One of the main limitations of turbocharged engines is manifold pressure, which is limited to let's say 40 inHg. For example, the aircraft is stationairy at sea level, ISA conditions. The air is entering turbocharger with temperature 15°C and it has a pressure of 40 inHg, so we calculate density of the air:
T = 15°C = 273.15 + 15 = 288.15 K
p = 40" = 1.3544 bar = 135440 Pa
R = 287 J/(kg*K)
RhoMSL = p/(R*T) = 135440/(287*288.15) = 1.6378 kg/m^3
The TCDS for TSIO-360-EB shows that it has a critical altitude altitude of 12.000 ft (maximum altitude at which turbocharger can provide maximum manifold pressure), which means that the air is colder than at sea level and the density of the air is a bit higher:
T = 288.15 - 12 * 2 = 264.15
p = 135440 Pa
Rho12000 = p/(R*T) = 135440/(287*264.15) = 1.7865 kg/m^3
Since piston engine power is (very, very simplified) more or less a function of the density of the intake air (assuming constant air to fuel ratio, etc.), since if we have constant air to fuel ratio, increasing of density of the air will also increase the mass flow of the fuel, more fuel will burn and the power output will be higher.
So we can calculate difference between densities of the air at MSL and 12.000ft:
1.7865 / 1.6378 = 1.09 = 109%
So if the engine is producing 200hp at sea level, it will produce 200 x 1,09 = 218 hp at 12.000 ft, which is close to 215 hp which is stated in TCDS. Do note that this is over simplified just to show basic principles of increasing power with increasing altitude (up to critical altitude) in turbocharged engines.
Rating, ICAO or ARDC,
standard atmosphere
Max. continuous hp, r.p.m., in. Hg at:
Critical altitude, ft. 215-2575-40-12,000
Sea level pressure altitude 200-2575-40
Takeoff hp, 5 min., rpm, full 200-2575-40
throttle at sea level
pressure altitude
So basically, the maximum manifold pressure (40") and maximum RPM (2575) remains the same and the power output is higher at critical altitude than at MSL.