The proof certificate in manometrica
September 28th, 2009 Posted in internal Ballistics, cane manometrica, munitioning, reloading, tools
Cane example manometrica
In this article we will examine in the detail a proof certificate in cane manometrica (for munitions with metal case you destine to the ruled canes). As well as a short description of all the his sections, we will do particular reference to the meaning of the calculated parametres.
There exist different formats of the certificate of proof, we will examine what has seemed more complete to us. Like visible on the image to follow (Fig. 1), a test certificate is typically subdivided in four horizontal sections:
Fig. 1 - Example of certificate of proof in cane manometrica
Section 1 - the first section makes reference to the identified numbers of the State lottery of cartridges an object of the test. The cartridges producers are held to make tests to sample, be for the dimensional controls for which for the maximum exercise pressure. For the controls in manometrica, the normativeness foresees a sample of 20 blows for State lotteries up to 35.000 cartridges and of 30 samples for State lotteries up to 150.000 pieces. On sezione_1 of the certificate the general constitution of the munitions is described besides in proof: calibre, type of case, typology and quantity of dust, type of ogive, OAL of the cartridge and type of trigger.
Section 2 - the second section brings back the characteristics of the cane manometrica used: possible identificativo and length of the same one. There are indicated besides the environmental conditions in which the test is carried out in terms of: barometric pressure, temperature and relative dampness. It closes it sezione_2 a legend minimimes for the interpretation of the prominent parametres.
We will find:
- TC = cane time.
- RT = lighting delay.
It is the time that passes between the electric contact of the striker on the trigger, called instant T0, and the exit of the bullet with the flight. The surveyor to the flight, to interrupt the temporal count shared T0, can be realised him by means of one of the principal three techniques in succession detachable:
Optic barrier: it is constituted by a ray of light (visible or not visible, typically in the side of the infrared ones) that crosses, according to his diameter, the mouth of the cane. In closeness of the flight there will be then the accoppiameto between a transmitter and a photoelectric receiver, the interruption of the bright bundle of coupling, he generates the signal of stop of the count. The light bundle can be shaving to the flight, in this case the cane time will be deficient in the time necessary to cover the length of the bullet or, positioned over the distance therefore the whole length of the bullet, in the moment of surveying from the photoelectric barrier, can be considered only come out by the cane.
This system is sensitive to the projections of solid bodies or of smokes opachi that, preceding the bullet, can distort the surveying (it respects in default). The use of the laser, being a more intense and coherent light, returns the system least sensitive to such a problem.
Flash detector or transducer of pressure: the exit of the projectile with the cane is normally accompanied by an expansion of gas (change of the pressure) and by a bright flash. Fit electro-optic or piezoelectric transducers, they let notice one or another variation, generating the useful electric signal to the temporal count. These systems can be influenced at blazes or variations pressorie, precursorie to the real exit of the projectile.
It is the time that passes between T0 and the increase of the pressure in the chamber to dust. Typically the stop threshold to the count is represented by the overcoming of a pressure equal to 10 % of the recorded maximum pressure.
Considering that, it should be the time of cane TC, that the delay of lighting RT, they base on the same beginning event count, under the same conditions, a delay of greater lighting will determine a time of greater cane.
Fig. 2 - typical Times noticed in manometrica
- V1 = speed noticed to 2,5m on base 1m (or rather exploiting two distant chronographic barriers between them 1m - the middle point of the system of surveying coincides with the reference for the distance from the flight).
- V2 = speed noticed to 25m on base 1m.
- P1 = prominent maximum pressure, there is also indicated the typology of the used piezoelectric sensor and the positioning, compared to the living one of breech, of the catching of the gases in chamber to dust.
As well as the time of cane and to the lighting delay brought back on the proof certificate, pressure - time becomes often a reference to other intermediate times individualised on the graph and shown in Figure 2:
Time of lighting – time passed between T0 and typically 1 % of the maximum pressure (t1 in the image)
Slope time – time passed in the passage at 10 % to 90 % of the maximum pressure (t2 in the image)
Time to the peak – necessary time to pass from the initial instant T0, to the peak instant pressorio (t3 in the image)
Transition time – is the time difference between the time of cane Tc and the delay of lighting RT.
We return to other present indications on sezione_2 of the certificate:
Section 3 - the third section brings back the data noticed on each tested blow. We will have then the punctual values of: TC (cane time in µs); V1 (speed to 2.5m in m/s); V2 (speed to 25m in m/s); P1 (peak pressure in Bar); RT (time of delay of lighting in µs); the column PC mediated noticed pressorio was bringing back in past the maximum value crusher (deformation of the sample), such method is not more used; INT is the integral one of the curved pressure - time arrested to the instant Tc, in other words it represents the below area the curve pressoria so as shown on the figure to be followed (background in yellow):
Fig. 3 - Area that represents the integral pressure - time (in yellow) and area, over Tc excluded from the integration (in orange)
The integral pressure - time can be interpreted the total impulse, for unity of surface of the straight section of the cane, supplied to the bullet during the time with cane Tc (bringing near the section of the bullet equal to that one internal of the cane). To explain better how much I dictate, we give a numerical example:
Calculation example 1
We consider the middle value of the integral one brought back on the certificate of proof:
INT = 0.361 Bar•s
a Bar is defined as 10N/cm2, we will have then a middle total impulse applied to the bullet, for unity of basic surface, of 3.61N•s/cm2. In our case the calibre of the weapon is 0.45 thumbs, we will consider a middle diameter of the cane of 11.455 mm for a surface of his straight section of 1.03 cm2. The total impulse (It) applied to the bullet (and apart of the propellant), will be then:
It = 3.61•1.03 = 3.72 N•s
(useful datum for example, for the calculation indicative and a priori of the speed of the bullet or for an estimate on the recoil undergone by the weapon)
The datum of the total impulse (It), we try to determine the theoretical speed reached by the bullet:
for the “theorem of the impulse” we can write what the total impulse applied to a mass, there equals the variation of quantity of motion of the same one. In other words we will have:
It=Qp
indicating with Qp the quantity of motion assumed by the bullet. Then:
It=mp•V0 (mass of the bullet for speed to the flight)
The V0 will be then:
V0=It/mp
Considering the mass of the equal bullet to 202gr (exact value), being equivalent to about 13.09g, we will have:
V0 ≅ 3.72•1000/13.09 = 284.2 m/s (to the gross one of the losses)
near value to the middle result obtained in manometrica (clean losses) and you look to 260.1 m/s (-9 %).
The knowledge of the integral pressure - time lets go back also to the middle value, on the time, of the pressure in cane. Observing the Figure 4, we can think in fact the middle pressure how the height of the rectangle, of width equal to Tc, such that his surface should equal the tinged area at the pressure curve. In other words, the area of the rectangle (in green) will be equal to Pm•Tc and equal also to the value of the integral INT (area in yellow). It results from it that the pressure middle (Pm) will be equal to the report between the integral one of the curved pressure - time and the interval of integration that coincides with the time of cane (Tc): Pm = INT/Tc.
Fig. 4 - Calculation of the prassione mediates at the value of the integral one
When an example follows from calculation using the only shown relations:
Calculation example 2
We always leave from the middle valour of the integral one brought back on the certificate of proof:
INT = 0.361 Bar•s
The middle value of the time of cane Tc turns out to be equal to:
Tc = 1012 µs = 1.012 10-3 s
The middle pressure (Pm) will be given then:
Pm = 0.361/(1.012 • 10-3) = 356.7 Bars
A second interpretation of the integral one of the curved pressure - time, it can be shown if he becomes attached to the density dissect them of the bullet.
In this case we will consider how density dissect (Ds) the physical size given by the report between the mass of the bullet and the surface of his straight section (typically in ballistics he considers himself instead of the report between mass and diameter of the bullet to the square).
The integral one of the curved pressure - time (INT) will result about equal (except for the losses), to the product between the density dissect them so calculated and the speed to the flight of the bullet (we are ignoring the mass of the propellant). In definitive we will obtain that:
INT ≅ Ds • V0 (dimensionalmente will have “pressure x time” is to the first one that per second member)
We give an example:
Calculation example 3
The mass of the used pellet is equal to 202gr (exact value), being equivalent to about 13.09g. The section of an ogive trafilata to 0.451 thumbs is equal to 103.0 mm2 (1.03 cm2). The density dissect agreement as report between mass and section will be equal to Ds=13.09/1.03 = 127.1 Kg/m2
As far as I dictate, the integral pressure - time (INT) will have to be about equal to the next value:
INT ≅ Ds•V0 = 127.1•260.09 = 33057.44 Kg/mq • m/s = 0.331 Bar•s
The middle datum noticed in cane manometrica is equal to 0.361 Bar•s, like indicated, near and slightly in excess ( 9 %) compared to all that obtained considering: density dissect to her and speed to the flight.
Section 4 - The fourth section of the certificate of proof, brings back the statistical data calculated from the punctual surveying and the number of examined samples. Each column of the section 4, in corresponding way to the section 3, will be relative to the same parametres: TC, V1, V2 etc.
Fig. 5 - Certificate of proof, detail of the section 4
Like visible in Figura5, different horizontal lines of the section 4 will bring back the next values:
- Media - arithmetical average of the prominent values. For the overcoming of the test in manometrica, such a value must be inferior or equal to the pressure of exercise prescribed by the Interdepartmental Committee on Prices (permanent international committee) and specifies for ciscun calibre (Pmax_CIP). Then the relation will have to be verified:
- Maximum - maximum between the prominent values
- Minute - minimum between the prominent values
- Delta - difference between the extreme values (Delta=Max-Min)
- SD - standard deviation on the prominent samples. For a "normal" distribution, the interval (Media-SD) and (Media SD), it contains about 68.3 % of the population of the blows. In case of low numerousness of the sample, above all if he is inferior to 30 units, for a better correspondence with the reality, often it prefers to become a reference not to the "normal" distribution (of Gauss), but to that one that is called a T-Student distribution. (The calculated standard deviation is that one relative to the little samples: it mediates on n-1)
- C 95 % - represents the interval on the average with a confidence of 95 %. In other words, with a probability of 95 %, the true average of the sample, compared to the calculated average, will fall on the interval: (Media-C95 %) and (Media C95 %). Here is how it is calculated:
- PK1 - it represents the statistical maximum pressure, on a series of at least 5 measures, and comes calcolta according to the relation:
It mediates ≤ Pmax_CIP
C 95 % = ton (n-1; 0.975) • SD / √ n
where:
* n it represents the number of examined blows
* ton (n-1; 0.975) is the coefficient individualised by the numbers (n-1) and (0.975) on the matrix of the distribution of T-Student (there is the selection of the values to be used: link).
* √n is the root it balances of the number of examined blows
* SD is the standard deviation of the esteemed parametre (Tc, V1, V2, P1, INT or RT)
PK1 = It Mediates (K1n • SD)
The value of the coefficient of tolerance K1n is rilevabile on special tables (see below) and it depends on the numerousness of the sample.
For the test in cane manometrica cartridges destined to the use in smooth cane, it becomes a reference not to PK1 but to PK2, analogue to the precedent but, with inferior coefficients of tolerance less restrictive (values).
PK2 = It Mediates (K2n • SD)
For the test in cane manometrica cartridges to annular percussion, it becomes a reference to PK3, with still inferior coefficients of tolerance even less restrictive (values).
PK3 = It Mediates (K3n • SD)
For the overcoming of the test in manometrica, as well as the condition already citatata for the average of the pressures, it must be verified that PK1, PK2 or PK3, superiors are not any more than 15 %, to the prescribed maximum pressure. In other words the munitions will have to satisfy the next inequalities:
It mediates ≤ Pmax_CIP
PK1 ≤ 1.15 • Pmax_CIP (for ruled cane central percussion)
PK2 ≤ 1.15 • Pmax_CIP (for smooth cane)
PK3 ≤ 1.15 • Pmax_CIP (for ruled cane annular percussion)
extracting the values of K1n, K2n and K3n at the table normata the C.I.P.:
| Tolerance coefficients | |||
| n | K1n | K2n | K3n |
| 5 | 5.75 | 4.21 | 3.41 |
| 10 | 3.98 | 2.91 | 2.36 |
| 20 | 3.30 | 2.40 | 1.93 |
| 25 | 3.15 | 2.29 | 1.83 |
| 30 | 3.06 | 2.22 | 1.78 |
| 35 | 2.99 | 2.17 | 1.73 |
| 40 | 2.94 | 2.13 | 1.70 |
| For the intermediate values: to interpolate linearly | |||
Considering the distribution T-Student and the coefficients K1n and K2n, we can say that for a State lottery of munitions qualified by the test in manometrica, at worst, only 0.3 % of the samples will exceed 15 % of the maximum pressure admitted for the ruled canes and only 2 % for the canes sleekers.
Final considerations
Possible how much do we hope, for, to have done clearness to regard of the interpretation (also ours) present parametres on the proof certificate in cane manometrica. A great deal of the present information on this article have been found close to the companies that use and / or build the test systems: STAS, Northwest, Banco Nazionale of Proof, etc. Some of the conceptual involvement (integral and dissect density) and the calculation of the statistical values (C95 % and covering % of the coefficients normati) has been determined by them instead after our elaboration. As well as the rough datum of the alone maximum pressure, we discover how many information is ricavabili at the proof certificate, only if he is observed in more attentive and deepened way.
Speedy.






















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A Comment for “The proof certificate in manometrica”
Andrew on Oct 7, 2010
The perfect work!