NSST SPECIAL EVOLUTIONS TRAINING INSTRUCTIONAL MODULE MODULE MATH FOR THE OOD (I) (APPLICATIONS FOR UNREP OPS) REVISION DATE: 6 NOVEMBER 2015 1
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BEST PRACTICES / SHIP INFORMATION SHEET MODULE MATH FOR THE OOD (I) STUDENT HANDOUT Some Math for the OOD basic concepts and best practices: 1. The Radian Rule and its Applications. From high school math, we recall there are 2 pi radians in a circle. If we use a value of 3.14 for pi, through division we can calculate that there are 57.3 degrees in a radian or 60 degrees by rounding up. The Radian Rule, simply put, states that for every angle of one degree, the ratio of the long side of a triangle to the short side, within a circle, is 60 to 1. The basic equation or relationship in analyzing the one-degree segment of a circle is R/60. R equals the radius, or range for our purposes. If the long side of a triangle/radius of a circle is 600, a one degree angle subtends an arc that has a chord length of 10. Example: A contact 3 degrees off your starboard bow at 4000 yards is DIW. How close will you pass if present course in maintained? Three degrees, divided by 60, or 1/20 of a radian, is 1/20 th of the range to the contact, or 200 yards. Another way to do the math is to return to the mental circle diagram. We can state what we already know in slightly different terms; an angle of one degree will subtend an arc on the circle that has a length of 1/60 th of the radius, or R/60. In this example, the range divided by 60 (4000/60) is equal to 66.66 yards. This distance times the 3 degrees equals 200 yards. 2. The Radian Rule can be applied to several different operations, such as contact management, underway replenishment approach, and handling the ship alongside. The most common application of the Radian Rule is in UNREP operations. By calculation, desired lateral separation (from the delivery ship) can be used to build a table that provides angular offset for given ranges. This information can be used during an UNREP approach to determine the approaching/receiving ship s position relative to the desired approach path. The worksheet in this lesson s handout can be used to perform the calculations and construct a table that provides angular offset and true bearing to the delivery ship for given ranges. 3. During the alongside phase of UNREP operations, the 1-minute rule (speed in knots times 100 equals distance traveled in feet) can be combined with the Radian Rule to determine lateral closure/opening rate. For a replenishment (ROMEO) speed of 13 knots, the ship will travel 1300 feet in one minute. Let s return to the earlier discussion of analyzing a one-degree segment. For a radius/range of 1300 feet, the chord of a one-degree angular segment is equal in length to R/60, or 1300/60 = 21.66 feet. Let s round this value to 22 feet. At 13 knots, for every course adjustment of 1 degree, the ship will move 3
laterally 22 feet in one minute. As conning officer, if I feel I am too wide on the delivery ship and adjust my course by 2 degrees towards the oiler, after 1 minute, I will have reduced the lateral separation by 44 feet. 4. Surge Rate and its Application in Shiphandling. Surge rate refers to the distance a ship travels between the time a speed change is initiated and the ship is actually at the new speed. The surge rate can vary widely by ship class and by initial speed. Surge rates can be derived from the ship s acceleration tables. For gas turbine surface combatants, 25 yards per knot (of speed differential) can be used as a surge rate rule of thumb during UNREP ops. Based on the information from the acceleration tables or by using an established rule of thumb, the distance traveled while effecting a speed change can be determined by multiplying the surge rate (expressed in yards per knot) by the magnitude of the speed change (in knots). This figure can be used to calculate the relative position of the speed cut when making an approach on an UNREP ship. Proper utilization of surge rate enhances sharp and concise ship-handling, and results in effective underway replenishment approaches or the arrival on station in any maneuver requiring a speed change. 5. The Five Degree Maneuver and its Use. The five degree maneuver is used to expedite opening the distance between ships that have gotten too close during underway replenishment. As ships that are alongside get closer, the low pressure area between the hulls becomes more of a factor exerting greater attraction between the ships. At close separation, attempts to open the distance by changing course will cause the stern to swing even closer to the other vessel, increasing the possibility of a collision. For a six hundred foot ship moving ahead with its pivot point relatively forward, one degree of course change will cause the stern to swing in by 10 feet, but also add 22 feet to the opening vector as we discussed in paragraph 3 above. A five degree course change will cause the stern to swing in 50 feet, but also add 110 feet per minute to the opening vector. As such, the stern will not complete the swing through 50 feet as the opening vector takes effect quicker and the ship opens rapidly. The key step is to execute the five degree maneuver before the two ships reach 50 feet of lateral separation. Ordering the five degree maneuver. In this type of situation with a master helmsman who has been briefed on executing the maneuver, the five degree maneuver should be executed by giving a course order (i.e. Come right (or left) smartly to XXX (ROMEO CORPEN +/- 5 degrees). The helmsman will know what is required to smartly execute the course change. The challenge lies in returning to replenishment course before the ships have opened too far. 4
STUDENT NOTETAKING GUIDE MODULE MATH FOR THE OOD (I) The Radian Rule and its Applications From high school math class, we know there are 2 pi radians in a circle. From this value, we can calculate that one radian is equal to degrees. To keep things simple, we round this number to 60. To analyze a one-degree segment, i.e., determine the chord length, we use the equation: R/60 where R represents. The Radian Rule has two applications in UNREP operations. The first application is used to assist the conning officer in making the approach on the delivery ship. A table can be constructed (see the handout) that allows us to use a numerical constant based on desired lateral separation to provide angular offset (converted to true bearing) to the oiler for set ranges. The second application is used when alongside to fine tune lateral separation. By using the one-minute rule in conjunction with a standard replenishment speed of 13 knots, we know that for each course adjustment of one degree, our ship will move laterally feet per minute. Surge Rate for my ship is:. Surge Rate is used to: The Five Degree Maneuver and its Application The Five Degree Maneuver is used to prevent a collision during alongside operations. The critical timing decision in executing this maneuver is: The proper order to the master helmsman is, Come right / left smartly to (course). 5
HANDOUT, MATH FOR THE OOD (I) UNREP APPROACH, APPLYING THE RADIAN RULE 1. Desired lateral separation: ft. / yds. 2. Translate the desired lateral separation into what the angular offset will be at a range of 600 yards from the delivery ship. NOTE: At a range of 600 yards, one degree of angular offset equals 10 yards / 30 feet of lateral separation. Divide the desired lateral separation by 30 feet (or 10 yards). This gives you the angular offset in degrees. The angular offset at a range of 600 yards will be degrees. 3. Multiply 600 yards by the angular offset value determined in step 2. This value serves as a numerical constant that can be used to determine the angular offset for any given range. This constant can be expressed as the rule of. For example, for a desired lateral separation of 180 feet / 60 yards, the angular offset at a range of 600 yards to the delivery ship is 6 degrees. Multiply 600 by 6 to obtain a rule of 3600. Using the rule of 3600 (remember, it applies only for a desired lateral separation of 180 feet), the angular offset for any range can be calculated by dividing 3600 by the range: 3 degrees for 1200 yards, 4 degrees for 900 yards, 6 degrees for 600 yards, etc. 4. Now, a table can be created that will serve as a ready reference for range versus angular offset and true bearing to the delivery ship. Divide the value of the constant by the ranges listed below. This will give the angular offset for each range. Apply the angular offsets to ROMEO CORPEN to give a desired true bearing to the oiler for each range. NOTE: When using own ship s port side during replenishment, subtract the angular offset from ROMEO CORPEN to obtain true bearing. For evolutions using own ship s starboard side, add the angular offset to ROMEO CORPEN to obtain true bearing. VERY IMPORTANT POINT this true bearing is what the outer edge/outer most object on the delivery ship s engaged side will be if own ship is on the approach path, i.e., at the desired lateral separation. If the observed true bearing is too large or too small, make a slight course adjustment to correct this. Also, this observation must be made from your engaged side s bridge wing. ROMEO CORPEN: Own Ship s Engaged Side: P / S RANGE (YDS) VALUE OF THE CONSTANT ANGULAR OFFSET TRUE BRG 1200 1000 800 600 400 6
UNREP APPROACH, CHECKING STATION-TO-STATION LINE-UP APPLYING THE SURGE RATE 1. Checking Station-to-Station Line-up: a. Line-up provided by the CLF ship: Delivery ship stations: Receiving ship stations: b. Fore and aft separation between stations: Delivery ship stations: Receiving ship stations: 2. Applying the surge rate: a. Receiving ship s surge rate: yards/knot of speed differential b. Romeo speed: 13 knots c. Desired approach speed: knots d. Predicted distance traveled during deceleration: yards e. Predicted distance traveled during deceleration: feet f. Delivery ship s LOA: feet g. Speed cut reference point (on delivery ship): feet aft of bow h. Speed cut reference point (on delivery ship): feet forward of stern i. Speed cut reference point visual cue (on delivery ship): 7