Why do private jets typically have a maximum service altitude of 51,000 ft?

Engine aspect only. You can compensate the lesser lift with more velocity.

High altitude = less air density. High altitude gives you more mach number, is true, but the aerodinamic velocity decreases.

Mass flow = Cross sectional Area * Axial velocity (aerodinamic velocity) * density. Thurst = mass flow * axial velocity. So, with lower axial velocity and density, you have lesser mass flow and thurst. You could spin your compressor/turbine faster to compesate the lower density giving you more axial velocity by adding more fuel, but the turbine would tear apart. Ramjets doesnt have turbines to break, then it can fly at higher altitudes just by adding more fuel.

/r/aviation Thread