# Vy equals 1.32*Vx

Thread Starter

Join Date: Jan 2018

Location: Sweden

Posts: 3

**Vy equals 1.32*Vx**

Lets first agree on the following terminology:

Vy = speed for max rate of climb = speed for max range

Vx = speed for max angle of climb = max lift over drag = min drag

Furthermore it's possible for a jet engine, after a few assumptions and approximations, to mathematically conclude from the drag formulas that Vy=1.32*Vx.

All this seems to be generally accepted and I also find it relatively true when looking at speeds for the B737 and the A320 at lower altitudes. I have not been able to find the relevant data for high altitude.

The question is what happens at high altitude and why? The Oxford ATPL text claims Vy will decrease and eventually equal Vx. Is that true or is the factor 1.32 relevant for all altitudes?

Vy = speed for max rate of climb = speed for max range

Vx = speed for max angle of climb = max lift over drag = min drag

Furthermore it's possible for a jet engine, after a few assumptions and approximations, to mathematically conclude from the drag formulas that Vy=1.32*Vx.

All this seems to be generally accepted and I also find it relatively true when looking at speeds for the B737 and the A320 at lower altitudes. I have not been able to find the relevant data for high altitude.

The question is what happens at high altitude and why? The Oxford ATPL text claims Vy will decrease and eventually equal Vx. Is that true or is the factor 1.32 relevant for all altitudes?

Join Date: Sep 2016

Location: USA

Posts: 440

The higher you climb, performance decreases until it necessarily reaches a point when you you cannot climb any more, i.e., rate and angle are both zero and the best you can do is level flight.

If you get even a knot off Vy, rate becomes negative.

If you get even a knot off Vx, angle becomes negative.

You see why, in this situation, Vx has to equal Vy?

If you get even a knot off Vy, rate becomes negative.

If you get even a knot off Vx, angle becomes negative.

You see why, in this situation, Vx has to equal Vy?

Join Date: May 2005

Location: France / UK

Age: 64

Posts: 925

Given enough thrust, a jet-powered aircraft could reach ‘coffin corner’, an altitude where controlled level flight is only possible at one speed. This altitude is the ‘absolute ceiling’.

At an altitude just below the absolute ceiling, flight at different speeds is possible but the available range of speeds will be small. A typical definition is that the ‘service ceiling’ is that where a rate of climb of 100fpm is still possible. It follows, therefore, that Vy and Vx will converge as altitude increases, eventually meeting at the absolute ceiling.

Sorry Vessbot, I think I crossed with your post.

At an altitude just below the absolute ceiling, flight at different speeds is possible but the available range of speeds will be small. A typical definition is that the ‘service ceiling’ is that where a rate of climb of 100fpm is still possible. It follows, therefore, that Vy and Vx will converge as altitude increases, eventually meeting at the absolute ceiling.

Sorry Vessbot, I think I crossed with your post.

Thread Starter

Join Date: Jan 2018

Location: Sweden

Posts: 3

Ok, this all sounds great but what about the claim that Vy = 1.32 * Vx when eventually Vy = 1.00 * Vx? I just assume the factor is not decreasing linearly with altitude to absolute ceiling or is it? What's the physics behind this?

Join Date: Sep 2016

Location: USA

Posts: 440

eckhard

What you say is true, but I think it's belaboring the point. If the OP is asking about Vx/Vy type stuff, then I think they're still trying to figure out how the performance-limited ceiling works; and talking about hitting a Mach ceiling instead, only introduces more confusion at this point. It's a more basic question.

In figuring out why Vx and Vy converge, I'd advise ignoring Mach and imagining a lower performance airplane that will climb until excess thrust and power reach zero.

What you say is true, but I think it's belaboring the point. If the OP is asking about Vx/Vy type stuff, then I think they're still trying to figure out how the performance-limited ceiling works; and talking about hitting a Mach ceiling instead, only introduces more confusion at this point. It's a more basic question.

In figuring out why Vx and Vy converge, I'd advise ignoring Mach and imagining a lower performance airplane that will climb until excess thrust and power reach zero.

Join Date: Sep 2016

Location: USA

Posts: 440

Yes you did, apparently without realizing it. "Coffin corner" means the speed-altitude point where the increasing stall speed converges with the decreasing Mach limit. There, you can only fly at one speed without exceeding one or the other of those limits. But it has nothing to do with running out of excess thrust or power, i.e. the performance ceiling.

Join Date: Sep 2016

Location: USA

Posts: 440

I missed this post earlier. Yes, 1.32 is only true at sea level, and only true as an approximation. There is no exact mathematical law by which it reduces to 1.00

Join Date: Sep 2016

Location: USA

Posts: 440

Yes. Interesting point about the U-2, which lived in coffin corner: separately from the wing aerodynamics, at its altitudes, idle power on the engine climbed so high that it met with the turbine temp limit of max power, so there was only one power setting. (One might call it a separate "coffin corner" of the engine.) Anyway, because of that, it could not reduce power and the only way to descend was to add drag!

Join Date: Nov 2015

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Vx = speed for max angle of climb = max lift over drag

**= min drag**Join Date: Jul 2013

Location: Everett, WA

Age: 64

Posts: 2,394

For a jet this may be close to (but still slightly less than) the minimum drag speed because jets have almost constant thrust at all airspeeds.

Join Date: Jun 2014

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I’m no engineer, but I think the original equation is not valid at all.

As others said, Vx is the speed of max excess thrust and Vy is the speed of max excess power. They do not depend only on aerodynamics, but also on engine/prop characteristics.

The famous 1.32 factor is the relation between “min drag” speed and “best range” speed for a jet

As others said, Vx is the speed of max excess thrust and Vy is the speed of max excess power. They do not depend only on aerodynamics, but also on engine/prop characteristics.

The famous 1.32 factor is the relation between “min drag” speed and “best range” speed for a jet

Join Date: Nov 2001

Location: Delta of Venus

Posts: 395

Yes, the 1.32 factor is the mathematical ratio between Vmd and LRC expressed as IAS values. (Because drag is proportional to IAS) It is also therefore valid at any altitude. In real life there is a few knots variation but thats up to an aeronautical engineer or test pilot to explain why! Vx & Vy maybe coincidentally similar but are different things.

Join Date: May 2014

Location: In thin air

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The factor 1.32 applies if the thrust is constant and the drag polar is 'parabolic'. A parabolic drag polar can be written as:

CD = a + b*CL^2

where a and b are constants, CD=drag coefficient and CL=lift coefficient

Constant a defines the parasitic drag which is proportional to airspeed squared.

Constant b defines the lift-dependent (or 'induced') drag which is inversely proportional to airspeed squared.

Most airplanes exhibit a nearly parabolic drag polar at low speed and low altitudes where Mach effects are insignificant. At high subsonic Mach numbers the parasitic drag

CD = a + b*CL^2

where a and b are constants, CD=drag coefficient and CL=lift coefficient

Constant a defines the parasitic drag which is proportional to airspeed squared.

Constant b defines the lift-dependent (or 'induced') drag which is inversely proportional to airspeed squared.

Most airplanes exhibit a nearly parabolic drag polar at low speed and low altitudes where Mach effects are insignificant. At high subsonic Mach numbers the parasitic drag

*coefficient*is no longer constant but increases rapidly with increasing Mach number, so the drag polar is no longer 'parabolic' and the 1.32 factor no longer applies.*Last edited by Gysbreght; 25th Jan 2018 at 08:38. Reason: "coefficient" added in last sentence (in italics)*