# Turboshaft Turbine Mathematical Model

Are there any simplified mathematical models for how two gas coupled turbines (also called a free power turbine) should interact with one another as the speed of the driving turbine changes.

(i.e.) How is the speed of a turboshaft engine's power turbine affected by the speed of it's gas turbine?

• If there's no gears between them (just the shaft) then however fast one spins is how fast the other spins. If there are gears, then the speed of one is related to the other by the gear ratio. – tpg2114 Jan 15 '13 at 20:51
• The question wasn't optimally stated, I've added the fact that the driving turbine is changing speeds. – Präriewolf Jan 15 '13 at 20:55
• I contend it's still not clear -- if the two turbines are linked by a rigid shaft, then the speed of one instantly determines the speed of the other. If there are gears in between then the gear ratio factors in, but the principle is the same -- as one spins, so does the other regardless of accelerations. – tpg2114 Jan 15 '13 at 21:07
• As the question states they are gas coupled, not shaft or gear coupled. – Präriewolf Jan 15 '13 at 21:27
• My bad -- I was not familiar with that term. I added an edit with another term for this design that may be more popular in certain parts of the world. – tpg2114 Jan 15 '13 at 21:34