![](https://blog.usni.org/wp-content/uploads/2015/06/Screen-Shot-2015-06-25-at-6.34.24-PM.png)
As a Junior Officer, it was very enjoyable to drive for an Underway Replenishment (UNREP) – with the sole exception, that is, of trying to make sense of the Radian Rule. I have strong memories of my attempts to internalize the relationship between the bearings and ranges. There always seemed to be one, but I never quite made it to a coherent understanding until much later in sea duty years. As an XO and CO recently, I finally had a more mature understanding of this important ship driving principle as well as numerous opportunities to train and coach Midshipmen and Junior Officers during UNREP events. In this article, I’d like to share a few approaches that take advantage of a more nuanced understanding of this well-known guidance.
The Radian Rule Equation and Its Uses
The rule of thumb that’s encoded in every table of Radian Rule values is laid out below. There are several ways to capitalize on this understanding as the team is either preparing for or executing an UNREP approach. I’ll start with a couple of the more common ones and then introduce three favored approaches to the problem. As a baseline assumption, the goal distance I’ll use for alongside separation is 180 ft. I think you’ll see soon, however, that they work equally well for any alongside separation distance.
Common Techniques
Technique #1: Make a List
From a new Conning Officer’s point of view, this was a fairly common approach to the problem of understanding and using the Radian Rule. Many Junior Officers arrived for both the brief and the evolution with a list of bearings and ranges that would indicate the ship was on track for the desired separation. Such a list might look like this:
This technique works well if the team is able to verify bearing to the oiler at each of the yardage milestones on the list, since a single data point is seldom as valuable as a series of consecutive observations. This method is less useful if the range for a given observation isn’t one of the milestones, or if the team misses a milestone.
Technique #2: Use a Radian Rule Table to Determine Separation Distance
This technique is by far the most common, and involves a third party (typically a Quartermaster) looking up each bearing and range combination in a table similar to the excerpt shown below. While it ensures that each data point is useful in determining the overall trend of the ship’s relative motion with respect to the oiler, this method – in my opinion – doesn’t help substantially to develop the Conning Officer’s understanding of that motion. Stated differently, the difference between a good and a great Conning Officer is the ability to add his/her own evaluation of a situation to the input they get from the rest of the bridge team. I believe there are more effective ways (discussed further below) to build this capability in our Junior Officers.
A Note on Advanced Techniques
Techniques #3 – #5 have one prominent feature in common – they all depend on mental math. While this may present a challenge, there are several advantages to these methods. First, mental math promotes independent judgment by the Conning Officer and/or coach for each observation throughout the approach evolution. Second, the mental math in these methods requires that the Conning Officer and/or coach build a mental model of the relative motion and internalize the relationships among bearing, range, and lateral separation. Third, from the Conning Officer’s point of view, these techniques offer a different way to learn the evolution and may appeal more intuitively to certain Officers. Finally, from the coach’s point of view, these techniques offer yet another mental tool for dispassionately evaluating the sight picture and ensuring the bridge team is appropriately focused on providing good inputs to the Conning Officer.
With these points in mind, I’ll introduce three non-traditional techniques. Each of these relies on the Conning Officer’s and coach’s ability to mentally exploit various forms of the baseline Radian Rule equation.
Advanced Techniques
Technique #3: “The Rule of 3600”
This technique works well in concert with either Approach #1 or #2 above. Since the separation distance for which we’re aiming is a constant (180 ft in this case), the right side of the equation becomes a constant:
Simplifying the Radian Rule equation, then, we get the following:
For any combination of bearing and range, we can multiply them and compare them to 3600. If the product is less than 3600, the ship is approaching the oiler at something less than 180 ft of separation. If the product is greater than 3600, the ship will approach the oiler wide of 180 ft separation. A few examples below illustrate this principle.
While it’s an imperfect measure, this technique allows the Conning Officer to corroborate his or her visual judgment with a quick check of the math, and then to combine those judgments with either of the first two approaches to refine the solution. This technique is very flexible with respect to desired separation distance, as well. If the goal is 200 ft, for instance, then the constant becomes 4000. Finally, this technique provides a good gateway to the next two approaches.
Technique #4: “Where Should You Be Right Now”
With range as an input, the Conning Officer works out the bearing he or she expects to see and then compares that prediction to reality (measured bearing separation). Direction and magnitude of any required course corrections follow relatively easily. The baseline equation, solved for bearing, follows.
This technique is a modification of technique #1, and it has two principal benefits. First, it helps the Conning Officer avoid the persistent need to divert attention from the approach to consult a list of bearings and ranges. Second, it helps to build the Conning Officer’s and/or coach’s comfort with mental math.
Technique #5: “Predict the Separation”
This technique is a modification of technique #3 and an extension of technique #4, using a different arrangement of the equation to anticipate the estimated separation for each bearing and range combination. Solving the Radian Rule equation for separation, the expression becomes:
Once the Conning Officer is adept at the mental math of multiplying the bearing and range, the only remaining step is to divide by 20. The simplest way to do this is to remove a zero and divide by two. A sample is shown below.
This is a mental math version of Approach #2. While this is more difficult than any of the four previous techniques, the principal benefit to this approach is that it gives the Conning Officer and/or coach convenient tools to mentally evaluate the geometry they are seeing on the bow. For the Conning Officer, the nuanced context available from each observation constructively builds the spatial judgment and physical intuition we call Seaman’s Eye. This technique allows the Conning Officer to take maximum advantage of sometimes-scarce evolutions and reinforces a more subtle understanding of the relative motion between ships that sometimes eludes the most seasoned veterans. I found it to be tougher than the other techniques to teach and use, at least at first, but it was infinitely more rewarding when the Conning Officer understood it and was able to use it.
Conclusion
It takes time and effort to learn how to safely conn the ship alongside. Proven techniques that have propelled ships alongside safely for decades are available to those who will take the time to learn and use them, and they can be improved with a small investment in systematic thinking about the geometry built into the evolution. Techniques #3 – #5 suggest ways to exploit the mathematical relationships inherent to the Radian Rule that offer two significant benefits. First, they build confidence in coaches by encouraging a more intuitive understanding of the relative motion throughout the UNREP approach. Second, they help build Seaman’s Eye in our Junior Officers by sharing those insights with the fertile minds of the Officers who drive the ship most frequently, and who are most apt to exploit them effectively.