CALCULATORS / AERODYNAMICS AND FLIGHT SCREENING

Multirotor hover power calculator

Ideal actuator-disc induced hover power plus supplied efficiency; no propeller curve.

aerodynamics-multirotor-hover.napkin / editable

SCENARIO COMPARISON

Compare the numbers.

This source describes an analytical model. Its quantities and checks are the view.

Scenario	thrustN	aream^2	powerW
	19.62	0.19635	208.833
	15.696	0.19635	149.429

All calculated quantities are listed with the inputs. Switch to Source to inspect the equations.

SCENARIOS / CALCULATED VALUESSAME SOURCE

Change an input to see the consequences.

hover power budget208.83 W✓ passes

BASELINE INPUTS

mass2 kgrotors4 diameter0.25 mdensity1.225 kg/m^3efficiency0.6 gravity9.81 m/s^2

CALCULATED

thrust19.62 N

area0.19635 m^2

power208.83 W

Edits change the baseline source.

THE SOURCE

Edits below update the same model.

# Multirotor hover power
# Scope: Ideal actuator-disc induced hover power plus supplied efficiency; no propeller curve.
# Status: illustrative worked example; engineering review pending.
# Inputs are example values. Checks are editable example requirements, not standards.

mass = 2 kg
rotors = 4
diameter = 0.25 m
density = 1.225 kg/m^3
efficiency = 0.6
gravity = 9.81 m/s^2

thrust := mass*gravity [N]
area := rotors*pi*diameter^2/4 [m^2]
power := thrust^1.5/sqrt(2*density*area)/efficiency [W]

check hover power budget: power <= 400 W

scenario alternative: mass = 1.6 kg

Calculated from your source · not saved

Baseline · Baseline

hover power budget208.83 W ✓ passes

alternative · alternative

hover power budget149.43 W ✓ passes

Illustrative first-order example. Checks are editable requirements, not design standards. The broader topic may require additional equations, data, and validation.

Formula and units

This example uses the following equations. Input names and units match the editable source above.

thrust: thrust = mass*gravity [N]
area: area = rotors*pi*diameter^2/4 [m^2]
power: power = thrust^1.5/sqrt(2*density*area)/efficiency [W]

Original worked example

These are the baseline values in the downloadable source. Edits above let you test your own values.

Given

mass: 2 kg
rotors: 4
diameter: 0.25 m
density: 1.225 kg/m^3
efficiency: 0.6
gravity: 9.81 m/s^2

Calculated

thrust: 19.62 N
area: 0.19635 m^2
power: 208.833 W

Assumptions and limits

Ideal actuator-disc induced hover power plus supplied efficiency; no propeller curve.

The requirement checks use the limits written in this example. Passing a check does not establish that the model covers every load, material behavior, or operating condition in a real design.

Download this .napkin example ↓

Take it further with your agent

Napkin keeps the inputs, equations, checks and assumptions together in one study. Your agent sets it up; you change the numbers.

Try with Claude ↗

codex 'Use Napkin (https://napkin.engineering/mcp, or the local Napkin plugin) to build a study: Multirotor hover power. Inputs: mass; rotor count and disk areas; density; efficiency. Outputs: ideal induced power; adjusted hover estimate. Model scope: Coefficient-based models over an explicitly limited flight regime. Read napkin_capabilities and the current snapshot. Ask me for the values that matter, label assumptions with units, author .napkin source, validate it and apply it with napkin_source using the current revision, then open the study. Add checks for the limits I supply. Keep unsupported analyses explicit.'

Claude needs the Napkin connector; Codex needs the Napkin plugin. Set up your agent ↗

The broader study

The topic brief below describes the broader scope. The worked example above states the particular calculation it implements.

Inputs: mass, rotor count and disk areas, density, efficiency
Outputs: ideal induced power, adjusted hover estimate
Modes: calculate, compare, sweep
Drawing: Force and flight-envelope plots

EXECUTABLE WORKED EXAMPLE · FIRST-ORDER MODEL · CHECK THE SCOPE & ASSUMPTIONS