0.48%
397.64
kJ/kg
397.64
kW
824.89
kW
280.61
kW
678.25
kW
0.41%
579.2
K
725.1
K
1.9307
:1
0.48%
397.64
kJ/kg
397.64
kW
824.89
kW
280.61
kW
678.25
kW
0.41%
579.2
K
725.1
K
1.9307
:1
The Brayton Cycle Calculator analyzes the idealized thermodynamic cycle for gas turbine engines — the powerplants behind jet aircraft, natural gas power plants, and industrial turbines. Named after George Brayton who patented a continuous-combustion engine in 1872, the Brayton cycle is the foundation of modern gas turbine technology.
The ideal Brayton cycle consists of four processes: (1) isentropic compression in the compressor, (2) isobaric heat addition in the combustion chamber, (3) isentropic expansion through the turbine, and (4) isobaric heat rejection (exhaust to atmosphere). The thermal efficiency depends solely on the pressure ratio and heat capacity ratio:
$$\eta_{\text{Brayton}} = 1 - \frac{1}{r_p^{(\gamma-1)/\gamma}}$$
A distinctive feature of gas turbines is the high back work ratio (BWR) — the fraction of turbine output needed to drive the compressor. Typically 40–60% of the turbine's work goes to powering the compressor, leaving the remainder as net output. This contrasts sharply with steam turbines (Rankine cycle) where the pump work is negligible.
Modern gas turbines achieve pressure ratios of 20:1 to 45:1 and turbine inlet temperatures of 1500–1800 K using advanced blade cooling and ceramic coatings. Combined-cycle plants pair Brayton and Rankine cycles, using turbine exhaust heat to generate steam, achieving overall efficiencies exceeding 60%.
This calculator computes all cycle state points, power quantities, and the critical back work ratio, making it essential for aerospace engineers, power plant designers, and thermodynamics students.
The calculator traces the four processes of the ideal Brayton cycle:
Process 1→2 (Isentropic Compression): $$T_2 = T_1 \cdot r_p^{(\gamma-1)/\gamma}$$
Process 2→3 (Isobaric Heat Addition): $$\dot{Q}_{\text{in}} = \dot{m}c_p(T_3 - T_2)$$
Process 3→4 (Isentropic Expansion): $$T_4 = T_3 / r_p^{(\gamma-1)/\gamma}$$
Compressor Power: $$\dot{W}_{\text{comp}} = \dot{m}c_p(T_2 - T_1)$$
Turbine Power: $$\dot{W}_{\text{turb}} = \dot{m}c_p(T_3 - T_4)$$
Net Power: $$\dot{W}_{\text{net}} = \dot{W}_{\text{turb}} - \dot{W}_{\text{comp}}$$
Back Work Ratio: $$\text{BWR} = \dot{W}_{\text{comp}} / \dot{W}_{\text{turb}}$$
The BWR is uniquely high for gas turbines because compressing a gas requires much more work per unit mass than pumping a liquid (as in the Rankine cycle). This makes gas turbine performance very sensitive to compressor efficiency.
The thermal efficiency increases with pressure ratio but has practical limits set by turbine inlet temperature and compressor technology. While higher pressure ratios give higher efficiency, they also increase compressor outlet temperature $$T_2$$, reducing the temperature rise $$T_3 - T_2$$ available for heat addition and thus the specific work output. An optimal pressure ratio exists that maximizes net work. The back work ratio of 40–60% means gas turbines are sensitive to component efficiency — even small drops in compressor or turbine efficiency dramatically reduce net output.
Inputs
Results
At pressure ratio 10:1 with TIT of 1400 K, the ideal Brayton cycle achieves 48.2% efficiency. The compressor consumes 41.4% of the turbine output, leaving 397.8 kW net per kg/s of air.
Inputs
Results
A high-performance turbine at 30:1 pressure ratio and 1700 K TIT achieves 57.2% ideal efficiency with 573 kW net output per kg/s.
The Brayton cycle is the ideal thermodynamic cycle for gas turbine engines. It consists of isentropic compression, isobaric (constant-pressure) heat addition in a combustor, isentropic expansion through a turbine, and isobaric heat rejection. It operates as an open cycle in jet engines (exhaust to atmosphere) or as a closed cycle in some nuclear and solar applications.
The back work ratio (BWR) is the fraction of turbine work consumed by the compressor: $$\text{BWR} = W_{\text{comp}}/W_{\text{turb}}$$. For gas turbines, BWR is typically 40–60%, meaning most of the turbine output just drives the compressor. This makes gas turbine net output very sensitive to component efficiencies — a 1% drop in compressor efficiency can reduce net power by 3–5%.
Higher pressure ratio increases thermal efficiency: $$\eta = 1 - 1/r_p^{(\gamma-1)/\gamma}$$. However, it also raises compressor outlet temperature, reducing the available temperature rise for combustion. For a given turbine inlet temperature, there's an optimal pressure ratio that maximizes specific net work output, and a different (higher) ratio that maximizes efficiency.
TIT is the gas temperature entering the turbine — the hottest point in the cycle. Higher TIT increases both efficiency and specific output. However, turbine blades must survive these extreme temperatures while spinning at high speeds. Modern blades use single-crystal superalloys, thermal barrier coatings, and complex internal cooling passages to withstand TIT up to ~1800 K.
A combined cycle pairs a Brayton (gas turbine) cycle with a Rankine (steam turbine) cycle. The hot exhaust from the gas turbine (~500–600°C) passes through a heat recovery steam generator (HRSG) to produce steam that drives a steam turbine. This recovers waste heat that would otherwise be lost, pushing overall efficiency above 60% — the highest of any thermal power technology.
The Brayton cycle uses isobaric heat addition and rejection (constant pressure), while the Otto uses isochoric (constant volume) for both, and the Diesel uses isobaric addition with isochoric rejection. The Brayton cycle operates with continuous flow (turbomachinery) rather than reciprocating pistons, enabling much higher power-to-weight ratios suitable for aviation and large-scale power generation.
Roboculator Team
The Roboculator Team explains calculations, planning tools, and practical formulas in clear language for real-life situations.
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