Oxford says Vy is the same as Vmd

[baleares]

Both the OAA textbook and video say that Vy is the same speed as Vmd for a propeller driven aircraft.

They illustrate that Vy is found by drawing a vertical line down to the axis of TAS from the tangent of a line drawn from the origin of the axes of Power and TAS to the curve of Power Required.

They also illustrate the same procedure for finding the Vmd and repeatedly state in the book and video that they are the same speed.

As far as I understand it, Vy is found at max. excess power which is not solely dependent on power required but also dependent on power available and the maximum difference between the two (i.e. the point of maximum distance between the two curves)

To complicate matters further, my instructor says that Vx is at Vmd! [Pretty sure this is wrong or at least the wrong way of looking at it as Vx is merely the speed for max. excess thrust as far as I understand]

The OAA book also states categorically that the IAS for Vx does not increase with altitude yet this is contradicted by many, including my instructor.

Who is right in all of this? - I don't want to screw up in the exams for misinformation!

:}

[BackPacker]

I do not have a definitive answer, but I do know that calculating the V-speeds is more complicated than just drawing a graph and identifying a specific point on the curve.

At the end of the day, for best rate of climb (Vy) or best angle of climb (Vx) calculations, you've got to superimpose three graphs on top of each other. You've got to start with the airframe efficiency graph (L/D at various airspeeds), and then superimpose engine efficiency (torque/HP at various RPMs) and propellor efficiency (net thrust at different airspeeds and RPMs). And of course things may be complicated further because at high airframe AoA the thrust vector is not in line with the flight path (drag vector), the whirlwind effect of the prop around the fuselage may create additional drag, the touch of right rudder required induces drag, and so forth.

My gut feeling is that the Oxford text and videos will only take the airframe efficiency graph into account, and assume that thrust (or drag) is a constant. They use that simplified model to argue that Vy = Vmd. And at that stage of training, that may well be the proper approach, especially if the students will eventually fly turbine driven aircraft, who have totally different characteristics than piston aircraft when it comes to power delivery at various airspeeds and altitudes.

In real life, I would assume that Vx and Vy are not calculated, but measured by the test pilots during the test program. And these real-world values will automatically take all inefficiencies into account. I can even imagine that test pilots / POH writers will fudge the numbers a bit, for instance if the real-world Vx number would only be achieved at airspeeds that would not allow for sufficient engine cooling.

In theory, there is no difference between theory and practice. In practice however, there is.

[Cows getting bigger]

In theory, there is no difference between theory and practice. In practice however, there is.

Now that's what I call a quote! :hmm:

[keith williams]

As far as I understand it, Vy is found at max. excess power which is not solely dependent on power required but also dependent on power available and the maximum difference between the two (i.e. the point of maximum distance between the two curves)

To complicate matters further, my instructor says that Vx is at Vmd! [Pretty sure this is wrong or at least the wrong way of looking at it as Vx is merely the speed for max. excess thrust as far as I understand]

The short answer is that you are correct in both cases.


A rather longer answer is provided below.


If we sketch the forces in a steady climb we will find that

The sine of the climb angle = Excess thrust / weight.

So for any given weight, we get max climb angle when flying at the speed at which excess thrust is a maximum. This speed is Vx.

And

Max ROC = Excess Power / Weight.

So for any given weight, we get max ROC when flying at the speed at which excess power is a maximum. This speed is Vy.


To find where Vx and Vy lie on our speed scale we need to look at how excess thrust and excess power vary with airspeed.

Props produce thrust by exerting a force on the air to accelerate the air backwards. The thrust produced is equal to the mass flow rate of air passing through the prop, multiplied by the acceleration given to that air. The acceleration is equal to the prop wash speed minus the aircraft TAS

For a simple fixed pitch prop and a normally aspirated piston-prop aircraft thrust is maximum before the start of the take-off run, when the air is given the maximum acceleration.

As the aircraft accelerates down the runway the difference between prop wash speed and TAS decreases, so the thrust decreases. So the thrust curve starts at a maximum when TAS is zero, then curves downwards as TAS increases.

Power available is thrust times TAS, so when we multiply the gradually decreasing thrust by the linearly increasing TAS throughout the speed range We get a hump-backed power available curve that starts at zero when TAS is zero, Curves up to a maximum at some intermediate speed, then curves back down to zero when prop wash speed equals TAS.

When we compare the downward curving thrust curve with the drag curve to get excess thrust, we find that the maximum occurs just below Vmp. The EASA ATPL exams assume that Vx prop is at about 1.1 Vs.

When we compare the hump-backed power available curve with the power required curve to get maximum excess power we find that this occurs at a speed that is slightly higher than Vmp. The EASA ATPL exams assume that Vy prop is Vmp.

So for a simple fixed pitch prop aircraft Vx is jaust below Vmp (about 1.1 Vs) and Vy is at or just above Vmp.


The use of variable pitch constant speed props extends the airspeed range over which thrust is close to maximum. This flattens out the top of the thrust curve, and moves Vx closer to Vmd. If we were able to maintain constant maximum thrust to Vmd and beyond, then Vx would be at Vmd.

The flatter thrust curve also extends the speed range over which power available is close to maximum. This also tends to increase the value of Vy.


So when OAA states that:

Vy is the same speed as Vmd for a propeller driven aircraft. They illustrate that Vy is found by drawing a vertical line down to the axis of TAS from the tangent of a line drawn from the origin of the axes of Power and TAS to the curve of Power Required. They also illustrate the same procedure for finding the Vmd and repeatedly state in the book and video that they are the same speed.

They are probably referring to a high performance aircraft with constant speed prop and turbocharger.

[BackPacker]

Keith, good explanation, but like I said, in practice there is a difference between theory and practice.

For a simple fixed pitch prop and a normally aspirated piston-prop aircraft thrust is maximum before the start of the take-off run, when the air is given the maximum acceleration.

I don't think this is necessarily true. At zero IAS part of the (fixed pitch) prop may be stalled as the blade angle (particularly near the root) is above the stall angle. Only once the aircraft starts moving and the IAS becomes larger than zero will this part be unstalled, which actually increases the thrust.

At the other end of the spectrum, at very high IAS, the tip of the blades may actually not be able to keep up with the airspeed, and may even generate a backwards force. Although my gut feeling is that fixed pitch propeller blades are designed so that this would only happen in a dive, at speeds well above normal cruise speeds.

So even at fixed RPMs, propeller thrust is far from a constant. In fact, there will probably be some sharp corners in the propeller thrust curve, which happen at the points where parts of the blade become unstalled, or go into beta.

As the aircraft accelerates down the runway the difference between prop wash speed and TAS decreases, so the thrust decreases. So the thrust curve starts at a maximum when TAS is zero, then curves downwards as TAS increases.

Another factor is that as the IAS goes up, the total thrust goes down, like you said. But that decreasing propeller thrust goes hand in hand with decreasing propeller drag. Which, in turn, means that the engine will turn faster. Which means that more air and fuel is sucked in and burned. Which will mean that the power exerted by the engine goes up. Until you reach an RPM where the combustion process is not finished when the exhaust port opens, and engine power actually goes down.

This all means that you now need to consider the engine power curve itself too, which alters the equation. I'm not arguing that the curve doesn't curve downwards or anything. I'm convinced the basic shape stays the same. It's just that the exact shape of the thrust curve is not just dependent on TAS and prop wash, but also on propeller efficiency and engine power output at various RPMs.

Adding a turbocharger will make things even more complex because it complicates the engine power curve to a great extent. While adding a constant speed prop may simplify things since you can now take the engine power curve out of the equation. And so far nobody has mentioned the mixture, which will alter the engine power output independently of RPM, IAS, density altitude and whatnot. (And you cannot simplify the model by assuming an optimum mixture - whatever that is - across the whole curve, since at certain power settings, an optimum mixture will cook your engine.)

It's stuff like this that will screw up the nice theoretical model.

[djpil]

If you'd like some data (for a C172) and graphs to go along with recent posts this is an excellent reference online: Propeller Aircraft Performance and The Bootstrap Approach: Performance Basics (http://www.allstar.fiu.edu/aero/airper-ba.htm)

At one, no several, stages of my life I had Hartzell's prop software coupled with engine dyno (and other) data to aid me in flight performance analysis.

At another stage in my life I trained some Oxford instructors and some would ask why their C172 POH speeds did not match theory. Apart from answering their queries I also stated that they need to teach their students stuff consistent with the exam questions and "correct" answers that they will encounter.