originally posted by orangeboy
why for a jet engine, point of Min Total Drag is equal to max endurance (i can see this since thrust is also lowest, and assuming fuel varies directly with thrust this would be the minimum required to keep the plane airborne), and on a piston plane, the point of min drag is used for max range since it gives the best L/D ratio?
from what i understand, max endurance on a piston plane comes from min power, but how come this min power doesn't correspond to the min point on the total drag curve? is it because the fact that piston engine doesn't provide the thrust directly?
sorry for the questions, just finding this really confusing, which it shouldn;t!
Well this whole thing certainly confused me when I was doing my ATPL.
We know that for props we can make the simplifying assumption that fuel flow is proportional to power required, whereas for jets we assume fuel flow is proportional to thrust required.
But props and jets are subject to the same laws of physics: they're both devices which create thrust by causing a mass of air to accelarate. There is really no fundamental difference between them. So the question becomes: why do the ATPL textbooks make different (and apparantly contradictory) simplifying assumptions for props and jets?
The answer to this question lies in propulsive efficiency. We can define propulsive efficiency as power_out / power_in.
For level flight, Power_out = power required = drag*TAS = thrust*TAS.
Power_in = the rate at which kinetic energy is added to the air to create thrust. Since the engine converts chemical energy in the fuel to kinetic energy in the air let's assume that fuel flow is proportional to the rate of adding kinetic energy to the air (another simplifying assumption!). So far no difference between props and jets.
How does propulsive efficiency vary with speed (TAS). This is where I would really like to draw a graph, but I'll try to describe it in words (if you have D P Davies' Handling The Big Jets, see p50).
Imagine you are at the beginning of the runway, running up the engine just prior to brake release. At this point you are creating thrust and burning fuel but going nowhere. Propulsive efficiency is therefore zero. So our graph of propulsive efficiency against TAS will begin at the origin (zero TAS, zero efficiency)for both props and jets.
In our prop aircraft, as TAS increases the propulsive efficiency rises steeply at first, then the graph bends over and the efficiency approaches a constant value. Eventually if the prop tips go supersonic the efficiency decreases. However, for speeds around Vmd we assume that we are on the bit of the graph where propulsive efficiency is roughly constant. This leads to the conclusion that fuel flow is proportional to power required and hence maximum endurance corresponds to minimum power required.
For the turbojet, the propulsive efficiency increases with speed at a much shallower gradient. Eventually, at very high speeds, the graph bends over towards a constant, but at speeds around Vmd we assume that we are on a bit of the graph where the propulsive efficiency is increasing roughly linearly with TAS. If propulsive efficiency is proportional to TAS and power out = thrust*TAS the speed term cancels and we are left with power_in proportional to thrust, hence fuel flow proportional to thrust. From this it follows that maximum endurance correspends to minimum thrust required or minimum drag.
But what about a modern turbofan at high altitude (High TAS, Low EAS). Which bit of the graph are we on now? Perhaps we are on the curved bit where neither simplifying assumption applies?
Simplifying assumptions are great provided you understand their origin and limitations.