Back to Basics: Rate of Closure (Vc)

This article is aimed mostly to new players, and it is intentionally simplified. The goal is introducing fundamental topics in, hopefully, a simple and concise way.

The Meaning of Life Closure Rate

Closure rate ( V_C ) is a concept every Pilot or RIO should be familiar with; it is the only parameter always present on the TID besides the antenna elevation angle and height.
Any fairly modern fighter aircraft shows it, but it is a variable often not understood or underappreciated.

The closure rate represents, in elementary terms, the rate at which the distance between the two aircraft is decreasing (closing) or increasing (opening).
A more appropriate definition can be found in the familiar P-825:

Rate of Closure (V_C) – Sum of the components of fighter and bandit velocities that contribute to downrange travel.

CNATRA P-825/17, 5-2

V_C tells a lot about an engagement. For example, a high closure rate probably indicates that the contact is hot (or has low TA). A minimal rate (to the point of becoming negative) probably means that the target is cold or even running away.

Maths time!

The closure rate depends on several parameters, and both aircraft can affect it. Not only speed and heading have an impact on the value of V_C, but the value that describes the relation between the two aircraft as a drastic effect on the rate of closure. This value is the bearing from one aircraft to the other.

The closure rate is determined as the difference of the two velocities (remember that Velocity &diff; Speed; the former is a vector, the latter a scalar, although they are often mixed and I’m very guilty of that).

V_C = V_{C_F14} – V_{C_TGT}

Each velocity can be calculated by using simple trigonometry (in order to keep the discussion short, I am skipping the steps used to determine the following formulas. They are quite straightforward, feel free to Google them yourself):

V_{C_F14} = V_F14 * cos (BRG – HDG_F14)
V_{C_TGT} = V_TGT * cos (BRG – HDG_TGT)

Finally resulting in:

V_C = V_F14 * cos (ATA – HDG_F14) – V_TGT * cos (ATA – HDG_TGT)

Let’s see a first example, using two generic aircraft, AC1 and AC2. It will be later used for further analysis:

Notable Scenarios

The following examples show some common but peculiar situations: True Head-on, a notching target and a target hiding in the ZDF.

Example I: True Head-On

HDG_F14	V_F14	HDG_TGT	V_TGT	BRG
360°	600 kts	180°	600 kts	0°

This scenario sees two aircraft flying head-on at the same speed. Intuitively, V_C will be equal to the sum of the two speeds. In fact:
V_C = 600 * cos (0 – 360) – 600 * cos (0 – 180) = 600 – (-600) = 1200 kts

Example II: Notch Filter

HDG_F14	V_F14	HDG_TGT	V_TGT	BRG
360°	600 kts	270°	450 kts	0°

In this scenario, TA = 90, so the Target’s component of the equation is zero.
V_C = 600 * cos (0 – 360) – 600 * cos (0 – 270) = 600 – (0) = 600 kts

Therefore, V_C depends only on the F-14.
However, note how this result is possible only because the cosine of the difference between BRG and HDG_TGT is zero. Since the two aircraft are moving, at some point the Target will appear again on the radar (if the status quo is maintained and the target leaves passes the gimbal limits).

Example III: Zero Doppler Filter

HDG_F14	V_F14	HDG_TGT	V_TGT	BRG
045°	600 kts	360°	600 kts	15°

I mixed up the number a bit in this example. The result is a closure rate of:
V_C = 600 * cos (15 – 45) – 600 * cos (15 – 360) = 520 – (580) = -60 kts

The target in this example is probably invisible to the F-14, unless the RIO switches to Pulse mode. The reason is the familiar Zero Doppler filter, which is ±100 kts wide, enough to include a target with V_C = -60kts.

V_C Over Time

Considering two aircraft flying at constant speed and heading, we may notice that V_C changes. As long as the relative positioning of the aircraft changes, then V_C will consequentially change. However, recalling the study about the Intercept Geometry, we know that there is a specific scenario where this does not happen: Collision course. The explanation is straightforward: when two aircraft are on a Collision Course, the ATA does not change; hence the target does not drift. Since we are already assuming that the other parameters (speed and heading) are constant, we then have that V_C is constant as well.

The following scenario instead shows two aircraft, one chasing the other. However, the pursuer is slower than its target. Let’s see how the closure rate changes if the status quo is unaltered.

HDG_T	HDG_AC1	V_AC1	HDG_AC2	V_AC2	BRG	V_C
T0	45°	250 kts	330°	300 kts	75°	294 kts
T1					65°	261 kts
T2					50°	197 kts
T3					24°	97 kts
T4					354°	-117 kts

When the BRG ≤ ~14°, V_C becomes negative.

Since the aircraft are not following a Collision Course, the angle is changing no matter the other parameters, ergo affecting V_C.

A proper and in-depth discussion of Collision and Drift is already available in this site; therefore I will not go into the details of the topic again.

Conclusions: Practical Usage

The closure rate is a topic discussed here multiple times. There are a few practical applications of this value or, even better, of the changes over time of V_C.
For example:

Improve your Situational Awareness: the closure rate can reveal important information about a target, such as his aspect. Along the mission intel, it can help to identify if the contact is, for example, a fighter or a bomber (a B52 hardly goes supersonic);
Bandit jinking or manoeuvring: variations in the V_C tell a lot about the target. Besides the point mentioned above, the RIO can identify a target jinking or manoeuvring (e.g. defending) even before the change is reflected by the track displayed on the TID. This can make the difference between a trashed and a connecting shot;
Controlling the fight: the RIO can actively and intentionally manipulate the closure rate, for example to slow down an approaching hostile or kinetically defeat a missile. The equation above shows how important the Bearing and how varying the Bearing immediately affect the V_C. A virtual RIO should now be more aware of the effects of a manoeuvre such as Cranking.

I hope this short article was clear and helped you to have a better understanding of this simple yet essential parameter.
Any question, feedback or anything else, give me a shout 🙂