How to use the Brayton Cycle Calculator
- 1. Enter the cyclePressure ratio, compressor inlet temperature and turbine inlet temperature.
- 2. Add lossesCompressor and turbine isentropic efficiencies, and a regenerator if there is one.
- 3. Read the resultsEvery state temperature, the works, efficiency and back work ratio.
Brayton cycle formulas
For the cold-air-standard cycle, with x = rp^((γ−1)/γ):
- T2s = T1·x and T4s = T3 / x
- With losses: T2 = T1 + (T2s − T1)/ηc and T4 = T3 − ηt(T3 − T4s)
- wc = cp(T2 − T1), wt = cp(T3 − T4) and wnet = wt − wc
- Ideal efficiency: η = 1 − 1/rp^((γ−1)/γ)
- Regenerator: the air is preheated to Tx = T2 + ε(T4 − T2), so qin = cp(T3 − Tx)
- Maximum net work (ideal cycle) at rp = (T3/T1)^(γ/(2(γ−1)))
Worked example and exam tips
rp = 8, T1 = 300 K, T3 = 1300 K, γ = 1.4, cp = 1.005. T2 = 543.4 K and T4 = 717.7 K, so wc = 244.6 kJ/kg, wt = 585.2 kJ/kg and η = 44.8%. The back work ratio is 41.8%, far higher than in a steam cycle. With ηc = 80% and ηt = 85%, T2 rises to 604.3 K, T4 to 805.0 K, and the efficiency falls a lot.
- Ideal Brayton efficiency depends only on the pressure ratio, not on T3.
- A regenerator helps only when the turbine exhaust is hotter than the compressor exit.
- Books that use air tables (variable cp) get slightly different numbers from this constant-cp method.
Frequently asked questions
Why is the back work ratio so high in gas turbines?
The compressor squeezes a gas, which takes much more work than pumping a liquid. Often 40 to 80% of the turbine work goes back into the compressor.
Does a higher pressure ratio always help?
It raises the ideal efficiency, but past the optimum the net work per kg falls, and with real losses the efficiency also peaks and then drops.
What is regenerator effectiveness?
The fraction of the largest possible preheating that the regenerator achieves: (Tx − T2)/(T4 − T2).
Is this calculator free?
Yes. You fill in a short form once to see your result, and the other Uncodemy tools then open without it. Every calculation runs in your browser and nothing you type is sent anywhere.