The Rule of 25

Introduction: One think I learned from the review of my second year of DP articles is that I am too ambitious. I tend to choose too big a subject, try to cover too many complications, and blab on too long as a result. Another thing that it reminded me was that the basics need to be constantly revisited and made clear and practical. This article is an attempt at that. I’m going to try cover a basic idea without blabbing on.

Tying My Hands: We always tell DPOs to monitor the load on thrusters, as well as the thruster feedback. Then we talk about curves and people’s eyes glaze over. So I want to cover a simple benchmark instead. I’m going to limit myself to fixed pitch variable speed thrusters in a rectangular ship or rig with an azimuth in each corner and a two split redundancy concept – port forward and starboard aft thruster in one redundancy group, starboard forward and port aft thruster in the other redundancy group, and the ship’s center of gravity dead in the middle if you draw a line from thruster to thruster. This limits what I can look at and allows me to introduce what should be a well-known rule of thumb, as it applies to many modern vessels.

Rule of 25: If I have a two split redundancy system and enough power to drive each thruster to 100%, then at what power level would I lose redundancy in this vessel? Some people might be tempted to say “2 split, so 50% load”, but that ignores the thrust/power relationship and need for dynamic margin. The ideal answer is 25% and the practical answer is less. Let me explain why.

Thrust/Power: Let’s start with the fixed pitch, laminar flow, thruster/pump relationships, water flow is proportional to blade rotation speed, pressure or thrust is proportional to the square of the blade speed, and power is proportional to the cube of the blade rotation speed. To simplify it, the % of full thrust is the (% of full speed) squared [% of full speed times % of full speed], and the % of full power is the (% of full speed) cubed. So a thruster running at 50% speed is producing 25% thrust (0.5x0.5) and drawing 12.5% power (0.5x0.5x0.5). 70.7% speed is 50% of full thrust is 35% of full power.

Dynamic Margin: Ships move around a bit because environmental loads vary and there are always some unknowns and limits to the DP control system reaction. To model this in DP capability plots, they take away 20% of the thrust to hold it in reserve to deal with these dynamic problems. The plots show the static capability with 80% thrust available, because they know that the extra 20% is needed to deal with dynamic variation. (If you have read my articles on DP plots then you know that many vessels require more, but we will ignore that for now)

WCF: This means that when you look at a worst case failure capability plot, it is showing what the vessel can hold at steady state with 80% thrust, if everything is modeled right. 80% thrust during the worst case is the thrust limit, so with a 2 split system, the maximum 80% WCF thrust becomes 40% redundant thrust limit with both groups intact, because 40% of full thrust plus 40% of full thrust = 80% WCF thrust after the loss of one redundancy group.

25: We know the relationship between % of full speed, thrust, and power, so if we know that 40% is the maximum redundant thrust for our simple example, then the maximum redundant speed is 63% and the maximum redundant load is 25%. A perfect, 2 split, vessel with fixed pitch, variable speed propellers loses DP redundancy when it exceeds 63% speed or 25% power.

Why not the Rule of 63? Mostly because the ships are limited by available power rather than shaft speed. Converting limited power to limited shaft speed redundancy levels takes more math, but if you know the thrusters are limited to 80% power, then you can use the 2 split, fixed pitch, variable speed rule of 25 to know that your new redundant power limit is 20% of full thruster power, or that a 60% power limit puts the maximum redundant power at 15%. When you are dealing with thruster power limits and trying to figure out redundancy, you are comparing like for like (power vs. power), so you can use simple mental math to determine the redundant limits, instead of using a chart or a calculator. It’s more intuitive when you are looking at power limits, and many ships are underpowered.

Ideal: This is a simple introduction to a basic relationship between available thruster power and redundant thruster power that can be a handy rule of thumb for DPOs maintaining redundant operation, but it is an ideal example and the real redundant power levels will be less than that. The rule changes for unbalanced thruster effectiveness and losses. I can look at them next week, if people are interested. The relationships also change for variable pitch, constant speed, and for more than 2 split groups. 25% is the maximum possible redundant power for an ideal 2 split vessel with fixed pitch, variable speed thrusters. The rule of 25% also makes FPP VSD vessels very dependent on power management systems, as engines don’t like low loads, but the system needs to respond to thruster demand quadrupling.

Conclusion: Real vessels have additional losses that need compensated for, but a DPO on a real 2 split FPP VSD vessel should know to be suspicious as thruster power approaches 25%. 25% of available thruster power as the redundant thruster power level is a handy initial guide for operators or designers dealing with power limited vessels and considering redundancy.