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A primary flight display (PFD) in a glass cockpit has an airspeed indicator (ASI) that doesn't just display the speed, but also a vertical arrow or bar that shows the "speed trend" i.e. the acceleration. But there's no extra "acceleration scale" shown behind it like there is for speed. What's the scale of this trend arrow and how do you read it?

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Direct answer from the A320 FCOM:

Speed Trend (yellow) This pointer starts at the speed symbol. The tip indicates the speed the aircraft will reach in 10 s, if its acceleration remains constant. The pointer only appears, when it is greater than 2 kt, and disappears when it is less than 1 kt. It also disappears, if the FACs fail.

It is also a good indicator during change of attitude. To understand what your aircraft is doing. Because you will see a change in the trend before seeing a change in the vs indicator which allow you to react to a deceleration or acceleration.

I have more data from OEM for the functionnality, unfortunately they are protected. I cannot diffuse more of that explanation.

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I found some training material on Airbus PFDs which explains:

A vertical arrow, called the speed trend arrow, indicates the aircraft's predicted speed in 10 seconds if the current acceleration or deceleration rate remains constant.

Put another way, if you measure the acceleration in knots per second, and then multiply it by ten, it's on the same scale as the speed tape.

If you want to reach a particular speed in ten seconds' time, adjust pitch or power to put the head of the arrow on that tick on the speed tape, then keep adjusting to keep it on the same tick as it approaches.

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    $\begingroup$ then keep adjusting to keep it on the same tick as it approaches. Then it will forever take another 10 seconds to get to that speed, i.e. you never get there. $\endgroup$ – DeltaLima Mar 29 '18 at 14:09
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    $\begingroup$ @DeltaLima: But it will lead to the target speed being approached exponentially, which is pretty good as control principles go, even though it doesn't exactly achieve "reach a particular speed in ten seconds' time". $\endgroup$ – Henning Makholm Mar 29 '18 at 14:44
  • $\begingroup$ Yeah, that's a good point. I was just trying to write another way of interpreting it, but as you say, it's not quite right. $\endgroup$ – Dan Hulme Mar 29 '18 at 15:34
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On the Garmin G5, used in many small airplanes, (under 12,500 lbs), the air speed trend is interprated thusly:

The Airspeed Indicator displays airspeed on a rolling number gauge using a moving tape. The numeric labels and major tick marks on the moving tape are marked at intervals of 10 knots. Speed indication starts at 30 knots, with 60 knots of airspeed viewable at any time. The actual airspeed is displayed inside the black pointer. The pointer remains black until reaching never-exceed speed (VNE), at which point it turns red.

A color-coded (red, white, green, yellow, and red/white “barber pole”) speed range strip is located on the moving tape. The colors denote flaps operating range, normal operating range, caution range, and never-exceed speed (VNE). A red range is also present for low speed awareness.

The Airspeed Trend Vector is a vertical, magenta line, extending up or down on the airspeed scale, shown to the right of the color-coded speed range strip. The end of the trend vector corresponds to the predicted airspeed in 6 seconds if the current rate of acceleration is maintained. If the trend vector crosses VNE, the text of the actual airspeed readout changes to yellow. The trend vector is absent if the speed remains constant or if any data needed to calculate airspeed is not available due to a system failure.

See the Pilots Guide, Para. 2.1.1, page 14. https://support.garmin.com/support/manuals/manuals.htm?partNo=K10-00280-00&language=en&country=US

Here's a picture of the G5 https://static.garmincdn.com/en/products/K10-00280-00/v/cf-lg.jpg

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