{"id":145,"date":"2021-11-24T23:51:25","date_gmt":"2021-11-24T23:51:25","guid":{"rendered":"https:\/\/agileaircraft.com\/?page_id=145"},"modified":"2024-01-03T00:51:50","modified_gmt":"2024-01-03T00:51:50","slug":"rotor-inertia","status":"publish","type":"page","link":"https:\/\/agileaircraft.com\/?page_id=145","title":{"rendered":"Rotor Thrust Response"},"content":{"rendered":"\n

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<\/a>. Usable torque may be limited more by motor temperature, but this best-case implies the following scaling rules:<\/p>\n\n\n\n

Property<\/td>Scaling factor<\/td><\/tr>
Motor Torque<\/td>L3<\/sup><\/td><\/tr>
Rotor Inertia<\/td>L5<\/sup><\/td><\/tr>
Time to spin-up<\/td>L2<\/sup><\/td><\/tr><\/tbody><\/table>
Scaling rules<\/strong><\/figcaption><\/figure>\n\n\n\n

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.<\/p>\n\n\n\n

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<\/a> design is intended.<\/p>\n\n\n\n

This novel design has an elastic-inertial critically-damped time constant; \u221a(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<\/p>\n\n\n\n

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<\/a> (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<\/sup> would suggest time constants from 180 to 900 milliseconds for a 16 inch fixed-pitch 2-bladed propeller and motor.<\/p>\n\n\n\n

However, Levi Burner pointed out (private communication) that \u201cthe long time constants correspond with small changes of applied voltage when operating at a low thrust\u201d and \u201cIn practice the drone would not fly at such thrusts, and so the lower time-constants were representative of our actual operating conditions\u201d. He also notes<\/p>\n\n\n\n

\u201c… the time constants measured are likely not representative of the state of the art.\u201d and \u201c… 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.\u201d<\/p>\n\n\n\n

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.
<\/p>\n","protected":false},"excerpt":{"rendered":"

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: Property Scaling […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-145","page","type-page","status-publish","hentry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/agileaircraft.com\/index.php?rest_route=\/wp\/v2\/pages\/145","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/agileaircraft.com\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/agileaircraft.com\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/agileaircraft.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/agileaircraft.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=145"}],"version-history":[{"count":5,"href":"https:\/\/agileaircraft.com\/index.php?rest_route=\/wp\/v2\/pages\/145\/revisions"}],"predecessor-version":[{"id":499,"href":"https:\/\/agileaircraft.com\/index.php?rest_route=\/wp\/v2\/pages\/145\/revisions\/499"}],"wp:attachment":[{"href":"https:\/\/agileaircraft.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=145"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}