Mon Feb 23, 2004 12:21 pm by Ut
You can't. It's sort of like asking which vehicle is faster, a Pinto, or a Mack truck, and then only judging based on max speed, or only on how quickly one can get out of the gate over the other. Max speed and acceleration have to be taken into account.
Now, I'm pretty sure you can gauge the maximum angular velocity by simply dividing the torque by the drag. This is the impression I get, anyway. The time it takes to get to that speed, however, is a little more complicated. Observe.
τ=Iα
Tau is the torque, and alpha is the angular acceleration.
The angular drag can be thought of as a torque acting in the opposite direction, making sure the ship has a maximum turn rate. This rate occurs when
τ=βω, where β is the angular drag, and ω is the maximum angular velocity.
At this point, we can say that
α=βω/I
However, α is also ω/t, so t = ω/α, where t is the time it takes to accelerate to ω. This reduces to
t=I/τ=Iα
Tau is the torque, and alpha is the angular acceleration.
The angular drag can be thought of as a torque acting in the opposite direction, making sure the ship has a maximum turn rate. This rate occurs when
τ=βω, where β is the angular drag, and ω is the maximum angular velocity.
At this point, we can say that
α=βω/I
However, α is also ω/t, so t = ω/α, where t is the time it takes to accelerate to ω. This reduces to
t=I/β
So, ω=τ/β, and it takes the ship t=I/β to reach ω. Which ship turns better? The ship with a really high ω and the low t? Or the one with the high t, and low ω?
Basically, a low t and a high ω are best.