# Bullet stabilization

G center of mass,
c aerodynamic center, a current tangent of the flight path, b longitudinal axis, F air force

In ballistics, bullet stabilization means stabilizing the trajectory of bullets . In the earth's atmosphere , projectiles are subject to air resistance , which limits their range. Elongated bodies (e.g. long projectiles ) have a lower air resistance than spherical ones (e.g. cannon balls ) with the same mass , but without stabilization they get into violent spin movements during flight, which has a strong negative influence on the direction and distance of flight. The reason for this is that gravity acts on the projectile and the center of mass is usually below the aerodynamic center , which means that the projectile lowers at the back and rises at the front until it overturns. Stabilization can be achieved through various measures.

## Twist stabilization

0: center of gravity, 1: longitudinal axis, 2: direction of flight, Ψ: angle of attack, 3: nutation, 4: precession

With twist stabilization , also known as rotation stabilization, the bullet is stabilized by rotating around the longitudinal axis . If the bullet is set in rotation around its longitudinal axis, it behaves like a top and what has a stabilizing effect due to the gyroscopic effect (see top theory # twist stabilization ). If the angular velocity is large enough, the angular momentum vector lies in the longitudinal axis. The orientation of the axis of rotation initially remains unchanged because of its twist (conservation of angular momentum). The angular momentum leads to a gyratory motion, the precession , which turns the tip of the bullet around the axis of motion. The precession is superimposed by faster and smaller movements, the nutation . Nutation is caused by small disturbances in flight, e.g. B. by uneven acceleration due to propellant gases when leaving the mouth. As a rule, the nutation fades slowly in flight. The superposition of the two movements cause the bullet tip to move in cycloid trajectories.

The precession creates an angle of attack which , together with the air resistance, leads to a buoyancy of the projectile below its tip. The buoyancy is not constant; it changes depending on how the angle of attack is to the flight path. The abrasion generates a torque to one side depending on the direction of rotation; right twist to the right. This ultimately causes an increasing lateral deviation from the rail tangent.

There are other forces at work, above all the Magnus effect , which works contrary to precession. These additional forces generally only have an insignificant influence on the twist stabilization.

In the case of projectiles, the precession frequency is somewhat around one revolution per second, so it is often greater than the flight time, which for artillery guns averages around 20 seconds.

### obedience

The speed of rotation and thus the stability of the bullet must be adapted to the application. As a rule, the longitudinal axis of the bullet should follow the ballistic curve , ie always fly with the tip first. An insufficiently stabilized projectile will go into a tailspin; an over-stabilized projectile, on the other hand, will retain its longitudinal axis and hit the ground laterally. An important parameter here is the starting angle of the ballistic curve. Thus, a projectile may start at a low angle ( direct shot or flat fire) stabilized and be obedient, at a high starting angle ( angle fire ) it is, however, over and stabilizes the ballistic curve may not follow more.

### Swirl generation

Trains and fields in a 9 mm pistol seen in the direction of fire

There are different ways to generate the twist. Basically, a distinction is made between the generation of twist during launch and in flight. For most gun that happens over in the run helically cut features . The speed of rotation is between 20,000 and 180,000 / min, depending on the caliber. Small caliber bullets rotate faster than large caliber bullets.

In the case of a spear , the twist can be created by a short roll strap that is wrapped around the shaft. When throwing the thrower holds the sling in his hand, the sling unwinds and sets the spear in rotation.

In flight, the twist can be generated with the help of air resistance. This is done through oblique holes at the top or through oblique fletching .

In the case of propelled projectiles such as rockets , the twist can be generated with inclined nozzles .

### steering

During the Second World War, the Ruhrstahl X-4 was developed as a future- oriented guided missile . Guided missiles that work according to this principle are made to rotate aerodynamically (e.g. via appropriately shaped guide surfaces) and thus stabilized in flight. The steering takes place via spoilers on the control surfaces. These spoilers can vibrate according to the speed of rotation of the guided missile. The control signals (right / left and up / down) are converted into control pulses by means of a control unit. A gyroscope supplies the control unit with the current rotational position; the control unit can therefore deflect the corresponding spoilers in the corresponding direction. The stabilization by means of rotation was easier to implement despite the more complex steering compared to a twistless stabilization because the demands on manufacturing tolerances were far less high, which simplified mass production .

## Twistless stabilization

Bullets without a twist are stabilized by the air force generated by the air resistance. The bullet achieves stability when the aerodynamic center is behind the center of mass. The bullet keeps settling on the trajectory and follows it with its nose ahead. A lateral deviation as with the twist stabilization does not exist. Twistless stabilization can be achieved constructively by the following measures:

• Arrow stabilization: The center of gravity is shifted forward through the distribution of mass. (e.g. firework rocket , Congreve rocket )
• The air attack point is shifted backwards through the use of air force at the rear.
• Wing stabilization: Stabilization is provided by the tail unit at the rear. The tail unit is available in two versions; as a wing control unit with lateral control surfaces and as a ring tail unit. The wing stabilization is mostly used for strongly curved flight paths and / or at low initial speeds. (e.g. mortar shells , rifle grenades and rocket weapons ).
• Resistance stabilization: permanent increase in air resistance at the rear (e.g. blowpipe arrow )

Wing stabilization is most commonly used in technology.

## literature

• R. Böhm: The German Guns 1939-1945. Edited by FM von Senger and Etterlin . Bechtermünz, Augsburg 2002, ISBN 3-8289-0524-2 , p. 18.
• C. Cranz : Textbook of Ballistics. Teubner, Leipzig et al
• Volume 1: External ballistics or theory of the movement of the projectile from the muzzle of the weapon to penetration into the target. 1910;
• Volume 2: Internal Ballistics. The movement of the projectile through the barrel and its accompanying phenomenon. 1926;
• Volume 3: Experimental ballistics or teaching of the ballistic measurement and observation methods. 1913;
• Volume 4: Atlas for tables, diagrams and photographic snapshots. 1910.
• Jürgen Gebauer, Egon Krenz: Marine Encyclopedia. 2nd revised edition. Brandenburgisches Verlags-Haus, Berlin 1998, ISBN 3-89488078-3 , p. 194, p. 296.

## Individual evidence

1. a b c
2. ^ A b c d Heinz Dathan: Weapon theory for the Bundeswehr. (4th revised edition), Mittler & Sohn Verlag , 1980, ISBN 3-87599-040-4 , pp. 41–45
3. a b Beat Kneubuehl (ed.), Robin Coupland, Markus Rothschild , Michael Thali: Wundballistik. Basics and Applications. 3. Edition. Springer Medizin Verlag, 2008, ISBN 978-3-540-79008-2 . Pp. 78–79 [1]
4. Karl Sellier, Beat P. Kneubuehl : Wound ballistics and their ballistic basics. 2nd completely revised and expanded edition. Springer, Berlin et al. 2001, ISBN 3-540-66604-4 , pp. 142-146. [2]
5. ^ A b Mark Denny: Their Arrows Will Darken the Sun: The Evolution and Science of Ballistics , Johns Hopkins University Press , 2011, ISBN 9780801899812 , pp. 110–117 [3]
6. ^ A b c Robert Wichard Pohl : Introduction to mechanics, acoustics and heat theory , Springer-Verlag , 1942, p. 84 [4]
7. Hans-Hermann Kritzinger, Friedrich Stuhlmann (Ed.): Artillery and Ballistics in Key Words Springer-Verlag , 1939 ISBN 9783642907944 , pp. 108-109 [5]
8. ^ A b Max Dreger: Waffensammlung Dreger: With an introduction to the systematics of weapons , Verlag Walter de Gruyter , 1926, ISBN 9783111401676 , p. 68 [6]
9. Thomas Enke: Landmines and ammunition in crisis areas: Safety manual for emergency and auxiliary forces , Walhalla Fachverlag , 2017 ISBN 9783802944956 , p. 50 [7]
10. ^ Bill Gunston: The Illustrated Encyclopedia of Rockets and Missiles , Salamander Books Ltd, 1979, pp. 212-213, 239
11. ^ Ian Hogg: German Secret Weapons of the Secret World War: The Missiles, Rockets, Weapons & New Technology of the Third Reich , Verlag Frontline Books, 2015, ISBN 9781473877672 , p. 53 [8]