# Intercept Geometry – Part II: Definitions

This article is a (hopefully not too boring) list of definitions, some of which have been already discussed in the past. A thorough understanding of definitions, acronyms and relations is unfortunately a necessary evil.

This article is a (hopefully not too boring) list of definitions, some of which have been already discussed in the past. A thorough understanding of definitions, acronyms and relations is unfortunately a necessary evil.

## Basic Definitions: Recap

The following concepts have been discussed in-depth already in previous articles. They are reported for completeness’ sake and as a refresher.
Definitions about the timeline are from different sources; the definitions about the geometry instead are reported in the previous part of this series.

Note: I always try to include the sources I base my work on. It is good to give credit to other authors or institutions, and it is very important for any of you interested in going deeper into the topics I cover in my articles. When it comes to DCS and content creators, this is even more important.

#### Definitions related to the Timelines

Note: these definitions were discussed in the article about the BVR Timeline.

• DR= Decision Range: “The minimum range at which a fighter can execute the briefed notch maneuver, remain there for a pre-briefed period of time in an attempt to defeat spikes, and then execute an abort maneuver. This maneuver will kinematically defeat any missiles shot at the fighter and momentarily keep the fighter outside the threat’s maximum stern weapons employment zone (WEZ) once the abort maneuver is completed. This definition does not address an adversary’s capability to eventually enter a stern WEZ by continuing to run down the fighter.” (Korean AF BEM A1-41)
• FR = “FR (factor range)—During merge tactics, the minimum acceptable distance between the group being merged with and the next the nearest group. Groups outside of this range are unlikely to affect the merge with the targeted group. FR should allow engaging and killing the targeted group, egressing tail aspect to the second group, and remaining outside that group’s maximum stern WEZ. FR is driven by threat weapons capability, fighter weapons capability, closure, and proficiency.” (AFTTP 3-1.1)
• MAR = “Minimum abort range (MAR) – The range at which an aircraft can execute a maximum performance out/abort manoeuvre and kinematically defeat any missiles and remain outside an adversary’s WEZ.” (AFTTP 3-1.1)
• DOR = “DOR (desired out range)/MOR (minimum out range)—Range from the closest bandit where an aircraft’s “out” will defeat any bandit’s weapons in the air or still on the jet and preserve enough distance to make an “in” decision with sufficient time to reengage the same group with launch-and-decide tactics. This also gives trailing elements a “clean” picture, reducing identification problems when targeting.” (AFTTP 3-1.1)
• LAR= “is a three-dimensional volume of space around a hostile aircraft into which the fighter must fly in order to have a chance to successfully employ its weapons. The fighter will maneuver in altitude, airspeed, and heading in order to achieve the best weapon solution for his opponent. The LAR is largest (i.e., longest RMAX) with 0 TA, at high airspeed and high altitude and is smallest (i.e., shortest RMAX) in the rear quarter at low altitude and low airspeed. Missiles like altitude, airspeed, and closure to achieve maximum kinematics.” (P-825 12-1)
• Skate = “Informative or directive call to execute launch-and-leave tactics and be out no later than desired out range (DOR)/minimum out range (MOR).” (AFTTP 3-1.1)
• Short Skate = “Informative or directive call to execute launch-and-leave tactics and be out no later than minimum abort range (MAR)/decision range (DR).” (AFTTP 3-1.1)
• Banzai = “Informative/directive call to execute launch and decide tactics.” (AFTTP 3-1.1)
• Out (w/direction)= “Informative call indicating a turn to a cold aspect relative to the known threat.” (AFTTP 3-1.1)
• Abort (w/direction)= “Abort is maximum performance, 135 degree overbank, nose slicing turn to put the threat at the6 o’clock position and accelerating to .7 IMN” (P-825 14-45)
• Crank (w/direction) = “F-Pole maneuver; implies illuminating target at radar gimbal limits.” (AFTTP 3-1.1)
• Notch (w/direction) = “Directive (informative) for an all-aspect missile defensive maneuver to place threat radar/missile near the beam.” (AFTTP 3-1.1)
• Pump (w/direction) = [AF] “A briefed maneuver to low aspect to stop closure on the threat or geographical boundary with the intent to reengage.” (Korean AF BEM A1-41)
• Bugout (w/direction) = [AF] “Separation from that particular engagement/attack/operation; no intent to reengage/return.”
• Extend (w/direction) = [AF] “Short-term maneuver to gain energy, distance, or separation normally with the intent of reengaging.”
• A-Pole = “The distance from the launching aircraft to the target when a missile begins active guidance.” (AFTTP 3-1.1)
• E-Pole = “The range from a threat aircraft that an abort maneuver must be accomplished to kinematically defeat any missile the bandit could have launched or is launching.” (AFTTP 3-1.1)
• F-Pole = “F-Pole is the separation between the launch aircraft and the target at missile endgame/impact.” (AFTTP 3-1.1)
• M-Pole = (not applicable) Fighter-Target range when the missile activates its seeker (MPRF).
• N-Pole = Notch-Pole.
• WEZ = Weapons Engagement Zone. “The three-dimensional volume of airspace around a fighter into which the hostile aircraft must fly to employ weapons.” (P-825 15-2)

#### Definitions related to the Geometry

• FH, Fighter Heading. “Heading of the fighter which, if extended through space, defines the fighter’s flight path”.
• FFP, Fighter Flight Path, “The logical extension of the direction of the fighter’s travel through space on its current FH”.
• BH, Bandit Heading. “Heading of the intercepted aircraft”.
• BFP, Bandit Flight Path, “the logical extension of the bandit’s travel through space on the current BH”.
• BR, Bandit Reciprocal Heading or Bandit Recip, it “is 180 degrees in the opposite direction from BH”.
• BB, Bandit Bearing. “Line of sight (LOS) bearing between the fighter’s position and the bandit’s position. BB is independent of both FH and BH”.
• SR, Slant Range. “Direct LOS distance between fighter and bandit”.
• Rate of Closure (ROC or VC), “Sum of the components of fighter and bandit velocities that contribute to downrange travel”.
• Range Rate of Closure (RROC), “[..] is the speed at which the contact moves down the attack display”.
• Lateral Separation “is the horizontal distance from the fighter to the BFP”. It is expressed in thousands of feet and is calculated as Target Aspect * Slant Range * 100.
• Vertical Separation (VD), “is the perpendicular distance the fighter is located above or below the bandit’s flight path”. It is calculated as the LS. VD = Elevation * SR * 100.
• Antenna Train Angle (ATA) is defined as “the position left or right of the fighter’s nose on the radar attack display”.
• Target Aspect (TA) is defined as “The bandit’s perspective pertinent to the fighter”. “The angle from the bearing line of the fighter to the nose of the target”.
• Aspect Angle (AA) is the supplementary angle of the TA. “The angle from the bearing line of the fighter to the tail of the target”.
• Cut: “The angle from fighter heading to bogey reciprocal.” (FH to BR).
• DTG (or HCA) (Degrees To Go or Heading Cross Angle): “is the shortest number of degrees the fighter needs to turn to parallel the bogey’s flight path, or turn to the bogey’s heading.”
• DOP: “is the direction the bogey would pass from one side of the fighter’s flight path to the other.”

#### Relations, Formulas and Synonyms

1. Cut = Fighter Heading (FH) to Bogey Reciprocal (BR)
Cut = FH to BR
2. Target Aspect (TA) = Bogey Reciprocal to Bogey Bearing
TA = BR to BB
3. Collision Bearing (CB) when co-speed = ½ Cut
CB = ½ Cut
4. Collision Bearing = Collision Antenna Train Angle (CATA)
CB = CATA
5. Lateral Separation or Lateral Displacement
LS = TA x SR x 100
6. Vertical Separation or Vertical Displacement
VD = Elev x SR x 100
7. Angle Off (AO) = Antenna Train Angle
AO = ATA
8. Degrees to Go (DTG) = Fighter Heading to Bogey Heading
DTG = FH to BH
9. Degrees to Go (DTG) = Heading Crossing Angle (HCA)
10. If SR → 0, TA and ATA increase.

### The best part: Maths!

Note: The following relations are taken from the official documentation but they are not always applicable “out of the box”. They are meant to be used by the RIO for assessing the parameters in his head.
This passage clarifies the potential issue:

[..] The computations require little mathematics beyond simple arithmetic. However, certain angular values are labelled either left or right with reference to either the fighter or enemy aircraft’s compass heading. The determination of Left-Right labels for Target Aspect, Antenna Train Angle, and Cut may be accomplished by a simple rule. Unfortunately, this rule does not hold true for all conditions, due to the discontinuity of compass values at a heading of North (3600). Under this condition the problem of reference labelling (RIGHT or LEFT) of values quickly becomes non-trivial for the neophyte RIO.

NAVTRAEQUIPCEN 71-C-0219-1 p7

In some cases, the modulo would have been better, in others, “mentally checking” directions and labels is simply more efficient.

Usually the RIO starts the intercept knowing at least the first three of the following parameters (ATA is obtained from the TID as soon as there is radar contact):

 Value Name Abbreviation Source Fighter Heading FH BDHI Bogey Bearing BB GCI / AIC Bogey Heading BH TID or GCI / AIC Antenna Train Angle (or Angle Off) ATA / AO TID

Starting from those values, other parameters can be easily calculated:

 Value Name Abbreviation Formula Bogey Reciprocal BR BR + 180° (if BH < 180°) BR – 180° (if BH > 180°) Target Aspect TA |BR – BB| TA is labelled Left (L) or Right (R) if BB is Left or Right of BR. Collision Course CC BB + TA (if TA is Right) BB – TA (if TA is Left) Cut (Cut) |FH – BR| Cut is labelled Left (L) or Right (R) if BR is Left or Right of FH. Degrees To Go DTG 180° – Cut Cut label is not considered Antenna Train Angle ATA |FH – BB| Labelled Left (L) if BB < FH Labelled Right (R) if BB > FH Note: ATA is displayed on the TID but this formula is useful when there is no radar contact. Bogey Bearing BB BB = FH – ATA (if ATA is Left) BB = FH + ATA (if ATA is Right) Note: useful if no tactical controller is available.

These relations are fundamental but not always necessary as some information can be obtained by means of the avionics or the AIC/GCI. Since there can be exceptions, the RIO should be able to calculate every parameter with the data he can extrapolate.
These are to simple scenarios where the RIO has to calculate those parameteres on his own:

• Lack of controller: if a controller is not present, the BB has to be calculated, or different formulas used;
• Ground (or Air) Controlled Intercept: the RIO must be able to perform most of the intercept guided by the GCI/AIC (and even without radar contact). This means calculating the necessary parameters using information from the tactical control.
• ## Considerations and Clarifications

### Aspect Angle vs Target Aspect

This is an incredibly common source of confusion.
Target Aspect and Aspect Angle are supplementary angles created by the intersection of the BFP with the CB. By definition, they are inversely proportional and therefore they are not interchangeable. The only occasion when they are equal is the case of the CB being the bisector of the aforementioned angle, therefore TA = AA = 90°.
Therefore, Aspect Angle (AA) = 180 – Target Aspect (TA), and they maintain the same direction (or label).

Fun fact: American Navy and Marines tend to use the Target aspect, the Air force uses primarily the Aspect angle (at least in the past, not sure if applicable to the modern doctrine as well).

### Cut, DTG and HCA

The Heading Cross Angle is the angle between the FH and the BH and is equal in value to the familiar DTG, as they are opposite angles. This means that the supplementary angle of both the HCA and the DTG is the Cut.
Additional observation: if the F-14 wants to turn perpendicular to the BFP, the turn radius is equal to 90° – Cut (labelled α in the sketch above, I not found the official labelling yet).

When FFP and BFP intersect in front of the aircraft (lead pursuit and TA and ATA are opposite in sign), the triangle formed by TA, ATA and DTG is known as the Intercept Triangle. The relations between the angle and the postulates of the Euclidean geometry allow to calculate any angle once two or them are known (or sides are known, but this requires basic trigonometry). In a co-speed scenario, the triangle is isosceles, so TA = ATA with opposite sign.

### Pursuit

There are three type of pursuit: lead, pure, lag. The difference is dictated by where the flight paths intersect relative to the target:

• Lead: the FFP intersects the BFP in front of the bandit.
This is the typical intercept when collision course is established and is used primary to increase closure and decrease range and for forward-position employment of ARH/SARH missiles. It is also used in order to obtain a valid gun solution from the rear quarter.
• Pure: the FFP intersects the BFP on the bandit’s position.
This is the primary means for positioning In LAR for a rear-quarter employment of IR missiles. It is also a form of collision when both actors are following pure pursuit or when the fighter has a speed advantage over the bandit.
• Lag: the FFP intersects the BFP behind the bandit.
It is used primarily to decrease closure and increase range (opposite of Lead pursuit) or to extend range in the rear quarter for an IR missile solution.

### Lexicon Notes: Overtake, Jinking, Position Advantage

• Overtake: descriptive definition of the Overtake (VC) used in the AREO report (but not exclusively there). If closing (e.g. VF-14 > VTGT dead ahead; or VC reading > 0) it can be omitted. The rate of closure is discussed later;
• Jinking: the contact changes heading, airspeed and/or altitude during the course of the intercept. The contact can jink into the F-14 (decreasing TA) or away;
• Position advantage: Position Advantage is described as “the fighter’s ability to attack a bandit or to defend a target in a beyond visual range (BVR) engagement.”. It is a recurring concept of the intercept geometry.

### Cranking

The Crank manoeuvre, so often mentioned, consists in placing the target at a minimum of 50 ATA and has the primary effect of reducing the closure rate hence decreasing the rate at which the distance between the fighter changes.
At the same time, it increases the chances of kinetically defeating any hostile missile flying towards the F-14, as the fighter decreases its TA relative to the bandit: the relation between VC and TA is similar (if you flip the scenario, by cranking the fighter changes its TA relative to the target).

### Rate of Closure (VC)

The ROC is affected by a number of variables. Besides the intuitive Fighter TAS and Bandit TAS, TA and ATA both impact the ROC: the smaller the TA and the ATA, the higher the rate of closure.
If TA = ATA = 0° the ROC is equal to the sum of the aircraft speed. Imagine increasing the DTG until it equals to 90°. In such a situation the closure rate is equal to the Fighter’s speed. This situation sounds familiar, and we have met it already discussing notching and Main Lobe clutter. With DTG=90° in fact, the relative speed of the bandit is zero, exactly as the ground.

VC can also be defined as the rate at which the SR changes.
VC decreases when the target is drifting and the higher the drift rate, the faster the VC loss and vice versa.

#### Rate of Closure and the TID AS

Note: the Tactical Information Display in Aircraft Stabilized mode is a topic I mentioned in several articles. In order to keep this short, I will not discuss why the information are presented as they are.

Let’s have a look at the three scenarios just mentioned from the point of view of the TID AS. To keep this simple, I will assume that VF14 = VTGT.

It is immediate how the length of the vector is proportional to the closure rate. Note that the second and the third example are hard to visualize on the TID: the first one falls into the ZDF, the second one in the MLC filter.
Fun fact: when I first discussed the TID AS, I also tried to use the proportions of the vector and the symbology to eyeball the value of the VC but I soon abandoned the idea.

### Drift

The effect of the contact moving on the display is called “Drift“. It has two main causes:

1. the fighter manoeuvring: Turn Drift;

2. the absence of collision course: Intercept Drift.
The following image shows the evolution of a contact not on collision. As you can see it is “shifting” towards the left side of the Display. This is even more evident on a B-Scope, rather than the TID, as the contact leaves a curved trail as it approaches the bottom part of the display.

This sketch represents a target on collision. Its position is consistent and on the B-Scope it appears as a contact moving vertically but not horizontally.

1. Turn Drift and Intercept Drift combined are called Displayed Drift. Understanding the Drift and compensating for it is a basic requirement for any RIO interested in a more simulative experience.

The Drift has been profusely discussed in this article. The effects on B-Scope are visible in the video I made when I discussed the Simple “Casual” Intercept (there are several examples, timestamps: 4’22”; 8’07”; 11’30”).

### Collision Course

Collision Course is another topic I discussed profusely already, so I will not spend too much on it. To recap it, if on collision course:

• The target does not drift;
• if co-speed, CB = Cut / 2;
• if co-speed, |TA| = |ATA| but opposite in sign.

If not on collision course:

• The target always drifts away from the Collision Bearing (CB);
• eventually the fighter will fly in front of the bandit (bad!) or vice versa (good at shorter ranges);
• if co-speed, CB doubles as the SR halves;
• if co-speed, for every degree the target drifts in ATA, the TA changes by the same amount.

#### CB when not co-speed

Update 13/02/2021
I put together a short study about the effects that different speeds have on CATA here.

As we know from previous articles, when co-speed, |TA|=|ATA| but opposite in sign and CB = Cut / 2. This relation is quite handy but not always applicable. What happens when the fighter and the bandit are not co-speed?

The following example should (hopefully) clarify what happens when the aircraft are not co-speed. I started by considering the formula that defines the speed (Distance/Time). In a set and common time quantum, they will cover different distances. Therefore, if the collision course has to happen (and in some cases it will not happen), the angles must change. The faster the F-14, the more we have to turn towards the bandit. By doing so, DTG becomes wider and therefore Cut shrinks. CB therefore will become closer to FFP rather than the BR.

• Image I shows a typical collision course (Note: in my infinite wisdom and luck I managed to randomly draw a sketch with TA=ATA=37.5° so I truncated them to 37°). As per the precedent definition, Cut / 2 = TA = ATA = 37.5°.
• Image II shows instead a very fast F-14 on collision with a slower aircraft (a bomber, perhaps). If the same TA and ATA of the previous example are maintained, the F-14 will fly at the previous CP (Collision Point) much earlier than the bandit. Therefore, the angles must be adjusted and the fighter must reduce the lead pursuit (in theory for S → ∞, the pursuit becomes pure).
• Image III shows a scenario opposite to the previous: the bandit is faster than the fighter, so the FFP and BFP intersect each other further away from the position of the bandit.
Moreover, if the bandit’s speed is much higher than the fighter’s, the collision will not happen at all.
##### Observations
• TA does not change, unless the bandit is actively manoeuvring;
• Note how in Example II, Cut / 2 > ATA whereas the third example shows the opposite result.
• I was curious about how the trend of the relation between ATA and Cut/2 changes as DGT increase:

This chart represents what happens in the examples above. DGT decreasing implies an increasing Cut but the ATA increases much faster.

This short discussion confirms the rule of thumb: the greater the ΔV, the smaller the ATA. If the fighter and the bandit are on a collision course and the controller directs “Gate” to expedite the intercept, then the RIO should know already how the target will change on the display (the intercept drift soon appears) and how to manoeuvre to compensate for the increasing speed of the F-14 (turn towards the target, decreasing the ATA).
Moreover, knowing that drift occurs when there is no collision and that the drift will always be away from CB, then it is understandable how, for every degree of drift, the TA increases by 1°. In a co-speed situation this information is directly applicable, as CB and TA are immediately calculated even on the F-14 either by means of the BDHI or from the TID AS.

This concludes the recap of the fundamental terms and concepts used in Intercept Geometry. Part III of this series is an overview of the Target Aspect and the Lateral Separation and several of the formulas and relations just described will be finally applied.