Exterior Ballistics Software For Mac

03.10.2019
  1. Ballistic Software Free
  2. Exterior Ballistics Software For Mac

Shooter is a highly accurate ballistics calculator for the iOS (iPhone, iPod Touch and iPad) and Android mobile platforms and is currently for sale in the Google Play Store, Amazon Appstore and Apple App Store for $9.99. Shooter is far above the competition by not only it's unparalleled accuracy, but it's great user interface that just makes sense to a shooter and gets you to a solution quick. GNU Exterior Ballistics Computer A graphical interface for solving exterior ballistics Arrowmatcher Arrowmatcher is a ballistics software for crossbow Voxengo Span for Mac OS X SPAN is a real-time 'sfast Fourier transform' audio spectrum. Aug 05, 2015  Download GNU Exterior Ballistics Computer for free. A graphical interface for solving exterior ballistics problems, based on the excellent GNU exterior ballistics library. This software generates valid 3-DOF solutions to small arms trajectories, including wind and atmospheric corrections.

My brother is pffereing to sell me an iphone he just picked up on ebay. He is the 'technological' one, I have trouble with these gadgets, however, since I don't usually go far without my ipod or phone, this sounds like a good idea. The fact the my current cell phone is being held together with duct tape, and that is not a figure of speech, I need to get a new one anyway. This thing will doa lot of things, amongst wich it will navigate on the internet.

So it brings me to my question, does anyone know if they are suitable for using with a ballistics program? My bro tells me they are Mac format. Here's a list of ballistic software titles: Several for macs are listed. Which i think will work on the iphone. But I'm not 100% for sure.

However, I'm partial to a pocket pc simply for the stylus input and written text recognition ability. It's way more handy then the iphone (in my opinion). My wife has a verizon vx6800 for $250 which is a phone and Pocket PC together. I know that there are lots of ballistics software programs will work on this.

There's also so cellphone/pocketpc's with gps capability - which might be more handy for hunting? I ran into a couple guys at the range the other day who had these phone and a program call Ballistic FTP ( I think). It was incredible. The app get your atmos data via the internet based on you your location (via it's gps capability) and automatically inputs the values.

This by passes the need for a Kestrel. It also had the ability to calc Coriolis without the need of carrying a compass.

That phone and app eliminated the need for extra tools. The only downside is you need cell service for it to work.

I use an app called BulletFlight on my iPhone. It retrieves local weather if you tell it to.

You can put your own loads / gun in. It has a database too. It's not Loadbase but it is pretty good. Even though I have the app on my phone I also typed in the range tables for my scope / rifle combo calculated from LoadBase. I just used the built in Notes app on the phone and typed in the info after Loadbase calculated it. Kind of handy to have a range card right there. Mac's in my opinion do photo's and movies very well.

They are also great for networking and internet connectivity. I use a Mac for my photography stuff and PC's for my 'real job' but only because I don't want to trash out my Mac's with PC software. About us My family and I welcome you. I started LRH back in 2001 to provide a friendly place where like-minded individuals could share information and ideas to help take their long range shooting and hunting to the next level. We work hard to provide an enjoyable place to spend your time.Len, Andy, Chris and Kathy Backus-. Site Functions. Useful Links.

Advertise Your Business LRH is the website of choice for many of the sharpest minds in modern shooting and hunting. We have a high renewal rate among our Advertising Sponsors indicating that they feel the advertising is effective. They recognize our over 100,000 members as serious buyers who help set trends.

Contents. Forces acting on the projectile When in flight, the main acting on the are, and if present. Gravity imparts a downward acceleration on the projectile, causing it to drop from the. Or the air resistance decelerates the projectile with a force exponentially proportional to the square of the velocity. Wind makes the projectile deviate from its trajectory. During flight, gravity, drag and wind have a major impact on the path of the projectile, and must be accounted for when predicting how the projectile will travel. For medium to longer ranges and flight times, besides gravity, air resistance and wind, several meso variables described in the paragraph have to be taken into account.

For long to very long ranges and flight times, minor effects and forces such as the ones described in the paragraph become important and have to be taken into account. The practical effects of these variables are generally irrelevant for most firearms users, since normal group scatter at short and medium ranges prevails over the influence these effects exert on firearms projectiles. At extremely long ranges, must fire projectiles along trajectories that are not even approximately straight; they are closer to, although air resistance affects this. In the case of, the altitudes involved have a significant effect as well, with part of the flight taking place in a near-vacuum. Stabilizing non-spherical projectiles during flight Two methods can be employed to stabilize non-spherical (ball shaped) projectiles during flight:. Projectiles like or like the achieve stability by forcing their (CP) behind their (CG) with tail surfaces.

Ballistic Software Free

The CP behind the CG condition yields stable projectile flight, meaning the projectile will not overturn during flight through the atmosphere due to aerodynamic forces. Projectiles like small arms bullets and artillery shells must deal with their CP being in front of their CG, which destabilizes these projectiles during flight.

To stabilize such projectiles the projectile is spun around its longitudinal (leading to trailing) axis. The spinning mass makes the bullets length axis resistant to the destabilizing overturning torque of the CP being in front of the CG. Small arms external ballistics. Typical trajectory graph for a and using identical cartridges with identical projectiles.

Though both trajectories have an identical 25 m near zero, the difference in muzzle velocity of the projectiles gradually causes a significant difference in trajectory and far zero. The 0 inch axis represents the line of sight or horizontal sighting plane. The effect of on a projectile in flight is often referred to as bullet drop. It is important to understand the effect of gravity when the sighting components of a gun. To plan for bullet drop and compensate properly, one must understand shaped. Due to the near parabolic shape of the projectile path, the line of sight or horizontal sighting plane will cross the projectiles trajectory at two points called the near zero and far zero incase the projectile starts its trajectory (slightly) inclined upward in relation to the sighting device horizontal plane, causing part of the bullet path to appear to rise above the horizontal sighting plane. The distance at which the firearm is zeroed, and the vertical distance between the sighting device axis and barrel bore axis, determine the apparent severity of the 'rise' in both the X and Y axes (how far above the horizontal sighting plane the rise goes, and over what distance it lasts).

Many firearms ballistics tables and graphs show a rise in trajectory at distances shorter than the one (far zero) used for sight-in. This apparent 'rise' of the projectile in the first part of its trajectory is relative only to the sighting plane, and is not actually a rise. The laws of physics dictate that the projectile will begin to be pulled down by gravity as soon as it leaves the support of the barrel bore at the muzzle, and can never rise above the axis of the bore. The apparent 'rise' is caused by the separation of the plane of the sighting device axis and that of the bore axis and the fact that the projectile rarely leaves the bore perfectly horizontally. If a firearm is zeroed at 100 meters, then the far horizontal sighting plane and the projectile path must 'cross' at that distance; the sighting line must be adjusted to intersect with the projectile path at 100 meters. In the case of a bore axis that is maintained in a perfectly horizontal position, the sighting device must be inclined downward to achieve this intersection. The axial separation distance between the line of sight and the bore axis and trajectory of the projectile dictate the amount of angular declination required to achieve the required intersection.

Fixed drag curve models generated for standard-shaped projectiles Use of ballistics tables or ballistics software based on the Siacci/Mayevski G1 drag model, introduced in 1881, are the most common method used to work with external ballistics. Bullets are described by a, or BC, which combines the air resistance of the bullet shape (the ) and its (a function of mass and bullet diameter).

The deceleration due to that a projectile with mass m, velocity v, and diameter d will experience is proportional to BC, 1/ m, v² and d². The BC gives the ratio of ballistic efficiency compared to the standard G1 projectile, which is a 1 pound (454 g), 1 inch (25.4 mm) diameter bullet with a flat base, a length of 3 inches (76.2 mm), and a 2 inch (50.8 mm) radius tangential curve for the point. The G1 standard projectile originates from the 'C' standard reference projectile defined by the German steel, ammunition and armaments manufacturer in 1881. The G1 model standard projectile has a BC of 1. The French Gavre Commission decided to use this projectile as their first reference projectile, giving the G1 name.

Exterior Ballistics Software For Mac

Sporting bullets, with a d ranging from 0.177 to 0.50 inches (4.50 to ), have G1 BC’s in the range 0.12 to slightly over 1.00, with 1.00 being the most aerodynamic, and 0.12 being the least. With BC's ≥ 1.10 can be designed and produced on CNC precision lathes out of mono-metal rods, but they often have to be fired from custom made full bore rifles with special barrels. Is a very important aspect of a bullet, and is the ratio of frontal surface area (half the bullet diameter squared, times ) to bullet mass. Since, for a given bullet shape, frontal surface increases as the square of the calibre, and mass increases as the cube of the diameter, then sectional density grows linearly with bore diameter.

Since BC combines shape and sectional density, a half of the G1 projectile will have a BC of 0.5, and a quarter scale model will have a BC of 0.25. Since different projectile shapes will respond differently to changes in velocity (particularly between and velocities), a BC provided by a bullet manufacturer will be an average BC that represents the common range of velocities for that bullet. For bullets, this will probably be a velocity, for pistol bullets it will be probably be.

For projectiles that travel through the, and flight regimes BC is not well approximated by a single constant, but is considered to be a BC(M) of the M; here M equals the projectile velocity divided by the. During the flight of the projectile the M will decrease, and therefore (in most cases) the BC will also decrease. Most ballistic tables or software takes for granted that one specific drag function correctly describes the drag and hence the flight characteristics of a bullet related to its ballistics coefficient. Those models do not differentiate between, flat-based, spitzer, boat-tail, etc. Bullet types or shapes. They assume one invariable drag function as indicated by the published BC.

Several drag curve models optimized for several standard projectile shapes are however available. More advanced drag models Pejsa model Besides the traditional drag curve models for several standard projectile shapes or types other more advanced drag models exist. The most prominent alternative ballistic model is probably the model presented in 1980 by Dr.

Claims on his website that his method was consistently capable of predicting (supersonic) rifle bullet trajectories within 2.54 mm (0.1 in) and bullet velocities within 0.3048 m/s (1 ft/s) out to 914.4 m (1,000 yd) when compared to dozens of actual measurements. The Pejsa model is an analytic closed-form solution that does not use any tables or fixed drag curves generated for standard-shaped projectiles. The Pejsa method uses the G1-based ballistic coefficient as published, and incorporates this in a Pejsa retardation coefficient function in order to model the retardation behaviour of the specific projectile. Since it effectively uses an analytic function ( modelled as a function of the ) in order to match the drag behaviour of the specific bullet the Pesja method does not need to rely on any prefixed assumption. Besides the mathematical retardation coefficient function, the Pejsa model adds an extra slope constant factor that accounts for the more subtle change in retardation rate downrange of different bullet shapes and sizes. It ranges from 0.1 (flat-nose bullets) to 0.9.

If this deceleration constant factor is unknown a default value of 0.5 will predict the flight behaviour of most modern spitzer-type rifle bullets quite well. With the help of test firing measurements the slope constant for a particular bullet/rifle system/shooter combination can be determined.

These test firings should preferably be executed at 60% and for extreme long range ballistic predictions also at 80% to 90% of the supersonic range of the projectiles of interest, staying away from erratic transonic effects. With this the Pejsa model can easily be tuned for the specific drag behaviour of a specific projectile, making significant better ballistic predictions for ranges beyond 500 m (547 yd) possible. Some software developers offer commercial software which is based on the Pejsa drag model enhanced and improved with refinements to account for normally minor effects (Coriolis, gyroscopic drift, etc.) that come in to play at long range.

The developers of these enhanced Pejsa models designed these programs for ballistic predictions beyond 1,000 m (1,094 yd). 6 degrees of freedom (6 DOF) model There are also advanced professional ballistic models like available. These are based on 6 Degrees Of Freedom (6 DOF) calculations. 6 DOF modelling needs such elaborate input, knowledge of the employed projectiles and long calculation time on computers that it is impractical for non-professional ballisticians and field use where calculations generally have to be done on the fly on with relatively modest computing power.

6 DOF is generally used by military organizations that study the ballistic behaviour of a limited number of (intended) military issue projectiles. Calculated 6 DOF trends can be incorporated as correction tables in more conventional ballistic software applications. Doppler radar-measurements For the precise establishment of drag or air resistance effects on projectiles, -measurements are required.

1000e are used by governments, professional ballisticians, defence forces and a few ammunition manufacturers to obtain real world data of the flight behaviour of projectiles of their interest. Correctly established state of the art Doppler radar measurements can determine the flight behaviour of projectiles as small as airgun pellets in three-dimensional space to within a few millimetres accuracy. The gathered data regarding the projectile deceleration can be derived and expressed in several ways, such as ballistic coefficients (BC) or (C d). Doppler radar measurement results for a lathe turned monolithic solid.50 BMG (Lost River J40.510-773 grain monolithic solid bullet / twist rate 1:15 in) look like this: Range (m) 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 Ballistic coefficient 1.040 1.051 1.057 1.063 1.064 1.067 1.068 1.068 1.068 1.066 1.064 1.060 1.056 1.050 1.042 1.032 The initial rise in the BC value is attributed to a projectile's always present yaw and precession out of the bore. The test results were obtained from many shots not just a single shot.

The bullet was assigned 1.062 for its BC number by the bullet's manufacturer Lost River Ballistic Technologies. Doppler radar measurement results for a Lapua GB528 Scenar 19.44 g (300 gr) 8.59 mm (0.338 in) calibre look like this: 0.000 0.400 0.500 0.600 0.700 0.800 0.825 0.850 0.875 0.900 0.925 0.950 0.975 1.000 1.025 1.050 1.075 1.100 1.150 1.200 1.300 1.400 1.500 1.600 1.800 2.000 2.200 2.400 Drag coefficient 0.230 0.229 0.200 0.171 0.164 0.144 0.141 0.137 0.137 0.142 0.154 0.177 0.236 0.306 0.334 0.341 0.345 0.347 0.348 0.348 0.343 0.336 0.328 0.321 0.304 0.292 0.282 0.270 This tested bullet experiences its maximum drag coefficient when entering the transonic flight regime around Mach 1.200. General trends in drag or ballistic coefficient In general, a pointed bullet will have a better (C d) or (BC) than a round nosed bullet, and a round nosed bullet will have a better C d or BC than a flat point bullet. Large radius curves, resulting in a shallower point angle, will produce lower drags, particularly at supersonic velocities. Behave much like a flat point of the same point diameter. Bullets designed for supersonic use often have a slight taper at the rear, called a boat tail, which further reduces drag.

Cannelures, which are recessed rings around the bullet used to crimp the bullet securely into the case, will cause an increase in drag. The transonic problem When the velocity of a rifle bullet fired at muzzle velocity approaches the speed of sound it enters the region (about 1.2–0.8). In the transonic region, the centre of pressure (CP) of most bullets shifts forward as the bullet decelerates. That CP shift affects the (dynamic) stability of the bullet.

If the bullet is not well stabilized, it can not remain pointing forward through the transonic region (the bullets starts to exhibit an unwanted or coning motion that, if not dampened out, can eventually end in uncontrollable tumbling along the length axis). However, even if the bullet has sufficient stability (static and dynamic) to be able to fly through the transonic region and stays pointing forward, it is still affected. The erratic and sudden CP shift and (temporary) decrease of dynamic stability can cause significant dispersion (and hence significant accuracy decay), even if the bullet's flight becomes well behaved again when it enters the region. This makes accurately predicting the ballistic behaviour of bullets in the transonic region very hard.

Because of this marksmen normally restrict themselves to engaging targets within the supersonic range of the bullet used. Testing the predictive qualities of software Due to the practical inability to know in advance and compensate for all the variables of flight, no software simulation, however advanced, will yield predictions that will always perfectly match real world trajectories. It is however possible to obtain predictions that are very close to actual flight behaviour.

Empirical measurement method Ballistic prediction computer programs intended for (extreme) long ranges can be evaluated by conducting field tests at the supersonic to subsonic transition range (the last 10 to 20% of the supersonic range of the rifle/cartridge/bullet combination). For a typical.338 Lapua Magnum rifle for example, shooting standard 16.2 gram (250 gr) Lapua Scenar GB488 bullets at 905 m/s (2969 ft/s) muzzle velocity, field testing of the software should be done at ≈ 1200 - 1300 meters (1312 - 1422 yd) under sea level conditions ( ρ = 1.225 /m³). To check how well the software predicts the trajectory at shorter to medium range, field tests at 20, 40 and 60% of the supersonic range have to be conducted. At those shorter to medium ranges, transsonic problems and hence unbehaved bullet flight should not occur, and the BC is less likely to be transient. Testing the predicative qualities of software at (extreme) long ranges is expensive because it consumes ammunition; the actual muzzle velocity of all shots fired must be measured to be able to make statistically dependable statements.

Sample groups of less than 24 shots do not obtain statistically dependable data. Doppler radar measurement method Governments, professional ballisticians, defence forces and a few ammunition manufacturers can use Doppler radars to obtain precise real world data regarding the flight behaviour of the specific projectiles of their interest and thereupon compare the gathered real world data against the predictions calculated by ballistic computer programs. The normal shooting or aerodynamics enthusiast, however, has no access to such expensive professional measurement devices. Authorities and projectile manufacturers are generally reluctant to share the results of Doppler radar tests and the test derived (C d) of projectiles with the general public. In January 2009 the Finnish ammunition manufacturer Lapua published Doppler radar test-derived drag coefficient data for most of their rifle projectiles. With this C d data engineers can create algorithms that utilize both known mathematical ballistic models as well as test specific, tabular data in unison.

When used by predicative software like, Lapua Edition this data can be used for more accurate external ballistic predictions. Some of the Lapua-provided drag coefficient data shows drastic increases in the measured drag around or below the Mach 1 flight velocity region. This behaviour was observed for most of the measured small calibre bullets, and not so much for the larger calibre bullets.

This implies some (mostly smaller calibre) rifle bullets exhibited coning and/or tumbling in the transonic/subsonic flight velocity regime. The information regarding unfavourable transonic/subsonic flight behaviour for some of the tested projectiles is important. This is a limiting factor for extended range shooting use, because the effects of coning and tumbling are not easily predictable and potentially catastrophic for the best ballistic prediction models and software. It should be noted that presented C d data can not be simply used for every gun-ammunition combination, since it was measured for the barrels, and ammunition lots the Lapua testers used during their test firings. Variables like differences in rifling, twist rates and/or muzzle velocities impart different rotational (spin) velocities and rifling marks on projectiles.

Changes in such variables and projectile production lot variations can yield different downrange interaction with the air the projectile passes through that can result in (minor) changes in flight behaviour. It should be noted that this particular field of external ballistics is currently (2009) not elaborately studied nor well understood. Predictions of several drag resistance modelling and measuring methods The method employed to model and predict external ballistic behaviour can yield differing results with increasing range and time of flight. Wind Wind has a range of effects, the first being the effect of making the bullet deviate to the side.

From a scientific perspective, the 'wind pushing on the side of the bullet' is not what causes wind drift. What causes wind drift is drag. Drag makes the bullet turn into the wind, keeping the centre of air pressure on its nose. This causes the nose to be cocked (from your perspective) into the wind, the base is cocked (from your perspective) 'downwind.' So, (again from your perspective), the drag is pushing the bullet downwind making bullets follow the wind. A somewhat less obvious effect is caused by head or tailwinds.

A headwind will slightly increase the of the projectile, and increase drag and the corresponding drop. A tailwind will reduce the drag and the bullet drop. In the real world pure head or tailwinds are rare, since wind seldom is constant in force and direction and normally interacts with the terrain it is blowing over. This often makes ultra long range shooting in head or tailwind conditions difficult. Vertical angles The (or ) of a shot will also affect the trajectory of the shot. Ballistic tables for small calibre projectiles (fired from pistols or rifles) assume that gravity is acting nearly perpendicular to the bullet path. If the angle is up or down, then the perpendicular acceleration will actually be less.

The effect of the path wise acceleration component will be negligible, so shooting up or downhill will both result in a similar decrease in bullet drop. Often mathematical ballistic prediction models are limited to 'flat fire' scenario's based on the, meaning they can not produce adequately accurate predictions when combined with steep elevation angles over -15 to 15 degrees and longer ranges. There are however several mathematical prediction models for inclined fire scenario's available which yield rather varying accuracy expectation levels.

Gyroscopic drift (Spin drift) Even in completely calm air, with no sideways air movement at all, a spin-stabilized projectile will experience a spin-induced sideways component. For a right hand (clockwise) direction of rotation this component will always be to the right. For a left hand (counterclockwise) direction of rotation this component will always be to the left. This is because the projectile's longitudinal axis (its axis of rotation) and the direction of the velocity of the center of gravity (CG) deviate by a small angle, which is said to be the equilibrium or the yaw of repose. For right-handed (clockwise) spin bullets, the bullet's axis of symmetry points to the right and a little bit upward with respect to the direction of the velocity vector as the projectile rotates through its ballistic arc on a long range trajectory.

As an effect of this small inclination, there is a continuous air stream, which tends to deflect the bullet to the right. Thus the occurrence of the yaw of repose is the reason for bullet drift to the right (for right-handed spin) or to the left (for left-handed spin). This means that the bullet is 'skidding' sideways at any given moment, and thus experiencing a sideways component. The following variables affect the magnitude of gyroscopic drift:. Projectile or bullet length: longer projectiles experience more gyroscopic drift because they produce more lateral 'lift' for a given yaw angle. Spin rate: faster spin rates will produce more gyroscopic drift because the nose ends up pointing farther to the side. Range, time of flight and trajectory height: gyroscopic drift increases with all of these variables.

Exterior Ballistics Software For Mac

Magnus effect Spin stabilized projectiles are affected by the, whereby the spin of the bullet creates a force acting either up or down, perpendicular to the sideways vector of the wind. In the simple case of horizontal wind, and a right hand (clockwise) direction of rotation, the Magnus effect induced pressure differences around the bullet cause a downward force to act on the projectile, affecting its point of impact. The vertical deflection value tends to be small in comparison with the horizontal wind induced deflection component, but it may nevertheless be significant in winds that exceed 4 m/s (14.4 km/h or 9 mph). Magnus effect and bullet stability The Magnus effect has a significant role in bullet stability because the Magnus force does not act upon the bullet's center of gravity, but the center of pressure affecting the yaw of the bullet. The Magnus effect will act as a destabilizing force on any bullet with a center of pressure located ahead of the center of gravity, while conversely acting as a stabilizing force on any bullet with the center of pressure located behind the center of gravity.

The location of the center of pressure depends on the flow field structure, in other words, depending on whether the bullet is in supersonic, transonic or subsonic flight. What this means in practice depends on the shape and other attributes of the bullet, in any case the Magnus force greatly affects stability because it tries to 'twist' the bullet along its flight path. Paradoxically, due to their length have a tendency to exhibit greater Magnus destabilizing errors because they have a greater surface area to present to the oncoming air they are travelling through, thereby reducing their aerodynamic efficiency. This subtle effect is one of the reasons why a calculated C d or BC based on shape and sectional density is of limited use. Poisson effect Another minor cause of drift, which depends on the nose of the projectile being above the trajectory, is the Poisson Effect. This, if it occurs at all, acts in the same direction as the gyroscopic drift and is even less important than the Magnus effect.

It supposes that the uptilted nose of the projectile causes an air cushion to build up underneath it. It further supposes that there is an increase of friction between this cushion and the projectile so that the latter, with its spin, will tend to roll off the cushion and move sideways. This simple explanation is quite popular.

There is, however, no evidence to show that increased pressure means increased friction and unless this is so, there can be no effect. Even if it does exist it must be quite insignificant compared with the gyroscopic and Coriolis drifts. Both the Poisson and Magnus Effects will reverse their directions of drift if the nose falls below the trajectory. When the nose is off to one side, as in equilibrium yaw, these effects will make minute alterations in range.

Coriolis drift The causes drift related to the spin of the Earth, known as Coriolis drift. Coriolis drift can be up, down, left or right. Coriolis drift is not an aerodynamic effect.

It is a result of flying from one point to another across the surface of a rotating sphere (Earth). For, this effect is generally insignificant, but for ballistic projectiles with long flight times, such as extreme long-range rifle projectiles, and, it is a significant factor in calculating the trajectory. The that is used to specify the location of the point of firing and the location of the target is the system of latitudes and longitudes, which is in fact a rotating coordinate system, since the Earth is a rotating sphere. During its flight, the projectile moves in a straight line (not counting gravitation and air resistance for now). Since the target is co-rotating with the Earth, it is in fact a moving target, relative to the projectile, so in order to hit it the gun must be aimed to the point where the projectile and the target will arrive simultaneously. When the straight path of the projectile is plotted in the rotating coordinate system that is used, then this path appears as.

The fact that the coordinate system is rotating must be taken into account, and this is achieved by adding terms for a 'centrifugal force' and a ' to the. When the appropriate Coriolis term is added to the equation of motion the predicted path with respect to the rotating coordinate system is curvilinear, corresponding to the actual straight line motion of the projectile. For an observer with his frame of reference in the northern hemisphere Coriolis makes the projectile appear to curve over to the right. Actually it is not the projectile swinging to the right but the earth (frame of reference) rotating to the left which produces this result.

The opposite will seem to happen in the southern hemisphere. The direction of Coriolis drift depends on the firer's location or on the sphere, and the of firing. The magnitude of the drift depends on the location, azimuth, and time of flight. The Coriolis effect is at its maximum at the poles and negligible at the of the. The reason for this is that the Coriolis effect depends on the vector of the angular velocity of the Earth's rotation with respect to xyz - coordinate system (frame of reference). Lateral throw-off Lateral throw-off is caused by mass imbalance in applied spin stabilized projectiles or pressure imbalances during the when a projectile leaves a gun barrel.

If present it causes dispersion. The effect is unpredictable, since it is generally small and varies from projectile to projectile, round to round and/or gun barrel to gun barrel. Maximum effective small arms range The maximum practical range of all and especially high-powered depends mainly on the aerodynamic or ballistic efficiency of the spin stabilised projectiles used. Long-range shooters must also collect relevant information to calculate elevation and windage corrections to be able to achieve first shot strikes. Evaluation small arms external ballistics software. 'Precision Shooter's Workbench©' and 'Field Firing Solutions©' fully functional 30-day free evaluation programs for Windows and PDA - Pejsa model. 'BallistiX' fully functional time limited evaluation program for Windows and MAC using US customary units - Pejsa model See also.

The behaviour of the projectile and propellant before it leaves the barrel. The behaviour of the projectile upon impact with the target. Basic external ballistics mathematic formulas. Procedures or 'rules' for a rifleman to accurately engage targets at a distance either uphill or downhill. Most spin stabilized projectiles that suffer from lack of dynamic stability have the problem near the speed of sound where the aerodynamic forces and moments exhibit great changes. It is less common (but possible) for bullets to display significant lack of dynamic stability at supersonic velocities. Since dynamic stability is mostly governed by transonic aerodynamics, it is very hard to predict when a projectile will have sufficient dynamic stability (these are the hardest aerodynamic coefficients to calculate accurately at the most difficult speed regime to predict (transonic)).

The aerodynamic coefficients that govern dynamic stability: pitching moment, Magnus moment and the sum of the pitch and angle of attack dynamic moment coefficient (a very hard quantity to predict). In the end, there is little that modelling and simulation can do to accurately predict the level of dynamic stability that a bullet will have downrange. If a bullet has a very high or low level of dynamic stability, modelling may get the answer right.

However, if a situation is borderline (dynamic stability near 0 or 2) modelling cannot be relied upon to produce the right answer. This is one of those things that have to be field tested and carefully documented. G1, G7 and Doppler radar test derived drag coefficients (C d) prediction method predictions calculated with QuickTARGET Unlimited, Lapua Edition. Pejsa predictions calculated with Lex Talus Corporation Pejsa based ballistic software with the slope constant factor set at the 0.5 default value. The C d data is used by engineers to create algorithms that utilize both known mathematical ballistic models as well as test specific, tabular data in unison to obtain predictions that are very close to actual flight behaviour. The website defines effective range as: The range in which a competent and trained individual using the firearm has the ability to hit a target sixty to eighty percent of the time.

In reality, most firearms have a true range much greater than this but the likelihood of hitting a target is poor at greater than effective range. There seems to be no good formula for the effective ranges of the various firearms. The US Army Research Laboratory did a study in 1999 on the practical limits of several sniper weapon systems and different methods of fire control. An example of how accurate a long-range shooter has to establish sighting parameters to calculate a correct ballistic solution is explained by these test shoot results. A.338 Lapua Magnum rifle sighted in at 300 m shot 250 (16.2 g) Lapua Scenar bullets at a measured muzzle velocity of 905 m/s. The ρ during the test shoot was 1.2588.

The test rifle needed 13.2 mils (45.38 ) elevation correction from a 300 m zero range at 61 latitude ( changes slightly with latitude) to hit a human torso sized target dead centre at 1400 m. The ballistic curve plot showed that between 1392 m and 1408 m the bullets would have hit a 60 cm (2 ft) tall target. This means that if only a 0.6% ranging error was made a 60 cm tall target at 1400 m would have been completely missed.

When the same target was set up at a less challenging 1000 m distance it could be hit between 987 m and 1013 m. This makes it obvious that with increasing distance apparently minor measuring and judgment errors become a major problem. External links General external ballistics. Tan, A., Frick, C.H., and Castillo, O. 'The fly ball trajectory: An older approach revisited'.

American Journal of Physics 55 (1): 37. (Simplified calculation of the motion of a projectile under a drag force proportional to the square of the velocity). Retrieved September 26 2005. basketball ballistics.

Small arms external ballistics. Speer Reloading Manual Number 11, Omark Industries, 1987 (no ). Artillery external ballistics. Doppler radar tracking systems.

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