*Intercept Geometry: Table of Contents*

**Part I**: Introduction**Part II**: Definitions**Part III**: Target Aspect & Lateral Separation

Part II of this study refreshed some basic concepts related to the Intercept Geometry. Out of many, the *Lateral Separation* is probably the most important variable at this stage of our learning process.

The Lateral Separation is calculated as *Target Aspect * Slant Range * 100*, thus it is directly dependant from the value of the Target Aspect, and that’s where we start from.

### The Target Aspect

Defined as *the bandit’s perspective pertinent to the fighter*, there are several ways to calculate this variable. Two of the most common can be visualized on the BDHI. However, the RIO should be able to calculate the TA mentally rather than re-creating the scenario on the BDHI every time.

Unfortunately, this is not the only value the RIO has to calculate and monitor and feeling overwhelmed is very easy especially when approaching these concepts for the first time, but practice definitely help (or, at least that’s my experience). Eventually, calculating TA and LS becomes a matter of a bunch of seconds:

“

High aircraft speeds bring the two aircraft into close proximity within a maximum of 2 to 3 minutes, and usually less. The RIO must learn to calculate rapidly, and with little error. An error, once made, seldom can be fully corrected within the time remaining to intercept. Rapid closure, numerous calculations, and the need to continually manipulate the radar, essentially prohibit recording calculated values. The RIO must hold the results in his memory as he progresses through the list of operations. The outcome is a high information-processing rate for the RIO’s mental processes.”NAVTRAEQUIPCEN 71-C-0219-1 p10

Two formulas are used to calculate the Target Aspect. They are actually identical as both use the BR (or Cut) as the starting point and the BB (or ATA) as the finishing point.

The context in which this formulas are applied is the typical Lead Pursuit where BB, FFP and BFP create the familiar intercept triangle, featuring TA, ATA and DTG as internal angles.

**Cut to ATA = TA (L or R)**

This formula works best on the DDD or other B-scope attack display. Problem is, the TID is not one of them and the information displayed on the DDD are functions of V_{C}in non-Pulse modes, making the drift hard to identify.**BR to BB = TA (L or R)**

This formula is should be used when the BRAA is passed. It is very simple as the BR is immediate (the documentation stresses the importance of being able to calculate the BR in a second), then it is just a matter of “moving to” the BB. If no tactical control is available, then BB can be calculated as FH ± ATA (add if ATA Right, subtract if Left).

#### What does “to” mean?

“*to*” is not a mathematical operator of course, it literally means “jumping” between two values, logically measuring the direction as mathematically we would do by means of the modulo.

Consider the application of the second Formula to this scenario:

- BR = 355°;
- BB = 030°.

The simplest solution is to mentally visualize the BDHI and assess how many degrees there are between BR and BB: 5° from 355° to 360° then 30° more for a total of 35°. This exercise is also useful to visualize the label (Left or Right) of the TA. In this scenario we moved from Left to Right so TA is *35R*.

If we invert BR and BB instead, we still have 35°, but we would be moving from 30° to 355°, therefore from Right to Left. The TA in this case is *35L*.

After some practice, this becomes second nature.

At the end of the day, use the procedure you prefer. I usually follow the doctrine and use BR → BB if a controller is available (and therefore BRAA is routinely provided unless Judy is called), otherwise Cut → ATA which is very easy to visualize both mentally and on the BDHI.

The BDHI is invaluable when first approaching the long list of parameters that can affect the geometry, use it!

### Determining the Bandit Reciprocal: the +2/-2 Rule

This is a simple but useful trick to calculate the BR. The Bandit Reciprocal can be in fact mathematically obtained by using the modulo but when calculating the result in your head, using the modulo may not be the fastest way.

Since ±180° are added depending on the BH, the +2/-2 rule can be effectively used:

- If 20° < HDG < 180°: add 2 to the hundreds, subtract 2 from the tens;
- If HDG > 190°: subtract 2 from the hundreds, add 2 to the tens.

As you can see, it’s simply a more structured way to add or subtract 200 and compensate for the remaining 20 degrees.

#### Examples

- HDG 347 → "3"
**– 2**and “4”**+ 2**. “7” is carried over. Reciprocal:**1 6 7** - HDG 125 → “1”
**+ 2**and “2”**– 2**. “5” is carried over. Reciprocal:**3 0 5** - HDG 220 → "2"
**– 2**and “2”**+ 2**. “0” is carried over. Recip:**0 4 0** - HDG 021 → “0”
**+ 2**and “2”**– 2**. “1” is carried over. Recip:**2 0 1**

Alternative means of calculating the BR are, for example, the already discussed BDHI or memorizing a table with Headings and Reciprocals, similarly to what we all did back at the elementary school.

### Undiscussed Scenarios

The sources I used and mentioned in Part I take for granted that in this phase the intercept triangle is present and built as usual by ATA, TA and DTG (angles). What if, instead, the standard intercept triangle is not applicable due to how FFP and BFP are oriented?

To answer this question, I put together a bunch of different scenarios and checked whether the formulas can be applied or the geometry changed in such a way that new formulas are required.

Note that I represented Target Aspect, Cut and DTG as per their definition (out of simplicity, in some cases I drew the opposite angle):

*TA*: the angle between BB and BR;*Cut*: the angle between FFP and the BR;*Degrees To Go*: the angle between FFP and BFP.

As you may have noticed already, the conundrum is understanding where the intersection between FFP and BFP is located: unless fighter and bandit are flying parallel, in fact, the two paths will always intersect at one point.

**Scenario II**, included for reference, is the standard Lead Pursuit (whether collision course is established, or it does not matter in this context).

Applying the first formula, we find that *TA = Cut – ATA*.

**Scenario I ** see the BFP intersecting the FFP behind the fighter.

The angles involved are Cut, TA and *α*, the supplementary angle of the ATA.

*α*

*α*is equal to: 180° – ATA

Thus: TA = 180° – Cut – 180° + ATA = ATA – Cut

**Observation I**: although Scenario I and II provide different results Maths-wise, in practical terms there is no difference as the absolute value of the difference is considered when determining the TA.

**Scenario III** resembles a Lag Pursuit and the usual intercept triangle is again not applicable. We notice that the triangle’s angles are AA, Cut and ATA:

AA in this case is equal to: 180° – Cut – ATA

Thus: TA = 180° – 180° + Cut + ATA = Cut + ATA

The result is different from the previous scenarios as in this case Cut and ATA are added up rather than subtracted.

**Observation II**: if Lag Pursuit is established, ATA and Cut are discordant*. This makes understanding the current geometry immediate and can affect how the RIO decides to manage the TA and eventually the Lateral Separation.

*****: this is a purely empirical observation. If you find examples where this is not applicable, please let me know!

For completeness’ sake, let’s have a look at what happens in two more peculiar scenarios:

**Scenario IV: Pure Pursuit**

This scenario is quite simple since BB = FH, the simplest solution is using BR → FH.

**Observation III**: in this scenario, TA = Cut – ATA with ATA = 0, therefore TA = Cut (in fact, the TA is the opposite angle of the Cut).

Note that Pure Pursuit should be maintained by adjusting FH, otherwise the situation falls into either Scenario II or Scenario III.

This scenario can be useful to quickly assess the aspect of the target at the beginning of the BVR Timeline (*Point and Assess*).

Remember also that the TA does not change instantaneously when the ATA changes.

**Scenario V: Parallel Flight**

Fighter and bandit can fly following parallel flight paths, therefore *DTG = 180°* or *DTG = 0°* depending on the directions:

- When
*DTG = 0° and FH = BH*, the scenario is called True Stern; - When
*DTG = 0° and FH ≠ BH*, the scenario is called Parallel Stern; - When
*DTG = 180° and FH = BR*, the scenario is called True Head-On; - When
*DTG = 180° and FH ≠ BR*, the scenario is called Parallel Head-On.

In the head-on scenarios, where the fighter is flying parallel to the bandit and HCA = 180°, TA is equal to ATA not only in value but in direction as well.

Moreover, the parallel flight prevents the determination of a DoP, as the two aircraft will not intersect each other.

**Observation IV**: no matter the scenario, TA can be always calculated by using Formula 2, BR to BB; whereas the relations between TA, ATA and DTG may change depending on the geometry.

### Examples

The considerations and observations made so far can help to understand how the TA changes as the intercept progresses, especially in case CB is not established.

Let’s now have a look at a few practical examples. I used both Formula 1 (DTG to Cut to TA) and Formula 2 (BR to BB), plus a variant of the first formula skipping the determination of DTG.

## Lateral Separation: Axis Mundi

The Lateral Separation (LS), sometimes called Lateral Displacement (LD) is one of the most important concepts of the Intercept Geometry. Defined as the distance from the Fighter Flight Path to the Bandit Flight Path, the LS puts into relation two other fundamental basic concepts: Target Aspect (TA) and Slant Range (SR).

The LS can be expressed in feet of nautical miles, and it is calculated as:

[nm] > LS = TA * SR / 60

Besides the geometrical concept, what is the meaning of the lateral separation? Simply put, it expresses the **manoeuvring space available to the fighter**, in relation to the target.

As mentioned above, the Lateral Separation is drastically affected by the TA: variations of the Antenna Train Angle or the Slant Range do not affect the LS immediately, whereas if the bandit turns and therefore the TA changes, it impacts the LS instantaneously.

Consider the following examples:

SR=50nm, TA=35° → LS = 175,000 SR=30nm, TA=35° → LS = 105,000 SR=10nm, TA=35° → LS = 35,000 |
SR=50nm, TA=35° → LS = 175,000 SR=50nm, TA=10° → LS = 50,000 SR=50nm, TA=0° → LS = 0 |

It is clear how the Slant Range can’t change in a bunch of seconds whereas the Target Aspect can, and by doing so, it drastically affects the Lateral Separation. This effect is fundamental as *an aware bandit may try to deny the fighter’s intercept* by, for example, jinking, turning cold or head-on.

The following sketch further emphasises this concept.

Since the Lateral Separation describes the turning space available to the fighter, it should be more clear now how important it is and, intuitively, we can foresee already how a big chunk of the Intercept Geometry relies on the ability to manage and manipulate the two components of the LS: Target Aspect and Slant Range.

The “goal” LS and how it is managed change depending on the objectives of the mission, tasking, commit directive from a controller, ROE and VID requirements and so on.

## Managing Lateral Separation

Before diving into the doctrinal techniques used to manage the LS, let’s have a quick look at the relation between LS and other actors.

**Notes**: each of the sources I used as reference approach the management of Lateral Separation slightly differently, and sometimes set different goals in terms of separation. The rest of the article is based on the P-825/17.

The following LS management observations are fundamentally a series of applications of the basic concepts of Euclidean geometry and trigonometry.

The differences and “quirks” pertinent to each technique are discussed in the following parts of the series.

Note also that the relations are based on the fact that the intercept is co-speed, co-altitude, conditions that rarely happen in DCS. On the other hand, this scenario simplifies the relations and the calculations required to determine collision and LS.

### Relation between Cut, DTG, ATA and LS

The CNATRA P-825 shows how different types of Cut vs Collision affect Lateral Separation and Target Aspect over time (you have probably seen it already. Moreover, when I discussed the “sides” of the Tactical Information Display, I mentioned part of this disquisition).

# |
Category |
Type of Cut |
LS |
TA |

1 | Cut Into | Cut > Collision | Decreases | Decreases |

2 | Cut Into | Cut = Collision | Decreases | Unchanged |

3 | Cut Into | Cut < Collision | Decrease | Increases |

4 | Cut equal to BR | Cut = 0 | Unchanged | Increases |

5 | Cut Away | Cut Away/Zero Cut | Increases | Increases |

The three categories are easily explained: a *Cut into* decreases the Lateral Separation (BFP and FFP intersect), a *Cut away* increases the LS (the fighter moves away from the BFP), the *Cut equal to BR*, maintains LS.

These five relations provide simple means to manipulate the Lateral Separation in order to achieve the desired objective.

The following sketches describe the relations mentioned above:

#### #1 – Cut Into: Cut greater than Collision

*► LS and TA reduced over time*

- FFP well in front of the bandit;
- This is the only Cut that reduces TA;
- The bandit is place in the Hot side of the display.

#### #2 – Cut Into: Cut equal to Collision

*► TA unchanged, LS decreases*

- As TA remains unchanged, the LS decreases due to the SR;
- TA = ATA but opposite in sign;
- If co-altitude, the aircraft will (theoretically) collide mid-air;
- This is the most efficient geometry to close with the bandit;
- Bandit’s vector in TID AS points towards the F-14.

#### #3 – Cut Into: Cut less than Collision

*► LS is reduced whilst TA increases*

- Pure and Lag pursuit are always less than collision;
- There can be Lead pursuit if within Pure and collision;
- Useful when approaching WVR (if bandit unaware of the fighter);
- The Target is placed in the first part of the Cold side of the TID.

#### #4 – Cut equal to Bandit Reciprocal

*► TA doubles as range halves*

- This is not a type of pursuit;
- FFP and BFP are parallel;
- It is the only occasion when the bandit’s TID AS vector is perpendicular to the bottom edge of the screen.

#### #5 – Cut Away

*► Only way to increase LS*

- It is not a type of pursuit (since LS is being generated);
- It is used by the fighter when LS needs to be increased.

### A Familiar Tool: Tactical Information Display in Aircraft Stabilized mode

These considerations are immediately understandable when applied in the scenarios described by the P-825, but what happens on the TID in Aircraft Stabilized mode when the fighter and the bandit are not co-speed?

Whist putting together these examples I collected data relative to the TA and the SR after 30″ and 60″. I ran the first series of tests with the fighter flying faster than the bandit and then I repeated the test collecting a second series with the aircraft flying co-speed (GS).

*Modus operandi. Notes:*

- I set up the flight paths from the ME, so they are not perfectly accurate but close enough (ref. collision and FFP = BR);
- The F-14 spawned in exactly the same position every time, I only changed FH and speed;
- Values are taken from TacView, I used RBRG from the target to the fighter as it is more precise (float) than the AA provided (int);
- LS is expressed in a thousand of feet.

These are the results of the first test:

The second test saw both aircraft flying at the same speed:

### Observations

**Note**: NCS = Non co-speed; CS = Co-speed.

*Case 1: Cut > CB*. In this scenario, both TA and SR decrease over time, and it is the quickest way to reduce LS. The SR does not decrease as much as in the other cases as the FH points almost away from the bandit, rather than towards the bandit itself;*Case 2: Collision*. This is a well-known situation, where the loss of LS is mostly due to the decrease of the SR;*Case 3: Cut < CB*. In this scenario the TA is increasing (eventually the F-14 will fly at the 3/9 of the bandit, rather than on its nose). This reduces the loss of LS caused by the decreasing SR;*Case 4: Cut = BR*. Besides a small error positioning the aircraft, the LS is almost unchanged. There is, in fact, a balance between the decreasing SR and the increasing TA. Moreover, as range halves, the TA doubles. This is an important consequence, since, for example, we can use Cut = BR as a mean to maintain the desired LS until it is time to perform a conversion turn;*Case 5: Cut Away*. This scenario is the simplest to imagine: the F-14 is flying away from the bandit and therefore the ratio at which the TA is generated drastically increases and, at the same time, slows down the SR decrementation, resulting in an increase of LS. This manoeuvre can therefore be used ante conversion to generate enough room for the turn.

## New Kneeboard page

At the end of this discussion I will put together a new kneeboard page that hopefully will make the new RIO’s job simpler by featuring info and reference tables for LS, VD and so on.

We should now have most of the basic tools needed to start putting into practice the gameplans suggested by the various sources.

Although it may sound complicated, calculating TA and LS eventually is done by means of rules of thumb, approximations and even just at a glance, for the most experienced. That being said, what is going on under the hood is nevertheless very important to be able to improve the crew’s understanding and, ultimately, the Situation Awareness.

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