We in the business of fighting submarines have become increasingly reliant on gadgets to arrive at estimates of target motion. Whether it’s the ultra-sophisticated BSY-1 fire control system or the Hewlett Packard 9020 with its lovely multi-color display or even the Sharp calculator, more and more we find ourselves waiting for these machines to tell us the answer.

Mental agility, far from dated, has become the benchmark against which the successful Commanding Officer is measured. His ability to rapidly arrive at an estimate of target solution which is “good enough” clearly sets the standard to which the rest of his wardroom will be held. To this end I offer a couple of simple thumbrules which might prove useful, and describe a ranging concept which may enhance the pursuit curve type of target closure without sacrificing the confidence of frequent ranging.

D/E Ranging: The straight line DIE range problem is represented as figure 1. The equation which describes the geometry is; tan(D/E) = Water Depth /(1/2 Range)

Assuming water depth is given in fathoms, we can solve for target range in yards as;

Target Range = 4 * Water Depth/ tan(D/E)

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It doesn’t take a rocket scientist to see that I’ve used a liberal amount of RADCON math to arrive at the DIE factor column in the table above. My defense, sometimes referred to as ‘Fischbeck’s Rule’ is that an easily remembered falsehood is often better than a difficult to remember truth. I would simply point out to the user that the easy to remember falsehood gives ranges which are a little too long.

Granted there are more accurate means available to determine DIE range. Corrections for SVP are developed in the 9020. Bottom slope approximations can be made. In fact, the fire control system can give us a better straight line approximation automatically.

However, consider some of the benefits this simple estimate gives us. ICs quick. Pick the best DIE and multiply the DIE factor by water depth to get range. It provides an invaluable check against all other range sources. Perhaps most importantly, it provides a reasonable bracket for the Approach Officer. If the target is showing up best somewhere between -2ff’ and 45° his range is between four and 12 times water depth. Surprisingly this bracket estimate may be ‘good enough’ for certain combinations of weapons and targets.

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**VIRTUAL RANGING**

Classic target ranging methods employed in solving the TMA problem rely, in one sense or other, on changing ownships speed across the line of sight. While yielding rather accurate estimates, they no longer meld with newer methods of target approach (pursuit). In other words, the TMNapproach problem now consists of distinct and somewhat disjointed phases. A line of sight ranging maneuver is performed to establish both target range and direction of motion. Based on this classical estimate, own-ship will follow a collapsing spiral into the targets stem area and establish a reasonable firing position. Finally, another range estimate is obtained to verify solution and, if favorably positioned, the target is engaged.

PXO class 90040 found that while this methodology generally worked, there was a definite discomfort in the long pursuit phase. The absence of classic, across the line of sight ranging maneuvers lent the sense that you were stumbling into the target rather than conducting a deliberate approach. The following methodology, to be used in bottom bounce towed array situations, relies upon a ranging method which requires a steady speed across the line of sight. This seems more in keeping with the pursuit approach methodology.

We enter the problem after having established initial target range and DRM. We assume that the target is abeam to port. Own-ships speed is six knots. With the target abeam we gain both an accurate bearing and bearing rate. The ship is now maneuvered to put the target 30 degrees off the port bow, speed is increased to twelve knots. Note that own ships speed across the line of sight remains unchanged. With the array steady a best bottom-bounce bearing or hyperbola is derived. If we had a direct path bearing at the same instance we could accurately determine target range (Hybrid hyperbolic cross-fJX).

Let’s pretend that own-ship had remained on it’s initial course and speed. If certain assumptions are invoked (namely linearity of bearing rate) then we could have predicted bearing at any time in the future. Clearly as the time interval over which we make this prediction grows the extrapolation will increasingly suffer from non-linearity effects. However, if we keep the prediction interval reasonable (generally less than 15 minutes, strongly a function of geometry) and accurately estimate bearing rate on the initial leg, our estimate of target bearing in the not-too-distant future should be close to actual.

It follows, then, that while as actual direct path bearing is not available with our hyperbola, there is a virtual bearing, generated from a virtual own-ship, which provides a reasonable approximation. The key clearly is keeping a relatively constant own-ships speed across the line of sight and minimizing the interval over which the direct path bearing is predicted. Given these rather liberal constraints, an accurate estimate of range is derived from cross bearings.