Reproduced from FINNFARE March 2002

Swinging in Marblehead

Peter Hinrichsen

Introduction

The Lamboley swing test, which measures the position of the centre of gravity, CG, and the gyradius, ρ of the hull, has been a standard part of Finn measurement at Olympics and Gold Cup regattas since it was introduced by Gilbert Lamboley in 1961. For the 2001 Gold Cup, at Eastern Yacht Club in Marblehead, the tests were performed in a container with a system which is almost identical to that belonging to the Finn class. It was therefore initially surprising that many hulls which had previously passed Lamboley tests, were not passing. The ensuing discussions and remeasurement with altered correctors, lead to unacceptable delays. The equipment and procedure were therefore carefully checked, but nothing was found to be wrong. We are now convinced that this problem was because modern Finnsters insist on their gyradii being within a few millimetres of the minimum combined with the heavy rain causing the wet hulls to gain weight in the middle and change gyradius.

For measurement we carefully set up the system and initially make measurements as quickly as possible. If the hull passes, good, however, if it is close then more careful measurements which take time are made. To measure to 10% takes 1 minute, to measure to 1% takes 10 minutes to measure to 0.1% takes half an hour and even then is difficult under regatta conditions. The moral is to think carefully whether you really need to be that close to the limit, that measurement will require much more of your time, which could be better spent sailing. To put this in perspective calculations of the pitch moment of inertia of the whole boat, and the contributions of each part, have been made. After all it is the whole boat, with you in it, which pitches when you sail, not just the Lamboley tested hull.

The Lamboley Test

When the hull is brought in for swing testing three quantities are measured: I) the horizontal distance λ> 2100 mm that the CG is forward of the AMP (aft measurement point, i.e. the intersection of the keel line with the transom), ii) The pitch radius of gyration or gyradius ρ > 1100 mm of the hull and iii) the height h = (d - a) > 210 mm of the CG above the keel. The latter, although a part of the rules has not up till now been checked at regattas, but be warned d and hence h will be measured in the future.

The hull is suspended on knife edges by two hangers so that it is free to swing in pitch. When the hull is hanging freely the CG is in the vertical plane of the knife edges, however, to determine if the weight is concentrated in the middle, or spread out to the ends one has to swing the hull like a pendulum and time the swings. The period of swing, T, depends on two properties; the distance a that the CG is below the knife

edges and the gyradius ρ. By swinging the hull about two axes 200 mm apart and measuring the two periods T1 and T2 these two quantities can be calculated. The Finn class has a chart which allows this calculation to be done, however, modern calculators can be programmed to do this, in my opinion, more precisely and quickly.

What does the weight distribution do? In flat water nothing, only in waves when the boat rotates in pitch will the distribution of weight affect the motion. If the weight is twice as far from the axis it's effect on the rotation is four times as big, i.e. it is important to remember that it depends on the square of the radii, i.e. distance from the axis of rotation. The gyradius squared is then the average of the squares of the radii of the mass of each part of the boat. The pitch gyradius is then a measure of the weight distribution, i.e. how far the weight is from the CG. As far as the pitching motion is concerned, the hull can be thought of as a dumbbell with two ends, each of half the hull mass, and at the gyradius either side of the CG, as shown in figure 1. Adding weight anywhere closer to the CG than the gyradius the dumbbell shrinks and your gyradius becomes less, while if you add mass at the bow and stern, i.e. farther from the CG than the gyradius, then it will increase. If you want to reduce the gyradius then first think of weight which is as far from the axis as possible, i.e. for a whole Finn at the top of the mast. Taking away 100 gm there, i.e. from the sail headboard, will have the same effect on pitching as removing 800 gm from the transom.

Figure 1

For a Lamboley test the hull is suspended from horizontal knife edges and two periods of oscillation T1 and T2 about two axes, a vertical distance b = 200 mm apart, are measured. The pitch gyradius ρ and the vertical position a of the CG can then be calculated using the above formulae or the Finn chart. With the hull horizontal the distance λ from the transom to the CG, and h = (d - a) from the keel to the CG, can also be measured.

Levelling and fore and Aft position λ of the CG

Many Finnsters feel that the hull must be accurately levelled for the test, but this turns out not to be that important. We normally level the first boat very carefully and then measure the height of the bow (or transom) and mark this on a gauge. Then all other hulls are adjusted so their bows are within a couple of cm of this height. Now you could hang the hull vertically and you would still get the same gyradius (provided nothing moved), so levelling is not important for the gyradius measurement.

Next the value of a will only change by the secant of the tilt angle θ, and as all present a values are still well within the Finn rule this is not a problem. For example if the bow is off by a huge 10 cm, the tilt is 2.4° and a will only increase by Δa = 0.6 mm which is smaller than we can measure. Finally remember that even when the hull is tilted the CG is still in the vertical plane of the knife edges and the change in λ is Δλ = (λØ/2) which even for the bow again off by a huge 10 cm, leads to an error in λ of Δλ = 1.8 mm, so the measurers will be out by much less than this, and if the bow is down this is an increase in λ so in your favour! The moral of the story is that, yes the hull should be eyeballed level, but better than that will not make a measurable difference.

Adjusting the Gyradius

If you come to measurement with your new Finn, which you have now personalised, and find that it does not pass the swing test, how should you adjust it to become legal? Most modern Finns carry the maximum corrector weights of 5 kg (typically as four pieces in the tanks at the traveller and the aft end of the cockpit), but as they get older tend to put on weight in the middle (somewhat like their owners). The first thing is to check is that you are at the minimum weight (120 kg) and, if you are overweight, ask the measurer for permission to take lead out and record this on your certificate. Keep the lead, or better still give it to the measurer so he can pass it on to one of your competitors! Now if your bow is too light, i.e. λ < 2100 mm, move the correctors at the traveller forward. This will change ? without changing the gyradius significantly. Finally if you do not pass the swing test you have to move the correctors outwards from the CG, preferably to the transom. Remember it depends on the square of the distance from the CG, so you get the maximum effect if you move the corrector all the way to the transom, or the bow. If you have to add or remove mass it really pays to put it right on the transom or remove it from the traveller. Think of drawing lines at ρ = 1100 mm forward and aft of the balance point of the hull which is about at the traveller. Then adding weight outside these lines or removing weight inside these lines will increase the gyradius, and the converse is also true. For instance adding a heavy compass at the front of the centreboard case actually makes things worse, as this is inside the lines.

Figure 2 Ways to move the CG forward, i.e. increase ?, and to increase the gyradius ?

Wet Hulls

In Marblehead the hulls were wet for measurement, despite the competitor's best efforts to dry them, and the water caused the gyradii to become illegal. For a Lamboley test the mainsheet and painter are placed on the traveller and the control lines wrapped around it. We found that a damp mainsheet weighs 500 gm more than a dry one. The pussy pads take up similar amounts of water, which is also well inside the gyradius lines. The addition of 1.5 kg at the centre of a 120 kg Finn hull will reduce the gyradius by 7 mm, which is more than enough to make most new Finns (which have gyradii of less than 1105 mm) illegal, hence the problem. In order to increase the gyradius of such a wet hull to 1100 mm more than half a kilogram of lead has to be added at the transom. This is just the effect of absorbed water. Even small amounts of free running water in the bilges or buoyancy tanks plays havoc with a swing test. What is the moral of this experience? Accept a Finn with a gyradius at least 5 mm above the minimum, keep your Finn undercover and make sure that your lines and pussy pads remain really dry for measurement.

The Finn sailing to windward

The Lamboley test only measures the hull with the centreboard in the up position It is the whole boat, with you in it which pitches as you go to windward. With some simplifying assumptions, the effect of the mast, sail rudder etc. were calculated and are shown in table 1 and figure 3.

Figure 3 The assumed configuration of a Finn sailing to windward in conditions where pitching is significant. The centres of gravity of the hull, C/B, rudder, Mast, boom, sail and of the total Finn are shown.

Table 1

The CG positions, gyradii and moments of inertia of the components of a Finn Dinghy when going to windward.

The weights, CG positions and gyradii of each component has to be known. The mast, centreboard and rudder with tiller were hung up, their periods of oscillation measured and the CG determined by hanging them up from two points. A Latini and a Wilke mast were swung and found to be similar. A Victory sail was weighed, a batten weighed and the weight of the headboard was estimated at 200 gm from which the CG and gyradius were calculated. The rig was drawn according to the class rules and then the web photo of Sebastien finishing the heavy air race was scanned and a spline fitted to his mast bend to set up the rig as shown in figure 4. The distance forward, x, and up, y, from the AMP to the CG of each component in sailing position were found and listed together with their mass and gyradii in table 1. Column 7 lists the moment of inertia of each part about itÕs own CG while column 8 lists the contribution to the whole moment of inertia. For example for the mast the first term is 25.1 kgm2, while the second is 48.3 kgm2, so about two thirds of the effect of the mast, which is 26 percent of the total. The best way to reduce the effect of the mast is to reduce the weight and then lower the mast CG to their minimum values. This is part of the advantage of the carbon masts.

So What does it mean?

Well if you really insist that your Lamboley gyradius is within a millimetre of the minimum then you had better pay equal attention to the effects of the other components, after all the hull is only 52 percent of the total. Some examples are: going from an aluminium to a carbon headboard will save 100 g, but a long way from the CG and is equivalent to 10 mm in ρ, Strapping your paddle athwartships under the traveller instead of putting it in the aft tank is equivalent to 7 mm in ρ, moving the painter, bailer and your lunch and water bottle (1 kg) to the centre of the boat will have similar effects, and you better have a minimum weight rudder as it is on the transom.

Should you do all these things? Well I think most Finnsters would be better off thinking about the next wind shift. The point of my saying these things is to suggest that a fixation on getting right into the bottom corner of the Lamboley chart is not worth the effort, and may cause you endless measurement grief. Finally, your weight and position seriously affects the total gyradius. Just moving for and aft a few cm will have the same effect as a mm or so in hull gyradius.

Reproducibility, Accuracy and Precision of Lamboley tests

In the 1980s most Finns were in the middle of the diagram so precision was not too important, however, now Finnsters want their hulls to be within a few mm of the minimum and so we have to measure at least this precisely. That is a tall order under regatta conditions. The first thing you need is a measurer who understands what he is doing, and in Juri the Finn class has him. He has to ensure the hull is really dry, the lines and fittings are all secure in their specified places. Then you need a system which rigidly supports the knife edges so they are level and do not move when the hull swings. The Finn class system, and that used in Marblehead are I believe rigid enough provided they are on a solid floor, but we are going to compare it with the system at DevotiÕs which is firmly cemented into the floor.The hull should be levelled and also aligned in yaw (I estimate that to produce an error of Δρ = 1 mm would require a misalignment of 2.5° or 10 cm at the bow, and so is easily visible). Misalignments in roll are also negligible. The hooks must be of the Finn design and thickness, with bearing surface spacing b precisely 200.0 mm, and in my opinion their weight should be specified in the rules to be say 2.8±0.2 kg. Clearly the, and this should be checked with a vernier calliper or gauge. The hooks should not be moved when changing axes (do not put the hull down).

Some Finns have solid or filled gunwales and although this will change the deduced a, it does not have any effect on λ, ρ or h (as d also changes). Tim Tavinor and I have made measurements at Devoti's to check this. Most physics students will tell you that the period of a pendulum is independent of the amplitude, however, it is not true for a Finn dinghy, and figure 4 shows the change in the periods with amplitude of a Finn hull If the calculated gyradius is to be reproducible to within 1 mm then the amplitude should be within 3 mm, and it even changes by more than this over the ten swings used for hand timing of the period. I believe most Finn swing measurers use a bow amplitude of 20 cm but have also seen 50 cm and 5 cm used. Clearly such differences will alter the results. This is again an area in which the class rules should be tightened up and I suggest that a bow amplitude of 20±2 cm be specified for future measurements. Initially hand operated stop watches were used to time ten swings and a skilled and fresh measurer can achieve a precision of 1/100 seconds in this way. However if you change the two periods by 0.01 s each the calculated gyradius changes by 5 mm so for modern Finns this is not really good enough. Most measurers now use calibrated electronic timers with a photogate to start and stop the timer and this should be mandatory. The periods then have to be converted to CG positions and gyradii and although Finnsters still prefer the chart it is more convenient to use a programmable calculator or laptop computer and this is to be preferred because the value of g which occurs in the equations varies slightly with latitude (9.819 m/s2 in Helsinki and 9.785 m/s2 in Acapulco). Such a variation would lead to a change of 3 mm in the calculated gyradius but could be eliminated with a GPS to get the height and latitude.

What about the reproducibility of the periods? If there is even the slightest breeze it affects the measured period, so a completely enclosed space such as a container is essential. But man did it get hot in there in Marblehead, luckily I had Tom to help because without him we would never have finished all the hulls. It is my opinion that the reproducibility of the period measurements, even under ideal conditions is not better than ±4 milliseconds (±10 milliseconds with a stop watch) which corresponds to ±2 mm in the gyradius. If you want to avoid. hassles then make sure your gyradius is at least 1105 mm, that way even if you are unlucky your hull will be found legal 99 percent of the time.

Conclusion

I hope I have convinced you that the delays during Lamboley testing in Marblehead were not only due to my advancing years but because Finnsters want gyradii within a few mm of the 1100 mm minimum, and that the hulls were unavoidably wet from the rain. You should consider if being close to the limit is really essential, and to help you I have tried to put the effects of hull gyradius into perspective. If Finnsters want precise Lamboley tests then only hooks which conform to the Finn drawing and weight should be used, and I suggest that the bow amplitude of swing be specified in the rules. Although most measurers now use 20 cm, if it is not specified a competitor could legally insist that it be 50 cm, and this could get his boat through. A longer more detailed version and the spreadsheet for the calculation are available from hinrichsen@videotron.ca.

The Finn is a great class, a great boat and a super bunch of sailors with whom it has been a pleasure to be associated, please invite me again sometime!

Figure 4 The percentage change in the periods T1 and T2 with swing amplitude of a Finn hull.