After discussing the first two models, it’s now time to go into the details of the mathematical model. The radar antenna elevation table resulting is still an approximation: as mentioned in Part I, there is an expected inducted error in the elevation boundaries calculation and it increases the wider the angle gets. Nevertheless, it’s still precise enough to find a target in most conditions.
School is useful!
I have applied very basic trigonometry and the theorems or right-angled triangles to calculate both the limits and the elevation angle to set in order to spot a target at a certain range and altitude.
By splitting the radar cone in two following the bisector, we obtain two right-angled triangles.
- a is half width of the radar cone;
- b is the distance between our aircraft and the target;
- α is the angle covered by the 4 BARS setting (6.3°);
- β is α/2.
a is calculated as the tangent of β angle, times the distance b. By doubling the value of a we obtain the width of the radar cone at that particular distance.
Back to the original goal
The idea behind the model was understanding the elevation angle to set in order to find a target at a particular range and altitude; for instance a target that might be outside of the radar cone at default elevation but shown on the TID thanks to the DL.
The same basic trigonometry can be applied to calculate the elevation angle instead of the width; the width in this case is the ΔAltitude.
The example shows how trigonometry can be applied to get the new approximated elevation. The radar cone boundaries are instead calculated without taking into account the radar elevation, only the number of bars.
The final result can be downloaded as PDF or Kneeboard page from the Download section. Feel free to download and test it and advise if you find mistakes or have additional considerations.