Rotor Thrust Response

Rotor rotational inertia is expected to be very significant; at least 10 times that of the motor even with lightweight carbon-fibre blades.
For length-scale L, motor torque is assumed to scale proportional to volume of the motor. Usable torque may be limited more by motor temperature, but this best-case implies the following scaling rules:

PropertyScaling factor
Motor TorqueL3
Rotor InertiaL5
Time to spin-upL2
Scaling rules

For example, a 6-times bigger rotor and motor requires 36-times longer to spin-up to a target rotation speed. So 36-times longer to generate a target percentage thrust increment when using fixed-pitch blades.

However, variable-pitch blades can eliminate delay of thrust due to spin-up. Variable-pitch is potentially extremely quick because the pitching-inertia of blades plus pitch control mechanism can be significantly smaller than the inertia of the motor. Conventional blade-pitch control may be slow, but a very quick novel variable-pitch rotor design is intended.

This novel design has an elastic-inertial critically-damped time constant; √(J/k) independent of the initial state, where J is the inertia of the motor plus blade-pitching mechanism, and k the torsional stiffness of the elastic drive element. This is approximately 4 milliseconds for the model 16 inch 5-bladed rotor. The electrical time constant of the motor is even shorter. Thrust is nearly proportional to blade-pitch, with an aerodynamic delay of only milliseconds at 3000 RPM. So the delay to 60% of a target thrust increment is expected to be around 7 milliseconds for the 16 inch 5-bladed rotor

Fixed-pitch rotors have no comparable state-independent response time constant. The ratio of inertial rotation energy to power defines a time, but this ratio varies with rotation rate, and thrust is not proportional to inertial rotation energy.

The delay to 60% of a target thrust increment for a fixed-pitch rotor can however be measured for particular initial and target states as in Figure 4, page 10 of 6 Degree of Freedom UAV Thrust Model Summary (Levi.S.Burner). That figure shows state-dependent time constants spanning a range from 70 to 350 milliseconds, for a 10 inch 2-bladed propeller. Scaling up as L2 would suggest time constants from 180 to 900 milliseconds for a 16 inch fixed-pitch 2-bladed propeller and motor.

However, Levi Burner pointed out (private communication) that “the long time constants correspond with small changes of applied voltage when operating at a low thrust” and “In practice the drone would not fly at such thrusts, and so the lower time-constants were representative of our actual operating conditions”. He also notes

“… the time constants measured are likely not representative of the state of the art.” and “… later in that project we were used 12-16 inch propellers (with much better motors and active braking) and got slightly large time-constants but not nearly as large as 180-900 milliseconds.”

So as a rough guide from this information, I expect a typically 10 times quicker thrust-response of the novel 5-bladed variable-pitch rotor compared to an equal diameter fixed-pitch 2-bladed propeller.