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An Estimation of the Recoil of the Main Centerline Gun on the Galley |

Reexamination of the Recoil in order not to Kill the Sixteenth Century Galley Crew |

The maximum muzzle velocity |

on the Galley

The main centerline gun of the galley is on the bow where is so small space. This is 52-55 pounder weighing 5,500 pounds and the length is longer than 4 m.
I doubt whether such big gun could be safely operated by the gunners in the small space. There is little knowledge about the main centerline gun. However, it is known that the gun barrel is installed in the wooden box and the box is in the track. The recoil is restrained by the friction between this box and the track and the tension of the breeching rope. I estimated the main centerline gun how to move after shooting. |

According to action-reaction low

On the otherhand, the velocity

Since the gun in the wooden box is being decelarated by friction between the wooden box and track,

: the coefficient of kinetic friction

*g* : gravitational accelaration coefficient

Therefore, the velocity

Then, the energy of the gun carrage is described as next equation.

These figures indicate that the recoil distance without breeching is 3.4 m for

The initial kinetic energy of the gun barrel is 17,000 J at

When a force

Therefore, if we know the relation between the tension of the rope and stretch length, the energy can be calculated.

At the age of the Battle of Lepanto, hemp or Manila ropes were used.

There is little data about these ropes. But I found the data about a 20mm diameter Manila rope

force(kg) | force(N) | stretch(%) |

0 | 0 | 0 |

150 | 1470 | 5 |

1000 | 9800 | 15 |

2750 | 26950 | break |

As shown in this table, the stretch length is not linearly proportional to the force. This means that the stretched rope longer than several percent is not in the elastic region but in the plastic region. (Young's modulus of the hemp rope is 32 GPa

So, I made a following second order approximation equation using these numerical data.

The curve made by this equation is shown in the following figure. In this figure, the stretch at the breaking point is an estimated value.

Since the equation 9 is for the 20 mm diameter rope, the equation for ropes with the diameter

Therefore, using equation 8, the energy of the rope is as follows.

According to "The Arming and Fitting of English Ships of War 1600-1815", "Normally a breech rope was three times the length of the gun." "Each end of this thick piece of rope was fitted by means of an eye-splice to a ringbolt on the side of the ship, either side of the gun. The rope passed through eyebolts on each side of the gun, and was spliced to the button of the cascable."

In the case of the galley, there is no reason to recoil the gun for reloading.

Therefore, the length of the breeching rope is not required to be so long. I think that the shortest breeching rope is the most reasonable in order to operate the gun on the small space deck on the galley. Because the distance between the trunnions and the breech is about 2 m, the shortest rope length would be about 5 m.

I calculated the relation between the energy and the stretch length of the ropes with various diameter from 20 mm to 100 mm using equation 11. The calculated result is shown in the following figure.

This figure shows that the thicker rope is shorter stretch length.

The next figure is the dependency of the stretch length on the diameter of the rope where the cannonball velocities are 1,800 ft/s (

This result indicates that 15% stretch ( 40% of breaking strain ) requires diameter of 50-70 mm (circumference of 6-9 inches).

According to "The Arming and Fitting of English Ships of War 1600-1815", "it was said that a 32-pounder gun (without breeching) with a normal charge on a level platform would recoil 11 ft."

Of course, the 32-pouder gun is on the carrage with trucks. So, my calculation results are a little longer. This means that the coefficient of kinetic friction of 0.2 I used might be too small.

In order to restrain this recoil action, a very thick rope with the circumference of 6-9 inches is needed. By using these thick ropes, the recoil distance restrained shorter than 40 cm (= 5 m x 0.15 / 2). However, the stretch length of 15% is equivalent to the 40 % of breaking strain and is not in the elastic region but in the plastic region.

Therefore, the several times of firing might break the breeching rope.

I think that the operation of the gun on the galley must have been very dangerous!!

But then, neither Robert Hook nor Isaac Newton were born in 16 th century. Such dangerous situation might be not surprising.

2)Brian Lavery: The Arming and Fitting of English Ships of War 1600-1815, p139 (2000) Conway Maritime Press

3)ibid p141

4)Sailing Smacks-Rope:http://www.alberta-ck318.freeserve.co.uk/rope.htm#manila20

5)Ropes:http://www-materials.eng.cam.ac.uk/mpsite/short/OCR/ropes/default.html

6)Private comminucation from Prof. Dr. John Francis Guilmartin, Jr.

the Sixteenth Century Galley Crew

I used several assumed values in the above estimation. However, these values lack sufficient basis. Therefore, I will try to modify them in order not to kill the sixteenth century galley crew.

The shooting range

The height of the gun would be reasonable to be about 1.5 m.

The calculated results are shown in the following table.

velocity (ft/s) | range (m) |

1,800 | 299 |

1,200 | 199 |

The dash speed of the galleys is about 7 knots. When the galley is oared with full speed, it takes about a minute for 200-300 m. It means that there is no time for reloading the gun. Therefore the extremely strong rope might have not been needed.

I calculated the dependency of the recoil distance on the coefficient of kinetic friction.

The calculated result is shown in the following figure.

I think that the recoil distance of the main centerline gun without breeching would be around 1 m from the recoil of the British 32-pounder

Because the coefficient of static friction is less than the coefficient of static friction (Amontons-Coulomb's Low), the coefficient of kinetic friction must be less than 0.5. So, the initial velocity of 1,200 ft/s, recoil distance of 1.4 m and the coefficient of kinetic friction of 0.5 are considered to be reasonable.

In these conditions, the velocity and the energy of the gun barrel is shown in the following figure.

I calculated the energies in the case of the rope length of 5 m (Case A) and in another case of the rope length of 6 m (Case B). In the Case B, the gun barrel is restrained in the first stage up to 50 cm of the recoil only by the frictional force, then reatrained by the sum of the frictional force and the tensile stress of the rope.

The calculated result is shown in the following figures.

Case A : rope length = 5 m |
Case B : rope length = 6 m
Up to 50 cm restrained only by friction and then restrained by the friction and rope tension. |

The energy at the strech=0 in the Case B is the energy caused by the frictional force for the initial sliding distance of 50cm. That is 16,700-10,600=6,100 J .

The relations between the rope stretch and the rope diameter which are obtained from above two figures are shown in the following figure.

The safety factor of the rope is normally selected between 12:1(8% of breaking force) and 6:1(16%) in present day

If we select the safety factor of 6:1, the rope diameter of 80 mm is required in the Case A, and the diameter of 50 mm in the Case B. Although, the 80 mm diameter is too thick at this age, 50 mm (circumference of 6.2 inches) would be reasonable.

In the Case B using 50 mm diameter rope, the recoil distance is 0.5+6x0.09/2 = 0.77 m.

The kinetic energy of the gun barrel in this case is shown in the following figure.

The diameter of the breeching rope: 50 mm
The length of the breeching rope: 6 m The energy decreases up to 50cm by the friction of wood on wood. Longer than 50 cm, the energy is absorbed by the sum of the friction and the tension of the breeching. |

If they used a 6 m long rope and up to 50 cm recoil was restrained only by the frictional force then restrained by the sum of the frictional force and the tensile stress of the rope, the 6.2 inches circumference rope could be used in the safety factor 6:1. In this condition, the repetitive firing would be possible and the recoil distance would be only 77 cm.

No trouble !!

On the otherhand, the track length is considered to be nearly equal to the length of the raised fighting platform above the guns. This length is about ten feets

I decided to search for the maximum muzzle velocity in the condition using 50 mm diameter rope, with the safety factor of 6:1 under the recoil distance of 1 m.

The kinetic energy of the gun garrel in the case of the cannonball velocity of 1,600 ft/s is shown in the next figure.

The orange curve shows the energy where the rope length is 6 m and up to 50 cm recoil is restrained only by the frictional force then restrained by the sum of the frictional force and the tensile stress of the rope.

The tensile stress of the rope oversteps the safety factor 6:1 at the recoil distance of 80 cm.

The green curve shows the energy where the rope length is 6.4 m and up to 70 cm recoil is restrained only by the frictional force. In this condition, the gun stops at the distance of just 1 m and the tesile stress is not beyond the safety factor.

Therefore I conclude that the maximum muzzle velocity of the main centerline gun is 1,600 ft/s.

The shooting range becomes about 270 m.