So, why do Vx and Vy change with altitude?

The answer's really simple, and it has to do with how induced drag and parasite drag change as you climb.

As You Climb, The Air Gets Rare

First - let's quickly hit what happens to the air density as you climb...

It decreases. (I know, you knew that. But I had to say it.)

So, how does that affect drag? Let's start with parasite drag.

Parasite Drag Decreases As You Climb

Since the air is less dense, there are fewer air molecules to cause friction. So, the parasite drag for any true airspeed decreases as you climb.

Net benefit: you have less parasite drag the higher you go.

Induced Drag Increases As You Climb

For every benefit, there's a cost. When air density decreases, there are fewer air molecules flowing over your wing at a given true airspeed. So, fewer molecules means less of a pressure differential and less induced lift for a given angle of attack. But your weight's the same. So how do you make up for the loss of lift?

You increase your angle of attack. At higher altitudes, because of the less dense air, you need to fly at a higher angle of attack for a given true airspeed.

And, if you're flying at a higher angle of attack, you're generating more induced drag.

So, as you climb, your angle of attack for level flight increases and you generate more induced drag.

Awesome. What Does This Have To Do With Vx?

Remember that bowl shaped drag curve, also known as the "thrust-required curve?" That was drawn at sea-level.

As you climb, the shape of that curve changes and it moves up. At the same time, your engine and propellor are less efficient, so the thrust available line shifts down. Take a look.

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Vx is located where you have the most space between the thrust required and thrust available lines. So, if you plot it for several altitudes, you can see it move to the right slightly as you climb. Vx's true airspeed increases as you climb.

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But, that's true airspeed, not indicated. Remember, there are fewer air molecules hitting the pitot tube at higher altitudes. So, for a given true airspeed, indicated airspeed gets slower as you climb.

What's that mean here? It means that Vx's indicated airspeed increases slowly, or stays almost the same, as you climb.

How About Vy? It Increases AND Decreases

Since the thrust required curve changes shape as you climb, you'd probably guess that the power required curve does, too. And you're right. (Remember that the power required curve is just the thrust required curve times the airspeed.)

As you climb, the power required curve shifts up, moves to the right, and tilts. The power available curve drops straight down. Check it out:

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And, if you plot Vy as you climb, you'll see that it moves slightly to the right. It gets a little bit faster as you climb.

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But, remember that this is true airspeed. As you climb, your indicated airspeed falls further behind your true.

So, as you climb, Vy's indicated airspeed decreases slightly.

The Absolute Ceiling: Where Vx and Vy Meet

Your "absolute ceiling" is the highest altitude you could possibly fly. At this altitude, the power available curve crosses through the lowest point of the power required curve. Now you can't climb anymore because you're out of excess power.

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At the absolute ceiling, your Vx and Vy are the same speed. And by the way, if you try reach your absolute ceiling, it will take you quite a while to get there.