Vy flight path angle greater than Vx ???

[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/deta...il=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.