# slope dope

## Inclined Fire, part #4: 2I2R in practice (prototyping)

Now that we have mastered the arcane science of the world's best heuristic method to estimate slope dope, how would we live with this knowledge in real life? Even the best method is pointless without an action plan.

Let's start with border conditions, where heuristics still make sense. The logic is simple:

## Inclined Fire, part #3.5bis: 2I2R for victims of MOA

And now folks, a special edition of the 2I2R for unfortunate owners of scopes with clicks graduated in ¼MOA. (Many of my good friends fell victims of this perversion; US manufacturers of [otherwise excellent] scopes seem to love this.)

Improved Rifleman's rule:

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 by cos(α).

## Inclined Fire, part #3.5: Even Better Rifleman's Rule

Here it comes.

EBRR?

or

Increasingly Improved Rifleman's Rule = IIRR? 2I2R = two-eye-two-arr?

Naming contest is still ongoing, suggestions are welcome.

When analyzing errors of Improved Rifleman's Rule (which appeared the most promising), I noticed that they are more or less (well enough for a *heuristic* method) linear in distance, at least for angles beyond ±20º.

**GP11 Improved Rifleman's Rule errors, 0.1 mrad clicks**

## Inclined Fire, part #3.4: Sierra's

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.

## 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**

## Inclined Fire, part #3.2: Rifleman's rule

Moving on to the most popular empirical method - Rifleman's rule.

The idea is very simple:

1. Measure inclination α;

2. Measure distance to target D (along line of sight);

3. Calculate equivalent horizontal distance De = D * cos(α);

4. Look up compensation as if shooting horizontally at distance De.

## Inclined Fire, part #3.1: NDS, or the fall of the favorite

I started with NDS method first because their other methodologies seem to be simple,

straightforward, and highly applicable. I consider their sniper/DMR training and Perotti's

book on sniping top of the line.

In that book, "From 1 to 1,000", inclined fire is covered by a couple of paragraphs that say approximately the following:

## Inclined Fire, part #3: Options

Now let's see when inclination does matter.

The table below shows what happens when slope is ignored, i.e. there is no correction for inclination. (Errors in cm, same color coding as above).

**GP11 vertical miss distance, cm**

## Inclined Fire, part #2: When it doesn't matter

It's easy to google gory details on gyroscopic precession and Coriolis force and analyze every minute factor, but when (and if) is it worth doing?

Case study: standard army issue Fass 90 assault rifle, 300 m battle zero. How does it behave when shooting at an angle?

The Swiss army manual responds with exactly one concise sentence: "when shooting at an angle beyond ±30º, aim low". Not much for a mountainous country.

## Inclined Fire, part #1: Definitions

Before jumping into formulas it makes sense to get an intuitive understanding of forces at work. School-level knowledge of Newton's laws of motion and basic trigonometry will suffice.