Best Angle Vs. Best Rate Paradox?

[hevansrv7a]

At reasonable altitudes, Best Angle and Best Rate of Climb speeds are different, with best rate being higher by about 30%. However, at absolute ceiling or just before it, the speeds converge (again, per others). One article (for Bonanza's) showed this change as a straight line graph. Since these speeds match up to two different angles of attack that are not supposed to change with density altitude or with weight, how can this be?

[jcoloccia]

Actually, Vy and Vx both go up as you increase altitude, but they go up at different rates. Much of it has to do with your engine and what it can put out with altitude.

Where the Vy and Vx airspeed curves cross is also the point that the plane's maximum ROC drops to 0 (i.e. you've hit your ceiling).

[4kilo]

Both best climb and best angle are dependant on available power plant output. Because available power changes with altitude, the angles of attack for best climb and best angle DO change with altitude.

Pat

[hevansrv7a]

Originally Posted by 4kilo

Both best climb and best angle are dependant on available power plant output. Because available power changes with altitude, the angles of attack for best climb and best angle DO change with altitude.

Originally Posted by jcoloccia

Actually, Vy and Vx both go up as you increase altitude, but they go up at different rates. Much of it has to do with your engine and what it can put out with altitude.

Where the Vy and Vx airspeed curves cross is also the point that the plane's maximum ROC drops to 0 (i.e. you've hit your ceiling)

According to: http://web.usna.navy.mil/~dfr/flying/weight1.pdf The speed for best angle Vx goes from 91 to 97.5 while the speed for best rate Vy goes down from 112.5 to 97.5 in the example of a Bonanza. They converge at zero climb at about 20,000 feet. And he shows them as straight lines, not curves. That contradicts John's statement.

My understanding of Best Angle of Climb Vx is that it is found roughly at the point on the drag or HP polar where maximum endurance is found and that it is variable with weight and air density but pretty much a constant with respect to angle of attack. Also, my reading seems to tell me that Vy is found approximately at best L/D which is also found at a constant AOA.
http://selair.selkirk.bc.ca/aerodyna...ce/Page10.html
Power declines with altitude - we all agree. That in turn means that as we go up, rate of climb goes down. But I don't agree that AOA for minimum HP required changes.

I thank you both for trying to help, but I don't think the paradox is resolved, yet. I still don't understand how we get to a single AOA when the AOA of each is supposed to remain steady while speed changes.

[RVbySDI]

Originally Posted by hevansrv7a

I thank you both for trying to help, but I don't think the paradox is resolved, yet. I still don't understand how we get to a single AOA when the AOA of each is supposed to remain steady while speed changes.

I think part of the paradox is that although AOA and speed are measurements of lift that are somewhat correlationally related, they are really two different aspects of measuring the lift capacity of a wing. We tend to use the speed indicator as a measure of lift generation capacity of the wings on our aircraft but the real component of lift that is important is the AOA of the wing which is a measurement of the angle of the wing in relation to that of the relative wind. As much as we use the airspeed indicator to tell us where this angle is, the reality is that this measurement is independent of speed.

[jcoloccia]

Originally Posted by hevansrv7a

According to: http://web.usna.navy.mil/~dfr/flying/weight1.pdf The speed for best angle Vx goes from 91 to 97.5 while the speed for best rate Vy goes down from 112.5 to 97.5 in the example of a Bonanza. They converge at zero climb at about 20,000 feet. And he shows them as straight lines, not curves. That contradicts John's statement.

My understanding of Best Angle of Climb Vx is that it is found roughly at the point on the drag or HP polar where maximum endurance is found and that it is variable with weight and air density but pretty much a constant with respect to angle of attack. Also, my reading seems to tell me that Vy is found approximately at best L/D which is also found at a constant AOA.
http://selair.selkirk.bc.ca/aerodyna...ce/Page10.html
Power declines with altitude - we all agree. That in turn means that as we go up, rate of climb goes down. But I don't agree that AOA for minimum HP required changes.

I thank you both for trying to help, but I don't think the paradox is resolved, yet. I still don't understand how we get to a single AOA when the AOA of each is supposed to remain steady while speed changes.

Are you talking TAS or IAS? I'm talking TAS. I can be confused...it's possible.

re: AOA etc... Let's say you're at your maximum ceiling...20,000 ft say. By definition Vx=Vy. If this were not so you would either be loosing altitude or you wouldn't yet be at your absolute ceiling. You simply run out of power to have any climb at all, and your best ROC = best angle ROC = 0. It's not AOA that makes you climb in the long run...it's excess power. As the amount of excess power you have goes to 0, so does the difference between Vx and Vy.