FDC
Why Two Vertical Speeds?
on February 20, 2017

Following on from last week’s blog about rates of change, it occurred to me that I should have mentioned the second computed vertical speed and explained why we have two measurements for the same thing. After all, surely the vertical speed is exactly that. Why have “Vertical Speed” and also “Vertical Speed Inertial”?

Quick Look

Let’s start with a  quick look at the two vertical speeds during a descent. A perfectly standard descent profile for the last five minutes of an approach is shown below. (The grid spacing is 30seconds).

The Vertical Speed of the aircraft is plotted in blue as described in the previous blog, and the Vertical Speed Inertial shown in red. The blue calculation comes from a smoothed version of the pressure altitude, which is also used to compute the height above the airfield, Altitude AAL, and we carefully differentiate this to avoid introducing noise or phase offsets so that the blue line is effectively the slope of the grey altitude line.

The far noisier red line represents the actual vertical speed of the aircraft instantaneously, as accurately as we can compute it.

Events

Imagine we had a rate of descent threshold of -1100 fpm. The blue line never crosses this line, so the pilot would not have triggered an event on the smoothly flown approach. If we used the red line, he would have triggered this event six times. Of course, on a turbulent day it would be impossible for the pilot to avoid triggering such an event, which is why this signal is not used for normal rate of climb or rate of descent events.

There are some cases, however, where we do use the inertial signal and this is where ground effect comes into play. For events close to liftoff or touchdown, and where the ground effect makes pressure altitude signals inaccurate, we can use the inertial signal to determine the actual motion of the aircraft.

Height Loss Liftoff To 35 Ft; At these low altitudes, the aircraft is in ground effect, so we use Vertical Speed Inertial to identify small height losses. This means that the algorithm will still work with low sample rate (or even missing) radio altimeters.

The KPV Rate Of Descent 50 Ft To Touchdown Max (or for helicopters 20 Ft To Touchdown) measures the most negative vertical speed between 50 or 20ft Altitude Radio and touchdown. Again, ground effect makes the normal pressure altitude based vertical speed meaningless, so we use the more complex inertial computation to give accurate measurements within ground effect.

Rate Of Descent At Touchdown is also based on the Vertical Speed Inertial. As these are all related to the final moments of the approach, let’s zoom into the last seconds of the trace I drew earlier. This graph is just over 12 seconds in time (the grid is at 1sec spacing).

I have added the left and right Gear On Ground signals, and put the cursor where the right mainwheel has touched, but the left has not. The slowly-responding pressure altitude based vertical speed shows -580fpm, and the Altitude AAL is also still positive but the inertial signal responds more quickly to the flare and shows +92fpm. In fact, at the point where the wheels were being recorded as making contact with the runway, the inertial signal was already indicating the onset of a bounced landing. Even with gear signals recorded at 4Hz as in this case, the delay between aircraft motion and recorded data is significant.

The bounce motion can be seen in the Vertical Speed Inertial, going up then back down before  resonant response of the aircraft as it finally lands.

For Maintainers

On some aircraft the maintenance manual limits for hard landing inspections are based on vertical speed, and so you can see that the Vertical Speed Inertial gives a more accurate measurement of the motion of the aircraft, although estimation of the actual point of landing is always problematical!

Weakness of Vertical Speed Inertial

To compute the inertial signal we have to use a lot of contributing signals. First, the three body-referenced acceleration signals are resolved into the true vertical using pitch and roll angles, so if any one of these five parameters is corrupt, the resulting Acceleration Vertical will also be affected. Furthermore, as the calculation of vertical speed involves integration of this signal, long term errors will be amplified so we use a complementary filter arrangement to keep the parameter “in step” with the pressure altitude based normal vertical speed at above 100ft.

Then we convert from a pressure based reference to a purely inertial signal at low heights. The full algorithm is given at an earlier blog on inertial-smoothing.

So we have used:

• Acceleration Normal
• Acceleration Lateral
• Acceleration Longitudinal
• Pitch
• Roll
• Altitude STD