Formula & Calculator
Propeller Thrust Coefficient
Dimensionless coefficient expressing propeller thrust normalized by density, rotational speed, and diameter.
Interpretation
Propeller thrust coefficient: C_T = T/(ρ·n²·D⁴), where T is thrust, ρ density, n rev/s, D diameter. It non‑dimensionalises thrust. Example: T=1000 N, ρ=1.225, n=25, D=2 → C_T = 1000/(1.225×625×16)=1000/12250=0.0816.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| C_T | Thrust coefficient | |
| T | Thrust | N |
| ρ | Air density | kg/m3 |
| n | Rotational speed | rev/s |
| D | Propeller diameter | m |
What it means
The thrust coefficient is a dimensionless parameter used to characterise propeller performance. It depends on the advance ratio and blade pitch. It is used in performance charts to determine thrust for given operating conditions. The coefficient is also used in scaling laws for similar propellers. Understanding C_T is essential for propeller analysis and for predicting thrust at various flight speeds.
Worked example
Propeller Thrust Coefficient – Two Examples
Real‑World| Parameter | Value |
|---|---|
| T | 3000 N |
| ρ | 1.225 kg/m³ |
| n | 25 rev/s |
| D | 2.0 m |
| Parameter | Value |
|---|---|
| T | 4000 |
| n | 30 |
| D | 2.2 |
Common mistakes
- Propeller thrust coefficient: C_T = T / (ρ·n²·D⁴).
- Dimensionless – used in propeller performance maps.
- ρ: Air density (kg/m³).
- n in rev/s, D in m.
- Typically from experimental data.
Applications
Propeller thrust coefficient, C_T = T/(ρ·n²·D⁴), normalises thrust by density, rotational speed, and diameter. It is used in propeller performance maps together with advance ratio to predict thrust. Engineers use this coefficient to compare different propeller designs and to compute thrust for given conditions. By using C_T, aerospace engineers can scale propeller performance from model tests to full‑scale, and design propellers that meet thrust requirements efficiently.
- Propeller performance analysis and comparison
- Scale‑up from model tests to full‑scale
- Design of propellers for specific thrust requirements
- Integration with engine performance models
- Optimisation of blade geometry for thrust and efficiency
Frequently Asked Questions
It is a dimensionless coefficient expressing propeller thrust normalised by density, rotational speed, and diameter. It is used in performance charts.
T = thrust (N)
ρ = air density (kg/m³)
n = rotational speed (rev/s)
D = diameter (m)
It allows comparison of propellers of different sizes and speeds. It is used to compute thrust from known operating conditions.
- Mixing up rotational speed units (rev/s vs rad/s), which enters the formula raised to the second power.
- Using the wrong density (e.g., sea level instead of altitude).
- Confusing thrust coefficient with power coefficient.
A propeller produces T = 2000 N, ρ = 1.225 kg/m³, n = 30 rev/s, D = 2 m. CT = 2000 / (1.225 × 30² × 2⁴) = 2000 / (1.225 × 900 × 16) = 2000 / 17640 ≈ 0.113.
Typically, CT decreases with increasing J. The performance chart shows CT vs. J for a given propeller.
Propeller efficiency ηp = J × CT / CP, where CP is the power coefficient.
Measure thrust, speed, density, and rotational speed, then compute CT.
CT is inversely proportional to D⁴, so a larger diameter gives a smaller CT for the same thrust.
Given CT from a chart, thrust = CT × ρ × n² × D⁴.