ΔV in non co-speed intercepts: Empirical Assessment

As we have seen multiple times, the basic documentation (such as the P-825/17) covers only the co-speed intercepts. In such scenarios, the Collision Bearing is determined very easily by using the relation: CB_COSPD = Cut / 2.
However, in DCS this is very rarely the case. Therefore, when the speed of the fighter (V_F14) and the speed of the target (V_TGT) are different (Δ_V > 0), the relation is no longer applicable.

This simple study aims to quantify the difference between CB and CB_COSPD. In other words, help the RIO to better understand this situation by having an idea of how much, what he can expect and what he can do to compensate such difference.

Let’s start from the beloved TID in Aircraft Stabilized mode, as it shows very clearly when Collision Course is established no matter Δ_V. By comparing that angle and CB_COSPD, we can understand the magnitude of the impact of Δ_V on CB.

Testing scenario

These are the parameters set for recreating the TID AS display below. In this scenario, the two variables are V_F14 and V_TGT.

The image above clearly shows how the CB changes depending on the speed of the fighter and the bandit.

Hey, hey kid! Wanna calculate some angles?!

The question is how we find the angle. The answer can be found in the geometry, by doing some poor man’s reverse-engineering on the TID Vector:

We already know that, then CB is established, the vector points towards the F-14 and the triangles defined by the vectors and the one defined by the headings and the CB are geometrically similar (my coolest discovery so far :p ).
Let’s consider the third image. The thick black line is the FFP, the red thick line is the FFP used to construct the vector. Therefore, they are parallel. CB, the thinner black line that connects the vector to the F-14, is therefore cutting two parallel lines. The angles originated are congruent (“γ”, the green one, plus the red, which is the opposite angle). We also know b, c and α.

The Cosine rule allows to easily calculated the hypotenuse (the “length” of the Vector, “a“). From there, we can calculate γ.

I chucked the formulas on Google Spreadsheet (I can share the spreadsheet, but there’s really not much to see there) and then filled a table with different values of speed:

Then determined Δ_CB:

Practical Test

A simple test to check if the model makes sense:
Altitude: Co-altitude, value non-factor;
V_F14 = 400;
V_TGT = 200;
I set up the geometry a bit randomly, let’s see what the TID said:

True Course: 167
True Heading: 19

DTG = 148°

Cut = 32° → CB_COSPD = 16°

However, due to the speed difference, CB must be adjusted. The model should tell us how much:

I measured the CATA graphically, htherefore there is a double chance of introducing imprecisions: CB in-game and measurement with GIMP. However, the resulting value is 10.26°, quite close to what the model suggested.

Practical Utility?

The issue here is that there is no linear relation between the parameters (at least I can’t see one). If, for example, the values of Δ_CB expressed as a percentage were constant for different values for DTG, then it would be easy. Unfortunately, this is not the case and the simplest solution in this scenario is using the avionics (e.g. the Collision option on the TID).
There are still some interesting things to notice. Let’s start by looking at how the values change for different DTG.

V_TGT is constant at 400, DTG is calculated between 80 and 170:

It gets even more interesting when we look at the Δ:

Observations and Conclusions

After this quick dive into the geometry, what can we conclude?

1. No simple relation: unfortunately the lack of a simple relation describing the variations of the CATA as a function of Δ_V makes the creation of a single model impossible (it would require too many pages: assessing the drift and correcting is much more efficient).;
2. Maths & Geometry. The relation between the parameters is purely geometrical. It does not matter if the values are IAS, TAS, CAS, GS, mm/day; as long as both speeds are measured using the same unit;
3. Δ_V: considering an equivalent Δ_V, CB varies more from CB_COSPD when the target is slower than the F-14.
4. Higher DGT = Less Variation: it may be taken for granted, but there is more: if you look at the Δ percentages of the test right above, they are quite similar after a certain magnitude of DTG, although in reality the variation consists of several degrees. For example, V_TGT = 350, DGT = 80 → -9.1%, DGT = 90 → -8.5%. The same interval instead includes from DTG 120 (-7.3%) to DTG 170 (-6.7%). This is important because the RIO can expect a greater variation between the Cut / 2 and the actual CB when Cut is high.
   Therefore, low DTG requires more corrections, since it impacts the angles the most;
5. Low Target Speed: when V_TGT is low, the difference between CB_COSPD and the new CATA is higher.
   For example, considering the Δ for DTG = 130, V_TGT = 200 → CB = -8.84°; for V_TGT = 600 = 5.33;
6. Combining the last two points, we can now identify the case where CB diverges the most from CB_COSPD: low Speed, high Cut (or low DTG). This case is the trickiest as the two parameters make the CB diverge the most from CB_COSPD. On the other hand, the difference decreases along the Cut, to the point where, in extreme cases, reference tables are not even useful anymore.

New Kneeboard Page

The quantity of parameters and the lack of a simple, intuitive and linear relation that does not require the RIO to do any abstruse calculation, makes creating a dedicated kneeboard page quite hard. In theory, dozens of pages are required to satisfy the combinations of the variables, which is honestly a waste of time when we can use the Tactical Information Display in Aircraft Stabilized mode to monitor the CB and the DDD (or the attack display in a modern aircraft) to monitor the drift and correct if necessary.
Nevertheless, a couple of reference tables can help new RIOs to have an idea of the magnitude of the difference between the actual CB and CB_COSPD.

This page is quite simple to use: the columns’ header with inverted colours is the speed of the F-14 (I choose 400, 500, and 600). The headers are the speed of the target. The rows’ header is the Cut. The column having a grey background is the co-speed CB.

Examples

The following are three simple examples of how the page can be used to determine the CATA.
Example I

Example II
This is the same example discussed above in the Practical Test.

Example III
For the last example I put together a simple scenario:

When values are not exactly what reported in the tables (it never will), they can be rounded following the usual procedure. At the end of the day, this is a tool aiming to help the RIO to better understand what to expect, not SOP-worthy material (in my opinion, of course).