Turbocharger Pressure Ratio and Charge-Air Temp
Why boost is a gauge number and why it needs an intercooler: PR = (ambient_abs + boost) / ambient_abs, so the ambient must be added before dividing -- 15 psi at sea level (14.7 psia) is PR 2.02, but the same 15 psi a mile high (12.2 psia) is PR 2.23, a hotter outlet for the identical boost. Compressing air heats it: T_out = T_in x [1 + (PR^0.283 - 1)/efficiency], so 15 psi at 80 F inlet and 70% efficiency reaches 250 F -- a 170 F rise from compression alone, why an intercooler is mandatory on a serious build. Reports the compressor-outlet (not manifold) temperature. A planning estimate; the compressor map and engine build govern.
Formula and source
PR = (ambient_psia + boost_psi) / ambient_psia; T_out = T_in x [1 + (PR^0.283 - 1) / (efficiency/100)] with temperatures absolute (Rankine); temp_rise = T_out - T_in.
Turbocharger pressure-ratio and charge-air-temperature model (compressor-map sizing; ideal-gas adiabatic compression with gamma = 1.4), first-principles, by name; the compressor map and the engine build govern.
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