General Principles - Cruise — Page 246, Lesson 296

Let’s start with the definition that anchors this whole topic. Endurance is the ratio of airborne time to the fuel used for that time. So the basic formula is endurance equals time in hours divided by fuel in kilograms. That gives you hours per kilogram, which is a bit awkward to work with directly, so we make a small adjustment. We define specific endurance as one divided by fuel flow. The units of specific endurance are airborne hours per kilogram of fuel consumed. So endurance is simply a function of fuel flow, or fuel consumption. An aeroplane that minimizes its fuel flow will achieve maximum endurance. So to analyse maximum endurance, we need to understand what controls fuel flow. Now, here’s a key point: fuel flow calculations are different for a jet and a propeller aeroplane. Let’s examine the jet first. For a jet, fuel flow equals fuel flow per unit thrust multiplied by total thrust. In other words, fuel flow is a function of the fuel used per unit of thrust, times the total number of thrust units. If we could reduce both the fuel used per unit of thrust and the total thrust required, total fuel flow would drop. Fuel used per unit of thrust is most commonly known as specific fuel consumption, abbreviated SFC. So the formula becomes fuel flow equals SFC times total thrust. Now, we want SFC to be small — we want to reduce the amount of fuel used to produce each unit of thrust. For a jet engine, this happens when ambient temperature is very low and engine rpm is very high. That combination only occurs at high altitude. So flying at high altitude minimizes the fuel used per unit of thrust. Having minimized the fuel per unit of thrust, the next aim is to fly the aeroplane using the minimum possible total thrust, because each unit of thrust requires fuel. This problem is comparatively simple to solve. In level flight, the forward-acting force of thrust is balanced by the rearward-acting force of drag. If drag is small, the aeroplane needs only a small amount of thrust. And since drag is equal and opposite to thrust, we can replace thrust with drag in the formula. So fuel flow equals SFC times total drag. To minimize drag, the jet aeroplane flies at the velocity for minimum drag. That speed is VMD. So VMD is the speed to fly for maximum endurance for a jet aeroplane. In summary, for a jet to maximize endurance by minimizing fuel flow, the pilot flies at VMD and as high as possible. That’s the whole chain: high altitude minimizes SFC, VMD minimizes drag, and together they minimize fuel flow, which maximizes endurance.