Now we proceed to the most accurate approximate method used by Sierra Bullets. Only proper ballistic calculator can do better.
But there's no free lunch - we'll need information not normally found in ballistic tables, namely vertical bullet drop at various distances. See the following picture for explanation.
As before, red line (LOS) goes straight from shooter's eye to target. Green line is bore axis.
Blue arrow d is bullet path, perpendicular to LOS. Coyote brown arrow d' is vertical drop. In absence of gravity, the bullet would continue along bore axis and drop would remain zero. On Earth drop is zero at the muzzle and negative throughout the rest of trajectory -- that is, below the bore axis. Bullet path, on the other hand, can be either positive or negative (above or below the LOS).
To calculate drop table in JBM, set sight height to 0 and zero distance to 1 m.
Sierra's correction is calculated as follows:
1. Measure inclination α;
2. Measure the slant distance (along LOS) D;
3. Look up in regular ballistic table bullet path d that corresponds to distance D;
4. Look up in drop table drop d' that corresponds to distance D and flip its sign;
5. Sierra's correction = d + (1 - cos(α)) * d'
GP11 vertical miss distance, cm
Terrific, isn't it?
Domain: as far as the eye can see
Complexity: complex! 2 table lookups, 3 mathematical operations
Pros: accuracy is as good as it gets
Cons: too complex to be useful, requires extra data (regular ballistic tables are not enough)
Shooting rules of thumb should work under stress. Sierra method is too complex to be of much use in such scenario. Even setting aside practicality of two sets of tables, the chance of getting the calculation wrong or not fast enough is too high.
So none of the methods so far is acceptable. It does not appear possible to have your cake and eat it, too. Yet there is light at the end of the tunnel. Read on.