Home/Aerospace Engineering/Propulsion/Propeller Aircraft Range (Simplified)

Formula & Calculator

Propeller Aircraft Range (Simplified)

Simplified Breguet-type range estimate for propeller-driven aircraft as a function of propulsive efficiency and aerodynamic efficiency.

Written by the Vorzep Team

PropulsionAircraft PerformanceRange

Breguet Range Calculator Propeller Aircraft

R = (ηp / cp) · (CL/CD) · ln(Wi / Wf)
R = range  ·  ηp = propeller efficiency  ·  cp = specific fuel consumption  ·  CL/CD = lift‑to‑drag ratio  ·  Wi = initial weight  ·  Wf = final weight
⟹ Solve ⟷ R, ηp, cp, L/D, Wi, Wf
km
—
kg/kW·h
—
kg
kg
Please fix the errors above.
Solve for:
Aircraft Presets: Scenarios:
Range —
—
R: — ηp: — cp: — L/D: — Wi: — Wf: — Wf/Wi: —
✓ Copied!
Range vs Lift‑to‑Drag Ratio At current parameters
Range Current L/D
Range Gauge —
Short (< 1000 km) Medium (1000–5000 km) Long (> 5000 km)
R = (ηp/cp)·(L/D)·ln(Wi/Wf)  ·  Assumes constant L/D, cp, and cruise conditions.

Interpretation

Propeller aircraft range (simplified): R = (η_p/c_p)·(C_L/C_D)·ln(W_i/W_f), where η_p is propeller efficiency, c_p is specific fuel consumption, C_L/C_D is lift‑to‑drag ratio, W_i/W_f is weight ratio. Example: η_p=0.85, c_p=0.0001 s⁻¹, L/D=15, ln(1.2)=0.182 → R = 0.85/0.0001×15×0.182 = 85,000×15×0.182 ≈ 232,000 m.

R = (η_p/c_p) * (C_L/C_D) * ln(W_i/W_f)
Propeller Aircraft Range (Simplified)

Variables

SymbolQuantityUnit
RRangem
η_pPropeller efficiency
c_pSpecific fuel consumption (power-based)1/s
C_L/C_DLift-to-drag ratio
W_iInitial weightN
W_fFinal weightN

What it means

The Breguet range equation for propeller aircraft is similar to that for jets but uses power‑specific fuel consumption (c_p) and propeller efficiency. Range is maximised by flying at the speed for maximum L/D. This equation is used in conceptual design to estimate range for a given fuel fraction. Understanding this relation is essential for aircraft sizing and for performance analysis of propeller‑driven aircraft.

Worked example

Propeller Aircraft Range – Two Examples

Real‑World
Scenario: η_p = 0.8, c_p = 8×10⁻⁸, L/D = 15, Wᵢ = 15,000, W_f = 11,000. Find range.
ParameterValue
η_p0.8
c_p8×10⁻⁸
L/D15
Wᵢ/W_f15000/11000 = 1.364
1R = η_p/c_p × (L/D) × ln(Wᵢ/W_f) = 0.8/8e-8 × 15 × ln(1.364) = 10,000,000 × 15 × 0.310 = 46.5×10⁶ m = 46,500 km
Result 46,500 km ✓ Very long
Scenario: η_p = 0.82, c_p = 7.5×10⁻⁸, L/D = 16, Wᵢ = 20,000, W_f = 14,500. Find R.
ParameterValue
η_p0.82
c_p7.5×10⁻⁸
L/D16
ln(20000/14500)0.321
1R = 0.82/7.5e-8 × 16 × 0.321 = 10,933,333 × 16 × 0.321 = 56.2×10⁶ m = 56,200 km
Result 56,200 km ✓ Excellent
Key insight: Propeller range = (η_p/c_p)·(L/D)·ln(Wᵢ/W_f) – high L/D gives long range.

Common mistakes

  • Propeller aircraft range (simplified): R = (η_p / c_p) · (C_L/C_D) · ln(W_i/W_f).
  • η_p: Propeller efficiency.
  • c_p: Specific fuel consumption (kg/(W·s) or similar).
  • Assumes constant L/D and c_p.
  • Maximum range occurs at (C_L/C_D) max.

Applications

Propeller aircraft range (simplified) gives the cruise range for a propeller‑driven aircraft. It is similar to the Breguet range but uses propulsive efficiency and brake specific fuel consumption. Engineers use this to size fuel tanks, to compare aircraft designs, and to optimise cruise speed. By maximising range, aerospace engineers can meet mission requirements with lower fuel consumption, improving operational efficiency and cost.

  • Preliminary design of light aircraft, turboprops, and UAVs
  • Range‑payload trade‑off studies
  • Optimisation of cruise speed and altitude
  • Engine and propeller selection for long‑range missions
  • Performance benchmarking of propeller aircraft

Frequently Asked Questions

Q01What is the Propeller Aircraft Range (Simplified) used for?
A01

It is a simplified Breguet‑type range estimate for propeller‑driven aircraft as a function of propulsive efficiency and aerodynamic efficiency.

Q02What do the variables ηp, cp, CL/CD, Wi, Wf represent?
A02

ηp = propeller efficiency
cp = power‑specific fuel consumption (kg/s·W)
CL/CD = lift‑to‑drag ratio
Wi, Wf = initial and final weights

Q03Why is the range formula for propeller aircraft different from jets?
A03

It uses power‑based fuel consumption and the range is proportional to (CL/CD)·ln(Wi/Wf), similar to jets but with a different constant.

Q04What are common mistakes when using this formula?
A04

  • Using jet‑engine TSFC (thrust‑based) directly in the propeller‑aircraft (power‑based) range equation without proper conversion.
  • Assuming constant ηp over the flight.
  • Optimising range at the same CL as for jets (max L/D) instead of propeller‑specific.

Q05Give a worked example.
A05

ηp = 0.8, cp = 0.00001 kg/(s·W), L/D = 15, Wi = 15,000 N, Wf = 10,000 N. R = (0.8/0.00001) × 15 × ln(15000/10000) = 80000 × 15 × ln(1.5) = 1,200,000 × 0.4055 ≈ 486,600 m ≈ 486.6 km.

Q06How does the range depend on weight?
A06

It increases with the natural log of the weight ratio. A higher fuel fraction gives longer range.

Q07What is the optimal speed for maximum range in a propeller aircraft?
A07

It is the speed for maximum L/D, which gives the maximum range.

Q08How does altitude affect propeller range?
A08

Higher altitude improves engine efficiency and increases true airspeed for a given Mach, but may reduce ηp; the net effect is an optimum altitude.

Q09How do you convert power‑specific fuel consumption to thrust‑specific?
A09

They are not directly convertible; use the appropriate fuel consumption for the engine type.

Q10What is the effect of wind on range?
A10

A headwind reduces the ground speed, reducing the range; a tailwind increases it.