Page:EB1911 - Volume 20.djvu/244

Rh ii. 𝑛S𝑛+1 denotes the shrinkage between the 𝑛𝑡ℎ and (𝑛 + 1)𝑡ℎ hoops.

Here M can be taken as 12,500 tons per square inch for gun steel. In the example already calculated the shrinkage between the jacket and barrel is 0·009 in.

S＝$2𝑟_{𝑛}⁄M$ 6·43 + 11·25 + $2𝑟_{𝑛}⁄M$(−11·25 + 3·4) ＝0·009 in.

In that portion of the gun in which wire is used in the construction, exactly the same principles are involved. It may be assumed that the tube on which the wire is wound is so large, in comparison to the thickness of the wire, that the compression of the concave surface of the wire and the extension of its convex surface may be neglected without

sensible error.

The greatest advantage is obtained from the wire coils when in the Firing Stress the tension T is uniform throughout the thickness of the wiring. The Firing Stress T in the wire may be as low as 25 tons per square inch and as high as 50 tons, but as the yielding strength of the wire is never less than 80 tons per square inch nor its breaking strength less than 90 tons, there is still an ample margin especially when it is remembered that the factor of safety is included in the calculation.

If the wire is wound direct on to the barrel and is covered by a jacket, 𝑟0, 𝑟1 being the radii in inches of the barrel, 𝑟1, 𝑟2 the radii of the internal and external layers of wire, and 𝑟2, 𝑟3 the radii of the jacket; then for the Firing Stress in the wire

or

By combining these the gunmakers’ formula for the wire is obtained

As T is to be uniform, when the gun is fired, the Initial Tensions of the wire are arranged accordingly, and the tensions at which the wire must be wound on to the guns have now to be determined.

It is assumed that M is uniform for the gun steel and wire.

Then

where

and

By means of these two equations and (9) the expression (11) becomes

where

To compare with the previous example, the stress for a 4·7-in. Q.F. wire gun will be calculated. This consists of a barrel, intermediate layer of wire and jacket.

Here 𝑟0＝2·5; 𝑟1＝3·75; 𝑟2＝5·5; 𝑟3＝7·5 inches; the firing tension T1 to T2 of the wire＝25 tons per square inch, suppose.

Take P0 = 21 tons per square inch and consider that the jacket fits tightly over the wire, but has no shrinkage. Then for the Firing Stress, from (2), P2＝2·25 tons, and from (9) and (10), T1(𝑟2-𝑟1) = P1𝑟1-P2𝑟2

P1＝14·97, say 15 tons;

from (4) we can obtain T0 and T2 since P0, P1 and P2 are known; from (3) T0 = 0·6 tons. T2 = 7·5 tons.

T′2＝−5·4 tons (a compression),

and

T3＝5·25 tons.

The Powder Stress is obtained in the same way as in the previous example, so also is the Initial Stress; therefore we may tabulate as follows:—

As the wire is wound on, the pressure of the external layers will compress those on the interior, thus producing an extension in the wire which is equivalent to a reduction in the winding tension of the particular layer at radius 𝑟 considered. If represents this reduction then ＝(𝑡) − , where

＝−$𝑟_{𝑛}^{2} − 𝑟_{𝑛}^{2}_{−1}⁄𝑟_{𝑛}^{2} + 𝑟_{𝑛}^{2}_{−1}$(𝑝)

At the interior layer of wire is the initial stress on the exterior of the barrel and the winding tension must commence at

＝ 11·875 + 18·525＝30·4 tons per square inch.

As the jacket is supposed to have no shrinkage T＝0 and consequently

＝(𝑡)＝17·5 tons per square inch.

These winding tensions can be found directly from formula (14) and then

E＝−149·875; F＝34·875; G＝264·875.

Sir G. Greenhill has put these formulas, both for the built-up and wire-wound guns, into an extremely neat and practical geometrical form, which can be used instead of the arithmetical processes; for these see Text-Book of Gunnery, Treatise of Service Ordnance, 1893, and Journal of the United States Artillery, vol. iv.

The longitudinal strength of the gun is very important especially at the breech end; along the forward portion of the gun the thickness of the barrel and the interlocking of the covering hoops provide ample strength, but at the breech special provision must be made. It is usual to provide for this by means of a strong breech piece or jacket in small guns or by both combined in large ones. Its amount is easily calculated on the hypothesis that the stress is uniformly distributed throughout the thickness of the breech piece, or jacket, or of both. If 𝑟0 is the largest radius of the gun chamber, 𝑟01 the radius of the obturator seating, 𝑟1 the external radius of the barrel, and P0 the maximum powder pressure, then, with the usual form of chamber adopted with guns fitted with obturation other than cartridge cases, there will be a longitudinal stress on the barrel at the breech end of the chamber due to the action of the pressure P0 on the rear slope of the chamber, of

$2 × 4·1⁄12,500$(𝑟02 − 𝑟012)P0 tons

this is resisted by the barrel of section $(4·1)^{2} − (2·5)^{2}⁄(4·1)^{2} + (2·5)^{2}$ (𝑟12−𝑟02) so that the resistance

R＝$𝑟_{2} − 𝑟_{1}⁄𝑟_{1}$ P0 tons.

This portion of the longitudinal stress is not of great importance as the breech end of the barrel is supported in all modern designs by the breech bush. In Q.F. guns, i.e. those firing cartridge cases, the breech end of the chamber has the largest diameter, and 𝑟0−𝑟01 so that there is no longitudinal stress on the chamber part of the barrel.

For the breech piece or outer tube of radii 𝑟1 and 𝑟2, the resistance

R＝$𝑟^{2} + 𝑟_{0}&#8202;^{2}⁄𝑟^{2} − 𝑟_{0}^{2}$ P0 tons for B.L. guns &numsp;＝$𝑟_{0}^{2}⁄𝑟^{2}$ P0 tons for Q.F. guns

If the longitudinal stress is taken by a jacket only, the resistance is found in the same way.

Generally for ordinary gun steel, the longitudinal stress on the material is always kept below 10 tons per square inch or 13 tons for nickel steel; but even with these low figures there is also included a factor of safety of 1·5 to 2. In large guns it is best to consider the jacket as an auxiliary aid only to longitudinal resistance, as, owing to the necessary connexions between it and the breech bush and its distance from the centre of pressure, there is a possibility that it may not be taking its proportionate share of the stress.

The thread of the breech screw and of the breech bush (or opening) must be so proportioned as to sustain the full pressure on the maximum obturator area; V or buttress shaped threads are always used as they are stronger than other forms, but V threads have the great advantage of centring the breech screw when under pressure.

In most modern B.L. guns fitted with de Bange obturation the