PYTHON · NUMPY

Hover a Quadrotor

Size the four rotor speeds so total thrust exactly cancels weight, holding a hover to machine precision.

01Challenge

A 0.5 kg quad has four rotors, each producing thrust k_f·Ω². Find the rotor speed Ω that makes the four rotors together hold the aircraft's weight. Too low and it falls; too high and it climbs away.

Predict firstA quadrotor's four rotors don't all spin the same way — two clockwise, two counter-clockwise. If instead all four spun the SAME direction at hover thrust, what happens?

02Model

A quadrotor is a rigid body with one force you control: the sum of four rotor thrusts, pointing up out of its belly. Each rotor makes thrust proportional to the square of its speed, T = k_f·Ω². Hover is the single condition where the four thrusts add up to exactly m·g. Get that number and the aircraft hangs in the air; everything else in autonomy is a correction on top of it.

03Guided practice

Worked: write the thrust model T=k_f·Ω². Faded: solve 4·k_f·Ω² = m·g for Ω. Independent: confirm the net vertical force is zero to machine precision.

04Feedback

PASS WHEN The solved rotor speed makes total thrust equal weight to machine precision — a stable hover.

If your run fails, check:

FAIL: net force is positive — Omega too high, the quad would climb. Divide m*g by 4 rotors before the square root.
FAIL: net force is negative — Omega too low, the quad would fall.

05Retrieve & space

If mass doubles, does Omega double? (No — thrust ~ Omega², so Omega scales with the square root of weight.)
Why square the rotor speed? (Rotor thrust is proportional to Ω²; it is the aerodynamic thrust law.)
What single force does a quad actually command? (The total thrust along its body-up axis; attitude aims it.)

06Mastery & project

Solves the hover condition 4·k_f·Ω² = m·g and verifies zero net vertical force (L1: derive and check the equilibrium of a thrust-driven rigid body).

The hover Omega is the trim point every controller in Module 1+ commands around; reused as the feed-forward term in the altitude loop.

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PYTHON · NUMPY

Hover a Quadrotor

Solve for the hover rotor speed, then check the net vertical force is zero.

You read

the arrays and values already in scope

You change

the code you write in each cell

Fixed

the dataset and the checks that grade you