Vy flight path angle greater than Vx ???

[Waldo Pepper]

A while back I decided to analyze runway design for obstacle clearances (angle to 50' vs distance vs climb rate vs speed, etc.) using my trusty spread sheet.
In so doing I decided to incorporate data from various POHs.
In so doing I found that in all cases Vy yielded a steeper flight path angle than Vx.


Apparently Vx is NOT the "airspeed for best climb angle" it is the airspeed to use at LIFT OFF to give the shortest ditance to 50' of altitude.
In other words; the sortest distance to 50' from the BEGINNING OF THE GROUND ROLL is attained by lifting off at the Vx speed.
The basic idea to clear 50' on takeoff is to get off the ground as soon as possible and establish an IAS of Vx.


This is very different from being "the best angle of climb speed" since while inflight if you need to clear the obstacle above you, you would go to Vy, not Vx.


Comments, agree/disagree welcome.

Poll is: agree Vy angle > than Vx
disagree, Vy angle not > Vx, Vx is greater than Vy
Other: ?

[martymayes]

In other words; the sortest distance to 50' from the BEGINNING OF THE GROUND ROLL is attained by lifting off at the Vx speed.

Actually, the Cessna max performance takeoff procedure in later FAA approved AFM's calls for "lifting off" at a speed less than Vx.

Additionally, at 50 ft the recommended speed is > than Vx for envelope protection in turbulent conditions. I believe the distance numbers in the AFM reflect the published procedure.

Also agree there is probably a lot of confusion on when, where and what speed to use. Therefore, all points considered, I voted "other"

[Waldo Pepper]

Actually, the Cessna max performance takeoff procedure in later FAA approved AFM's calls for "lifting off" at a speed less than Vx.

Additionally, at 50 ft the recommended speed is > than Vx for envelope protection in turbulent conditions. I believe the distance numbers in the AFM reflect the published procedure.

Also agree there is probably a lot of confusion on when, where and what speed to use. Therefore, all points considered, I voted "other"

Agree Marty, but the question wasn't about flying techniques, it was just simply "If you fly at the POH Vx speed is your flight path angle greater or less than if you fly at the POH Vy speed?"

[Dana]

I don't know what numbers are in any particular POH, but by definition Vx is the speed for the steepest climb angle, so unless Vy happens to be at the same speed, Vx will be steeper. The POH numbers may include fudge factors for expected pilot skill, averaging for varying conditions, etc. But I also see errors in your spreadsheet; for example, the formula in column J should be ATAN not TAN... not that it greatly affects the results at these small angles (as the tangent of a small angle is very close to the angle itself in radians).

I suspect that the POH numbers to clear the obstacle, from which you take the C-150 Vx climb rate (I didn't look further) include the time it takes to initiate the climb (accelerate the aircraft upwards) from zero ROC on the ground, i.e. the actual ROC at Vx is probably greater than you calculated from the published obstacle clearance distance. The faster the aircraft, the more ground you'll cover during that transition.

[Waldo Pepper]

I don't know what numbers are in any particular POH, but by definition Vx is the speed for the steepest climb angle, so unless Vy happens to be at the same speed, Vx will be steeper. The POH numbers may include fudge factors for expected pilot skill, averaging for varying conditions, etc. But I also see errors in your spreadsheet; for example, the formula in column J should be ATAN not TAN... not that it greatly affects the results at these small angles (as the tangent of a small angle is very close to the angle itself in radians).

I suspect that the POH numbers to clear the obstacle, from which you take the C-150 Vx climb rate (I didn't look further) include the time it takes to initiate the climb (accelerate the aircraft upwards) from zero ROC on the ground, i.e. the actual ROC at Vx is probably greater than you calculated from the published obstacle clearance distance. The faster the aircraft, the more ground you'll cover during that transition.

Good catch on TAN v ATAN, I guess I was too busy coloring the spread sheet.
But as you pointed out for small angles it doesn't make much difference in the result (some of the angles over ~4 degrees decreased by 0.1 degree).

I too always thought Vx was the speed yielding the steepest climb angle (as it's label states), but the data says otherwise.

[martymayes]

The value for Vx is just a point on a curve plotted on a graph. The theoretical value may not = the practical value.

[Waldo Pepper]

For anyone wishing to check the numbers in the SS or add some new planes, here's a link to Cessna POHs:

https://www.manualslib.com/brand/cessna/aircrafts.html

[Marc Zeitlin]

A while back I decided to analyze runway design for obstacle clearances (angle to 50' vs distance vs climb rate vs speed, etc.) using my trusty spread sheet.
In so doing I decided to incorporate data from various POHs.
In so doing I found that in all cases Vy yielded a steeper flight path angle than Vx...
I would be very interested in understanding where you got the #'s for climb rate when at Vx. I looked at two different C-172 manuals:

https://static1.squarespace.com/static/565f5233e4b0a69070fb2525/t/56e5c1294c2f8502d98477ee/1457897798070/1978-Cessna-C172N-+POH.pdf

and:
http://www.lanierflightcenter.com/wp-content/uploads/172S-POH.pdf

Both of them have tables for Vy rate of climbs, and both have tables for Vx and Vy at different altitudes, but NEITHER have a table of actual climb rates when flying at Vx. If you don't have this #, you cannot calculate the angle of climb.

Maybe some of the other aircraft have these #'s, but you claimed ALL cases to have Vy steeper than Vx (which others have pointed out is the opposite of the definition of Vx and Vy).

When testing my COZY MKIV in Phase I, I did complete climb tests at airspeeds from 60 KIAS to 140 KIAS and at fwd, center and aft CG, as well as lightweight, mid-weight and MGW. In ALL cases, the maximum climb angle occurred at a speed lower (by about the right amount) than the maximum climb rate speed - IOW, Vx is always below Vy, and Vx's climb angle is always higher than the climb angle at Vy.

So I think that you're confusing something in the POH with the climb rate when at Vx.

Can you point me to a specific POH where they give the climb rates at both Vx and Vy, and where, if you calculate the climb angle at both speeds, you come up with a steeper angle at Vy?

[Waldo Pepper]

I would be very interested in understanding where you got the #'s for climb rate when at Vx. I looked at two different C-172 manuals:

https://static1.squarespace.com/static/565f5233e4b0a69070fb2525/t/56e5c1294c2f8502d98477ee/1457897798070/1978-Cessna-C172N-+POH.pdf

and:
http://www.lanierflightcenter.com/wp-content/uploads/172S-POH.pdf

Both of them have tables for Vy rate of climbs, and both have tables for Vx and Vy at different altitudes, but NEITHER have a table of actual climb rates when flying at Vx. If you don't have this #, you cannot calculate the angle of climb.

Maybe some of the other aircraft have these #'s, but you claimed ALL cases to have Vy steeper than Vx (which others have pointed out is the opposite of the definition of Vx and Vy).

When testing my COZY MKIV in Phase I, I did complete climb tests at airspeeds from 60 KIAS to 140 KIAS and at fwd, center and aft CG, as well as lightweight, mid-weight and MGW. In ALL cases, the maximum climb angle occurred at a speed lower (by about the right amount) than the maximum climb rate speed - IOW, Vx is always below Vy, and Vx's climb angle is always higher than the climb angle at Vy.

So I think that you're confusing something in the POH with the climb rate when at Vx.

Can you point me to a specific POH where they give the climb rates at both Vx and Vy, and where, if you calculate the climb angle at both speeds, you come up with a steeper angle at Vy?



Hi Marc, Very insightful questions,

As I think I noted in the SS none of the manuals I looked at gave the climb rate for Vx, nor did they give the ground roll distance for a Vy TO.
Looking further into why all the manuals had pretty much the same format and types of data (or lack thereof) I found that GAMA has a spec for POHs.
It seems to be the source for not specifying the inclusion of those 2 essential bits of information:

Link to GAMA Specification No. 1 for POHs (+ others):
https://gama.aero/facts-and-statistics/publications/gama-and-industry-technical-publications-and-specifications/

Not having those numbers available from the POHs I derived them as follows:

Vx gives the Vx IAS, ground roll distance and total distance over a 50' obstacle, 4 pieces of info.
1) Subtracting ground roll distance from total distance gives the distance from lift-off to the 50' obstacle, taking the ATAN of 50/that delta distance gives the flight path climb angle.
2) Converting the IAS in mph or Kts to fpm for common units then correcting (reducing) the air speed to Ground speed due to the climb angle.
3) Now knowing the GS from lift-off to the obstacle and the distance from lift-off to the obstacle I ratio distance to speed and get the time (fraction of a minute) from lift-off to the obstacle.
4) Now knowing time from liftoff to the obstacle and that the obstacle is at 50', I divide the fraction of a minute into 50' and get the Vx average rate of climb from Lift-off to 50'.

One set of numbers in the spread sheet (left side) assumes that the Vy Lift-off occurs at the same lift-off point as Vx (clearly not true) - but the point here is to determine which speed gives the greater angle of climb so the answer here is valid.

Having some concern about how much longer the unstated Vy ground roll might be than the Vx ground roll a friend of mine assumed a constant acceleration to Vy, thos numbers are the yellow and blue high lights to the right.

The Vy numbers were then derived similarly to the Vx numbers.

I realize it's a PITA to try and figure out what the thinking is behind someone else's spread sheet formulas, hope these alleviates the pain somewhat.

[Dana]

I too always thought Vx was the speed yielding the steepest climb angle (as it's label states), but the data says otherwise.

Then the data is wrong, or includes other assumptions not factored into your calculations. Vx is, as I said above, by definition the speed for steepest climb, but the distance given to clear an obstacle (from which you calculated the ROC at Vx) may include other factors.

[WLIU]

The GAMA format manual for the C-150M book describes a maximum performance take-off as lifting off, then accelerating to 60 KIAS with flaps retracted, to climb over an obstacle. Interestingly, the stated Vx is 56 KIAS. So we can deduce that the take-off distance numbers include the expectation that the technique described is used. Which makes attempting to back out the climb rate invalid.

If you are looking for an excuse to go fly, you can find the explanation of how to fly the saw-tooth climb and descent profiles in this web site's info on flight testing your homebuilt, and I think on other web sites. You can gather real world data for your spreadsheet that describes the individual airplane that you fly in your typical load configuration. A good learning exercise.

Best of luck,

Wes

[Marc Zeitlin]

Not having those numbers available from the POHs I derived them as follows:...
I realize it's a PITA to try and figure out what the thinking is behind someone else's spread sheet formulas, hope these alleviates the pain somewhat.Well, yeah, thanks.

But I'll say, as others have, that your methodology is flawed with respect to trying to DERIVE climb rates from the data stated - there are too many confounding parameters, and not enough information, and too many assumptions.

Since your conclusions are in opposition to both axioms as well as to measured data from actual testing of aircraft, it seems clear that the methodology to reach those conclusions is flawed. Obstacle clearance after a takeoff roll can't be used to derive climb RATE at a particular airspeed.

Having been involved with a number of various aircraft flight tests, I can tell you that the angle of climb at Vx is ALWAYS steeper than the angle of climb at Vy, and Vy is ALWAYS higher than Vx, by pretty close to the predictions of the formulae that calculate them.

[Waldo Pepper]

Hi Dana,
I fully understand why it's so difficult to accept that Vy gives a steeper climb than Vx, but using the definition of Vx to validate Vx is circuitous reasoning.
I don't quite believe it myself but I can find no evidence to support Vx yielding a steeper climb angle, only ~100 years of the aviation community stating it does.
I think what may have happened back in the day is someone determined that to clear obstacles on TO it was best to use a climb speed such as Vx, and rather than call it "best climb speed to clear obstacles on TO" it got shortened to "best angle of climb speed"

[keen9]

So given your few hours with a spreadsheet, you negate the work of the Wright Brothers, NACA, NASA, and entire aerospace industry?

The CAFE Foundation has detailed test reports on a number of aircraft. They include Vx and Vy tests. They do not agree with your assessment:
http://cafe.foundation/v2/research_aprs.php

[Waldo Pepper]

Hi Marc,
"
Obstacle clearance after a takeoff roll can't be used to derive climb RATE at a particular airspeed."

Evidence of why not is why I posted this question.

BTW, If you would, I would be very interested in knowing how you determined the distance from one altitude to another at a constant airspeed in order to determine the flight path angles at both Vy and Vx.
For example; Was wind considered? e.g. not knowing the wind exactly were 2 runs made in opposite directions as soon after the other as possible starting at the same altitude, then flying the same course and starting altitude at the other airspeed?

[Waldo Pepper]

Hi Keen9,
I looked through some of those CAFE reports (Thanks for the link) and didn't run across the one(s) you are referring to for Vx and Vy, would you mention which ones do?
Thanks

[Waldo Pepper]

Hi WLTU,
Good point on the 60 then 56 KIAS and I fully expect that, assuming the manufacturers actually fully test their aircraft for the numbers they put in their Handbooks, that there is variation in the techniques used to obtain the numbers and in the execution of those techniques; However,
the climb rates in my spread sheet are average climb rates for both Vx & Vy. If the manufacturers statements for ground roll and total distance over a 50' obstacle are fairly accurate and correct (and the 50' is accurate and correct), then the angle of climb for Vx should be fairly accurate.
Changing (for instance) the '64 150 IAS from 64 to 60 changes the average climb rate from 433 fpm to 406 fpm, which for the 60 to 56 KIAS you quoted would band the uncertainty in the spread sheets average climb rate numbers - IOW a possible error in average climb rate of +/-14 fpm or +/-3.3% in the '64 150 case.

This point does bring up 2 other problems:
1) If one were to fly the Vx obstacle clearance numbers in POHs EXACTLY (somehow) would the wheels be rolling over the top of that 50' obstacle? - or is there some margin of safety built into the numbers the POH is silent about. e.g. is it actually a 55' or 60' obstacle the POH numbers are good for?
2) Why is there no specification of ground roll distance for a lift off at Vy in any of the POHs I looked at and not required in the GAMA specification? It seems that this distance would be closest to the distance of a normal TO roll, and therefore an important number to include.

[Dana]

Hi Dana,
I fully understand why it's so difficult to accept that Vy gives a steeper climb than Vx, but using the definition of Vx to validate Vx is circuitous reasoning.
I don't quite believe it myself but I can find no evidence to support Vx yielding a steeper climb angle, only ~100 years of the aviation community stating it does.
I think what may have happened back in the day is someone determined that to clear obstacles on TO it was best to use a climb speed such as Vx, and rather than call it "best climb speed to clear obstacles on TO" it got shortened to "best angle of climb speed"

The aerodynamics of a climbing aircraft are well understood. The best rate of climb will always happen at the airspeed (Vy) where excess power (power above that required for level flight) is greatest. The best angle of climb will always happen at that airspeed (Vx) where excess thrust is greatest. The calculations are fairly straightforward, and well proven by real world testing. Yes, there will be real world variations from theory, but the basic relationships (including the one that says Vy will be faster than Vx) don't change.

The numbers in the POH are based on theory as verified by real world testing. As such, they include assumptions and/or adjustments (as Wes described) that invalidate any attempt to back calculate numbers not provided (like ROC at Vx, or actual climb angles).

Take a look at this graph. It shows a plot of ROC vs. airspeed for typical light plane. The very top of the curve (point B) is the best rate of climb (700 fpm) at a TAS of 80 knots. That's Vy. The best angle, however, is where the line from 0,0, is tangent to the curve at point A (the highest angle the line can be and still touch the curve), and the corresponding speed (Vx) is always slower (69 knots in this case). The actual numbers vary with each aircraft and I don't know if this is real data or a made up example, but it doesn't matter, the general relationship is always the same.

[Waldo Pepper]

Hi Dana,

The graph you presented is obviously for illustration purposes.
A more to the point statement is that Vy is the peak of the L/D curve for the entire aircraft at full power (not just the airfoil L/D peak, although the airfoil is the dominate contributor by far)
and Vx is at the Maximum CL (coefficient of lift for the entire aircraft at maximum power) with only the airfoil CL curve being the dominant contributor in this case.
The main reason for Vy and Vx not being at airfoil peak L/D and Cl respectively is the angle of the thrust vector to the earth tangent, or pitch angle assuming the thrust vector is parallel to the longitudinal axis.
The thrust vector angle ,or pitch angle, is then the primary determinate of the flight path angle, gamma, after subtracting out the AOA.
I perfer to view the primary reason I climb and how fast is where I point the thrust vector and how long I make that vector with the throttle setting - since I've never flown a general aviation A/C I thought had "excess" thrust. :-) maybe a T-6, but that's not GA.

Here's a good site for airfoil curves (the basis for all flying things):
http://airfoiltools.com/airfoil/details?airfoil=naca2412-il

While all this is I'm sure fascinating, saying that we don't know how the numbers in a POH were arrived at so we can't empirically derive numbers is the same as saying we can't rely on the number/data in a POH,
ESPECIALLY when you consider the 50' number and the ground roll number and the total distance over an obstacle number - if those 3 numbers aren't reliable what numbers in the POH could be reliable?

Incidentally, those 3 numbers are the numbers which give the net flight path angle to 50' and the spread sheet shows Vy flight path being steeper than the Vx flight path angle.

To simplify this whole discussion does anyone know why those numbers are wrong in all the POHs (looked at anyway)?

[Marc Zeitlin]

BTW, If you would, I would be very interested in knowing how you determined the distance from one altitude to another at a constant airspeed in order to determine the flight path angles at both Vy and Vx.Well, the distance from one altitude to another is determined by subtracting the lower altitude from the higher altitude.

When doing climb tests (which is what validates Vx and Vy), you fly at a given CAS, starting 500 ft. below your starting altitude (let's say it's 2000 ft MSL). You begin a climb at that IAS and when reaching your starting altitude of 2000 ft., you mark the time, to the second. When you pass through 3000 ft., you mark the time again, to the second. Continue that until you're tired of climbing. Do that at IAS's from 5 kt. above stall speed until the speed at which you can't climb much anymore.

Once you've got the climb RATES at each airspeed, you then use the pythagorean theorem to determine the climb angle - your flight path, using your TAS (determined in the standard way using CAS, DA, temp and humidity) as the hypotenuse and the climb rate as the vertical distance. Voila' - climb angle.


For example; Was wind considered?For Cthulu's sake, really? Do we not know the difference between Groundspeed and Airspeed? I don't give a crap about wind - I'm measuring aircraft performance, here. See above - distance moved over the ground is not taken into account - all I need is climb rate and TAS - both measured in ft/sec, m/sec, or some set of consistent units. Do the math, and the climb angle magically appears.


e.g. not knowing the wind exactly were 2 runs made in opposite directions as soon after the other as possible starting at the same altitude, then flying the same course and starting altitude at the other airspeed?Unnecessary. In Phase I, we've done our airspeed calibrations so that we know the IAS - CAS translation, then use standard atmospherics to determine TAS. Once I know TAS and climb rate, I'm done.

You insist on using data for takeoff to clear a 50 ft. obstacle as some sort of indication of the climb RATE for Vx, and it's not (as others have more than once pointed out), anymore than seeing a snake outside my window is an indication that one of the dragons from Game of Thrones is about to incinerate my house.

MEASUREMENTS of real planes prove you wrong. There is no discussion to be had here - the facts have long been known, measured, and verified, in many (in fact all) aircraft.

[Marc Zeitlin]

To simplify this whole discussion does anyone know why those numbers are wrong in all the POHs (looked at anyway)?They're not wrong. You're just misinterpreting what they mean.

To quote Inigo Montoya from "Princess Bride:

"... I do not think it means what you think it means."

[Dana]

Hi Dana,

The graph you presented is obviously for illustration purposes.

Yes, of course. But ignoring the numbers, it looks just like the real curves for real aircraft, I posted it simply to illustrate why Vx is always slower than Vy.


While all this is I'm sure fascinating, saying that we don't know how the numbers in a POH were arrived at so we can't empirically derive numbers is the same as saying we can't rely on the number/data in a POH,
ESPECIALLY when you consider the 50' number and the ground roll number and the total distance over an obstacle number - if those 3 numbers aren't reliable what numbers in the POH could be reliable?

It's not that those numbers aren't "reliable", but they don't contain enough information to derive the information you're looking for. It's probably like the "maximum demonstrated crosswind" in the POH, which is not necessarily the max the plane can handle, but that max that was demonstrated, and intended to be representative of what a typical pilot in typical conditions can safely expect to handle.

[martymayes]

To simplify this whole discussion does anyone know why those numbers are wrong in all the POHs (looked at anyway)?

Define "wrong"

The numbers accomplish exactly what the manufacturer intended.

[Ron Blum]

Dana posted a great graph of ROC (rate of climb) versus airspeed. It shows the relationships between Vx (best angle of climb) and Vy (best rate of climb).

The best rate of climb (Vy) is simply the highest value of rate of climb. This value is independent of wind.

The best angle of climb (Vx - for clearing obstacles) is the point on the ROC data curves where a line drawn from the origin (zero airspeed, zero rate of climb) tangents the ROC curve. The ROC at Vx is always lower than the ROC at Vy (or Vx would be Vy by definition). Wind greatly affects the ANGLE of climb, but the best angle of climb is always at Vx.

MANY people confuse angles and rates of climb. Angle of climb (altitude change per distance) is based on an earth reference, which is why wind changes the angle of climb (increases with headwind; decreases with tailwind). Rate of climb (altitude change per time) is independent of wind.
.

[Marc Zeitlin]

Wind greatly affects the ANGLE of climb...Only with respect to ground position - NOT with respect to aircraft performance. We're ONLY talking about the aircraft's performance here, NOT where it ends up over the ground.


... but the best angle of climb is always at Vx.Yes, by definition, as Dana and others have pointed out multiple times. Wherever the best angle of climb is is by definition called Vx.


MANY people confuse angles and rates of climb. Angle of climb (altitude change per distance) is based on an earth reference, which is why wind changes the angle of climb (increases with headwind; decreases with tailwind). Rate of climb (altitude change per time) is independent of wind.See above. They're BOTH completely independent of wind when discussing AIRCRAFT PERFORMANCE. The airplane does not know if or which way the wind is blowing (unless we're going to start having downwind turn discussions again).

If you're talking about clearing an obstacle on the ground, then you care about which way the wind is blowing. If you only care to know what your airplane's best climb angle is, then the ground and the wind are meaningless.

[keen9]

Hi Keen9,
I looked through some of those CAFE reports (Thanks for the link) and didn't run across the one(s) you are referring to for Vx and Vy, would you mention which ones do?
Thanks
The RV-9A Report (clearly the finest of the aircraft tested) has the climb data on page 11. I'm sure there is similar data in the others.

[Ron Blum]

If you're talking about clearing an obstacle on the ground, then you care about which way the wind is blowing. If you only care to know what your airplane's best climb angle is, then the ground and the wind are meaningless.

Marc: By your definition of aircraft performance, Vx is not an aircraft performance number because it is the airspeed to fly to produce the largest climb ANGLE (with respect to the ground).

I am curious to know what your aircraft performance climb angle is referenced to?

[WLIU]

All aircraft performance numbers are referenced to the air mass that you are flying in. When we are close to the ground, or we are trying travel across the ground, then we factor in the wind vector. But when calculating or demonstrating a pure performance number, we assume that we are moving in an air mass whose horizontal motion (N-S & E-W) is not a factor.

Best of luck,

Wes

[Marc Zeitlin]

Marc: By your definition of aircraft performance, Vx is not an aircraft performance number because it is the airspeed to fly to produce the largest climb ANGLE (with respect to the ground).You do understand that the aircraft's performance is a function of the air that it's in, not the ground that it's over, yes? If my TAS is 100 Kts (169 ft/sec) and my climb rate is 800 fpm (13 ft/sec), then my climb angle is:

sin^(-1)(13/169) = 4.5 degrees

For my COZY MKIV at Vx, SL, standard day, if my TAS is 80 Kt. (135 ft/sec) and my climb rate is 1300 fpm (21.7 ft/sec), then my climb angle is 9.2 degrees.

Same plane, same day, Vy, TAS of 95 Kt. (160 ft/sec) and a climb rate of 1400 fpm (23.3 ft/sec), my climb angle is 8.4 degrees. Climb RATE is higher at Vy, but climb ANGLE is lower.

See? Vx is steeper than Vy, and I don't care about the ground, or wind, or trees, or 50 ft. obstacles. It's the airplane's performance we're measuring - nothing else.


I am curious to know what your aircraft performance climb angle is referenced to?The air in which the aircraft is flying. Same as ALL aircraft performance, except landing and takeoff rolls. Once the wheels are no longer touching the ground, the air is all that matters. TAS is not referenced to the ground; climb rate is not referenced to the ground; glide ratio is not referenced to the ground; etc.

Does wind affect the travel over the ground? Sure. But the OP's question was about Vx and Vy and climb angles, not distance traveled over the ground for a given altitude increase.

[Ron Blum]

The original poster (Waldo) posed a question relative to Vx, Vy and clearing a 50’ ground obstacle (regulation). Angle of climb (with respect to the air) is both irrelevant to aircraft performance and the original posters question/statement.

Flying an airspeed of Vy will produce the highest rate of climb (altitude gain per time).
Flying an airspeed of Vx will produce the highest angle of climb (altitude gain per distance travelled)

Yes, I understand aircraft performance. Heading Flight Test, Aerodynamic and Engineering departments and being an FAA Flight Analyst DER at major GA manufacturers across the country over the past 30 years, I think I know aircraft performance, but I am ALWAYS open to learn from others.

[Marc Zeitlin]

The original poster (Waldo) posed a question relative to Vx, Vy and clearing a 50’ ground obstacle (regulation). Angle of climb (with respect to the air) is both irrelevant to aircraft performance and the original posters question/statement.

Flying an airspeed of Vy will produce the highest rate of climb (altitude gain per time).
Flying an airspeed of Vx will produce the highest angle of climb (altitude gain per distance travelled)
If you accept that Vy has a lower angle of climb than Vx, then what's the discussion about? Angle of climb (with respect to the air) is what will determine angle of climb over an obstacle on the ground.

The OP said:

"In so doing I found that in all cases Vy yielded a steeper flight path angle than Vx."

This is the incorrect part. Vy, as you know, does NOT yield a steeper flight path angle than Vx. This is what all of us took exception to, and it has nothing to do with distance over the ground, just distance (as defined by TAS per unit time).

Because the OP used inappropriate information to attempt to DERIVE the Vx climb rate (since that information is not in any POH), he then got inaccurate data for climb performance over a 50' obstacle, which was his original goal. Conflating inappropriate data was the problem with his calculations. If he actually tested for Vx and Vy in a particular airplane and then measured the altitude above a 50' obstacle, he'd realize that climbing at Vx would get him higher over an obstacle than Vy would.

And the OP stated, with respect to the POLL:

"Poll is: agree Vy angle > than Vx
disagree, Vy angle not > Vx, Vx is greater than Vy
Other: ?"

As you've clearly articulated, the angle of climb at Vx is ALWAYS higher than the angle of climb at Vy - there can be no other answer. And that's NOT a function of wind, ground, or anything else.

[Ron Blum]

All: This thread has given me a great idea (yes, I am bias). I was just thinking of ideas for OSH forum topics. The making of AFM/POHs would be a great topic. Agree?

i don’t want to mess up this thread, so email fly-in-home@att.net or call (316) 295-7812 with comments, questions or concerns. I’d even do it jointly with Marc as I think that he has done great work with his Cozt Mark IV, and we could both learn from each other ... I really think that we are saying the same thing. It’s just hard to put complex thoughts (and all the background/history/assumptions into short text.

[PNelson]

This discussion has been very interesting. I have done flight testing on my Kitfox during its Phase 1 flight testing. Part of the Phase 1 testing is doing the timed climb testing to determine Vx and Vy. I did this several times at different weights and flap settings. After collecting the data you create a TAS vs. ROC graph like the one that Dana posted. Vy was very easy to determine, it is the point at the greatest ROC. Vy is determined by drawing a tangent line from the 0, 0 point to where it touches the ROC curve (just like the graph).

What these numbers mean in flying, regardless of aircraft type, is:

Vy gives us the greatest rate of climb, period.


We use it if we want to get to altitude ASAP
ROC changes with weight. Lower weight = higher ROC
Vy changes with altitude (it decreases as altitude increases)
Wind doesn’t affect Vy, but . . . we may chose a different speed due to:

Wanting better visibility over the nose
Desire to reduce engine temperatures (CHT, oil temp, etc.)
Terrain, turbulence, etc.


Most POHs only give us takeoff & climb charts only at gross weight, the worst case scenario.


Vx is the best angle of climb and is always a steeper angle than Vy.


Vx has to do with climbing to get over an object (tree, mountain, antenna, etc.)
Vx is always given in a POH with zero wind, but Vx is actually wind dependent. We rarely fly that way.

The wind component can be drawn on the ROC graph. If you have a 20 knot headwind than you would draw the tangent line from the 20 KTAS point, which would intersect the ROC curve at a lower speed. Even if you don’t fly the lower speed you will have a better angle of climb due to the headwind component.
An extreme example would be a 50 knot head wind with a plane that has a Vso of 40 KIAS. If you climb at 50 KIAS it will be a vertical climb (10 knots above stall). If you increase your IAS above 50 you will be moving forward and have an angle less than vertical.
With a tailwind Vx increases. Again, if you had a 20 knot tail wind, you would draw a tangent line from the -20 KTAS point of the graph. It will intersect the ROC curve at a higher speed. With an increasing tailwind Vx increases, and approaches Vy.


Vx increases with altitude (Vx & Vy eventually will be the same speed when you can’t climb anymore)
Vx decreases with weight.

Theoretically speaking if you reduce the weight of a plane enough it will climb vertically (like an F-15).
Remember, as we decrease aircraft weight, Vso also decreases. Therefore, a different ROC curve has been established

Vso is lower
Peak ROC is higher
This changes where the tangent line intersects the curve (at a lower KIAS)


These are actual numbers from a Cessna TU206G POH

Best angle of climb / Vx – 55 KIAS
Weight vs. Lift off speed (from the Takeoff Distance tables)

3600 lbs. – 55 KIAS (notice this speed = Vx @ GW)
3300 lbs. – 53 KIAS
3000 lbs. – 50 KIAS





Lastly, the distance a POH gives for clearing a 50’ obstacle has several factors that make up the total distance.


The ground roll to liftoff (sometimes a liftoff speed is given, see to TU206G example above)
Continued acceleration to Vx (or another speed published)
Pitching from liftoff to an appropriate climb angle or pitch
Going from zero ROC at liftoff to the Vx ROC

Due to these factors the published 50’ obstacle distance isn’t just calculated as (takeoff roll) + (horizontal distance in a Vx climb to 50’). It includes the transition from one to the other. I believe this number is determined by actual flight testing data.

[Marc Zeitlin]

The making of AFM/POHs would be a great topic.It would be. The main thing here, though, is understanding aerodynamic and aircraft performance basics, which in my experience as a pilot and engineer (and A&P) seem to be sorely lacking in a large minority of the pilot population.


I’d even do it jointly with Marc ..."Even", huh? :-). Let me know how I can help. I'd be happy to review documents, and as far as a presentation at OSH is concerned, I do the COZY forum each year on Friday, and generally get there on Wednesday, so it could be possible to squeeze something in.


as I think that he has done great work with his Cozy Mark IV...I followed in the footsteps of many others. Then, after working at Scaled for 6 - 7 years, I learned a lot more. The best Phase I test program document that I've seen (and I know that EAA is working on something, but I haven't seen a finished product yet) is Kevin Walsh's test plan for his COZY MKIV, available at:

http://cozybuilders.org/docs/

third bullet point down. It could obviously be modified for any aircraft.

The results from the Phase I test program should be used to populate the fields in a generic POH for EAB aircraft.


and we could both learn from each other ... I really think that we are saying the same thing. It’s just hard to put complex thoughts (and all the background/history/assumptions into short text.I thank you for your civility. I should have been less strident in my postings, and for that I apologize.

[Ron Blum]

I’m excited about this now ��. I’ll checkout the links you sent, look at the deltas between the homebuilt and certificated worlds and see what EAA is doing.

I love when people tell me that they have 5 hours on their new airplanes and their box isn’t big enough to cruise around for the remainder of the test time.

This is going to be fun. Thanks!

[Marc Zeitlin]

I love when people tell me that they have 5 hours on their new airplanes and their box isn’t big enough to cruise around for the remainder of the test time.Don't get me started. I can't tell you how many times I've heard folks say "it's a Long-EZ - Burt tested it in 1980" or "what do you mean, did I test it at the rear CG limit?". Sigh. If it doesn't take you 30 - 40 hours to finish all the tests that should be statutorily required (IMO) then you haven't completed Phase I. Flying around in circles for 30 hours at mid-weight and mid-CG (and not having any idea what Vx and Vy, for example, and to keep us vaguely in the same state as the OP's mission statement) is not Phase I testing.

And you kids get off of my lawn!

[Ron Blum]

And you kids get off of my lawn!

Amen!!! LOL LOL LOL

[Frank Giger]

As the dumbest guy in the thread, can I see if I've sorted this out, as I'm knee deep in Phase I testing?

Okay, so Vx - getting to altitude quickly to go over an obstacle - one is going to be more nose high, a tad slower, but with a higher climb rate. It's effectiveness over efficiency.
Vy is getting to a higher altitude efficiently, so one is going to gain the most altitude over time. It's not as effective, though, in the short term, as Vx.

Now, then, these are the "book" numbers.

How we use those numbers in the real world are dependent on, well, the real world. Once an aircraft leaves the earth it is in the air and of the air, moving with it as much as through it.

So if it takes me 200 feet at 60 miles an hour* to clear a 50 foot tall tree and I'm looking at a 10 mile an hour headwind, it really only takes me 165 feet in ground distance. The plane doesn't know any better, and thinks it's traveled the whole 200 feet.

The opposite is true with a 10 mile per hour tailwind, as it would take me 235 feet on the ground to clear the same tree. Again, the airplane is ignorant of this, as it's only flown for the 200 feet. The air itself did the rest of the work.

* As stated previously, this is a lie. The takeoff roll has to be taken into account. Determining this requires a patient and diligent helper (at least for me), or video taken from the ground, and one has to use an average. Bonus plan: air density matters.

Between late October through April, my little airport in Alabama has an altitude of around 530 feet above sea level. Between mid-April to mid-October the density altitude can be as much as 3,400. What that means to me, a stick-and-rudder guy wearing goggles and a leather flying helmet, is that there's a lot of fudging on climb rates and distances in the summertime, as I don't have a graph with me. But knowing that graph as it relates to altitude is pretty dang important if I want to visit some of the short fields around here.

So tell me if I got it right!

[Dana]

Okay, so Vx - getting to altitude quickly to go over an obstacle - one is going to be more nose high, a tad slower, but with a higher climb rate. It's effectiveness over efficiency.
Vy is getting to a higher altitude efficiently, so one is going to gain the most altitude over time. It's not as effective, though, in the short term, as Vx.

No, Vx has a higher climb angle, in degrees, but a lower climb rate, in feet per minute. Otherwise correct.

[Ron Blum]

Frank: You’re not dumb, and you got it correct! (except as Dana pointed out in the second paragraph “climb rate” should be “climb angle”). Great job!

Now you brought up that summer and winter performance is different. Yes! ��. Since climb rates (and angles) are based on excess power - power above and beyond what it takes to fly at that airspeed), rates (and angles) will decrease as engine horsepower decreases (due to altitude, temperature, humidity, etc. effects). OEMs have engine decks (programs that tell them power available under various conditions) and propeller maps to calculate power/thrust available. Not so simple ��. You’ll have to test under various conditions.

Here’s a simple, totally made up example. If a 160 HP airplane takes 100 HP to fly 70 MPH, it has 60 excess HP to climb. We’ll say it climbs at 600 FPM. Now, if the engine is only putting out 150 HP, the airplane only has 50 excess HP to climb. Climb rate will decrease to 500 FPM (down 17%). At 100 HP the airplane will not climb (absolute ceiling).

Be safe.

[Waldo Pepper]

Hi Frank,


You've made a number of interesting observations which are usually not examined in much detail.
One is that an aircraft once free of the ground becomes a part of the air mass, it no longer experiences any effect of "wind", as wind is something experienced by an observer on the ground witnessing the movement of the air mass and interpreting that as "wind".
The airplane is almost like a balloon released into the air. Almost in that the balloon has essentially no mass so with little inertia it moves almost instantly with any change in the air mass from any horizontal shear or up/down drafts, i.e. localized changes within the air mass.
The aircraft on the other hand has a significant amount of mass and thus inertia so it resists any fast change in it's flight path from horizontal shear or up/down drafts.
An illustration of this is a 747 going through localized changes within an air mass might report "light chop", while a J-3 going through that same area might report "Severe Turbulence".
The less mass an object has which is experiencing localized air mass changes, the greater the g loading on the object due to those changes.


And taking off with a tail wind can be ah "interesting". You're of course right that once the aircraft leaves the ground at it's normal lift off airspeed it flies no differently than when it lifts off at that same airspeed into a head wind.
But in order to attain that normal lift off airspeed it has to be rollin along the runway at that noraml airspeed plus the tail wind speed.
If the tail wind is just 1 or 2 knots it's not much of a problem but say 10 or 20 knots means the airplane will be on the ground roll 10-20 knots faster than normal and can get quite squirrley (difficult to control) while in contact with the ground.
The other factor with tail wind take offs (and landings) is that as the wind increases in velocity a given percentage change in the tail wind velocity component effects the aircraft exponentially.
e.g. a 20% change in the tail wind component (twc) with a 5 knot tail wind will show up for a few seconds as a 1 knot gain (if a twc decrese) or loss (if a twc increase) in airspeed until the aircraft overcomes it's inertia stabilizing at the airspeed prior to the twc chnge.
OTOH, if it's a 20 kt tail wind component there would be a 4 Kt change and the aircraft's ability to overcome a 4 Kt change would take significantly longer than the few seconds of the 1 Kt change, which could result in premature unintentional ground contact (crash or incident).


...and yes, the Vx speed(s) determined for various gross weights, CG locations, and density altitudes you determine will provide the steepest angle of climb through the air mass at those conditions in any wind conduition.
it will also be the steepest angle relative to a ground observer or a 50' obstacle;
however, if you're climbing at Vx with a 20 knot twc your climb angle relative to a ground observer and a 50' obstacle will be much less steep than under no wind conditions even though the air mass relative angle hasn't changed at all,
this because your performance perspective has changed to ground relative and not the normal in flight air mass relative.


A suggestion for recording ground relative measurements of speed and distance is to use a GPS receiver that optimally records it's measurements at a 10Hz rate.




Everyone,


Since I started this string from an admittedly poor (wrong) thesis, let me add to the endeavor to develop POH standards.


I'm afraid most comments on this thread were addressing the thread title and not it's intended subject - which is my fault, I expected the double question marks to convey too much meaning.


I should have entitled the message "Defecient POHs due to lack of specifications, particularly techniques used to obtain data."
The subject POHs are the Commercial GAMA Speciifcation No.1 required POHs, which are not exactly of much interest per se to the EAA community, but anyway something may be learned from others errors.


If I recall I attached a spread sheet (ss) in my original post which (if anyone is actually interested can be analyzed and in so doing demonstrate specifically what I'm talking about).
I'm attaching an expanded ss which may be easier to understand and a '78 C172 POH used in the ss and representative of all POHs due to GAMA specfication No. 1., and the GAMA Spec.


To simplify, or at least vebalize what's contained in the SS:


If you take the "Total distance to clear a 50" obstacle" minus the "Ground Roll Distance" (specified as such in all POHs) you would expect to have the distance from "Lift Off" to the obstacle. -
Right?


Then if you take the specified Vx KIASs converted to KCASs either specifically or averaged, convert to fpm then divide that into 50' (x 60) you have the number of seconds from lift off to 50' -
Right?


Now with number of seconds to climb to 50' you have the average climb rate from "Lift Off" to 50' -
Right?


Now take the arcsine of that climb rate (in fpm) and divide it by the previously determined fpmCAS and you have the average climb angle from "Lift Off" to 50' -
Right?


Doing the same process for Vy speeds you find the Vy angle is always greater than the Vx angle - Right? - Wrong!


So whats wrong?


1) the above logic?
2) Trigonometry?
3) the numbers specified in the POH?
4) or something NOT specified in the POH?


The attached spread sheet votes for 4) and possibly 3).


What is apparently being left out of ALL commercial POHs is the technique that was used to obtain the POH 50' obstacle clearance numbers.


The bottom line for Commercial GAMA specificatio No. 1 POHs is "trust" - BUT VERIFY.
IOW: You should flight test for about 5-50 hours depending on the A/C before using the POH specifications for any critical flight operation.


...dropping the mike

[Ron Blum]

So whats wrong?
1) the above logic?
2) Trigonometry?
3) the numbers specified in the POH?
4) or something NOT specified in the POH?

"4)" is not correct. Everything that an operator needs is in the AFM/POH. Angle of climb relative to the air mass that the airplane is flying through is useless information.

"3)" is not correct. It is highly unlikely that the entire industry has been in error since the beginning.

"2)" Trigonometry is correct and unchanging for anyone, as is physics. OTOH our use of it may be incorrect.

Which leaves only "1)" and our use of "2)".



If you take the "Total distance to clear a 50" obstacle" minus the "Ground Roll Distance" (specified as such in all POHs) you would expect to have the distance from "Lift Off" to the obstacle. -
Right?

Kind of ... The total distance is comprised of 3 segments - time/distance to: acclerate to Vr, rotate and transition to Vx, and climb to 50'.




Then if you take the specified Vx KIASs converted to KCASs either specifically or averaged, convert to fpm then divide that into 50' (x 60) you have the number of seconds from lift off to 50' -
Right?

Now with number of seconds to climb to 50' you have the average climb rate from "Lift Off" to 50' -
Right?

Now take the arcsine of that climb rate (in fpm) and divide it by the previously determined fpmCAS and you have the average climb angle from "Lift Off" to 50' -
Right?

Doing the same process for Vy speeds you find the Vy angle is always greater than the Vx angle - Right?

And here is the improper use of trigonometry "2)" and a simple logic error "1)".

The angle of climb relative to the air (still a useless ... but fun number) is the inverse sine of the rate of climb divided by the calibrated airspeed (both in the same units). This is in error in the spreadsheets.



What is apparently being left out of ALL commercial POHs is the technique that was used to obtain the POH 50' obstacle clearance numbers.

AFM/POHs don't leave anything out. The more recent versions will state exactly how one has to fly the airplane to achieve book values. Along those lines (and this will raise eyebrows), everyone should be able to meet or exceed peformance numbers that are in the AFM sections (FAA approved data) of their AFM/POHs. We intentionally add time/distance to be conservative. In addition, our obsticals are at the exact beginning/end of the runway. IOW the landing distance starts at the top of the obstical over the runway surface.

An AFM/POH forum at Oshkosh looks like more and more fun every moment http://eaaforums.org/images/icons/smiley.gif

[martymayes]

What is apparently being left out of ALL commercial POHs is the technique that was used to obtain the POH 50' obstacle clearance numbers.

The non-GAMA format handbook for the 1970 Cardinal I fly specifies exactly how to obtain those book numbers. Once I obtain those numbers I'm going to do what we do in airline world and add 40-50% safety margin. That's for my less than perfect technique and mediocre piloting skills. I don't need to get anywhere bad enough to push the limit values. Then I'll feel safe, and clear whatever I need to clear by a comfortable margin.

[Marc Zeitlin]

The angle of climb relative to the air (still a useless ... but fun number) is the inverse sine of the rate of climb divided by the calibrated airspeed (both in the same units).Minor nit - it would be the arctan (inverse tangent), not the inverse sine, since the airspeed is measured along the hypotenuse of the triangle, not the leg parallel to the ground. But at the small angles at which our aircraft can climb, the difference between the two is negligible. Get a very high powered aircraft with large climb angle capability, however, and the difference is NOT negligible.

[Ron Blum]

Marty: LOL. Good way to stay safe.


Minor nit - it would be the arctan (inverse tangent), not the inverse sine
Marc: You've been out of school too long. The sine of an angle is the side opposite divided by the hypotenuse. I'm going to guess that you are teaching the great Waldo Pepper new math (trigonometry). Facts not flames.

[Marc Zeitlin]

Marc: You've been out of school too long.Oh for crap's sake. Of course you're right. 38 years is too long, I guess...

[Ron Blum]

It would be nice to just be able to thumbs up a post. There is probably a way, but I’m too old to figure it out.

My bottom line is to assure that Waldo Pepper has all the correct information that he was/is looking for.

[martymayes]

It would be nice to just be able to thumbs up a post.

I agree! I look for that all the time!

[Ron Blum]

LOL. You’re my hero. Thanks.:thumbsup:

[jedi]

.........

2) Why is there no specification of ground roll distance for a lift off at Vy in any of the POHs I looked at and not required in the GAMA specification? It seems that this distance would be closest to the distance of a normal TO roll, and therefore an important number to include.

Because no one expects you to accelerate to Vy before lift off. Rotation is prior to reaching Vy to an attitude that allows the aircraft to continue to accelerate to Vy and continue the climbout. A "normal" takeoff has a lift off speed that is less than Vx in many cases.

[Frank Giger]

I'm actually approaching this matter the same way I did CG - a max/min chart that has green for good. Bear in mind I have a single seat aircraft with no baggage. It's just the pilot and the fuel in a central tank.

I've just about worked out that I need about 450 feet from the halt to clear a 50 foot object, given my 500 foot altitude on a normal (50-70 degree) day. So let's fudge that up to 700 feet and then just say 1,000 to be safe.

[WLIU]

If you need an excuse to do some flying, you can do some simple testing. First make some simple markers by taking some brightly colored crepe paper, creating a pocket containing a few ounces of sand with tape, and leaving a couple of feet of tail. Balloonists use these to mark where they have been.

At an airport with not much traffic and clear space on the end(s) of the runway, pick a day with as little wind down the runway as you can get. Crosswind is OK.

Set your altimeter to zero at the end of the runway. Takeoff, lifting off as soon as airspeed allows, accelerate to Vy, climb, and at 50' on the altimeter, throw one of your markers out. Do this two or three times.

Using a hiking GPS, mark a waypoint at the end of the runway where you started your takeoff roll, go out to where the markers landed. That's your distance to takeoff and climb to 50'. If you look at a Cessna/Piper/Mooney manual, in the performance charts you can see the percentage that they correct for headwinds and tailwinds. Since the laws of physics are pretty constant, you can use those same percentages to calculate corrections from your data for the same headwinds and tailwinds.

So you will then have hard info vs a guess. And you can fly with more confidence that you know your airplane's performance.

Best of luck,

Wes