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To accelerate a gas turbine engine, you have to add fuel to the combustor to generate the additional energy to the turbine necessary to turn the compressor faster to increase airflow.I keep wondering why the early gas turbines failed to accelerate as quickly as late model piston engines and, why the hybrids failed to bridge the gap. I understand materials were a problem until quite late on but I reckon a lot of it came down to political decisions and strategic investment.
When that additional fuel is first introduced at the low power setting, it increases the combustor temperature, which challenges the turbine heat resistance, and the combustor pressure, which challenges the compressor stall margin at the low airflow condition. Early engines had low stall margin and low turbine temp capability, so they were limited on how fast the fuel flow could be increased for acceleration.