Since the invention of radar and sonar, most ship rangefinding methods have required the radiation of energy—electromagnetic or sound—that an adversary can intercept. In restrictive emissions control (EmCon) environments, remaining undetected may provide a crucial tactical advantage. As a result, finding the range to other vessels without giving away your position presents a particular challenge.
In the interest of increasing the variety of passive rangefinding options available to all surface ships, we propose three new methods of visual rangefinding. The first, known as the “pelorus rangefinder,” uses relative bearings from a known distance between two peloruses to measure the distance from the point midway between the peloruses to the target vessel. The second and third methods, called “half-length horizontal sextant angle” and “full-length horizontal sextant angle,” are similar to the vertical sextant angle and stadimeter methods but rely on the known length or breadth of the target vessel and an estimation of the relative bearing of the observer’s vessel to the target vessel (i.e., “target angle”).
All three methods require seeing the target. The “half-length horizontal sextant angle” method also relies on accurately estimating the midpoint of the length or breadth of the target vessel. These conditions are not ideal for determining range to an adversary from which a Navy ship is also trying to remain hidden. However, these methods are useful when operating with friendly forces or when piloting the ship in confined waters. Frequent underway replenishments while in EmCon as well as piloting near shoal water offer many opportunities to use these passive rangefinding methods to navigate safely.
Pelorus Rangefinder
The pelorus rangefinder is operated in a manner similar to that of the optical coincidence rangefinders of old. Instead of creating a right triangle with a movable base and measuring one angle with high precision, ship peloruses are used to measure the relative bearings to a target. This method has a limited maximum range, compared with other optical means, but it can be useful for measuring the range to aids to navigation, increasing the navigator’s options for fixing a ship’s position. One benefit over sextant angles is it does not require the bearing takers to shift between using sextants and using the telescopic alidade, resulting in faster observations. Furthermore, it can be used when there is a loss of gyrocompass and magnetic compass headings.
The first step is to measure the relative (R) bearings from the port bridge wing (P) and starboard bridge wing (S) to the target. (Note: If P or S = 270 degrees R or 090 degrees R, this method cannot be used because the bearings would be on the same line of bearing, and there would be no triangle.) Then, the inside angles of the triangle in Figure 1 (on page 82) are calculated with the following logic:
If TA = 090°R or 270°R, then the ABeam = 0°.
If TA > 000°R and < 090°, then ABeam = 90-TA.
If TA > 090°R and < 180°R, then ABeam = TA-90.
If TA ≥ 180 and ≤ 270°R, then ABeam = 270-TA.
If TA ≤ 360°R and ≥ 270°R, then ABeam = TA-270.
If TA = 000°R or 180°R, then ABow/Stern = 0°.
Next, sides aPR and bPR are calculated using the Law of Sines (Equations 2 and 3). Finally, the distance, mc, is calculated by solving for the median of the triangle (Equation 4). With a precision of 0.5 degrees, the minimum measurable angle (CPR) would be 1 degree. For peloruses 10 yards and 20 yards apart, this translates to maximum measurable range of 572.9 yards and 1,148.9 yards, respectively.
Horizontal Sextant (Half-Length)
The half-length horizontal sextant angle method starts with measuring the angular distance between midships and the bow or stern or the centerline and the port or starboard extremity (angle CHL of Figure 2). Then, index correction (I.C.) is applied and the observed sextant angle is converted from degrees-minutes to degrees using Equation 5. Next, the angle on the beam, ABeam, or angle on the bow/stern, ABow/Stern, is calculated from the estimated target angle, TA, using the following logic:
If TA = 090°R or 270°R, then the ABeam = 0°.
If TA > 000°R and < 090°, then ABeam = 90-TA.
If TA > 090°R and < 180°R, then ABeam = TA-90.
If TA ≥ 180 and ≤ 270°R, then ABeam = 270-TA.
If TA ≤ 360°R and ≥ 270°R, then ABeam = TA-270.
If TA = 000°R or 180°R, then ABow/Stern = 0°.
The remaining angles of the triangle are calculated using Equations 6 and 7. Finally, the distance to the target is calculated using Equation 8, where the half-length or half-breadth forms side cHL. A Flight IIA Arleigh Burke–class destroyer (509.5 feet long) observed broad on the beam 4,864.87 yards away will have 1 degree of sextant angle; at 9,730.49 yards, the same ship would be observed with 30 minutes of sextant angle.
Horizontal Sextant (Full-Length)
The second horizontal sextant angle method mimics the first, but instead of using half the length or breadth of a ship, it uses the length overall and greatest breadth (Figure 3). To account for this difference, the apparent length of the ship (cFL) is calculated from the angle on the beam or bow/stern using Equation 9. Because this method treats the observer as the vertex of an isosceles triangle, the supplementary angles to the observed sextant angle must be calculated (Equation 10). With cFL and angles AFL and BFL, sides aFL and bFL and the median of side cFL can be calculated with Equation 11.
A Flight IIA Arleigh Burke–class destroyer observed broad on the beam at 9,730.85 yards will have 1 degree of sextant angle and 30 minutes of sextant angle at 19,461.53 yards.
Learning and using these three methods will help surface warfare officers, especially navigators, determine range passively in restrictive EmCon environments, something that may be required in the near future.
