Hello everyone!

Our Early Access program for Bodenplatte begun recently with its first two aircraft become available - the Bf-109 G-14 and Spitfire Mk.IXe. They both have unique features – the G-14 has a water-methanol mixture injection system MW 50, and for the Spit has an optional G.G.S Mk. IID gyro gunsight. Many virtual pilots were surprised with the accuracy that can be achieved using it. Positive user feedback and their interest in this device and how it works motivated us to write this extensive description of how it works and what difficulties we had to overcome modeling it in the sim. It is also useful as a guide on how to use it in combat.

Let's see an overview of why this device was developed in reality. Obviously, shooting accuracy is paramount in an aerial engagement, that's why future fighter pilots spent a lot of time improving their gunnery skills. First, cadets learned the theory of estimating the deflection required to hit a moving target and then they practiced in it by attacking an aerial target. In the middle of the last century, they usually practiced on a towed fabric cone that was attached to another aircraft using a long cable. These cones were usually towed by low-speed aircraft that didn't attempt sharp maneuvers, so a fighter trainee could plan his attack conveniently. Of course, this led to a dramatic decrease in shooting accuracy when new pilots encountered a real enemy instead of fabric cones. Even Winston Churchill, himself noticed this problem in 1939. An average fighter pilot often chose a much smaller deflection than was required. Bomber gunners had the same difficulties in hitting enemy fighters.

As the result of this, the engineers of several countries were assigned a difficult task to make a gunsight that took the guesswork out of shooting. Eventually, the British found the most elegant, dependable solution that was quite effective - 

the gyro gunsight, namely the G.G.S Mk. II. C (for turrets) or D (for fighters). Later they were copied with minimal changes by American engineers and were named Mk.18 and K-14A gunsights.

Let's divide the following description into the following parts for easier understanding:

1. Gunsight construction;
2. How the target deflection is calculated;
3. Dynamic processes that happen in the gunsight during its work.

Gunsight construction

We begin the work on any aircraft or its instruments with a search for its technical documentation. As the main source for modeling G.G.S Mk. IID we chose the manual for its American counterpart then K-14A since it was the most complete description of such a gyro gunsight we could obtain by the required date. Their cores are the same. If someone has the original manual for G.G.S Mk. IID or have this gunsight itself in a working condition, please contact us to clarify the remaining questions we have for the British version of this gunsight.

Ok, let's take a look at the main parts of K-14A gunsight shown in Pictures 1 and 2.

Immediately we can see that it is a twin gunsight: there are two reticles on the reflecting glass, each one projected by its own optical system, the distance between them is close to user inter-pupil distance. Each eye could see only one reticle, so if a pilot moved his head to either side far enough, he could see the first mark disappear and then another. We wanted to model this peculiarity too, but it is impossible to show this behavior on a flat monitor and while in VR we run into graphics engine limitations. Therefore, we have decided to omit this feature in spite of wanting to have it for the sake of completion.

The reticle visible by the left eye is fixed, it is projected by a regular collimator system. It serves as a backup sight in case of gyro system failure or for firing in a head-on attack, setting up the gunsight and zeroing in the guns on the ground.

The second reticle is much more interesting - as you can see on the drawings, its position on the reflecting glass depends on the angle between the moving mirror and the gunsight lateral axis (Picture 3). This mirror is attached to the gyro rotor that has three degrees of freedom. The aluminum hemisphere of the rotor rotates in the magnetic field created by inductance coils, so the angle of the mirror is controlled by these magnetic fields (Pictures 4 and 5). These processes are shown in detail in the third part of this article.

Pictures 3, 4 and 5.

In addition to the fact that the second reticle is movable, it also serves as an optical rangefinder. There are two sets of slits that rotate independently of each other (Picture 6). The resulting openings form an image of the reticle of a variable size. The set with straight slits is controlled by the target base knob (that can be adjusted to set the size of a target) while the set with curved slits is controlled by the target distance knob. When a pilot changes the target base (wingspan), straight slits move along the curved slits and the visible reticle mark changes its size and slightly rotates at the same time. On the other hand, when you adjust the distance, only the curved slits move and you see that only the size of the reticle is changing without rotation.

Picture 6.

Let's see how the optical rangefinder works (Pictures 7 and 8). Our target will be a Bf 109 G-6 fighter, its target base is roughly 32 feet. We'll place it at the point C on our scheme, 400 yards away from the pilot eye (point O). Let's draw a circle around the target and then draw a cone with its apex at O and its base at that circle. The angular opening of the cone depends on the distance between the target and the eye and also on the target base circle, this angular opening is called the angular size of the target. If the target base remains the same, the angular size of the target will decrease as C-O distance increases.

Pictures 7 and 8.

To a human eye, different objects that have the same angular sizes appear to be the same size. For example, a coin you hold in a stretched-out hand would appear to have the same size as the Moon. The optical rangefinder is based on this principle. It should be noted that collimator sights have an important characteristic - the angular size of the visible reticle depends on the optical system and almost doesn't depend on the distance between the user eye and the reflecting mirror, so it's not required to keep your head in a certain position. As we saw above, the resulting size of the gyro reticle mark in K-14A gunsight is adjustable, so a user can adjust the size of the mark to be the same as the visible target size (the Bf 109 G-6 wingspan positioned at 400 yards). If a pilot identified the type of the target and set the target base correctly, adjusting the size of the reticle mark to be the same as the visible target size results in the precise measuring of the distance to the target.

It should be noted that exact match between the reticle size and the target wingspan is possible if you look at the target directly from the front, back, above or below. In other cases, the angular size of the target wingspan will be less than the size of the reticle because of the obvious geometrical reasons. The rules of correction while determining the distance to target are shown on Picture 9.

Picture 9.

The maximum angular size of the gyro reticle that can be set on this gunsight corresponds to a target with 120 feet base positioned at 300 yards. The target distance knob has the range of 200-800 yards, so if you set the target base knob to its maximum value of 120 feet and rotate the target distance knob to lower the distance, the visible reticle mark won't increase in size beyond 300 yards, but the set distance will be taken into account correctly. For the gunsight to function correctly in such circumstances, there is a coil spring link between the distance knob and the gears that control the slit sets. When the slit sets reach their limit, the coil spring stretches, allowing a pilot to adjust the knob further. As long as the distance know is set to less than 300 yards, the coil spring will remain stretched, pushing the slit set to its stop. If the target base knob is set to less than 120 feet, the slit set limit will also decrease (the mechanical stop is linked to the current angular position of the slit set).

Calculating the Deflection

The exact method of calculating the required deflection that has been used in K-14A construction is missing in all sources we could find. Nevertheless, after analyzing its manual and its internal construction we devised a method which is close to the original one as possible even if it doesn't correspond to it completely.

According to the manual, for a correct deflection to be calculated you need to keep the target inside the moving mark for at least 1 second, simultaneously correcting the set distance if needed (it goes without saying that the target base needs to be correctly set before). In short, you need to lead the target with the gunsight for some short time.

So, let's imagine we engaging that unlucky Bf 109 G-6 again: it flies in a more or less steady turn at some distance ahead of our fighter. We assume that you already identified the target and set the correct target base (Picture 10).

Picture 10.

To understand the principles of calculating the correct deflection, let's inverse this task and simplify it:

1. A pilot leads the target for the required time, the deflection is calculated already and the aiming line is positioned so when we fire the guns we hit the target 100%;
2. We disregard the gravitation that affects the flight of the projectiles;
3. Own aircraft is in the center of the target aircraft turn when it shoots;
4.  After firing, a pilot continues to lead the target until the projectiles hit and the deflection change during this time is negligible.

The point of inverting the task is to express the calculated deflection as a function of some dynamic characteristics or parameters we can measure before firing.

Let's take a look at the schematic that shows the target trajectory it travels between the time the shot is fired and the time of the hit. We'll draw the visible target line that goes through the center of the moving reticle and the aiming line that goes through the center of the stationary reticle (at the moment of firing). The angle between these lines is the deflection angle calculated by the gunsight. Also, the aiming line corresponds to the lateral axis of the firing aircraft.

The first conclusion we can make in this simplified task is that all dynamic processes in this system happen in the plane of the target aircraft turn. It is also apparent that while the projectile is in flight the direction of the target speed vector will change exactly by the pre-fire deflection angle. Since a pilot with the gyro gunsight continues to lead the target and during the time of firing his own aircraft was located in the center of the target aircraft turn, the aiming line rotates by roughly the same angle while the projectile is in flight. Therefore, we can conclude that the angular speeds of both aircraft are roughly the same.

From kinematics, we know that an object that rotates around a fixed center with a constant angular speed, in a given time rotates to the angle which can be calculated by multiplying the angular speed by the time. If we apply this to our situation, we can say that the deflection angle can be calculated by multiplying the angular target speed by the time of projectile flight. Considering our above simplifications, we can replace the angular target speed with the angular speed of your own aircraft, allowing us to solve this task: we can determine all the required data before firing to calculate a correct deflection angle. That's right: the time of the projectile flight can be calculated from ballistics tables if we know the target distance while the angular speed of the own aircraft is the same as the angular speed of the gunsight itself, naturally.

This solution may seem rough since we have made several simplifications for the inverted task. However, in a sustained turn when you pursue your target, your trajectories are approximately the same and these simplifications can be considered negligible. It should be also noted that the gunsight doesn't have any additional data from the outside world: only the distance to target, target base and the angular speed of the gunsight itself. Therefore, this solution is the only one possible with this limited amount of data available.

To understand the working principles of the gunsight fully, we need to find out how a ballistic table can be 'hidden' in its construction and how the angular speed of the gunsight can be converted into the corresponding angle between the lateral axis of the gunsight and the rotating mirror to show the moving reticle in a correct place.

Dynamic Processes in the Gyro Assembly

In the gunsight construction overview, we have noted that the mirror is attached to the rotor of the gyro that has three degrees of freedom (it is actually a part of the rotor) which rotates in the magnetic field. There is an aluminum hemisphere on the other side of the rotor. The rotor is balanced in relation to its gimbal suspension. Let's find out what processes happen in this electro-mechanical system.

To make the explanation simpler, let's imagine that the hemisphere is replaced with a flat part and all electromagnets except one (that is located at some distance from the rotor axis) are removed. When a conducting material moves in a magnetic field, vortex Foucault currents (eddy currents) are generated in it and their strength is proportional to the speed of this movement. If a thin disk made from conducting material rotates in the magnetic field of a single electromagnet, Foucault currents in it look like shown in Picture 11 These generated currents interact with the magnetic field, inducing the Lorentz force that is distributed along the disk surface the current flows through. The total Lorentz force is located in point A and is directed in the way to slow the disk rotation: modern magnetic brakes work using this principle. The gyro motor compensates for this slowing motion, keeping the RPM constant. It's important that Lorentz force is in direct proportion to the distance between the rotating axis of the rotor and point A: the further from the disk center, the linear speed of rotation is higher and the Foucault currents there are stronger.

Note that the point of application of the Lorentz force is located at some distance from the center of the gimbal suspension (point O), which creates the moment of force resulting in precession: rotor axis starts to change its position according to Picture 12 It looks like the rotating axis is drawn to the center of the electromagnet (the axis 'tries' to move through the point A and nullify Lorentz force and the created moment).

Pictures 11 and 12.

If we add another electromagnet from the opposite side of the rotating axis, the resulting moments of Lorentz force will compensate each other and the gyro rotor will remain right in the middle between the electromagnets. An interesting effect will happen if we start to rotate both electromagnets in a circle in OA1A2 plane as shown in Picture 13. The distance from one electromagnet to the rotor axis will increase while the distance from another electromagnet to the rotor axis will decrease and the moments of Lorentz force will no longer compensate each other. The total precessional moment will be directed in such a way so the rotor axis will precess towards the electromagnet that moves away. The angular misalignment between the center of the magnetic system and the rotor axis will build up until the speed of precession will reach the speed of the rotation of the electromagnets around the point O. The dependence between the value of the angular misalignment and the rotation speed can be considered linear with high accuracy.

Picture 13.

The system of four electromagnets and hemispheric rotor in the K-14A gyro gunsight operates on the same principles. Such system makes the rotor behave like described above for any orientation of the magnetic system rotation in 3D space while hemispherical rotor improves the linearity of the dependence. When your own aircraft and its gunsight enter a turn, the electromagnets attached to the gunsight body change their positions in relation to the rotating gyro, inducing its precession. The accumulated angular misalignment moves the rotating mirror in such a way so it shows the required deflection using a given distance to the gunsight user.

But how the distance knob influences the position of the gyro reticle? The distance to the target is regulated by the electric current that flows through the electromagnetic coils, and the dependence is quadratic: both the magnetic field strength and Foucault currents strength in the rotor depend on the amperage in electromagnetic coils. The distance knob controls the adjustable resistor that regulates that amperage.

It is somewhat ironic (or genial) that one of the keystones of the gunsight function is right there, in front of your eyes - the distance scale on the knob is non-linear (Picture 14). Thanks to this non-linearity, the gunsight takes into account the values from the ballistic table for projectiles and also the fact that the dependence between distance and amperage is quadratic. The target base knob also has a non-linear scale (Picture 15) and this is also required for the gunsight to function properly.

Pictures 14 and 15.

We attempted to model the gunsight with all its peculiarities described above, to have all the authentic transient responses and micro-dynamic movement of the gyro reticle, so the mathematical model of the rotor with the hemispherical dome that rotates in the magnetic field of four electromagnets has been created. The angular displacement of the rotor follows the vector differential equations which take into account all the described physical values and processes.

The only noticeable simplification that was dictated by the performance reasons is that the gyro movement between the electromagnets is limited by a pyramidal space instead of a cone, because of this the gyro reticle has square limits instead of circular ones. In the future, we may find a way to model the conical limit without an additional performance impact. Moreover, since Spit IX release with this gyro gunsight in update 3.003 we have improved the modeling of the influence of the tension in the gimbal suspension on the dynamics of the entire system. This peculiarity which pushes the virtual gunsight even closer to the real thing will be published in one of the coming updates.

In conclusion, we would like to point out that G.G.S. Mk.II D gyro gunsight has been created by the best British engineers of that time and it is unlikely that a modern engineer team could make such a device without using computers at all. Its final design that amuses any engineer has been developed for several years with many experiments, trials and errors on the way. We did our best to reconstruct its design and give you the feeling of operating a real, 'live' instrument.

To mix the nice visuals in the hard science of the today's blog, here are the first in-game shots of the two new planes.

First of them is German fighter/attack plane Fw 190 A-8/F-8 which is part of Bodenplatte planeset. Thanks to its array of modifications it's going to be two planes in one - both the fighter and attack variants. We plan to release it for all Bodenplatte owners in the next update.

The second aircraft is in development and will be ready this Autumn - Po-2VS Collector Plane, the legendary multipurpose (recon, liaison, ambulance, night bomber, psychological warfare) plane of the Eastern front that will have higher fidelity (4K) textures by default.