That's what I meant by "allows the quad a quicker response". I'll edit the wording.

Actually this is exactly backwards. Because of the longer rotational axis the pitch axis on a stretch X quad actually takes longer to change than a shorter distance would. What it allows is more precision of control on the pitch axis, which is why racers like it. It also means that when you're going very fast, small changes in stick movement for control are less likely to result in large changes in altitude. Which when you're pitched forward at a 85 degree angle is a very real problem :D

@QuadMcFly But the torque also increases with the increased moment arm length. I don't think the moment of inertia of the racing quad is mostly determined by the motors.

It's not a question of torque, it's a question of velocity per degree of rotation. The motor is inherently capable of a certain rate of change and max velocity. As you increase the distance, the motor has to travel more distance per degree of rotation. Hence, as you increase the lever arm, the rotation rate slows. The torque increase (less force required to hold against outside influences) and the effective higher resolution result in more control. I'm writing a more complete answer below.

@QuadMcFly Uh... Fd = Iα. Thus with an increased lever arm, and a moment of inertia which doesn't increase as much, the angular acceleration for a given motor force will be greater. AFAIK, motors aren't rated for a max angular rotation rate they can apply to the quad frame nor are they rated for a max linear velocity.

They may not be rated for it, but there is a hardware limitation for how much they can create based on the prop pitch, the motor torque, and the Kv.

Sorry, what I meant to say is that those quantities aren't inherent to the motor-prop combination. They're properties of the motor-propeller-quad system as a whole. Thus, the frame's dimensions play into the calculation of those values. Remember that the linear force the motor-prop system creates is directly related to angular acceleration of the quad by proxy of torque, not linear acceleration of the quad.

You're right. I wasn't taking the distributed moment of inertia into account initially. This is true of acceleration but not rotational velocity though. Velocity is still lower for a given linear velocity, but it will get there faster.

I'm afraid you're confusing physics terminology here. I stand by my claim here.

Hey I moved this to chat so we can talk without cluttering the thread. I'd like to explore this a bit more.

Can you explain what your claim is? In every experience I've had, a longer lever arm results in a slower rotation rate on the axis that is being extended. I have never experienced a longer axis making it feel faster on that axis in 3 years of frame design and prototyping.

It makes sense that rotational acceleration would be faster, but not the actual degrees per second once equilibrium has been reached.

Essentially at a static stick deflection, the axis with the extended distance will move slower than than the same static stick deflection with a shorter lever arm.

Given that a motor can reach full RPMs in approximately 100ms, it seems that the resulting rotation speed in DPS is more important than how quickly it gets to that DPS.