V_x and performance takeoffs - POH discrepancy

[Cat Driver]

...maybe they will draws some graphs for that new configuration of the prop Beef??

[Trematode]

Just out of curiosity: How do you reconcile the fact that max endurance/min power speed is very slow -- the boundary of slow flight, bascially -- and published Vy speeds for aircraft (even propellor driven ones) are significantly higher?

Wait a sec -- might have just blown a head gasket -- tell me if I am on the right track. I think I am having a bit of an epiphany (don't laugh).

I think I understand what you and denker are coming from now -- more of a nuanced starting point in the mathematical theory. All this time I've been thinking about these figures in terms of specific airspeeds. And not really anything else. I think all of the confusion and ineptitude I've displayed comes from this fundamental misunderstanding on my part.

The magic is that these three figures:

Minimum Sink
Max Endurance
Vy

Are really just the same RATE of power exchange that you get in combination with differing angles of attack (speeds) and power settings. The fact that they corellate to specific airspeeds is important, but not the whole story. I can see the relationship now, the one you were trying to illustrate with your initial diagrams. They are not the same speeds, they are very different speeds, but the same RATE.

Whereas:

Best Glide
Best Range
Vx

Are really just the same angle of attack (an actual concrete airspeed that doesn't change) related to the forces of Thrust and drag.

Except of cource in the case of Vx for prop driven aircraft, because of prop efficiency shaping thrust available curve. And I still maintain, in the same way that Vx is a little different in prop driven aircraft, Vy must be as well.

[Colonel Sanders]

The twisty prop does not maintain a constant power output!

Not sure I agree with that. The AEIO-540D4A5 Lycomings
that I am very familiar with, will happily develop max RPM
at zero MPH - say at the top of a vertical line, right before
I kick for a hammerhead. The MP is up there, and they are
moving plenty of air backwards, so I would wager that the
torque is right up there, too. So, by definition, it's power
output is up there, too - at zero MPH.

Now, how much thrust is it developing? Well, with the
3-blade constant speed props, plenty. They're a huge
improvement over the stock 2-blade metal props in
terms of slow-speed thrust and regaining energy during
a sequence.

But that configuration is probably as good as it gets, for
prop, in terms of a flat line as the airspeed decreases.

A fixed-pitch prop is terrible, because the RPM falls off
so badly as the airspeed decreases. At zero MPH, for
example, the max static RPM might be 2,200 RPM with
a 2,700 RPM redline. That's a long way down on the
horsepower curve, so the line is going to really badly
drop as the airspeed decreases. That's even before you
consider the prop efficiency decrease.

[Trematode]

The twisty prop does not maintain a constant power output!

Not sure I agree with that. The AEIO-540D4A5 Lycomings
that I am very familiar with, will happily develop max RPM
at zero MPH - say at the top of a vertical line, right before
I kick for a hammerhead. The MP is up there, and they are
moving plenty of air backwards, so I would wager that the
torque is right up there, too. So, by definition, it's power
output is up there, too - at zero MPH.

Now, how much thrust is it developing? Well, with the
3-blade constant speed props, plenty. They're a huge
improvement over the stock 2-blade metal props in
terms of slow-speed thrust and regaining energy during
a sequence.

But that configuration is probably as good as it gets, for
prop, in terms of a flat line as the airspeed decreases.

A fixed-pitch prop is terrible, because the RPM falls off
so badly as the airspeed decreases. At zero MPH, for
example, the max static RPM might be 2,200 RPM with
a 2,700 RPM redline. That's a long way down on the
horsepower curve, so the line is going to really badly
drop as the airspeed decreases. That's even before you
consider the prop efficiency decrease.

I don't disagree with any of that. It all sounds reasonable. I was thinking about what happens to their efficiency as speed increases, into best rate of climb territory. Would they be tuned to be most efficient at this point, as it's a good balance between hanging off the prop, and cruising?

I know most fixed pitch props are designed as a bit of a compromise for the flight envelope and are hideously inefficient at very low speeds, the fall off is a little less dramatic after they've passed their peak efficiency towards the higher speeds, as I understand it.

A variable pitch prop can offset this, as you mentioned. If you really want to you can swap out fixed pitch props tuned for climbs, or cruise, but I know you know that too.

[Colonel Sanders]

what happens to (prop) efficiency as speed increases, into best rate of climb territory.

I suspect that by the time you accelerate to Vy, the prop should be pretty efficient.

fixed pitch props are designed as a bit of a compromise ... hideously inefficient at very low speeds

The decrease in RPM (and resulting loss of horsepower) by itself is tremendously significant with fixed pitch props. That's even before you start factoring in prop efficiency.

you can swap out fixed pitch props tuned for climbs, or cruise, but I know you know that too.

Uh, yeah. I am not a fan of "cruise props" because of their horrible takeoff
and climb performance. Saving a GPH at cruise isn't always the best choice
if you've crashed into the trees after takeoff.

I like climb props that wind the engine up Real Good (tm). I used to fly a
single-seat Pitts with a 4 cyl Lycoming and a fixed pitch prop that I would
wind up 'way past redline, to 3200 RPM. Sounded marvellous!

[Colonel Sanders]

I was wondering if there was some really simple stuff that we could agree on:

Is Vx really less than Vy?

Is best endurance still less than best range?

Is minimum sink glide speed probably slower than best distance glide speed?

From all of the graphs and quotes above, I am no longer sure!

[Trematode]

Hey Photo:

Take a look at this PDF file I've attached -- I think it will answer all of your questions, and you can better see where I'm coming from. The math is all there too.

It's from this great resource:
http://backoff.pr.erau.edu/gallyt/aero301_old.html
Aerodynamics 301, by a Dr. Tom Gally associate prof at embry-riddle

The section I attached is focused on performance in level and climbing flight, and you can see what I meant about the power available curves, with examples from both propeller driven aircraft and jets. I can also see exactly where you were coming from at the start of the topic as well.

[Trematode]

Is Vx really less than Vy

In terms of airspeed to fly? Yeah, I'd agree, Vx is always going to be slower (till you get to your absolute altitude).

Is best endurance still less than best range?

I think yes, it has to be.

Is minimum sink glide speed probably slower than best distance glide speed?

Same as above.

I think we've all agreed on those ones. Where we have differed is in our attempts to understand their interelationships as a whole.

[photofly]

I was wondering if there was some really simple stuff that we could agree on:

Lol.

Is Vx really less than Vy?

Yes, agree with that.

Comment: the graph from the navy flight manual uses Vx in a enlarged way, even into the region where you don't have enough engine power to maintain level flight and therefore can't climb, and all the way to glide (no engine power at all). That means, for example, that best glide range is also labelled Vx (looking at the graph makes it clearer.) In that case Vx becomes > Vy for power less than that required for level flight, just like best glide (distance) > best glide (time). Personally I like that approach because it ties together gliding and powered flight. But it's not what most people would call Vx. So, yes we agree. With that proviso.

Is best endurance still less than best range?

Yes, it must be by definition. If best endurance was faster than best range then best endurance would both last longer and fly faster - and therefore further - than best range. Which wouldn't be best range any more. If you see what I mean.

Is minimum sink glide speed probably slower than best distance glide speed?

Yes. That was clear from the start - it's easier to analyze because you don't have to know or assume anything about the engine. You don't have one.

[photofly]

and you can see what I meant about the power available curves...

In that document, the prop curve looks reasonably flat to me!

Not sure I agree with that. The AEIO-540D4A5 Lycomings
that I am very familiar with, will happily develop max RPM
at zero MPH - say at the top of a vertical line, right before
I kick for a hammerhead. The MP is up there, and they are
moving plenty of air backwards, so I would wager that the
torque is right up there, too. So, by definition, it's power
output is up there, too - at zero MPH.

With respect, Colonel, if you're not moving, it's not producing any useful power, and it's efficiency is zero, by the definition of propeller efficiency. That's because the power output of the prop is force * velocity-in-the-direction-of-the-force. While stationary it's thrashing air and making a lot of noise, sure, but not adding even the slightest amount of energy to your airframe.

Even a twisty prop has zero efficiency while stationary. But its efficiency should rise much more quickly (as the speed picks up) than a fixed prop.

[photofly]

Even a twisty prop has zero efficiency while stationary.

Here's a conundrum for you then: if the prop has zero efficiency while stationary (like with the brakes on, at the start of a takeoff roll) it's obviously unable to transfer any energy to the airframe. Then how does the aircraft get the first amount of kinetic energy to get rolling in order for the prop efficiency to move off the zero peg?

There is a right answer, btw.

@Trematode: Is Denker off the hook now?

[Trematode]

In that document, the prop curve looks reasonably flat to me!

Did you actually look at the curves dude!!

there is quite a slope initially, and it keeps rising well after the lowest point in the power required curve. This is exactly the margin I was trying to explain. Notice in every single visual aid he has in the course notes, the area where max excess power is noted, it is further up from the lowest point of the power required curve.

This is precisely because the power available curve is not as constant as you think!

[Trematode]

Is Denker off the hook now?

Sure!

[Trematode]

Here's a conundrum for you then: if the prop has zero efficiency while stationary (like with the brakes on, at the start of a takeoff roll) it's obviously unable to transfer any energy to the airframe. Then how does the aircraft get the first amount of kinetic energy to get rolling in order for the prop efficiency to move off the zero peg?

Fart or hope for a head wind?

[photofly]

This is precisely because the power available curve is not as constant as you think!

I acknowledge it's an approximation that makes the maths possible. The question is, is it useful (and interesting)? I totally agree, that, even for a twisty prop, the power drops off at lower airspeeds.

Do you remember way back in this thread, that I pointed out that for the 172/M, Vy is 90mph and best glide (sink rate) is about 68-ish-mph? If the power-available curve were really constant they'd be at the same speed.

For the 182/P, with a constant speed prop, Vy is 80KIAS, and best glide (sink) is 65-ish KIAS. Clearly the power curve isn't very flat there, either.

(re: Denker - I'll email him now, I'm sure he'll be delighted. Nice chap actually, very patient answering my email queries about some of what he's written, btw.)

[photofly]

Fart

I'm tempted to ask if you've been flying with the Colonel, but I don't know him nearly well enough to make jokes like that.

or hope for a head wind?

Nope, that won't help you, because the "problem" is that the point of application of your force isn't moving yet. A strong headwind will reduce the thrust the propeller is producing, but it's not thrust that you're short of. A tailwind would do, but everyone knows not to take off with a tailwind.

[Trematode]

I acknowledge it's an approximation that makes the maths possible. The question is, is it useful (and interesting)? I totally agree, that, even for a twisty prop, the power drops off at lower airspeeds.

Do you remember way back in this thread, that I pointed out that for the 172/M, Vy is 90mph and best glide (sink rate) is about 68-ish-mph? If the power-available curve were really constant they'd be at the same speed.

For the 182/P, with a constant speed prop, Vy is 80KIAS, and best glide (sink) is 65-ish KIAS. Clearly the power curve isn't very flat there, either.

(re: Denker - I'll email him now, I'm sure he'll be delighted. Nice chap actually, very patient answering my email queries about some of what he's written, btw.)

But don't you mean best angle of glide? When they give you best glide in the book that's what they're talking about.

[photofly]

But don't you mean best angle of glide? When they give you best glide in the book that's what they're talking about.

No, I mean best (lowest) sink rate. That should be at Vy (check the curves from the navy flight manual for a reminder), but quite clearly isn't. Reminder: Vx and best glide (distance) are the ones where you draw the tangent lines on the excess power curve, through the origin: Vy, and best sink rate, are at the flat point on the excess power curve.

They don't give you best sink rate speed in the book, which is why I said "ish" in both cases, because I had to guess. However we know it's going to be slower than best glide distance, which is what I based my guesses on.

I could have pointed out that Vy is considerably greater than speed for best glide (distance) and used exact figures in both cases, but you'd correctly have wondered why I was comparing two speeds that don't have a direct relationship.

By the way, thank you for pursuing this. I've learned a hell of a lot of new stuff, and even the stuff that I knew previously I now know much better.

[Colonel Sanders]

if you're not moving, it's not producing any useful power

I don't buy into that. As pointed out above, if you're correct,
then no aircraft could ever take off, because it would never
be able to accelerate from zero to one mph, which is silly.

A prop or jet engine which is not moving but has all the knobs
forward, is pushing a considerable mass of air backwards per
unit time. That's work per unit time, and that's power.

I would like you to ask this person, sitting behind an L39,
if he thinks that a stationary engine produces zero power:

[photofly]

if you're not moving, it's not producing any useful power

I don't buy into that. As pointed out above, if you're correct,
then no aircraft could ever take off, because it would never
be able to accelerate from zero to one mph, which is silly.

A prop or jet engine which is not moving but has all the knobs
forward, is pushing a considerable mass of air backwards per
unit time. That's work per unit time, and that's power.

Colonel, I kind of hoped you say that (naughty me). The engine that's stationary is indeed pushing a considerable mass of air backwards, and doing a lot of work, and expending a lot of power. BUT it's not adding that power to the airframe. Clearly it isn't, because the airframe is stationary and therefore not gaining kinetic energy. Nor is it wearing the brakes, because they're not moving, and nothing is getting hot because there's no friction. All the energy is lost as a fast moving stream of air (and some noise) - which is wasted as far as the aircraft is concerned.

So the prop efficiency is zero. Thats equally obvious because of the definition of efficiency, which includes the important factor of "axial speed" on the top line. Axial speed - nill? efficiency: nill.

Take home message: for a force to do work, the point of application of the force has to move in the direction of the force. No move - no work.

I would like you to ask this person, sitting behind an L39,
if he thinks that a stationary engine produces zero power:
(interesting video clip)

It's producing a lot of power, and wasting it all, because the L39 isn't accelerating. Power produced: lots. Power added to the airframe: nil.

[Colonel Sanders]

So the prop efficiency is zero

If it were moving zero air backwards, then the
prop efficiency would be zero. But there is plenty
of air moving backwards, therefore the prop is
doing plenty of work, therefore it's efficiency must
be more than zero.

You seem to be proposing that air has no mass.

It's that kind of bizarre thinking that has stretched
this thread out so long.

BUT it's not adding that power to the airframe

Who cares?

According to you, it takes no horsepower for a helicopter
to hover That will come as good news to all the
helicopter pilots that I know - I will tell them that according
to the experts on Avcan, they can hover at 3 feet indefinitely.

They can turn off the engine and walk away, and the helicopter
will remain at 3 feet, because it didn't take any power to keep
it there.

[photofly]

I don't buy into that. As pointed out above, if you're correct,
then no aircraft could ever take off, because it would never
be able to accelerate from zero to one mph, which is silly.

That's the interesting part. As I said, the propeller is unable to add energy to the airframe while stationary. But that's ok. The amount of energy required to accelerate the airframe from stationary is also zero. If you know a little calculus you can prove it like this:

Kinetic energy = m.v^2 / 2
Rate of change of kinetic energy as the velocity changes is d/dv (m.v^2 / 2) = mv
Since v is initially zero, kinetic energy doesn't change as it moves off the block. Therefore no energy is required to move it off the block. So the propeller doesn't need to provide any energy at all in that first instant. Which is just as well, as ... it can't!

Physicists will note that the physical quantity "rate of change of kinetic energy with velocity" has a special name, in fact we call it Momentum. (Relativists will say E = p^2 / 2m, and calculate dE/dp, and then claim they've invented a new quantity called "velocity" but that's beside the point.) The point is that more momentum something has, the harder it get to accelerate it.

Why does this sound so kooky? Because we're looking at ratios of quantities that both tend to zero. Isaac Newton (and that French guy Leibnitz) had to invent differential calculus to be able to handle exactly that kind of problem.

A more straightforward way to look at what happens to the aircraft with the brakes on is not to think about the energy at all but to think about the thrust: the aircraft has a mass, the propellor produces considerable thrust, and when the brakes are released it accelerates in the tradition manner.

But if you do consider the energy - and you can - then it works out too. It just sounds a bit weird.

[Cat Driver]

It's that kind of bizarre thinking that has stretched
this thread out so long.

But it is like coming up on a horrendous wreck on the highway, you just can not resist slowing down for a look.

[Trematode]

No, I mean best (lowest) sink rate. That should be at Vy (check the curves from the navy flight manual for a reminder), but quite clearly isn't. Reminder: Vx and best glide (distance) are the ones where you draw the tangent lines on the excess power curve, through the origin: Vy, and best sink rate, are at the flat point on the excess power curve.

They don't give you best sink rate speed in the book, which is why I said "ish" in both cases, because I had to guess. However we know it's going to be slower than best glide distance, which is what I based my guesses on.

I could have pointed out that Vy is considerably greater than speed for best glide (distance) and used exact figures in both cases, but you'd correctly have wondered why I was comparing two speeds that don't have a direct relationship.

By the way, thank you for pursuing this. I've learned a hell of a lot of new stuff, and even the stuff that I knew previously I now know much better.

Ok I see that you're comparing the function Vy to minimum sink -- which is ok. I do believe you've shown me that they are both the same function, and with different power settings give you the Maximum Performance Rates of climb, or rate of keeping your altitude!

But I don't think it's ok to say that the speed for Vy will be the same or even related to the speed that gives you minimum sink. If I managed to learn anything, it's explained by understanding Vy is a function that describes the rate of power exchange, and not a specific airspeed (denker says exactly that).

So if you're wondering why the speeds are so different, don't!

I think part of the general misunderstanding we are having (at least I am), is that Vy is published in POHs as a hard and fast airspeed to use in a climb. And this belies what it really represents (an exchange rate).

If you're wondering why Vy (the climb speed they publish for you) is what it is, you've just got to look at that excess power curve, and understand it is derived in part from the thrust power available, and this is not a straight line!

But, it's good we both know Best Glide in the book is refering to angle! At least we've got that straight.

and I agree it's been fun, thanks for the interesting discussion -- I feel like I've learned a lot.

I'm going to make one last attempt to sway you, Standby!

[photofly]

If it were moving zero air backwards, then the
prop efficiency would be zero. But there is plenty
of air moving backwards, therefore the prop is
doing plenty of work, therefore it's efficiency must
be more than zero.

Colonel - please look at the dictionary definition of propeller efficiency. It's all in there. Promise. The amount of air moved backwards doesn't figure in the equation. Only the energy added to the aircraft.

According to you, it takes no horsepower for a helicopter
to hover That will come as good news to all the
helicopter pilots that I know - I will tell them that according
to the experts on Avcan, they can hover at 3 feet indefinitely.

They can turn off the engine and walk away, and the helicopter
will remain at 3 feet, because it didn't take any power to keep
it there.

It may surprise you to learn that they can. All they need to do is put three foot blocks under the skids. The blocks do exactly the same job as the rotor system, and they do it considerably more quietly and without churning up all the air. It's not the keeping of the aircraft at three feet that's consuming the energy, it's churning up all the air and making all that noise that requires the energy. The actual act of hovering is free.

Same point I'm afraid: the blocks exert a considerable upwards thrust on the helicopter. According to you they must be generating a considerable amount of power! In fact they're not, because the point of application of the force isn't moving.

My sofa is (as we speak) thrusting upwards on my posterior with a considerable thrust : about 200lbs of it, in fact. No energy source required, and no power imparted to me.