Why is the ratio of TSFC at altitude vs. sea level different for hi-bypass vs. lo-bypass turbofan engines?

Question

I've read up on how the thrust-specific fuel consumption of turbofan/turbine engines increases with altitude, and the Georgia Institute of Technology plot in particular seems to indicate that, for most modern airliners, the TSFC at cruise is 1.6 to 1.7 that of static thrust at sea level.

Now, I've come across this site (courtesy of the Wikipedia page for TSFC) and noted some wide variations with $TSFC_{cruise}$ vs. $TSFC_{0}$.

Some examples (data from the page linked above):

• GE CF6-50C2: $\dfrac{TSFC_{cruise}}{TSFC_{0}} = \dfrac{0.630}{0.371} = 1.698$.
• P&W PW2040: $\dfrac{0.582}{0.330} = 1.764$.
• RR RB.211-535E4-37: $\dfrac{0.598}{0.324} = 1.846$.
• P&W JT8D-15A: $\dfrac{0.810}{0.590} = 1.373$.
• RR Conway RCo.12 Mk.508: $\dfrac{0.822}{0.726} = 1.132$.
• RR Spey RSp.4 Mk.511-5: $\dfrac{0.770}{0.600} = 1.283$.

The upper three examples are high-bypass turbofans, and the lower three are low-bypass. Notice the big differences in the TSFC ratios.

What causes this difference?

Answer 1

The factor affecting TSFC is speed, not altitude. Altitude is indirectly responsible because the lower density requires a higher flight speed.

Low-bypass engines have a higher exit speed, so the change in speed affects their efficiency less. High-bypass engines double their TSFC between static and Mach 0.8 and only the lower temperature at altitude reduces the difference a bit. If you look at the formula for thermal efficiency in this answer, you see that efficiency drops more over speed for high-bypass engines. Only the much better propulsive efficiency of high-bypass engines makes them overall better for airliners.