Found this while I was browsing for ways to chrono an air-rifle.
Click Here! to go to the original website.
Peter May penned this document. All Credit goes to him.
I've copied the info here so that we wont have any of those 'cant access the link' issues.
This should be a good project if you have some time to spare.
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Chronograph
Peter May has been involved with shooting for over 25 years. After graduating, in 1978, from Heriot-Watt University he shot with the Dunfermline Rifle Club for 5 years and was Secretary for a brief period before joining the, Edinburgh based, Balerno & Currie Rifle Club, where he was Secretary between 1989-96. He is a collector of pre-World War 1 air rifles, manufactured by the Birmingham Small Arms Company between 1904-18, often under the Lincoln Jeffries Patent. These rifles show the development of systems still used today. Often highly serviceable, their operation is a testament to the quality engineering of the time. Many modern air rifles are based on designs developed by BSA.
Introduction
Commercial chronographs can be expensive, often costing hundreds of pounds. This article demonstrates it is possible to build a working device using common materials. As with any chronograph it can be used to determine the muzzle velocity and hence the muzzle energy of a projectile.
To illustrate the chronograph's operation it was used to compare the performance of different commercial pellets, fired from a rifle.
Types of Chronograph
Most chronographs, since World War 1, have used a gate system, where the missile passes through 2 or more gates, and where the distance between the gates is known. The missile trips timing devices allowing the velocity of the missile to be measured.
One of the most convenient means for tripping a chronograph uses photo-electric screens. These were developed in Canada before World War II, and were used in the first Potter counter chronograph.
The photo-electric screen uses an electronic photo sensitive element that is focused on a Lumiline or other suitable light source. The bullet passes between the light source and the photo cell, causing an interruption of the light. This is detected by circuitry, which starts the chronograph counter. A similar light interruption at the closing gate stops the counter. Today, photoelectric switches are used for nearly all "professional" chronographs. Avtron and Oehler among others, furnish small photo screen units for amateur use.
Photoelectric cells have the advantage that since they rely on a light beam there is no hindrance to the projectile which could affect its performance.
However, the distance between the gates is important with any chronograph, since the shorter the distance, the quicker the time taken for the projectile to pass from the first gate to the second gate. Where too short a distance is allowed the time to cover the distance may be so short as to introduce a large percentage error into the result.
Therefore the term muzzle velocity is misleading, since the projectile has to travel some distance beyond the barrel to allow accurate measurement to take place.
Muzzle Velocity & Muzzle Energy
These 2 characteristics are often quoted or referred to by manufacturers wishing to promote their product. The muzzle velocity is simply the speed at which a projectile leaves the muzzle of a weapon. Muzzle energy is a measure of the energy possessed by the projectile just after it leaves the barrel. The energy will depend on the speed of the bullet as well as its weight and is sometimes referred to as kinetic energy. Muzzle energy is given by the formula:
where:
m = mass of pellet
v = velocity of pellet
Depending upon the units used the result will give the energy in Joules. The higher the value the greater the kinetic energy of the pellet.
Metric units have been used, although many readers may be familiar with imperial measures. Using these imperial measures the maximum permitted energy for an air rifle is 12 ft/lbs. Weapons exceeding this figure require a firearm certificate.
The muzzle velocity and energy of a rifle are dependent on 3 variables:
the shape and weight of the bullet
the propellant
the rifling
For a spring loading air rifle the effectiveness of the compression cycle is related to the weight and shape of the pellet, and the pellet's resistance to the compressed air in the chamber.
Too little resistance at the breech and in the barrel, due to the weight and shape of a pellet, would not allow optimum pressure to build up and too great a resistance by a pellet would cause a high build up of pressure causing escape of air at the breech seal and subsequent reduction in the energy imparted to the pellet.
The dimensions of the pellet will affect the velocity and muzzle energy. For every air weapon, it should be possible to find a given shape and weight of pellet which best suits that rifle and which allows the muzzle energy to reach its optimum level.
For pellets of identical shape there should be an optimum weight of pellet most suited to a particular rifle.
Similarly for pellets of constant weight but of different shape there should be a particular shape most suited to a given rifle.
The variety and range of commrcial pellet shapes are enormous. These tests compare 4 pellet makes of dissimilar characteristics and analyses their performance. It is not feasible to make a series of individual pellets of identical shape and different weights. It is necessary to rely on commercially produced pellets. However the wide variety available allows pellets of different characteristics to be selected.
It was intended to determine the muzzle velocity and subsequently the muzzle energy of a pellet.
In addition, the chronograph can be moved, some distance from the muzzle of the rifle, to enable the loss of velocity and energy over a distance to be measured, to determine which pellet, if any, best maintains its energy.
It should be stressed that performance is true only for this particular air rifle and another rifle may better suit a different pellet. The important point is that any air rifle will perform differently with different pellets and it is worthwhile trying a range of different makes, shapes, sizes and weight of pellet to discover which one(s) best suit your individual air weapon.
In many cases this is done by target shooters on an "ad hoc" basis. Using a chronograph may allow a shooter to more rapidly select a commercial pellet which performs consistently with their weapon.
The "Home Made" Chronograph
The sketch shows the chronograph design. It consists of a shaft, driven by an electric motor the shaft revolves in 2 bearings. Two circular paper discs, at either end of the shaft, are mounted at right angles to the shaft. The original design used tin plates to hold the paper in place. However, these proved too heavy and were replaced by lighter plastic discs.
If the distance between the 2 paper discs is known, together with the rotation speed of the shaft, then a horizontally fired pellet travelling through both discs will produce an between the cutting of the 1st disc and the cutting of the 2nd disc.
This angle Ø can be measured and the pellet velocity calculated.
The apparatus was constructed over a period of weeks. It had been intended to use a inch diameter shaft but only inch bearings could be obtained. This meant that the shaft was less rigid then desired which made it more susceptible to vibration and distortion. Minimising the vibration was one of difficulties encountered at speeds exceeding 1400 rpm.
A support for the barrel of the rifle to rest upon was built and a box of papers used to stop the pellet after it has passed, through the discs.
The discs were made of cartridge paper. These were supported on the shaft by plastic discs to ensure their rigidity with the vertical plane.
The Rifle
The rifle used was an Original Model 35 breakbarrel spring system, of a calibre 5.5 mm (.22 in). This type of rifle generates its power by compressing the mainspring which on release compresses air in the chamber so propelling the pellet.
The photo shows the breech detail and the all important breech seal. This seal eventually wear and should, on older rifles, be replaced at intervals. With all breech loading rifles it is important to ensure that pellets are seated correctly and the pellet skirt is not nipped when the breech is closed. Some rifles may benefit from a small amount of grinding our to improve the pellet seating. Carborundum paste can be used to good effect.
Underlever rifles where the barrel remains inline with the cylinder are less prone to leakage since they do not require a breech seal. A "tap" allows the pellet to be inserted so that it too is inline between the barrel and cylinder.
However, the breech loading rifle is normally quicker to load because the task can be done as a single smooth operation.
It is prudent with all types of weapon to fire a few "warm up" shots before undertaking any experiment or engaging in target shooting. This will have the effect of warming up the barrel, remembering that the rifle may have been stored unused for a period in a cool environment. It is common practice amongst .22 targetshooters.
With air weapons this is particularly important since the temperature of the cylinder will affect the gas stored in the chamber. Piston washers especially may require their lubrication warmed up to ensure that they compress the gas and none escapes past the mainspring washer.
Pellets
Four types of pellet were chosen. These were:
Type 1 Champion round-headed
Type 2 RWS flat-headed
Type 3 Marksman round-headed
Type 4 Bulldog round-headed
Type 1 is relatively light weight; type 2 is common in target shooting for its consistency and types 3 & 4 are both heavier.
To find the average weight of a pellet, the pellets were weighed in groups of 10 and for each type of pellet this was repeated 10 times. The average weight was used since it would be impractical to weigh each individual pellet before firing. In addition it had been found to be impractical to weigh 10 individual pellets to find the average weight. The small variations in weight would require a machine of considerable accuracy.
All pellets were examined carefully to ensure that no deformed or out of gauge pellets were weighed.
A flashing stroboscope was used to measure the speed of rotation of the shaft.
The enlarged illustration above shows a typical pellet. Note that the pellet skirt is slightly wider than the top indeed it is slightly larger than the barrel bore and will deform to create a tight seal so that no gas encases past the pellet. Evidence of this is shown in the below photograph showing rifling marks.
Required Rotational Speed
It is assumed, from manufacturers' values, that the velocity of an air rifle pellet is 170 m/s.
Assuming the length of the shaft to be 1 metre, the time taken to travel a metre is seconds.
The disc should rotate at a speed so that 1 revolution of disc is completed in second.
Ø = wt
assume Ø< 360°, say 90° (360° = 2¼ radians 90° = radians)
w = = = 85 radians
N = 30 * 85 radians = 2550 revolutions per minutes
The shaft should rotate at a speed of 2550 revolutions per minutes. This will produce an angle of approximately 90°. If the speed falls to 1250 rpm then the angle generated will be about 45°.
As large an angle as possible is desirable. The angle should not be less than 45°, since little change in the angle would occur for corresponding changes in velocity. This means that the minimum speed for the shaft must be 1250 rpm.
A speed more than 1500 rpm would allow greater accuracy of measurement and allow small variations in speed to be measured. Ideally, the angle Ø should be as large as possible.
Procedure
A datum line was drawn across the diameter of each paper disc to be used. When each disc was placed in position, on the shaft, the vertical distance between baseboard and the datum line was measured so ensuring that the datum line was horizontal. This would later allow each pair of discs to be correctly aligned, relative to each other, to measure the angle, following removal.
In addition one disc was marked with a broad band across the radius. This would be used to determine the rotation speed of the shaft. The discs were securely fastened and both vertical and horizontal distances checked. Once started the rotational speed of the shaft was measured using the stroboscope.
The stroboscope reading was set at 1700 revolutions per minute and the shaft speed adjusted by varying the motor speed using a rheostat. The speed of 1700 revolutions per minute was considered suitable to give a reasonably high value for the angle Ø. This speed was checked by making 2 or 3 lines appear using the stroboscope. The reading given by the stroboscope would then be 2 or 3 times the shaft speed. The speed was checked before and after each set of discs used.
The first series of tests were carried out with the nearest disc 0.22 metres from the muzzle and all 4 makes of pellet were used.
Some 36 discs were prepared.
Several pellets were fired into the collection box, to allow the rifle to warm up before firing through the chronometer. Test shots were fired with the rifle on its rest and with the motor switched off, to ensure the apparatus and rifle rest were aligned, before these were clamped to the bench.
Two discs were placed on the shaft as described and the speed adjusted to 1700 revolution per minute.
A pellet was examined and selected if uniform, and then placed in the cocked rifle. The pellet was fired through the discs and the hole each pellet made in each disc was marked. This procedure was repeated so that 4 pellets were fired through each pair of discs. The discs were then removed and placed one on top of the other with the datum diameter in line. The holes made in the first disc were then marked on the second disc and the angle Ø measured.
Eight firings for each type of pellet were made, using some 16 discs.
The second series of tests were carried out with the apparatus moved so that the first disc was 10.22 m from the muzzle. This would allow any drop in velocity, over the 10 metre distance, to be measured. Only 2 makes of pellet were used, a light and heavy pellet. For these tests, the rifle was laid on its rest and with the shaft not rotating, test shots were fired at the disc to ensure proper alignment. Telescopic sights ensured that the pellet passed through the first disc at approximately 3 cms from the circumference, and to make sure the pellet passed through the corresponding point on both discs. Again angles Ø were measured for each pair of discs used.
Typical Calculation
Speed of discs = 1700 revolutions/second
= 178 radians/second
t = = time to travel from discs 1 to disc 2
Type 1 (Champion)
Mean angle = 65.65°
= 1.145 radians
t = = = 0.006425 seconds
Distance between discs = 1.03 metres
s = vt hence
v = = = 160 m/s
Mass of pellet = 0.7663 grams
Muzzle velocity = 160.5 m/s
Muzzle energy = 9.87 Joules
Discussion of Results
The flat-headed RWS match pellets (Type 2) have more consistent results as shown on table page 22.
This indicates that the air rifle was firing with consistent energy.
Comparing the 3 round-headed pellets there is an increase in the muzzle velocity up to a given weight and then the energy falls off. This does not of course take into account the variation in the shape of the 3 types of pellet but is consistent with what would be expected for any particular air-rifle.
The Type 1 and Type 3 pellets were compared over the 11 metre distance. The losses in muzzle velocity and muzzle energy are consistent with tables published by Eley. which indicates that over this range for a low velocity bullet there would not be a significant loss of energy or velocity. The fall in energy and velocity would occur over a greater distance.
Although variation in the weight of pellets was calculated in considering an individual type of pellet it would be very difficult to say if small reductions or increases in weight would increase the muzzle velocity and energy. To investigate this would require more elaborate pellet weighing equipment.
Only by making individual pellets or by skilfully adding weight to or from an individual type of pellet could an attempt be make to determine the effect of a small variation in weight on the muzzle velocity.
In theory the muzzle velocity will vary according to the type of pellet used, but the muzzle energy should remain constant since the same energy is being supplied.
It appears that a "shape and dimension" factor needs to be taken into account since the results give a range of muzzle energy. The variation in the type of pellets chosen has highlighted the difference in muzzle energy and it is considered that had similar type of pellet been used this difference in muzzle energy would not have been so pronounced.
The pellet photographs on page show the different external shapes of the 4 pellets shown.
It is considered that the difference in muzzle energy between the different types of pellet is due to the difference in force required to deform the particular type of pellet to fit the rifling.
It was not practicable to measure the pellets with a micrometer since the pellets deformed between the jaws of the micrometer. However, it is practical to measure the enlarged photographs of the pellets, and by doing so, a comparison of the relative pellet sizes can be made. The outside of the pellet is however not a true comparison since internal shape and wall thickness both play a large part in determining the force required to shape the pellet into the bore and rifling.
The mid mean angles corresponding to the average angle for each of the 4 types of pellets over 1 metre.
The trajectory of the pellet over the 10 metre distance would be very flat and although the total drop over the distance is 1.7 mm, the drop over any one metre would be small enough, approximately 0.17 mm, that the path of the pellet can be taken as horizontal.
In other words the distance travelled by the pellet over the 11 metres can be taken as the 1.03 metres measured horizontal distance between the discs of the chronometer/graph and it is not necessary to amend the calculation to include component to reflect this drop. This is true for this air rifle for distance up to some 30 metres or until the energy of the pellet was so small that the piercing of the rotating 1st disc would cause the pellet to deflect and give inaccurate readings. Obviously some energy is lost in piercing the discs but over the 10 metre range given in the results this would be very small.
It is generally accepted that for distances of over 50 metres an air rifle pellet becomes unstable and the project is only concerned with the stable part of its path.
The deformation of pellets caused by the rifling are shown in the photo on page. The rifled pellets were trapped by firing then into a mass of cotton wool.
Conclusion
This demonstration has shown it is practical to make a simple apparatus which would be of value to a keen amateur or a small gunsmith. More sophisticated means of measuring pellet or muzzle velocities are available. However, the apparatus has determined for a particular rifle, which of 3 round headed pellets are most suitable for sporting purposes. That is, type 3 gives the maximum muzzle energy and would be expected to have greater retained energy over a greater distance.
Unfortunately it was not possible to obtain a comparison between flat-headed pellets, but the consistent results with this type of pellet show that it would be very suitable for target shooting.
The shape of the pellet plays a part in its performance and photographs of these have been given to show the difference. Generally the longer and more uniform pellets give more consistent results. The shapes of these pellets have been determined by the manufacturers over a considerable number of years.
It is apparent that a more refined chronograph could be built on the lines adopted.
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Hope it helps!
Mo.
I hear you!! 
