In my free time, I often flying with the X Plane 11 simulator and recently I thought to create the Top of descent (TOD) calculator, to calculate descent path. TOD is the point when the aircraft should start to descent to approach or any other target altitude. The calculator which I created is not strictly accurate, because it just depends on aviation rules of thumb and simply trigonometry. But it is sufficient for the initial decision.
The calculator can be found on https://descent.now.sh
Here I shortly discuss how the calculator works.
TOD point is just a distance, how much nautical miles (or other units) take the descent procedure from altitude A to B.
The main parameters we should have are origin altitude, destination altitude, and glideslope:
By simple trigonometry formula, we can calculate the distance:
Usually, when aircraft descending, it not only decreases altitude but reduces speed too. By the rule of thumb, 1 nautical mile for a speed reduction of 10 knots is a good value to start with. So we include it to the distance calculation:
The same rule of thumb is used to add the wind impact on distance. 1 nautical mile for 10 knots of head or tailwind.
Now we know how much distance takes the aircraft descent. But we need to calculate how fast we should descent to maintain the glideslope profile. The descent speed is called vertical speed (feet per minute) and is calculated by the following formula:
The source code of the calculator can be found at my GitHub repository github.com/epranka/descent-app
If you have any questions, feel free to ask in the comments below or contact me directly.
Top comments (2)
what does the triangle means ? if D = distance what is △h / tan alpha?
From the beginning you don't know D. So you calculate distance D with △h / tan.