DFC,
Unfortunately you appear to have some gaps / confusions in your understanding of basic mechanics.
The way that I picture the situation is that an aircraft has to produce a force (let's call it thrust) to oppose the drag force.
For starters, there is no thrust in a glide. Although I suppsoe you might be talking more generally now, so I won't debate this point any further.
This Thrust force uses up stored energy.
Forces don't really
use energy. They
might be a mechanism that's involved in transforming energy from one form to another, but you can have a force existing quite happily without any energy being used, transferred or transformed.
It would be better to say something like "The effect of drag is to cause disturbances in the air as the object passes through it, so we can see that the air has gained some kinetic energy. Consequently the object must have lost some energy, so it must either descend or decrease in velocity. If it descends at a rate that compensates for the rate that energy is lost due to drag, then the objects speed will be constant."
To stay in the air as long as possible we need to use the energy as slowly as possible.
Agreed, but.....
This is done by using the minimum thrust.
No. This is the key to where you are going wrong.
The work done by a force is the product of the force multiplied by the distance the object moves in the direction of the force.
This is often difficult for people to visualise; it is a
very common misconception that the work done by a force must somehow be related to the
duration of application. This is not the case:
Force and Time are relevant when you want to know the relationship between an
unbalanced force and a change of velocity.
i.e. Forces and Times are related to Momentum changes.
If you want to know about
energy transfer though, you need to know the force and the distance.
Since Work (Energy) done = Force x Distance, we can divide both sides of the equation by time.
This gives us Energy / Time = Force x Distance / Time
But Energy / Time = Power
and Distance / Time = Speed
So Power = Force x Speed
So we can say that if we want our store of Gravitational Potential Energy to last as long as possible, we must be converting GPE to KE (disturbances in the air due to drag) at the lowest possible rate.
So we do NOT need minimum force (drag), but rather we need whatever speed gives us the smallest value for Drage multipled by Speed. This will be below Vmd.
In order to use the minimum thrust at a constant speed the drag must also be at a minimum at that speed.
Thus isn't your minimum power speed also the minimum drag speed.
OK, well, I was talking about gliding, but the principle is exactly the same for the aerodynamic considerations of flying for endurance (rather than gliding for endurance).
The key point about the discussion is that we are talking about power REQUIRED to compensate for teh effects of drag without a decrease in the aircraft velocity being needed.
As soon as you add engines into the situation its crucial to differentiate between what the airframe needs and what the engine can provide. The latter is also influenced by airspeed, strongly so if its a propeller engine.
Under power, the optimum range and endurance speeds are by necessity a compromise between what the airframe needs and what the engines can provide.
Thus isn't your minimum power speed also the minimum drag speed.
No, as discussed above. Although in a Jet, it'll be approximately so. In a propeller aircraft all bets are off; Propeller efficiency (especially for a fixed pitch prop) is a huge deal and so power plant optimisation often overwhelms aerodynamic considerations. Hence why in a jet you typically fly a target speed, but in a prop set a target power (or a parameter that is esentially a Power setting, e.g. RPM or MAP or Torque/RPM) and then set what speed you get.
So looking at the total drag curve (not including CL) there will be an airspeed where total drag is at a minimum. Faster or slower than this speed causes more drag.
Agreed.
Is it not true then to say that when flying at this minimum drag speed minimum thrust will be required since to fly faster or slower requires more thrust to offset the increased drag?
Yes.
But be careful... minimum thrust does not imply minimum power.
This is a basic foundation in powered flying regarding endurance, minimum sink
We know that best gliding range is achieved at the best lift drag ratio. Condider also that for a shallow glide angle, weight is very close to equally lift, and weight is fixed. Put this altogether, and we can see that Vmd is actually the speed for best glide angle, not best endurance.
For best endurance, (from a purely airframe point of view because we are mostly talking about gliders here) you need to fly slower than Vmd. You'll work your way back up the drag curve, and initially becuase you are close to the bottom of the U, you get a proportionally big reduction in speed with only a small increase in drag.
i.e. in the power = force x speed equation, force (drag) goes up less than speed goes down, so the power required value decreases.
and the old 2 speeds fro every power setting except when at min-drag.
Well, this demo illustrates a powerful point, namely the reverse side of the drag curve, so i would not dispute it as a teaching exercise. But at the risk of being pedantic, it's two speeds for a given throttle setting. Typically RPM and Prop efficiency will both change as the speed changes so its not really one power setting.
Hope that's of some help.
pb