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As gauss-building comes forward, models appear with relatively high initial velocities, I think it’s time to rise the question about accuracy of coilguns. To answer this question one should at first mention the important fact: in contrast to pneumatic and firearms, the projectile in coilguns is moving inside barrel with some gap (i.e. the diameter of the projectile is a bit smaller than one of the barrel). The reason is simple – it is just a way to reduce friction which degrades efficiency of acceleration (not so large itself).newLet us consider the gap as
The picture shows that the projectile leaving the barrel with deviation angle f = l ·sin α = D - d ·cos α (1)
Then, considering small α (i.е. cos α ≈1), we easily get
The same situation for spherical projectile (fig .2):
Now the trajectory of maximal deviation will be the tangent to the sphere crossing the end of barrel, and deflection angle is:
Let’s find out how the deviation
It is seen that
Inserting equations (1) and (2) for - for cylindrical projectile:
(5)
or
(5a) - for spherical projectile: (6)
(6a)
As we can see, deviation is proportional to Now let’s do some quantitative estimations: Suggest, we have 8 mm caliber projectile and gap of 50 microns ( in real amateur coilguns the gap makes 100 microns and more because of many reasons, the main of them - low rigidity and roughness of thin-wall tubes which the barrels are made of). Then The cylindrical one with diameter-to-length ratio of 1/3 in the same conditions will give only 2,1 cm deviation. Of course, these values are only qualitive, as the projectiles must not always fly along the trajectories of maximum deviation depicted earlier, but the tendency is clear - the deviation for cylinder is much smaller than for ball. It is intuitively obvious because elongated cylindrical body plays a role of "stabilizer" preventing projectile from large deviation while leaving a barrel. It is interesting to compare these speculative assessments to real experiments dedicated to investigations of accuracy of EM-3 coilgun which are situated d/l ratio of about 0.035, moving inside barrel of 5.9 mm inside diameter. According to (5), we get 2.56 cm deviation on 10 m distance, which perfectly coincides to the experimental results (2.5 cm scattering in single-arrow shooting). Such a precise agreement is of course accidental because we didn't account for many factors (for example flexibility of arrow in this specific case), but it illustrates correctness of the suggested method.
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