Calculator
Example data table
| Scenario | Radius (m) | Density (kg/m3) | Method | Key input | Notes |
|---|---|---|---|---|---|
| Small quadcopter hover | 0.15 | 1.225 | Power (hover) | Power 500 W, eta 0.75 | Good for quick hover estimates. |
| Bench test with Ct | 0.20 | 1.18 | Ct, RPM | Ct 0.0045, 2400 RPM | Use measured Ct for best accuracy. |
| Induced velocity estimate | 0.18 | 1.225 | Momentum | vi 6 m/s, Vc 0 | Relates thrust to induced flow directly. |
| Higher altitude air | 0.15 | 1.00 | Power (hover) | Power 500 W, eta 0.75 | Lower density reduces available thrust. |
| Axial climb | 0.18 | 1.225 | Momentum | vi 6 m/s, Vc 2 m/s | Use positive climb velocity for axial climb. |
Formula used
- Disk area: A = pi * R^2
- Momentum theory (axial): T = 2 * rho * A * vi * (vi + Vc)
- Ideal induced power: Pi = T * (vi + Vc)
- Power to thrust (hover): T = (P * sqrt(2 * rho * A))^(2/3), with P = Pin * eta
- Ct method: T = Ct * rho * n^2 * D^4, n = RPM/60, D = 2R
How to use this calculator
- Select a calculation method based on your known inputs.
- Enter air density and the number of rotors.
- Provide rotor radius or diameter and choose units.
- Fill method inputs, then press Calculate Thrust.
- Use the CSV or PDF buttons to save results.
Rotor thrust notes and practical guidance
1) What thrust means for your aircraft
Rotor thrust is the upward force produced by accelerating air through the rotor disk. For multirotors, total lift is the sum of each rotor’s thrust. A 1.5 kg vehicle weighs about 14.7 N, so you typically target at least 2× weight for responsive control and safe climbs.
2) Air density changes your results
Density enters every method because it sets how much mass flow the disk can move. Sea level standard is 1.225 kg/m³, while warm weather or higher altitude can drop density near 1.0 kg/m³. That reduction can cut available thrust noticeably for the same geometry and power.
3) Disk area and disk loading
The calculator uses A = πR² per rotor. Disk loading equals thrust divided by disk area, shown in N/m². Lower disk loading generally improves hover efficiency and reduces induced losses. Doubling radius increases disk area by 4×, which can significantly reduce required induced velocity for hover.
4) Momentum method when induced flow is known
If you have induced velocity estimates from testing or simulation, momentum theory is direct: T = 2ρAvi(vi + Vc). Hover uses Vc = 0. In axial climb, positive Vc increases the required power term and shifts thrust for the same vi, so enter realistic climb speed values.
5) Power-to-thrust for quick hover sizing
The hover power model estimates thrust from available aerodynamic power: T = (P·√(2ρA))^(2/3). Use efficiency to represent drivetrain and rotor losses. If your motor delivers 600 W but the overall efficiency is 0.70, the effective 420 W is what the model uses.
6) Ct and RPM for test-based accuracy
With a measured thrust coefficient, the Ct method is often the most repeatable: T = Ct·ρ·n²·D⁴, where n = RPM/60 and D = 2R. Ct typically varies with Reynolds number, blade pitch, and inflow, so prefer Ct values recorded near your operating RPM.
7) Interpreting outputs and sanity checks
Compare thrust per rotor to your required hover thrust (weight divided by rotor count). Watch unit consistency and keep inputs within realistic ranges. If results look extreme, verify radius/diameter selection, density units, and power efficiency. Use disk loading trends to compare design alternatives quickly.
FAQs
Q1: Which method should I use first?
A: Use the power method for quick hover sizing, Ct+RPM when you have test data, and momentum when induced velocity estimates are available. Cross-check two methods to spot input errors.
Q2: What air density should I enter?
A: Use 1.225 kg/m³ for sea-level standard conditions. For hot days or higher altitude, use a lower value if known. Even a 10–20% density drop can reduce thrust for the same setup.
Q3: Why does disk loading matter?
A: Disk loading (T/A) indicates how hard the rotor disk is working. Lower disk loading typically improves hover efficiency and reduces induced losses, which can translate to longer endurance and less heat in the power system.
Q4: Can I use this for ducted fans?
A: You can get a rough estimate, but ducts change inflow and effective disk area. If you have a thrust coefficient for the ducted system, the Ct method usually gives more realistic results than pure actuator-disk assumptions.
Q5: What efficiency value is reasonable?
A: Many small electric setups fall around 0.60–0.85 overall efficiency depending on prop/rotor, motor, ESC, and losses. If unsure, start with 0.70–0.75 and refine using measured current, voltage, and thrust.
Q6: Why do my results differ from a thrust stand?
A: Real systems include profile power, swirl, tip losses, and nonuniform inflow. Sensor calibration, battery sag, and RPM measurement error also matter. Use measured Ct near your operating point for best agreement.