the same amount of time to go from 0-50% as it does to go from 50-100%, or is the latter transition faster?
-Smaller engines spin at higher RPM, but because of their smaller diameter, they have less rotating inertia. Compared to large engines, do they take more time or less time to go from 0-100%?
Mri = Moment of Rotational Inertia.
Rotational Inertia = Mri * rotational velocity
Mri is a square law - sum of ( mass times distance (from axis) squared ),
Well the point mass (or cylinder, or other mass all at the same distance from the axis.) will do as the example.
So if you make the rotor twice the size it will weigh twice as much ,and the radius component of Mri will be quadrupled.
So double the diameter, then you multiply the Mri by EIGHT .
Thats got to affect spool up time,given the power to tap is not 8 times larger, its only 3 or 4 times larger.
The first thing to consider with the second part of your question is that a smaller engine may be a turbojet and not a turbofan engine. A turbojet is simpler in that the inlet compressor blades are connected directly to the exhaust turbine by a shaft. These engines will spool up very quickly. You move the throttle forward and the engine rpm accelerates quickly.
Now a turbofan engine is more complex. It basically has a turbojet engine inside of it. In the back of the inner engine is another exhaust turbine and spins a second shaft to drive the front compressor blades that you see on most modern jet aircraft. Thy two shafts are not mechanically attached to each other. You can spin the inlet blades without turning the inner engine. It’s even possible to put something like a 2"x4" piece of wood in the front blades and run the inner engine!
What happens is the exhaust from the inner engine first keeps it running. Next it hits the exhaust turbine of the big fan section to get it turning. This allows those big blades to pull in a lot of air. Now if you move the throttle forward on a turbofan engine, the inside engine does spin up pretty fast; however, it takes a while longer for the larger fan section to spool up. The big fan section produces a lot of the thrust on turbofan engines.
Think about putting two household fans of the same size pointing at each other. You turn one on and it spins up pretty fast. The second fan will start spinning also, but there will be a lag time. Now imagine that the first fan is smaller than the second. The second fan will take longer to spool up plus probably spin at a much slower speed.
I’ve simplified the above quite a bit and some techno-purists would have my head on a platter for the way I put it, but there it is.
IME the rate at which an engine spools up is fairly linear. That is to say that it takes about the same amout of time to go from 0%-50% as from 50% to 100%.
Engine spool up time (as with almost everything related to jet engines) is regulated by the FAA. The requirement that all certified engines must meet is no more than a 5 second spool up from flight idle to 95% of rated takoff thrust. (The relevant regulation can be found here and is FAR 33.73). Engineers have a few tools to meet this 5 second spool-up requirement, including compressor bleeds and compressor variable inlet guide vanes. Since adding these extra features adds cost and reduces the robustness of the overall system (more parts, more chances for failure) my guess would be that the spool-up time for an engine like this is not much better than the regulatory maximum.
I’m not arguing that, but I’ll point out that the engines will be less efficient at lower rotational speeds and if the time is linear there must be something to counteract that.