>So in reality does (T)SFC increase with altitude... and would i be correct in saying that as a jet airliner cruises at a high altitude , its engine efficiency actually decreases (due increase in sfc) , but its aerodynamic efficiency increases (thrust does not get too high due to the low air density).. and Overall the aircraft is more efficient at higher altitudes ??
For maximum specific range we need to be operating our engines and our airframe at their maximum efficiencies simultaneously. This means getting minimum SFC and maximum TAS/Drag ratio.
As altitude increase we have:
For the engines:
Decreasing temperature tends to decrease SFC.
Decreasing pressure and density tends to increase SFC.
Increasing RPM (to maintain thrust to maintain Vmrc) increases the RPM, taking it closer to the optimum 90% to 95%. This tends to decrease SFC.
The overall effect is that SFC actually increase slightly with increasing altitude.
For the Airframe:
Constant IAS at Vmrc maintains constant drag.
Increasing TAS at that constant Drag increases the TAS/Drag Ratio.
The overall effect is that TAS/Drag ratio increases with increasing altitude.
Ideally we want minimum SFC and Maximum TAS/Drag ratio simultaneously. But in reallity we have to do a bit of a trade-off between the two.
We do not actually get minimum SFC at the optimum altitude, but we do get the the best balance between SFC and TAS/Drag ratio. So we get best Specific Air Range.
(You will probably also find that your perforamnce notes are wrong about the getting the minimum SFC at the optimum altitude)