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General Photos |
Lifeboat Model Page |
Speedline Trent 14-14 Commission Build |
scale lifeboats |
January 2011 Alexandra Palace London |
Man Truck |
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General Photos |
Lifeboat Model Page |
Speedline Trent 14-14 Commission Build |
scale lifeboats |
January 2011 Alexandra Palace London |
Man Truck |
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Contributed by Steve Booty BSc CEng FIMechE Introduction Similar physical systems Scale speed Scale behaviour Distance covered Hull speed In conclusion It seems the question of scale causes confusion in our hobby. I have therefore put together this series of notes which explain the technical theory in an attempt to help you through this minefield. Introduction Firstly, let us consider what it is we are aiming for in our scale models. I hope we could all agree that as scale modellers ideally what we want is a model which looks like and behaves like the original prototype full sized vessel. To get a true scale representation of any prototype full sized object we need what engineers term similar physical systems. Similar physical systems For the prototype and the model to be similar three conditions must be satisfied: 1. Geometric similarity 2. Similar internal constitution 3. Similar conditions at the boundary (e.g. between the hull and the water) The basic rule that must be followed is that any property that describes both the prototype and the model (displacement, linear dimensions, speed, etc.) must have a relationship which is described by the equation: P1 = k x P2 where P1 is the property of the full size prototype P2 is the property of the model k is a constant ratio Geometric similarity This is the easy bit since everyone (I hope) wants their model to look like the full size prototype. To make the model geometrically similar we use the equation: L1 = kl x L2 where L1 is the prototype full size dimension L2 is the model dimension k l is the constant linear scale factor In other words if the model say of a 100 ft. vessel is to be built to the scale of 1:32, then the hull length will be: 100 x 12 = 37.5 inches 32 and of course all other linear dimensions are treated the same. The only limit to our success in achieving complete geometric similarity is our personal preference, ability as a modeller, the available materials and the amount of time, equipment and/or money we have available. Similar internal constitution This means, in our terms, similarity of structural behaviour and of weight distribution throughout the prototype and the model. Generally, the structural behaviour does not concern us as for conventional vessels the prototype is normally very stiff and by the nature of the construction techniques we use the model is similar. It is only if you are building a model of a vessels like the Egyptian reed boats which were deliberately made flexible to reduce bending stresses in the hull due to wave action, do you need to worry about this. Weight distribution is much more important as it affects stability. The diagrams below illustrate this point. Firstly consider the hull section (a) which is through a ship at rest in the water. Point B is the centroid of the displaced volume and is known as the centre of buoyancy. The resulting force exerted on the hull by the surrounding water is the force F which passes vertically upwards through B. This must be equal to the weight of the ship W for the ship to float. The weight of the ship W acts vertically downwards from the centre of gravity G. As the two forces F and W are equal and opposite and as they are perfectly aligned with each other this is a stable system and there is no movement. Now consider the diagram (b). The hull has rolled over. Because of the shape of the hull the centre of buoyancy has now moved to a new position B and the vertical buoyant force F has moved with it. G cannot move provided the internal weights of the ship do not move (i.e. that the cargo/ballast does not shift). The resulting force W therefore is offset from force F by a horizontal distance Gz (known as the righting lever). As the two equal and opposite forces F and W are not aligned this is an unstable system and therefore an anti-clockwise rotation is set up which rotates the hull back to the stable condition. The righting force is the result of the weight x righting lever which therefore decreases as the angle decreases. The point M where the vertical line through the centre of buoyancy intersects the centreline of the hull is known as the metacentre. The height h of this point above the centre of gravity G is known as the metacentric height. For a hull to float upright M must always be above G. In practice for most hull forms the position of M, and as G is fixed therefore the metacentric height, is virtually constant for angles of roll up to 20o. In practice therefore points G and M are fixed and are a property of the particular vessel. The greater the metacentric height the greater the righting level for any given angle of roll and the righting force resisting roll and therefore the greater the stability. Finally, diagram (c) shows an inherently unstable hull which has G above M and therefore will capsize. This is the typical hull form of a racing sail boat and illustrates why they capsize when they loose their fin and ballast weight. Modellers have the same problem as that faced by full sized ship designers, particularly with warships with their heavy top weight of armament, etc., in addition to which it was not unusual for additional armament, armour and equipment (radar aerials, etc.) to be added during the life of a warship, all of which raise point G relative to the waterline, reducing metacentric height and hence stability. The Admiralty has used several solutions such as adding ballast to lower G, adding bulges to the hull sides to increase the distance B moves during a roll and hence raise M, removing armament in a trade off, using aluminium topside structures, etc. Figures for these properties, particularly for warships, are usually readily available from references. Typical figures for metacentric height for a flower class corvette is 1.6 ft., whilst for a battleship it is typically 5ft.. You can see immediately why the corvette had such a bad reputation for rolling on a mill pond! To give a feel for this effect, during WWII Flower Class had a loss of operational time due to crew fatigue/illness as a result of motions in bad weather of 28%, the Castle class corvettes 21%, the River/Loch/Bay class frigates and older destroyers 15%, whilst the modern Leanders with stabilisers managed a loss of only 9%. On the other hand, several vessels have had extra top weight added to reduce the metacentric height, since if this is to great the resulting motion in a sea can be very 'stiff', i.e. violent and jerky. This can induce discomfort and severely affect crew efficiency as against a nice, low frequency roll. Typical of this were the WWII Captain class frigates, 78 of which were supplied to the RN by the USA but which were found to roll very violently making them lively and uncomfortable, and only perform as satisfactory gun platforms under favourable weather conditions. A programme to increase the depth of the bilge keels, increase top weight and move some weight outboard of the centreline overcame this problem, but at a cost of taking the vessels out of service for 3 months. Reducing the speed of the roll also dampens it, leading to a reduction in amplitude. In the case of the Captains, the modifications reduced roll on one trial from 56 deg. (out to out) to 40 deg. In more modern times stabiliser systems have been used on vulnerable full size vessels (large passenger carrying vessels, warships, etc.) to overcome this problem. As M is a property of the hull form which cannot be altered if we are achieving geometric similarity. Similarly, the rolling resistance is a function of the external attachments to the hull (keels, bilge keels, dead woods, etc.) which must also conform to full size practice for geometric similarity. The only influence on stability we have as modellers is the location of G. Obviously, the lower in the hull we get this the greater the forces are which resist roll and therefore the greater the stability. Hence on vulnerable models (warships, liners, ferries, etc.) top weight must be kept to a minimum and ballast (including batteries, motors, etc.) kept as low as possible in the hull. However, if you increase the metacentric height or lower the centre of gravity to increase the righting force to much you will have an unrealistically stiff model with a fast, jerky rolling motion. Note the speed of roll is a function of the both the righting force (the higher the force the quicker the roll) and the hull rolling resistance. Reducing this speed can be achieved by fitting items such as extended keels, dead woods and bilge keels which provide lateral resistance to roll as well as greater directional stability by resisting yaw. The message here is that you cannot reduce that rolling 'wobble' in your model every time you apply rudder or the model sees a small wave simply by lowering the ballast. This will slightly reduce the angle of roll but will increase the its speed to an unrealistic extent. To minimise this wobble you must also increase the rolling resistance. However, geometric similarity requires that items such as bilge keels and dead woods should only be used if fitted to the prototype. Ah but, I hear you say, what about scale sail. I agree there is an added problem here in that the wind is not to scale and therefore the overturning moment caused by the action of the sails is well over scale. In addition, scale sail suffers from surface effect. This basically means that the resistance of the water to being displaced is less near the surface because the water has the option of moving upwards and displacing lighter air, whilst at depth it can only move by displacing other much heavier water. This is why a scale sailing vessel will tend to crab (i.e. move sideways) more under influence of the wind than the prototype. Hence why such long fins are used on model racing sail boats both to lower G and increase the righting force, and to get some benefit from the greater lateral resistance from the deeper water. It is also why they use relatively deep rudders to increase their effectiveness. Scale sailors will want to be able to sail their craft in conditions the scale equivalent to gale to storm force (or even hurricane) winds. For smaller models it is undoubtedly true that keel extensions/fins, external ballast and/or rudder extensions may be necessary in order to be able to sail your model in anything above a light breeze. For the larger models however it has been proven possible to sail perfectly well in most conditions provided attention is paid to weight distribution and as in full size practice sail area is reduced as necessary. Finally, remember that weight is directly proportional to volume, so if you do know the displacement of the prototype, then this can be easily calculated for the model using the equation: M1 = (kl) 3 x M2 where M1 is the prototype weight/displacement M2 is the prototype weight/displacement kl is the constant linear scale factor In other words if the model say of a 300 ton displacement vessel is to be built to the scale of 1:32, then the model displacement will be: 300 x 2240 = 20.5 lb. (32)3 Similar conditions at the boundary This is rather more complex. What we are looking for here is known as dynamic similarity, i.e. that the flow of water round the model (e.g. the bow wave and wake) should be similar to that seen with the full size prototype. To achieve this a property known as the Froude number must be the same for both the prototype and the model. The importance of this property was discovered by the English hydrodynamicist William Froude who pioneered the scientific modelling of ships behaviour in model test tanks, enabling test results to accurately predict full size vessel performance. For a surface vessels or submarine the Froude number is given by the formula: F = Vsq x M where F is the Froude number L x R V is the vessel speed The Froude number may also be expressed as: F = V/sq.rt(gL) where F is the Froude Number V is the vessel speed M is the vessel displacement L is the water line length R is the wave making resistance g is the acceleration due to gravity Scale speed If we now assume that gravity is constant (which for model boat purposes it is) and that the density of the water is also constant (although it decreases with higher temperature and sea water is 1.028 times more dense than fresh, the differences have no major practical effect for us modellers), then by going through the mathematics we find that for a constant Froude number: (1) V1 = V2 x (square root kl) where V1 is the prototype speed V2 is the model speed kl is the constant linear scale factor and at this condition the wave making resistance of the model is expressed by the equation: (2) R1 = R2 (kl)3 where R1 is the prototype wave making resistance R2 is the model wave making resistance kl is the constant linear scale factor These equations illustrate Froudes Law of Comparison. This is what is used in test tanks to determine the relationship between a model and a full sized hull. When these two equations are true then the wave formation caused by the model forcing its way through the water is similar to that produced by the prototype. The model speed at which this occurs is called the reduced speed by engineers, but for our purposes it is the scale speed. Equation (2) is always satisfied if the model is geometrically similar, therefore we only need to consider equation (1). Equation (1) means that, for example, if the prototype had a speed of 12 knots and the model is to a scale of 1:32 then the model scale speed is: 12 = 2.1 knots sq.rt.32 If you use the commonly held belief that scale speed is the prototype speed divided by the constant linear scale factor then in our example you would get the answer 0.375 knots, a factor of 5.6 times to slow! No wonder this is difficult to achieve and does not look realistic! Note there are many other factors affect the motor power you require and it is not practically possible to accurately predict this using equation (2) or any other calculation. In full size practice this is often determined by model testing. You can measure the actual speed of your model if you know that a knot is 1 nautical mile (1852 m) per hour, therefore in 30 seconds a model travelling at 1 knot will cover 15.4 m. To check your model speed set up a measured distance of 15.4 m and time your model between these points. Say this time was 14.5 seconds then the speed of your model would be: 30 = 2.1 knots 14.5 It should not be difficult to time your models over such a pre measured distance and check your scale speed. Achieving this speed is NOT overpowering your model but producing one that performs and handles in a similar fashion to the prototype. As stated at the beginning this must be our aim as scale modellers. Scale behaviour It should also be noted that this ratio affects all factors reliant on time in relation to our model, including items such as the speed of roll. This means therefore that if you were to film or video your model to get a true appreciation of the motion of the prototype you need to slow down the film using the equation: t1 = t2 x sq.rt.kl where t1 is the prototype time period t2 is the model time period kl is the constant linear scale factor Taking our example again, if the model is 1:32 scale then the film needs to be slowed by a factor of sq.rt.32 = 5.6. If this was done you would see a very realistic depiction of what the prototype would behave like in these conditions. This is the technique used in both model test tanks and in commercial films where recordings of model behaviour are used to get a realistic portrayal of the behaviour and motion of the prototype Distance covered Finally, for those of you interested in endurance events, etc. if you want to calculate the distance the prototype would have covered in any given period you need to use the formula: D2 = V1 x T where V1 is the prototype speed sq.rt.kl D2 is the model distance covered T is the period kl is the constant linear scale factor Again using our example of a prototype making 12 knots modelled at 1:32 scale, the distance for the model to cover in 24 hours continuous steaming at a true scale speed is: 12 x 24 = 50.9 nautical miles or 94.27 km (1 int. nautical mile = 1852 metres) sq.rt.32 Hull speed Another interesting factor that comes out of the fluid mechanics of displacement hulls is known as the hull speed. The resistance to the forward motion of a ship is made up of the wave making resistance for the bow and stern waves, the skin friction resistance of the water against the hull and the eddy-making resistance created by the propellers in the wake. In practice, for displacement hulls the power required increases with speed. However, at a certain speed the wave-making resistance becomes the dominant factor and rapidly increases with speed. This occurs when the waves made by the hull, principally at the bow and the stern, reinforce each other greatly increasing the power absorbed. The speed at which this occurs is sometimes known as the hull speed. Getting a displacement hull to go faster than this speed takes a disproportionate increase in power as the hull has to be forced through or over the bow wave. This is why semi-planing or planning hulls and more exotic forms such as hydros, tunnel hulls, hydrofoils, etc. were developed. All of these have the same aim, i.e. finding a way to lift the hull clear of any bow/stern wave with minimum effort and hence allowing faster speeds at relatively moderate power. For displacement hulls the hull speed may be found using the formula: Vh = Kh x square root of L where Vh is the hull speed Kh is the hull form constant L is the waterline length The constant Kh is a function of the hull form, length/beam ratio, etc. and again is usually found by tank testing a model. In the case of waterline length measured in feet and speed in knots it is commonly around 1.3, which corresponds to a Froude Number of 0.4 which is the condition where the wave length of the generated wave pattern coincides with the vessel length and is the point where the wave making resistance starts to increase rapidly. Generally, full sized propulsion equipment for displacement hulls is sized to drive the ship at a figure some where near, but below this hull speed, hence the prototype speed and hull speed are usually nearly same. The one major exception to this rule is warships, particularly WWII destroyers and modern frigates. The penalty for this increased speed was much larger machinery and boiler spaces, together with much higher fuel consumption. Note that since the hull speed depends on the square root of the waterline length it has the same model/prototype ratio as the scale speed discussed earlier (i.e. is proportional to the route of the constant linear scale factor). Essentially this means that for any displacement hull model it is not worth putting in a more powerful motor than that needed to achieve the hull speed since the increased speed from that increased power will only be small, unless you get the hull planning. In practice all you are doing is putting in a more inefficient propulsion system which will shorten your running time. The exception to this are models where the prototype is overpowered due to the job they do (tugs, icebreakers, etc.). This is why many tugs when moving at full power on their own have that distinctive bone at the bow as they push their way through the bow wave. But note, tug skippers usually only push their tugs like this to impress the onlookers. In normal working they would cut back to an economic power level. And yes, we have all seen flower class corvette models planning like a fast electric, but don't they look daft! There is one interesting variation on this, the bow bulb seen on many modern merchant ships. This odd protuberance is specially designed to produce a second bow wave ahead of the true one. At a certain speed the crest of the real bow wave will coincide with the trough of the one from the bulb, effectively cancelling each other out and therefore reducing the wave making resistance of the hull. At this specific speed therefore the power required from the propulsion equipment reduces dramatically. This gives the ship a specific economic cruising speed. In conclusion Do remember when comparing dimensions to make sure the units of measurement are consistent. Also note where I have used the term displacement I mean the all up weight of the prototype or model. The basic message is that if you want a manoeuvrable and/or stable model, choose the right prototype (e.g. a Watson or Liverpool lifeboat, a modern tug, etc.). WWII Empire class tugs had a deeply immersed single screw and a barn door rudder, effective and efficient tugs but not manoeuvrable. Ships like RMS Titanic and HMS Nelson by all accounts manoeuvred like the brick proverbial in real life, so you cannot expect your model to behave any better. Warships always struggle to offset the requirement for ever greater top weight against stability, so the modeller will also struggle and be faced with poor stability. Commercial paddlers did not have separate paddle drives because the Board of Trade rules ban these for any passenger carrying vessels, and remember many commercial tugs used to supplemented their income by offering excursions, acting as tenders for liners, etc. Admiralty paddle tugs though did not have to comply with this and generally had independent paddle drive. So choose your prototype to match your requirements, or put up with the consequences. Modifying models to fit balanced or semi-balanced rudders in place of barn door ones, khurt nozzles, bow thrusters, independent paddle drives, dead woods, keel extensions and bilge keels where there were none, etc. to improve handling results in an interesting toy, not a scale model which performs in prototype fashion. I hope this provides some enlightenment and helps you all produce more accurate models that truly perform in prototype fashion. I certainly hope this gets us away from the common assumption that scale speed is simply the prototype speed divided by the constant linear scale factor, that models going faster than this speed are overpowered and that real overpowering brings you benefits. | The Model Build Part 2 | Model build Part 5 | Model Build Part 6 | Crew figures | Y-Boat | Sea Trials | | Motor Up Grade | 1/16th Scale Severn | 17-21 model Lifeboat Build | Tamar | Atlantic 21 | lifeboat photos on disc | | Return Home | Lifeboat General Photos | My Lifeboat Model Page | 1/12th Speedline Trent 14-14 Commission Build | Other scale lifeboats | LMEE January 2011 Alexandra Palace London | R.N.L.I. Man Truck | Lowloader | |
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