Sizing

Sizing Wizard | Sizing Model

Sizing a gyro stabilization system to obtain a given level of roll reduction in a specific boat is analogous to sizing the horsepower rating of the propulsion system to obtain a given level of speed in a specific boat. In both cases, sizing of the equipment depends upon the objective of the boat owner. You can under-gyro a boat just like you can under power a boat – in both cases the boat owner will be disappointed.

The Seakeeper gyro with its vacuum technology and active control makes it practical, for the first time, to virtually eliminate boat roll in any reasonable condition. Because prior roll attenuation gyros do not use these two important technologies, space, weight and power constraints have limited them to “Stability at Anchor”, meaning that effective stabilization is limited to low sea states.

Seakeeper recommends a higher level of stabilization where possible to achieve a superior level of roll reduction. We do however recognize that “Stability at Anchor” may meet the needs of many yachtsmen while still enjoying the benefits of Seakeeper technology.

A single Seakeeper Gyro system will provide excellent roll reduction for a boat of approximately 35,000 to 55,000 lb full load displacement. Boats with higher displacements will require multiple gyro systems to insure good roll reduction.

To evaluate how many gyro systems your boat will require to get effective roll reduction, go to our easy-to-use Sizing Wizard. This wizard will quickly and easily tell you many gyros are required on your boat by simply providing a few pieces of data.

If you are interested in the more technical details of gyro sizing, scroll down to Sizing Model.

Sizing Wizard

Sizing Model

Background

Fin stabilizers which control roll on monohull vessels operating in the displacement speed range are typical sized using a simple formula that treats ship rolling motion as a hydrostatic problem. This approach overlooks the underlying dynamics e.g. wave conditions, hull shape, boat inertia, added inertia, hull damping, etc. but is effective at sizing stabilizers.

Seakeeper has developed a similar approach for gyro system sizing to make it easy to select the number of Model 7000 Gyros required to provide adequate stabilization on a given vessel. Yacht designers and builders will be familiar with this basic methodology even if it bears little resemblance to the actual physics of the problem.

The Moment to Heel One Degree (MTH1) is a naval architecture term that defines the moment or torque required to statically heel or roll a given vessel one degree. For small angles (~+7 degrees), the Moment to Heel One Degree is calculated from the following formula:

MTH1 = x g x GMT x sin1

Where = Vessel’s displacement in Metric Tonnes (mt)

Where g (gravity) = 9.806 N/kg = 9806 N/mt

GM_T = Vessel’s transverse metacentric height in meters (m)

Sin 1 = 0.018

A fin stabilizer supplier knows how much Righting Moment (RM) their fins can supply at a given location on the hull for a given speed. Typically the supplier will design to supply enough fin area so the ratio of the fin system Righting Moment (FRM) to the Moment to Heel One Degree (MTH1) has a certain value at the vessel’s cruise speed. This ratio (FRM/MTH1) is referred to as the fin stabilization system’s Wave Slope Capacity (WSC).

Fin stabilizer suppliers typically attempt to achieve WSC values of between 3 and 5. A value of 3 usually provides very good stabilization at the cruise speed and a value of 5 provides excellent stabilization at cruise plus margin for slowing down in rough weather, etc. The stabilizer supplier is also attempting to match his product line to the vessel so his quote is competitive and therefore he cannot afford to always quote fin sizes that provide a wave slope capacity of 5 degrees.

Sizing a Model 7000 Gyro for Seakeeper’s 43 foot Viking Demonstration Boat

The system software limits the Gyro Righting Moment (GRM) of the Model 7000 Gyro to produce a maximum value of 15,000 N-m (11,067 ft-lb) by limiting the precession rate to 2.09 radians per second (120 deg/sec). Higher precession rates will shorten bearing life and will not improve roll stabilization since the forces could only act for a brief period before the available gimbal rotation is used up.

The Moment to Heel One Degree (MTH1) on the Seakeeper 43 foot Viking is:

= 19 mt (41,800 lbs)

GM_T = 1.03 m (3.38 ft)

MTH1 = (19 mt) x (9806 N/mt) x (1.03 m) x sin 1 = 3349 N-m/deg

The Gyro has a Wave Slope Capacity of:

Gyro WSC = GRM/MTH1 = 15,000 N-m/ 3349 N-m/deg = 4.5 degrees

Sizing a boat for the Model 7000 Gyro

If the boat’s displacement () and transverse metacentric height (GM_T) are known, compute the Moment to Heal One Degree from the following equation.

MTH1 = x g x GM_T x sin 1 (g = 9.806 N/kg = 9806 N/mt)

The boat’s builder or designer can provide the GM_T since they have to provide it in the vessel’s stability book and probably obtained it through an inclining experiment. If GM_T cannot be found, then assume a value of 1.5 m (4.76 ft) based upon data that shows for 40 to 80 foot (12 to 24 meters) boats the GM_T is typically around this value. However, boats in this size range can have GM_T values as low as 1.0 m and some well over 2 m so care has to be exercised when sizing without the GM_T value since a boat could be under-gyroed and not get the roll reduction expected or over-gyroed and paying for capability that does not provide perceivable improvement in roll reduction.

After calculating the MTH1 value for the boat, compute the Gyro Wave Slope Capacity as follows:

Gyro WSC = (15,000 N-m/gyro) × (number of gyros)/MTH1

Increment the number of gyros in the above equation until the Gyro WSC is between 3.2 and 5 degrees. If it is determined that the project cannot afford enough gyros to achieve a WSC of 3.2 (due to cost, weight, space, power, etc), the project can proceed with a lower WSC but we recommend that Seakeeper does a simulation to check that the solution will provide adequate stabilization and meet expectations.

Examples

1) 46 Ft Production Yacht with = 16.3 mt and GM_T = 1.29 m

Compute MTH1 MTH1 = (16 mt) x (9806 N/mt) x (1.29 m) x sin 1 = 3592 N-m/deg

Compute WSC for one gyro Gyro WSC = (15,000 N-m/gyro x 1 gyro)/(3592 N-m/deg) = 4.2 deg One gyro is sufficient

2) 68 Ft Production Yacht with = 40.4 mt and GM_T = 1.65 m

Compute MTH1 MTH1 = (40.4 mt) x (9806 N/mt) x (1.65 m) x sin 1 = 11,436 N-m/deg

Compute WSC for two gyros Gyro WSC = (15,000 N-m/gyro x 2 gyros)/(11,436 N-m/deg) = 2.6 deg Two gyros are required

In this case, the boat has over twice the displacement of the Seakeeper 43 foot Viking but it has a very high GM_T compared to the Viking probably due to a wide beam. The WSC is only 2.6 deg for two gyros versus 4.5 deg on Seakeeper’s Viking 43. Running simulations on this boat to check that the vessel will be adequately stabilized with two gyros confirmed that over 60% roll reduction can be achieved in a sea state having a significant wave height of 0.8 m. With one gyro, the WSC would only be 1.3 deg and barely a 40% roll reduction will be achieved which is not sufficient.

3) 68 Ft Production Yacht with = 40.4 mt and GM_T = 1.0 m (Same as Example 2 with GM_T = 1 m)

Compute MTH1 MTH1 = (40.4 mt) x (9806 N/mt) x (1.0 m) x sin 1 = 6914 N-m/deg

Compute WSC for one gyro Gyro WSC = (15,000 N-m/gyro x 1 gyros)/(6914 N-m/deg) = 2.2 deg One gyro may be insufficient

In this case, we have the same boat as Example 2 but with the GM_T reduced to 1 m. The WSC is only 2.2 deg for one gyro which is below our 3.2 deg lower limit. Running simulations in the same sea state as Example 2 confirmed that on this vessel because of the low GM we can achieve a 60% roll reduction with one gyro (versus barely 40% on the same vessel with one gyro and high GM_T in Example 2). Obviously, two gyros would be even better on this vessel but if cost or space was a major issue a one gyro installation could be acceptable from a performance point of view.

The simulation discussed above is a 1 degree-of-freedom boat motion simulation to predict the roll motions of a bare hull or a gyro stabilized hull in irregular beam seas at zero speed. In order to run this simulation, we need the following information from the designer or builder of the vessel:

- Full Load Displacement
- Transverse Metacentric Height (GM_T)
- Waterline Length (LWL)
- Waterline Beam Max (BWL_Max)
- Waterline Beam at Transom (BWL_Transom)
- Deadrise Angle at BWL_Max(ß_BWLmax)
- Deadrise Angle at Transom(ß_Transom)

What is Transverse Metacentric Height?

From the discussion above, you can see that Transverse Metacentric Height (GM_T) is an extremely important parameter in boat stability and in selecting the appropriate number of gyros to eliminate roll. Below is a brief, non-mathematical description of GM_T. More information can be found at www.wikipedia.org/wiki/Metacentric_height and www.navweaps.com/index_tech/tech-009.htm.

Note that boats actually have two metacentric heights, Transverse Metacentric Height (GM_T) calculated using the transverse moment of inertia of the water plane about a longitudinal axis section of the boat and Longitudinal Metacentric Height (GM_L) using the moment of inertia of the water plane about a transverse axis. GM_L determines the boat’s recovery behavior from pitching and GM_T controls the recovery behavior of a boat from heeling. For the gyro since we are only controlling roll, GM_T is the only Metacentric Height of interest in our application.

A boat, or any other object, floating in the water is acted upon by two forces; gravity and buoyancy. Gravity is acting to push the boat down into the water while buoyancy is acting to push the boat up out of the water. The length, beam, displacement, hull profile, center of gravity, and center of buoyancy all determine how these two forces interact and hence determine the stability characteristics of the boat.

Gravity and buoyancy are acting along a vertical plane that intersects the center of the boat’s hull. The boat’s center of gravity (G), which is the exact center of the ship in terms of the ship's weight distribution, and the boat’s center of buoyancy (B), which is the exact center of gravity of the volume of water displaced by the boat’s hull, both fall on a line that passes through the exact center of the transverse (port to starboard) section of the boat’s hull and points vertically downwards. This line is called the Transverse Metacenter.

When a boat is designed, it is designed in such a way that if the boat heels slightly, the distance (B) moves from the centerline is greater than the distance (G) moves from the centerline. This design will produce a force, the restoring moment, which pushes the boat back toward a level condition. As you heel the boat within a range of angles, (B) moves to the side an amount proportional to the angle. This movement of (B) as the boat heels can be described as if it were rotating around an imaginary point up above the waterline. This point is called the metacenter.

If the displaced (B) is designated as (Z), the distance between the level center of buoyancy (B) and the heeled center of buoyancy (Z) is defined as the transverse righting arm (GZ_T) and is calculated by (GZ_T) = (GM_T) x sine(s), where (s) is the angle of heel.

GM_T is the height from the center of gravity to the metacenter. If the GMT is positive, the boat is stable and will return to level unless heeled over very far or very hard.

Boats with high GM_T have a large GZ_T and are "snappy" i.e. they are resistant to rolling but are also very uncomfortable to ride since they snap upright very quickly when they roll. Boats with low GM_T have a small GZ_T and are “soft” i.e. they roll relatively easily but recover from roll is slower and gentler.