Vy angle greater than Vx angle??

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Vy angle greater than Vx angle??

Posted by John Whitson on Feb 20, 2018 2:58 pm

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.
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Re: Vy angle greater than Vx angle??

Posted by Allen Kittleson on Mar 12, 2018 8:51 am

 John your entire conversation is based upon a bunch of text matter. It may be correct. 

 Until I see it it proven by a flight test I won't believe it.

 So, John, has any of the stuff been flight tested? 


Re: Vy angle greater than Vx angle??

Posted by John Whitson on Mar 12, 2018 5:52 pm


I'm afraid no one can get past the subject title and address the 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."

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 '79 C172 POH used in the ss and representative of all POHs due to GAMA specfication No. 1.

To simplify:
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' -

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

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' -

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).

The bottom line for POHs is "trust" - BUT VERIFY.
IOW: about 5-50 hours of flight test depending on the A/C before using the POH specifications for any critical flight operation.

...dropping the mike
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Re: Vy angle greater than Vx angle??

Posted by Scott Opheim on Mar 12, 2018 9:11 pm

I think you are getting hung up on the terminology of "best angle of climb speed". 
The best angle depends on what your goal is. To climb to a given altitude in the shortest forward distance = Vx. To climb to that same altitude in the least amount of time = Vy.
Speed Vx < Speed Vy, Climb angle Vx > Climb angle Vy, and Angle of attack Vx > Angle of attack Vy.
Think of it this way...if you climb a vertical 500' cliff, you've traveled no distance forward but it would take a long time. If there was a slope up to the same peak that was at a much flatter angle, you could run up there before the climber but would cover much more horizontal distance.
You don't need fancy formulas to figure this out...
If after this comment you still believe that flying at a faster forward speed and flatter climb angle (Vy) will get you over a close-in obstacle quicker than a higher climb angle at a slower forward speed (Vx), remind me never to fly with you around any sort of terrain.