Bort62":3sdeimg2 said:
You are pumping air. In a vacuum, then yes - you would be right.
However, you aren't. A very small amount of effort is used to accellerate the mass of the turbine wheel/shaft/Compressor wheel. The rest is required to accelerate the working fluid. In this case, Air.
And the force needed to acclerate 1x air is .5 2x air.
That's linear.
I agree that the force needed to accelerate one pound of air will be half that needed to accelerate two pounds of air. But if an engine moves 60lbs/min with a single turbo at 10psi, it will move 60lbs/min with twin turbos at 10psi, all else being equal.
So here's the equations for accelerating air:
F=ma --> Force = mass*acceleration
Acceleration will be constant in this example. Mass of air through entire engine will be constant as well.
Twin turbos:
turbo #1 Force=1/2m*a
turbo #2 Force=1/2m*a
Total Force=(1/2m*a) +(1/2m*a)=m*a
So the sum of the forces is m*a
Single Turbo:
Force=m*a
Twin Turbo Total Force = m*a
Single Turbo Total Force = m*a
Twin Turbo total moment of inertia = (m*r^2)+(m*r^2)
Single Turbo total moment of inertia = m*r^2
So the force required to move 60lbs/min of air is the same for both the twins and the single (each twin only has to move half of total air). But the moment of inertia is going to be larger with the single due to the larger radius with the square on it. For equivalent turbo set ups, a single turbo's moment of inertia will be about 1.25 times that of the twins combined.
Sure, you can spin a turbo around by hand and it doesn't feel like it requires much force, but when accelerating up to and past 100,000rpm, the moment of inertia becomes very real.
Anyway, I'm fine with agreeing to disagree. But if you want to toss around some more math, I'm up for that too.