Underside Attack -- Maneuvering for the Attack

Best Type of Attack Against a Non-maneuvering Target with the 20MM Cannon

As you will recall, because of the characteristics of the pursuit curve, our fire control system limitations, and the capabilities of our opponent’s defensive fire, we consider the pursuit curve a poor attack at best, when using the 20mm cannon. If does not matter whether we are in an overhead, a high-side or an underside attack. The problem now is, how are we going to attack a non-maneuvering target if we do not choose to use the pursuit curve as illustrated previously. The solution we propose: Plan an attack in which we combine the characteristics of the pursuit curve and the collision course. To explain: On a collision course attack, the target will be allowed to fly right through our bullet stream. The bullet stream itself will have no angular velocity as generated in a pursuit curve type attack. A 100- foot target with a speed of 800 feet per second, at 30,000 feet will require approximately 1 ∕ 8 of a second to fly through our bullet stream. Assuming that we can fire 6,000 round per minute – the combined rate of fire of 4 M-39 cannon – this means we fire at a rate of approximately 100 round per second. If the target requires 1 ∕ 8 of a second to pass through our bullet stream, we can expect about 12 hits it we set up a perfect attack. This is not acceptable. In a pursuit curve attack, we do not have this problem, because the angular velocity of our bullet stream matches the angular velocity of our target. In other words, our bullet stream is constantly superimposed against the target which is being tracked. The only disadvantage of this attack is that it forces us into our opponent’s defensive cone of fire. To counter the disadvantages of the pursuit curve and the collision course, we assume attack conditions against an imaginary target and apply them against a real target. To illustrate: We set up an attack so that the angular velocity of our bullet stream matches that of a target going slower than .8 Mach – say .5 Mach. This allows us to fire at a higher angle off, at a given range, because of the slower target. Then we apply this imaginary attack – against a .5-Mach target – to the .8-Mach target. To do this, we place our reticle in front of the .8-mach target, generating the G necessary to track a .5-Mach target which means our real target (.8) closes upon our bullet stream (.5) with a delta Mach of .3 which, at 30,000 feet, is 300 feet per second. Firing 100 rounds per second, this allows us to put approximately 33 holes in the target with a perfect pass, as compared to 12 in a collision course. Our only requirement is to figure the amount of lead necessary, when firing. To determine lead, we need to know three components; 1. Lead for target motion 2. Lead for gravity drop. 3. Trajectory shift. If we use a fixed sight, we will have to determine all three components. If we use radar, or keep the sight pegged at the range from which we plan to fire, gravity drop and trajectory shift will be completely computed and lead for target motion partially computed. We’ll use pegged sight, to simplify our lead problem. Radar is not applicable because the overhead needed to set up the attack takes us out of our radar tracking cone.

To determine the additional lead we need to enable our pegged sight to indicate the bullet impact area, we use the following formula:

${\text{Lead}}={\frac {V_{t}\cdot \sin(\theta )\cdot 1000}{V_{p}}}$

Where

Vt = rate of closure of the target, in feet per second toward the bullet stream
Sinθ = Sine of the angle-off
Vp = average projectile velocity (dynamic gravity drop tables)
Lead = additional lead in mils

The lead in mils which we acquire from the above formula is placed in the sight reticle, so that the outer diamond indicates the bullet impact area as the target passes through the reticle. To compute the lead for insertion into out sight reticle we use the following formula:

${\frac {WS}{\text{Firing Range}}}={\frac {2\times {\text{Lead in mils}}}{1000}}$

In order to solve for both additional lead and reticle size, we need to know the firing range and the angle-off at which we’ll be firing. Assume that we attack a target which is traveling 0.8 Mach (at 35,000 feet) at .09 Mach with 3 Gr.

Step I

To find the firing range and angle-off, we assume a 0.5-Mach target and solve in the following manner: At 35,000’,

Vf = 0.9 Mach
VT = 0.5 Mach
N=3
θ = 30°, 25°, 20°

$S={\frac {V_{f}\cdot V_{t}\cdot \sin(\theta )}{32.2}}$ $=$ ${\frac {873\cdot 485\cdot \sin(\theta )}{96.6}}=4380\sin(\theta )$

At 30° S = 4380 (0.5) = 2190’
At 25° S = 4380 (0.423) = 1850’
At 20° S = 4380 (0.342) = 1500

Step II

To find the additional lead (in mils) needed against a 0.8 Mach target we solve in the following manner:

$l={\frac {V_{t}\cdot \sin(\theta )\cdot 1000}{V_{p}}}$
At 30°
$l={\frac {291\times 0.5\times 1000}{3840}}=38{\text{ mils}}$
At 25°
$l={\frac {291\times 0.423\times 1000}{3840}}=32{\text{ mils}}$
At 20°
$l={\frac {291\times 0.342\times 1000}{3840}}=25.5{\text{ mils}}$

Step III

To determine the additional lead to be incorporated into the sight reticle we solve in the following manner:

At 30° angle-off

$WS\times {\text{Firing Range}}={\frac {2\times {\text{lead in mils}}}{1000}}$
${\frac {WS}{2190}}={\frac {76}{1000}}$
WS = 166

At 25° angle-off

${\frac {WS}{1850}}={\frac {64}{1000}}$ WS = 118

At 20° angle-off

${\frac {WS}{1500}}={\frac {51}{1000}}$ WS = 76

From Step III we can see that it will be impossible to set up the additional lead by placing the wingspan lever on 166 since 120 is the maximum setting. This means that we can either fire at 1850’, 25° angle-off (steps I and II with the wingspan lever at 118) or at 1500’, 20° angle-off with the wingspan lever at 76. Since we want to fire at max angle-off, we’ll set the wingspan lever at 118 and fire at 1850’, 25° angle-off.

Now to perform the attack. We do not use the conventional pursuit curve approach, as this does not allow us to determine target speed and direction, and we need these factors to apply the attack we have just computed. To apply this attack correctly, we use a barrel-roll type of attack. To set it up, we fly in the same direction as the target and about 3,000 to 4,000 feet above it. From there we turn about 10° from his line of flight, barrel-roll — in the direction of the turn - down to a key point, trying to maintain an almost constant angular relationship between us and the target. See figure 15. From here, we place the sight reticle well out in front of the target, in line with his flight path, and pull the G necessary to track the imaginary target. As we close to our firing range and angle-off, the target will move toward our sight reticle. As the target starts to cross the outer diamond, we depress the gun trigger and hold it down until the tail of the target passes through the outer diamond. From there we recover and set up another attack by kicking in afterburner and rolling back to the same position on top of the target.

This attack has definite advantages: It allows the attacker to fire at a higher angle-off than in a pure pursuit curve attack. It allows the attacker to fly through the target’s defensive cone of fire at a faster rate than is possible in a normal pursuit curve attack. Since he is flying a combination of a pursuit curve and a collision course, another and probably the most important advantage is that the attacker finds it easy to reposition himself for consecutive attacks. This is possible because the attacker is always close enough to the target to judge relative positioning. The big disadvantage of the barrel-roll attack – as we employ it – is that it provides the attacker less time for lethal fire. However, in view of the fact that a fighter can perform more consecutive attacks than in a normal pursuit curve, this disadvantage does not appear to be too restrictive.

In summary, we do not advocate the barrel-roll attack as a cure-all for fire control problems encountered when firing against bomber-type aircraft. Instead, we consider it somewhat of a “Rube Goldberg” affair designed to surmount the problems associated with today’s normal pursuit curve attack, when using guns as the means for ordnance delivery. Although it appears difficult to perform, pilots are able, with just a minimum of practice, to set themselves up quite successfully.

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Underside Attack -- Maneuvering for the Attack