General Principles - Cruise — Page 246, Lesson 296

Let’s start with the definition of endurance, because everything in cruise performance hangs off this one idea. Endurance is the ratio of airborne time to the fuel used for that time. In other words, it tells you how long you can stay in the air for a given amount of fuel. The formula is endurance equals time in hours divided by fuel in kilograms. So the units come out as hours per kilogram. But to actually use that formula in practice, we make a small adjustment. We define specific endurance as one divided by fuel flow. So specific endurance, in hours per kilogram, is simply the reciprocal of fuel flow. The units are airborne hours per kilogram of fuel consumed. What this means is that the endurance of an aeroplane is simply a function of its fuel flow, or fuel consumption. If an aeroplane can minimize its fuel flow, it will achieve maximum endurance. So when we analyse maximum endurance capability, we need to understand what controls fuel flow. Now, a critical point: fuel flow calculations are different for a jet aeroplane and a propeller aeroplane. Let’s examine the jet first. For a jet, fuel flow equals fuel flow per unit of thrust multiplied by total thrust. So fuel flow is a function of the fuel used per unit of thrust, multiplied by the total number of thrust units. Obviously, if we could reduce both the fuel used per unit of thrust and the total number of thrust units required, then total fuel flow would be reduced. 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, the specific fuel consumption needs to be small. In other words, the aim is to reduce the amount of fuel used to produce each thrust unit. For a jet engine, this occurs when ambient temperature is very low and engine rpm is very high. And that combination can only occur at high altitude. So flying at high altitude minimizes the fuel used per unit of thrust. Having minimized the fuel used to produce each unit of thrust, the next aim is to fly the aeroplane using the minimum possible total thrust, because each unit of thrust requires fuel to be consumed. This problem is comparatively simple to solve. In level flight, the forward acting force of thrust is controlled and balanced by the rearward acting force of drag. If drag is small, the aeroplane need fly with only a small amount of thrust. So in the formula, thrust can be replaced by drag, since the value of drag is equal and opposite to the value of thrust. The formula becomes fuel flow equals SFC times total drag. To minimize drag, the jet aeroplane simply 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 then, for a jet aeroplane to maximize its endurance by minimizing its fuel flow, the pilot would fly the aeroplane at VMD and fly as high as possible.