V_x and performance takeoffs - POH discrepancy

[Cat Driver]

Landing on the water with a flying boat might under some circumstances be no problem, however if the wave action is large you are not to likely to have a successful outcome.

Long range over loaded flying always has the risk of going down and not surviving.

But it pays better than working for a FTU.

[photofly]

Photofly -- I am very confused.

The main discrepancy I see in your graphs is that the relationship between the speeds along the horizontal access is not in the proper order

In a propellor driven air craft the relationship between speeds should be as follows (slowest to fastest):

1. Minimum power required/max endurance/minimum sink glide
2. Vx
3. Minimum drag/max range/best glide
4. Vy

Your graphs show Vx as slowest, followed by Vy and Minimum sink together -- the two aren't directly correlated like this -- and then best glide

It's important to know the limitations of looking at graphs like these or you can come to some false conclusions. Because the graph slides left/right and changes shape (somewhat) as the power changes, it's not fair, and could be misleading, to compare points on the drag curve with different power settings. (I mentioned that, but maybe didn't make the point strongly enough.)

So the graph will show you that Vx < Vy, because they're on the same curve (full power).

The graphs will also show you that with the power off, i.e. in gliding flight, the speed for longest time in the air is slightly slower than the speed for best glide distance. This is certainly true, and easily demonstrated: if you slow up slightly from your best glide speed the VSI shows a slower rate of descent. That's because you're reducing the drag; you need to cash in altitude at a lower rate to pay for it. It's very obvious then that minimum drag speed doesn't give you the best glide angle, they must be two different speeds.

Max endurance (time) and best range are both determined from the drag curves obtained with two different, and intermediate, levels of power. Therefore I don't think it's fair to make any detailed claim about where, exactly, they lie in comparison with Vx etc. merely by looking at the graph. In other words, the graphs neither agree nor disagree with what you're saying there.

What it is true to say, is that for the drag curve obtained at the correct power for max endurance (time), the max endurance (time) speed is at the bottom of the curve (or top, depending on which way up you draw it).

Do you agree?

[Colonel Sanders]

Photofly:

Imagine if you removed the engine and prop from a 172
and replaced it with equivalent ballast and big-@ss hook.

Using the biggest fish scale in the world, hook the 172 to
the back of a DC-3, and go flying.

Sweep the ASI that is for every CAS from 30 mph to 180
mph, read the fish scale in pounds of drag, that the 172
pulls against the DC-3. I know, a DC-3 can't fly at 30 mph -
work with me.

Plot those numbers on a graph, with the x-axis airspeed
and the y-axis the pounds of pull you read on the fish scale.

Now take the engine and prop you removed from the 172
and mount them on the front of a railroad engine. Drive
the railroad engine down the track, with zero wind, at speeds
from 30 to 180 mph and measure the thrust that the engine
and prop could develop at WOT, in pounds of force, with one
of those new fancy thin sensor scales.

You could plot that data on the same graph.

What would those two curves look like?

[Shiny Side Up]

WTF do they talk about for all that time?

Do you mean you never sat in and actually watched?

[Trematode]

Photofly, I am just confused in general now.

This started when the colonel mentioned that he thought Vx was the equivalent of the Minimum power required and that Vy was the equivalent of the Minimum Drag airspeed.

This is wrong, and I think that was what you were getting at, but your graphs didn't make much sense to me.

There is not a separate "power on" and "power off" curve.

To find Vy you need to know your Power Required curve vs. your Power Available curve. The point at which there is greatest distance between these curves is Vy. You can also derrive minimum power required/max endurance/minimum sink glide from this curve -- the low point of the power required curve, like on the colonel's diagram. Importantly, the power required curve is NOT the same as the drag curve.

For Vx you need the trust required curve (which is the same as the drag curve), but you also need a thrust available curve -- which nobody has mentioned here. The max difference between these two is where you find Vx.

To find the Max L:D/Min Drag/Best Range/Best Glide (best glide angle, as you call it), it's simply at the low point onthe drag curve, or the tangent of the power required curve, as the colonel posted.

To sum up: Vx and Vy are not the equivalents of Minimum Power required, or Minimum Drag speeds, only with the power on instead of off.

They are completely separate speeds and are separate functions entirely.

Again, the order of speeds from slowest to fastests ends up being:

Minimum Power Required
Vx
Minimum Drag
Vy

All four are distinct from one another in a propellor driven aircraft.

[photofly]

work with me.

Colonel, always.

I'll have a think about it and sketch some graphs a bit later. But I want to point out some differences between the graphs I've been drawing, and the ones you're asking about. You're talking about measuring force - thrust/drag, and while we're talking about the "drag" curve, we're actually talking about power dissipated, which is force times velocity. So there's an extra factor of v in the shape of the curves.

Secondly, if you tow the 172 then changed the airflow over it, because you have no propwash. That changes the local airflow considerably, and also the trim. So the drag isn't going to be the same. Similarly, the propeller/engine on the front of the railway locomotive doesn't have the same airframe behind it, so the thrust it generates isn't the same as on a 172.

Whie I'm not entirely sure where your thought experiment is going, I'm very happy to play along (I like this kind of thing) but I have doubts about whether what it shows will be applicable to the real engine on the real 172.

[photofly]

There is not a separate "power on" and "power off" curve.

No, no - there absolutely is. They don't tell you that in "From the ground up", but there totally is. It's not vastly different, but different enough. That's extremely important to understand in the context of this discussion. See Denker, here:
http://www.av8n.com/how/htm/power.html#sec-vy-power

I'm sorry I have to head away from my keyboard now, but I'll come back later and see where we've got to.

[Trematode]

Photofly, to illustrate my point, the best graph I could come up with was actually in the TC flight training manual. It is absurdly hard to find anything similar online.

This shows the Power curves and Drag/thrust curves lined up on the horizontal axis, which depicts velocity. The only thing that was missing for the sake of this dicussion was the thrust available curve (necessary to find Vx), which I've sketched in roughly where it should be -- at very slow speeds it first increases, after that as speed increases, thrust available decreases.

where the excess thrust is at its greatest, you have Vx. This extra thrust being angled upward over the relatively smallest horizontal distance is what provides you with your best angle of climb performance.

When we are speaking of power required -- we must also look at power available to find out when we have the most in excess, See Vy in red -- power is a measure of thrust over time, and when the excess is greatest we get our best rate of climb performance.

You'll notice Minimum Power required and L/D max are also depicted as lines that intersect both diagrams.

Minimum power speed (lowest point on the power required cruve) = Maximum endurance = Minimum Sink Glide
L/D Max/Minimum Drag (lowest point on the total drag curve) = Best Range = Maximum Glide (distance over ground).



What I meant by there being no separate "power on" or "power off" curve is that the Drag Curve/thrust required curve stays the same for any given aircraft design. The Power required curve stays the same for any given aircraft design at a specific density altitude.

For simplicity's sake, aside from maybe some differences in drag profiles, the only thing that really changes with power settings, engines sizes, and propulsion types are the availability curves. It is interesting to note that jet engines thrust availability curves are a lot flatter, and the point of greatest excess thrust ends up being at the low point on the drag curve -- so in those cases Vx is at or close to your max L/D, or best glide speed.

I guess what I'm getting at is that you can't find Vx or Vy with just the Drag curve or the Power required curves (although you can find best glide, and minimum sink) -- you also need the thrust and power available curves.

[Cat Driver]

Do you mean you never sat in and actually watched?

Well actually when I first started the school I took an active interest in how they taught but eventually I came to the conclusion it was counter productive for me to become involved in how they taught flying.

My problem was two fold, because I did not hold an instructors rating they would not accept any of my suggestions and the second problem arose when T.C. phoned me and informed me that there were complaints from unidentified instructors that I was interfering in flight training and if I did not cease and desist from interfering they would suspend my FTU-OC .

I eventually did the smart thing and sold the flight school.

By the way when I sold it there were six single engine trainers one twin engine and one R22 Mariner on the OC.

[Cat Driver]

By the way Shiny, I do enjoy watching the mental masturbation that goes on here in this forum hopefully this gang are good enough hands and feet pilots to actually fly to those fine limits.

If I can think of even one of the instructors I had in my school over the six years I owned it who could fly that accurately I'll get back to you.

[Trematode]

Photofly -- I think I see where you are coming from. If you are refering to 7.5.2 in see how it flies, I think he is dead wrong.

It looks like he's forgone the traditional power required vs. available cruves, and drawn a single "excess power" curve. If that's what he's done, he is correct in noting that the high point of this curve is Vy, however -- he seems to make a logical leap and assume it is also equivalent to the minimum sink speed. This isn't right because excess power isn't the inverse of power required. You need to plot it against the power available to find it.

If he has simply flipped the power required curve upside down, then he's right about minimum sink, but WRONG about Vy.

For some nice graphs that will illustrate how denker is wrong, and how Vy is not the lowest point on the power required curve: http://www.boundvortex.com/ReadArticle. ... ticleID=55.

[Shiny Side Up]

Well actually when I first started the school I took an active interest in how they taught but eventually I came to the conclusion it was counter productive for me to become involved in how they taught flying.

My problem was two fold, because I did not hold an instructors rating they would not accept any of my suggestions and the second problem arose when T.C. phoned me and informed me that there were complaints from unidentified instructors that I was interfering in flight training and if I did not cease and desist from interfering they would suspend my FTU-OC .

I eventually did the smart thing and sold the flight school.

My mistake and apologies, I had assumed you were also the CFI of said school. Since this was not the case I am interested in hearing how it was set up, but that can be asked and answered somewhere else since its starting to get well outside the scope of this thread.

By the way Shiny, I do enjoy watching the mental masturbation that goes on here in this forum hopefully this gang are good enough hands and feet pilots to actually fly to those fine limits.

At least its a topic for discussion, I'd much rather see people discussing the finer points of the power curve and actual flying techniques than the usual things that pervade flight training these days. Again, another discussion, another time.

If I can think of even one of the instructors I had in my school over the six years I owned it who could fly that accurately I'll get back to you.

Unfortunate it was that way, and again I'd be interested in hearing about how it became that way. I'll reserve comment for then.

[photofly]

Photofly -- I think I see where you are coming from. If you are refering to 7.5.2 in see how it flies, I think he is dead wrong.

It looks like he's forgone the traditional power required vs. available cruves, and drawn a single "excess power" curve. If that's what he's done, he is correct in noting that the high point of this curve is Vy, however -- he seems to make a logical leap and assume it is also equivalent to the minimum sink speed. This isn't right because excess power isn't the inverse of power required. You need to plot it against the power available to find it.

If he has simply flipped the power required curve upside down, then he's right about minimum sink, but WRONG about Vy.

For some nice graphs that will illustrate how denker is wrong, and how Vy is not the lowest point on the power required curve: http://www.boundvortex.com/ReadArticle. ... ticleID=55.

The graph I drew way-back for power-on climb rate is based on the engine providing constant power at all air speeds of interest, which would make the power available curve a flat line (I did draw a dotted line marked "full power", to make it explicit) and then the excess-power available curve has the same shape as the drag curve. That approximation is probably best for a constant-speed prop, less good for a fixed pitch prop, and lousy for a turbojet.

So yes, Vy isn't the lowest point on the power-required curve, it's where the "power available curve" is highest above the "power required" curve. But if the the power available curve is a flat line then it's the same thing.

Are you happy now that to determine Vx (and best glide distance) it's appropriate to look at the tangent line to the "excess power available" curve? I take your point about looking at excess thrust curves to do that, but you can also look at them on the power curves, which lets you tie Vx to Vy, and best glide (distance) to best glide (time).

[Trematode]

The graph I drew way-back for power-on climb rate is based on the engine providing constant power at all air speeds of interest, which would make the power available curve a flat line (I did draw a dotted line marked "full power", to make it explicit) and then the excess-power available curve has the same shape as the drag curve. That approximation is probably best for a constant-speed prop, less good for a fixed pitch prop, and lousy for a turbojet.

Photofly, you are making a couple mistakes here:

You can't conflate brake horse power being generated by the engine with the "power" we are talking about with these curves. When we are talking about BHP we're talking about the torque generated by the engine, and transferred by the crankshaft to the prop per unit of time -- this is not what we're talking about on these curves.

The power we're talking about is actually THRUST * VELOCITY. It's pretty confusing, I know, and it took me a while to wrap my head around it. I think it is the flaw denker makes in his explaination, either out of ignorance or in an attempt to convey the concepts in a simple fashion.

Important thing to note is that thrust is not the same as power. Thrust is a force that opposes Drag, and its the maximum difference between these two that gives us Vx.

Power is a measure of thrust being generated over a distance, divided by time. This means that power curves cannot be substituted for thrust or drag curves in these charts. Denker treats them as the same in his book.

So which are you talking about here when you say power available is the same as the drag curve? You are comparing apples and oranges. Thrust opposes Drag, and the curve for power required is opposed by the curve for power available.

So yes, Vy isn't the lowest point on the power-required curve, it's where the "power available curve" is highest above the "power required" curve. But if the the power available curve is a flat line then it's the same thing.

But the power available curve is anything but flat: Look at the bottom of the two diagrams I posted -- the power required vs. power available curves.

Are you happy now that to determine Vx (and best glide distance) it's appropriate to look at the tangent line to the "excess power available" curve?

NO. Vx again is a function of thrust available vs. total drag -- the power curves have nothing to do with Vx except that we know Vx lies somewhere between minimum power required, and the tangent.

I take your point about looking at excess thrust curves to do that, but you can also look at them on the power curves, which lets you tie Vx to Vy, and best glide (distance) to best glide (time).

No, you can't. Which was my point. Vx and Vy are heavily dependant on the engine, and type of propulsion. You need to know thrust available, and power available -- two different things.

Best glide, both distance and time, are more functions of the airframe and angle of attack. They are the ones that can be found with the power required curve alone (point of minimum power, and tangent to the curve). Denker seems to be conflating both of these speeds with Vx and Vy.

To sum up, you can compare thrust to drag, but you can't compare power to drag -- it's apples and oranges.


Here's two more diagrams that may help:

Vx


Vy

[photofly]

Photofly, you are making a couple mistakes here:

Nope... don't believe I am ...

You can't conflate brake horse power being generated by the engine with the "power" we are talking about with these curves.

Absolutely you can. The connecting factor is the propeller efficiency, η. As Wikipedia correctly has it:

Screen Shot 2012-12-17 at 12.44.57 AM.png (14.73 KiB) Viewed 2632 times

Important thing to note is that thrust is not the same as power.

Indeed it's not....

So which are you talking about here when you say power available is the same as the drag curve?

By drag curve, I mean the rate of loss of energy due to drag. That's a measure of power required to maintain unaccelerated flight. It's drag time airspeed. I do know and the difference between a power and a force, trust me.

But the power available curve is anything but flat: Look at the bottom of the two diagrams I posted -- the power required vs. power available curves.

Well that's just a sketch, to illustrate a point. Let's look at a real graph, like figure 23, for a constant speed prop, from this 1947 NACA report entitled Prop Efficiency Charts for Light Aeroplanes": http://www.engbrasil.eng.br/index_arquivos/art10.pdf.

Screen Shot 2012-12-17 at 12.40.24 AM.png (60.51 KiB) Viewed 2632 times

There isn't a measurement for 2300rpm but you can see the way the trend goes. It's not exactly flat, but the efficiency is between .8 and .9 for a wide range of airspeeds. That means that your fixed shaft engine power, say 230hp, gives you a fixed propulsive power across that same range of speeds of 184 thrust hp, to within 15% or so. That's quite flat enough for me.

As far as looking at the tangents goes, I'm really really surprised you find that controversial. Consider the "excess power" curve. If we agree that the vertical axis measures vertical speed, and the horizontal axis is horizontal speed, then for any point on the curve the line that connects it to the origin has the same angle as the flight path. Look for the point on the curve that makes the greatest angle, and that's Vx, by definition of Vx. The same applies for the drag(power) curve in power-off gliding flight, in respect of the best angle of glide. Yes, you can pull those speeds off a thrust-drag vs. airspeed plot. But you can also get them from the tangents to a power - drag*speed vs. airspeed plot. The same landmark speeds, appearing as different interesting features on different graphs.

Wikipedia sums it up, here: http://en.wikipedia.org/wiki/Polar_curve_(aviation). See also the Colonel's graph in his earlier post, complete with tangent lines to show best angle.

[photofly]

On the subject of flat power curves, and whether they're "flat enough" - it doesn't make much odds. The "excess power" curve, that graphs the rate of production of energy in excess of that required to overcome drag, and which is converted into gravitational potential energy at some rate and therefore equivalent to a rate of climb - against airspeed - that graph:

- goes down at each end
- and has a hump in the middle.

Similarly, the power-lost-to-drag-in-gliding-flight vs. airspeed graph:

- goes down at each end
- and has a hump in the middle

The two curves don't have to have the same shape exactly, and nobody's claiming that in real life they do.

The best rate of climb and slowest rate of glide descent are at the top of the hump of each curve - and the best angle of climb - Vx - and the best angle of glide - are at the points where the tangent passes through the origin.

EDIT: actually with some elementary calculus it's easy to prove that when the tangent to the excess power curve passes through the origin, the excess thrust is at a maximum. I'll post the details tomorrow.

[Trematode]

Sorry man don't agree with any of that, and I don't think I'm getting my points across very well.

See also the Colonel's graph in his earlier post, complete with tangent lines to show best angle.

Actually all the Colonel's graph showed was:


Minimum power speed (max endurance, min sink)
Minimum Drag speed (best range, best glide)

Vbr == Best Range, and how it has to increase with a 30 knot headwind.

[Trematode]

I'll take one more stab at being succinct, before the thread careens out of control.

My issue with what you're saying, photofly -- that you can use the power required curve to find Vx -- is that the power required curve measures a rate. It tells us nothing about the forces of drag or thrust directly. If you accept this, and you accept that Vx is a function of excess thrust, then you will see you cannot find Vx by plotting the tangent against a curve that measures a rate.

The power required and drag polars look similar but they are not giving you the same information. It can be compelling to think so, and denker wraps it in a nice package that looks elegant because Vx and Vy are considered equivalent to the two glide speeds, but they are not. None of the literature I've read backs that up, at least.

I don't know what else to say, except that this is really just an academic exercise, and the numbers are so close together as to not really matter that much. We should all be flying with attitudes and not an airspeeds anyway.

[photofly]

Let's agree that Vx occurs at maximum excess thrust. Here's a mathematical proof that this is exactly equivalent to saying "Vx is the airspeed where the tangent to the excess power curve passes through the origin." Thus, you can read off Vx from a power curve.

work 1.png (21.83 KiB) Viewed 2618 times

Actually all the Colonel's graph showed was:...
Vbr == Best Range, and how it has to increase with a 30 knot headwind.

Well, what is Vbr if not an airspeed determined by maximizing or minimizing an angle of flight? And lo, there we are, finding it by drawing a tangent to a graph of power vs. airspeed. Just do the same exercise while the engine is producing power, using the excess power curve. Lo and behold, you just drew Vx on a power vs. airspeed graph. No need to draw a thrust graph.

then you will see you cannot find Vx by plotting the tangent against a curve that measures a rate.

I'm sorry, but your argument (which consists of "you will see...." ) is wrong - you quite simply can.

My issue with what you're saying, photofly -- that you can use the power required curve to find Vx -- is that the power required curve measures a rate. It tells us nothing about the forces of drag or thrust directly.

Here's the flaw in your argument. The excess power curve tells you everything about the excess thrust, because excess power is simply excess thrust multiplied by the airspeed. (That's a basic definition in physics.) When you take the gradient you divide the vertical measure by the horizontal - you divide the power by the airspeed - removing the extra factor of velocity that's worrying you. That's a wishy-washy hand-waving way to get you to think about what the concept of a gradient means. The solid maths is on the page I scanned above.

[Trematode]

Bear with me, as now I'm even more confused.

Are you talking about an "excess" power curve now? I don't disagree that you would be able to find Vy at the top of this curve, and Vx at the tangent.

But Before we were talking about the single power required curve -- not an excess power curve. And if you are plotting an excess power curve you aren't going to get the information about the glide speeds, correct?

Edit: Reading back through the posts I see you've been using the "excess" power curve for a while, sorry about that. I still have a couple questions though.

Re: see how it flies, and denker's depiction of the power curve: Is he describing an excess power curve as well? If it is, do you agree with his assertion that Vy occurs at the same speed as minimum sink?

I may have been focused too much on the diagrams you posted initially, and was interpreting them incorrectly. To clarify: Are you saying Vy and minimum sink are equivalent? That Vx and Best Glide are equivalent? Or were you just saying that you can find them in similar fashions by plotting them on separate curves and noting the high/low points of the arc and tangents?

[photofly]

Bear with me, as now I'm even more confused.

Are you talking about an "excess" power curve now? I don't disagree that you would be able to find Vy at the top of this curve, and Vx at the tangent.

But Before we were talking about the single power required curve -- not an excess power curve.

Hallelujah. Yes. We're talking about "excess power" curves. All the way along.

If you accept the "usual" simplification that propellor-driven aircraft develop constant power regardless of airspeed (and I accept that it's an oversimplification, but it appears in a huge number of basic texts) - then the "excess power" curve has the same basic shape as the drag curve, just turned over and lifted up. That's where I started.

Then you said, well, engines don't develop constant power with changing airspeed. I said, ok, the "power developed" curve isn't exactly flat, but it's not far from it. Even if the "power developed" curve isn't flat, the "excess power" still has the same basic shape - down at both ends, and a hump in the middle. And you can still find Vx from it, by looking at the tangent through the origin, just like you can find the best glide speed by looking at a tangent to the drag(power) curve.

I think we're in agreement now.

And if you are plotting an excess power curve you aren't going to get the information about the glide speeds, correct?

You can think of the drag(power) curve as an "excess power" curve of sorts. The excess is always negative, so you're never climbing, but it's the same idea, and the curve has the same basic shape, just in a different place. So I maintain that yes, you can get the information about glide speeds from an excess power curve - specifically, the one you get when the engine's producing no power.

[Trematode]

oh god yes. Ok. perfect sense now.

edit: well... more than it was making before. Thanks for taking it easy on me. Appreciate the discussion.

[photofly]

Re: see how it flies, and denker's depiction of the power curve: Is he describing an excess power curve as well? If it is, do you agree with his assertion that Vy occurs at the same speed as minimum sink?

I agree that it would do, if the drag didn't depend somewhat on angle of incidence etc, and if the power produced by the engine was independent of airspeed. (You rightly pointed out that's not a great assumption). Earlier I wrote that the minimum sink speed for the 172 is less than 74mph while Vy is 90mph - not really very close to each other. The very simple theory doesn't produce very realistic results, for sure. Denker admits as much.

I may have been focused too much on the diagrams you posted initially, and was interpreting them incorrectly.

I wasn't very clear to begin with, that in the graphs I was assuming a constant power output independent of airspeed from the engine, because I hadn't really thought about whether it was ok to assume that.

To clarify: Are you saying Vy and minimum sink are equivalent? That Vx and Best Glide are equivalent? Or were you just saying that you can find them in similar fashions by plotting them on separate curves and noting the high/low points of the arc and tangents?

Vy and minimum sink have a kind of correspondence, both being found at the top of the respective relevant curve, but no, they don't in reality occur at the same speed. Vx and best glide aren't equivalent because Vx is slower than Vy, and best glide is faster than min sink, but you can find each of them by using the same method of drawing the relevant tangent line on the relevant graph.

[Trematode]

Ok then I think we are largely in agreement.

Something about your diagrams threw me off. Maybe it's because visually, at least when I was interpreting them, they implied more relationship between the speeds than I thought was there. But I'm still always learning, and it's great to think about it in different ways.

[photofly]

I learned that you do have to take into account how the prop efficiency varies with airspeed in order to get the right shape for the power-on excess-power curve. I also learned that Vx can be defined by airspeed for maximum excess thrust (I didn't know that previously) and I had the satisfaction of proving mathematically that's identical to the way I had understood it previously, on the power curve. I also as a side-line now have a much better understanding of why jets get more efficient the faster they fly (constant thrust develops more power at speed), and why propellers get less useful (constant power develops reduced thrust at speed). We're all still learning