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Inclined Fire, part #3.3: Improved Rifleman's Rule

The next step towards perfection is attributed to señor Tiro Fijo of Paraguay. It's called "Improved Rifleman's Rule", the only difference being that correction is applied not to distance, but to correction. To wit,

1. Measure the inclination α;
2. Measure the slant distance (along LOS) D;
3. Look up bullet path (come-up) in ballistic table as if shooting at distance D
horizontally;
4. Multiply this correction (and not distance D) by cos(α).

And we get the following:

GP11 vertical miss distance, cm


15 20 25 30 35 40 45
300 1.1 2.0 3.3 5.0 7.1 10.0 13.5
400 1.4 2.7 4.5 6.8 9.7 13.6 18.5
500 1.6 3.1 5.3 8.2 11.9 16.8 23.0
600 1.7 3.5 5.9 9.4 13.8 19.6 27.2
700 1.5 3.6 6.4 10.2 15.3 22.1 30.9
800 1.2 3.2 6.3 10.5 16.3 23.8 33.8
900 0.5 2.5 5.7 10.3 16.5 24.8 35.8
1000 -0.7 1.2 4.3 9.1 15.7 24.6 36.6









-15 -20 -25 -30 -35 -40 -45
300 1.2 2.2 3.6 5.2 7.5 10.3 14.0
400 1.9 3.3 5.1 7.4 10.5 14.5 19.5
500 2.5 4.3 6.7 9.8 13.7 18.8 25.2
600 3.2 5.6 8.6 12.4 17.2 23.4 31.3
700 4.2 7.1 10.7 15.4 21.2 28.5 37.8
800 5.5 8.9 13.3 18.9 25.6 34.3 45.0
900 7.1 11.2 16.4 22.8 30.8 40.6 53.1
1000 9.0 14.0 20.1 27.7 36.8 48.1 62.2

Much better accuracy comes at a price:

1. No more rifle or caliber independence. Unlike Rifleman's Rule, come-ups at any given distances depend on specific weapon system. Can't implement such correction in a universal laser rangefinder.
2. Errors depend on zeroing distance. The further the zero, the more are the errors. (E.g. if rifle is zeroed at 300 and the target is also at 300, this trick is useless, as it gives zero adjustment and equals no slope dope at all.)

Example:

GP11 zeroed at 300 m vertical miss distance, cm


15 20 25 30 35 40 45
300 2.9 5.3 8.6 12.8 18.4 25.5 34.6
400 3.8 7.1 11.4 17.2 24.7 34.3 46.6
500 4.7 8.7 14.1 21.4 30.8 42.8 58.2
600 5.4 10.2 16.7 25.3 36.6 51.0 69.6
700 5.9 11.3 18.9 28.9 42.0 58.8 80.5
800 6.3 12.3 20.7 32.1 46.9 66.0 90.7
900 6.2 12.8 22.1 34.7 51.1 72.5 100.3
1000 5.9 12.8 22.8 36.5 54.4 77.9 108.6









-15 -20 -25 -30 -35 -40 -45
300 3.0 5.4 8.8 13.0 18.7 25.7 34.9
400 4.1 7.5 12.0 17.9 25.3 35.0 47.4
500 5.4 9.6 15.2 22.6 32.2 44.4 59.8
600 6.8 11.9 18.8 27.9 39.3 54.0 72.8
700 8.2 14.4 22.5 33.2 46.8 64.0 86.0
800 10.0 17.2 26.7 39.0 54.7 74.6 99.9
900 12.0 20.4 31.4 45.4 63.2 85.7 114.5
1000 14.4 24.0 36.7 52.6 72.6 97.9 130.1

Not nearly as good.

There are lower bounds on zero distance, both physical (sight height) and practical (existing range distance, pre-calculated tables with a given zero, etc.). Nevertheless this is the only method we tried so far that is acceptable beyond 500 m.

Just like its parent, Improved Rifleman's Rule can be applied to existing ballistic tables.

It is also predictable, although in different direction: underestimates the effect of inclination. Bullet still goes higher, therefore battle zero logic remains useful.

Accuracy: good.
Domain: up to ±30º -- all distances. Up to ±40º -- within 800 m with additional hold.
Complexity: low -- 1 table lookup, 1 mathematical operation.
Pros: reasonable accuracy, simplicity, can use existing tables.
Cons: dependence on zero distance.

Good, but can be even better. Read on.

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Article | by Dr. Radut