vx & vy converge at altitude

On Monday I am participating in a density altitude seminar, and I have
been tasked with explaining why vx and vy converge at altitude.
The explanation needs to be simple - i.e. no algebra calculations etc -
just stripped to the bare bones.

Here is what I have come up with.

VX utilises excess thrust.
VY utilises excess thrust hp.

As density altitude increases, VX angle of attack becomes lower,
VY angle of attack increases.
Somewhere between service ceiling and absolute ceiling they converge.

Can anyone explain it simpler (and/or more accurately in as few words)
than that?

Thanks

Tony
--

Tony Roberts
PP-ASEL
VFR OTT
Night
Cessna 172H C-GICE

"tony roberts" wrote in message
news:nospam-51A543.18490626022005@shawnews...

On Monday I am participating in a density altitude seminar, and I have
been tasked with explaining why vx and vy converge at altitude.
The explanation needs to be simple - i.e. no algebra calculations etc -
just stripped to the bare bones.

At the absolute ceiling of the aircraft, there's only one speed, the
minimum-power-required speed, at which the aircraft can avoid descending.
Thus just below the absolute ceiling, both Vx and Vy must be very close to
that speed. So Vx and Vy converge on that speed at the absolute ceiling.

Put another way, at lower levels, Vx is considerably less than Vy because
the excess power can be used in a way that trades slightly more power
required (and therefore slightly less climb rate) for less forward speed.
As excess power decreases, as it will at altitude, the ability to make that
trade-off reduces.

Julian Scarfe

"tony roberts" wrote in message
news:nospam-51A543.18490626022005@shawnews...

On Monday I am participating in a density altitude seminar, and I have
been tasked with explaining why vx and vy converge at altitude.
The explanation needs to be simple - i.e. no algebra calculations
etc -
just stripped to the bare bones.

Here is what I have come up with.

VX utilises excess thrust.
VY utilises excess thrust hp.

As density altitude increases, VX angle of attack becomes lower,
VY angle of attack increases.
Somewhere between service ceiling and absolute ceiling they converge.

Can anyone explain it simpler (and/or more accurately in as few
words)
than that?

Thanks

Tony
--

Tony Roberts
PP-ASEL
VFR OTT
Night
Cessna 172H C-GICE

Nope. Vx and Vy are equal (only) AT the absolute ceiling. So the
"topological" answer to your problem -- available even to the
algebraically untarnished -- is that since Vx Vy at MSL, and Vx = Vy
at absolute ceiling, and they are both increasing functions of density
altitude, they must converge (be getting closer together) at increasing
density altitude.. Your discussion won't even need to invoke arithmetic!

For details (for those who went to high school and actually learned
something)) see the Maneuvering chapter of Performance of Light
Aircraft, AIAA, 1999.

John Lowry
Flight Physics