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Why Vy Varies with Altitude
Category Miscellaneous
Posted by Taylor Grayson Submitted on 01/01/2008 12:00 AM
The greatest rate of climb in an airplane occurs at a velocity where the greatest excess power occurs, as shown by the orange points in the graph below.

Figure 1
At higher altitudes, the less dense air causes the Power Required curve to rise and rotate to the right, as shown below in figure 2. This occurs because
  1. Induced drag increases at every airspeed because the less dense air requires a greater angle of attack to ensure that lift = weight;
  2. Parasite drag decreases at every airspeed because less dense air provides a smaller frictional force at every airspeed.
Since induced drag predominates at low airspeeds, total drag within this speed range increases. At faster airspeeds, where parasite drag predominates, the total drag is reduced.

Figure 2
This shift in the Power Required curve causes the point of minimum drag to increase and shift right, meaning that it will occur at a higher true airspeed.

Increased altitude also changes the Power Available curve, but at least this change is straight-forward. At any given airspeed, there will simply be less power available because of the less dense air, as shown in figure 3. The point of maximum power available will still occur at the same airspeed because the shape of the curve does not change, only its height.

Figure 3
We can now put figures 2 and 3 together to see what happens the Vy, which will be the airspeed where there is the greatest difference between Power Available and Power Required. This chart is shown below in figure 4.

Figure 4
What this chart shows is the Vy shifts to the right, due to the tilting of the Power Required curve. This conclusion contradicts what we know from real airplanes, where Vy decreases with altitude.

How can we explain this result?

Important Point:
These charts are plotted using true airspeed, but Vy is normally provided as an indicated airspeed.

So these charts so far aren't very useful in explaining why Vy in indicated airspeed will decrease with altitude. We can, however, make these charts more useful by plotting the same data in indicated airspeeds, rather than true airspeeds, and this is shown below in figure 5.

The main differences between this chart and the one in figure 4 are

  1. The power required curves merely moves up when plotted in indicated airspeeds, it doesn't tilt right
  2. The power available curve now shifts left as well as down, instead of just moving down like it did when plotted in true airspeeds.

Figure 5
These differences cause the point of maximum excess power to move left, as we would expect.

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