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Scale Weight
I don't know if there is already a way of determining what the weight a truly scale mofel should be but i found a way of doing it. I wanted to determin how much a model would weigh before making it. If you know what the weight of the 1:1 ship/boat/etc then all you have to do is divide by the scale three times. It seems to have worked. These are my findings, I'll use the Titanic as an example:
The Titanic weighed 46000 tons so i used this as a starting point. A 1:150 scale rc model of a titanic is sold as a professional product(forget who makes it now). To determin how much it should weigh before hiting the waterline i take the weight of the real ship(92000000lb) and divide by the scale(150) three times. I get 271/4lb. The rc model is advertised as weighing 26.4lb. Not far off and if you look at a vid the model is sitting a little high(1/4 inch) below the waterline. I have used this to determin these scale weights of the Titanic: Scale  Weight 500  3/4lb 350  2lb 250  53/4lb 200  111/2lb 150  27lb 100  92lb 87  139lb 48  831lb Remember this is all highly theoretical process and if you can proove it wrong then let me know. Or if you have an example of this process calculating the correct weight i would also like to know.  MARCRACER 




Well, I was ready to gently burst your buble. But now that I've done the calculations (so long as you are sailing in salt water) the differences are miniscual.
Scale  Weight 500  0.736lb 350  2.146lb 250  5.888lb 200  11.500lb 150  27.259lb 100  92.000lb 87  139.711lb 48  831.887lb However, if you are going to sail in fresh water, the weight is proportionally less. To get the fresh water weight for proper displacement, see http://www.rcgroups.com/forums/showthread.php?t=1024644 Read Section 2.1 Displacement for the formulas. Calculations for the Titanic are: Scale  Weight 500  0.715 350  2.085 250  5.722 200  11.177 150  26.493 100  89.413 87  135.782 48  808.490 



The only difference is that ships are listed in long tons for displacement and a long ton (tonne) is 2,240 pounds.
Real ship disp x 2240 / scale^3 = model weight in pounds Dave PS: to figure model speed, take the real speed and divide by the square root of the scale. 



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If it did weigh 46,000 ling tons then it would have weighed 51,520 straight tons. 




Hi BoaterDave. I disagree about scale speeds; the speed the model skipper should shoot for should be, to be realistic, the actual ship speed/scale, not /sqrt(scale). I have read the Froude analysis published by a British boater S.J. Booty (he has a string of engineering degrees behind his name). Booty is often cited for the model speed calc you presented above, which is why I mention him specifically. He misapplies Froude's work wrt model boat speeds.
Froude investigated why shipbuilders could not use model results to predict actual boat speeds. The models always sailed faster than the real ship once it was built (that is, the equation real ship estimate=modelspeed * scale greatly overestimated the performance of the real ship). Froude calculated that if the ship builders did as you say (real speedestimate=modelspeed*sqrt(modelscale), then the equation would more closely predict the actual speed once the real ship was constructed. But, and here's the rub, you can't go the other way. If you want your model to mimic real ship speed, then you need to operate in the scale environment. For instance, 44ft/sec=30mph. If your real ship is 44' long, and it can travel at 30mph, then it is moving at 1hull length/sec. To mimic this in a 1:32 scale model, or in *any* scale, then the model must also move 1 modelhull length/sec. For a 1:32 model, 44/32=1.4fps. If you do the math, you find that the reverse Fronde calc would have your model skipper powering up his model to move faster than 1 hull length/sec (44/sqrt(32)= 7.8fps). For this specific example, the 1:32 model moving at a reverse calc Froude speed would be moving 5.5 hull lengths/sec. This would not look real. And explains why models often look zippy compared to the real ship they are trying to portray. Models live in the scale world. For distance and speed (and size of craft, eg LxWxD), simple linear adjustment is the appropriate calibration to use. For using a model to predict what a real ship of the same form will achieve, then use the Froude equations. To move a model at the speed that corresponds visually with the real ship, slow down :). Booty's article: http://members.fortunecity.co.uk/sjb...s_on_scale.htm 



Good article, but he obviously has the luxury of a more 'controlled' environment for sailing. It's worth repeating that you can't scale down the weather, so unless you want to build a huge model, you might have to add a bow thruster or independant paddles to maintain control.



Blackpool, Lancs
Joined Feb 2006
3,148 Posts

Brooks, if you consider that for the model, time is scaled, everything falls into place.
Take a 1:100 scale model for a 1 mile walk. If it looks right all the way, it will take about 1 hour. The model has sailed 100 scale miles. Using the square root rule, it has sailed at 10 mph. 100 miles at 10 mph gives a 10 hour cruise. The 10 hour model cruise has taken 1 real people hour. This works with all scales. 



First, I have no objection to whatever any modeler wants to do with his boat or his clock. It's a hobby, and you are free to pursue it anyway you please. My only objection is when someone tries to take towtank procedures and prove that they are somehow "real" and should be followed by all "rightthinking" modelers :) Tow tank procedures were designed to deal with a specific problem, and that problem is only real to the towtank. btw, towtanks are not held in the high regard they were held 100 years ago. Submarine designers, for instance, have learned to reject towtank results unless the model is 1/3 scale. That's right, a 300' sub (WW2 size) would need a 100' model to generate any useful prediction info. Nuclear subs, being much bigger, would need a correspondingly bigger model. No indoor towtank in the world is big enough for these models, of course, so computers have replaced traditional towtanks to some degree.
Adjusting clockspeed is common in model railroading; operators mimicing dispach ops will speed up the modeltime clock  otherwise it would take real hours to make up a train, just like the real railroad, and that would be no fun. If you want to adjust your clockspeed, using any formula you chose, there is certainly precedent in the model RR world. Even if there was no precedent, you can adjust to meet your modeling needs. But there is no "correct" formula for doing so. Physical items can be scaled (a 1:100 ship can look just like a real ship), but time can't be scaled (a 1:100 sec looks no different than a real second...they are both invisible). If you have time for a 1hr sail of your Titanic, and you wish to consider it a 10 hr cruise, no problem.  Now for your example: length real Titanic 882', speed 23knots=43.7fps., speed in seconds/hull length =20sec, time to travel 1 real naut.mile= 2.61 minutes=0.0435hr 1:100 Titanic model, length 8.8', speed .23knots my way (23/100), 1hull length/20 seconds. time to travel 1 real naut.mile = 4.35 hrs. Comment:looks good to my eye, but at the cost of a boring afternoon. If your 1:100 Titanic travels 1 real naut. mile in 1 hour, then it is traveling at 1 hull length/4.6sec. Comments: Your boat will send up a bigger wave than mine :). Does not look as good to my eye, but is a much more enjoyable way to spend an hour at the lake.  Perception of speed at sea  I've seen this, and it's played a role in many tragedies: Big ships don't appear to be moving fast, unless they are very close (less than a mile distant from your vessel). It is fatally easy to spot a big ship coming over the horizon, watch it for a minute and note that it is not appearing to move, and then dismiss it from your priority list. Then, all of a sudden, you look up from your chart and there the blighter is, RIGHT OFF YOUR BOW! Blub Blub..... This nasty peception problem is perhaps related to our terrestial experience over the past 1000 years  we just don't have practice gauging the speed of big objects. We are used to relating to speed in terms of "body lengths". That fly is perceived as speedy because he is covering several body lengths/sec. When the body is as big as a ship, though, we notice that it's not moving many body lengths per sec, so dismiss it as being a sloth. Titanic facts http://www.titanictitanic.com/titanic_statistics.shtml 


Blackpool, Lancs
Joined Feb 2006
3,148 Posts

The odd thing is, if you use the square root theory, it looks right when compared with pictures of the real thing. This why the cinema crowd, when using models, run the model at the square root speed, filming at a high frame rate, then playback at a normal frame rate. Result, best realism for the model.
Back to weight  Merchant ships have many tonnages  gross, deadweight, lading, registered and probably a few more. Occasionally displacement may be quoted. With military vessels, a displacement figure is usually quoted. This figure is usually manipulated by the government involved, upwards if there is a need to intimidate neighbours or bolster home appeal, downwards to lull aforementioned neighbours into a false sense of security or to fit in with a treaty. If a scale model is made, floated at waterline and weighed, you will probably have a more accurate figure than that published. If the drawings were, in fact, actually accurate. 



Wow, what a debate. All good, of course, because we do this to have fun. And yes, operate your model the way you enjoy, because that's all that really matters.
I agree that there is way too much going on for a single simple formula to accurately predict what the full size ship is going to do. But, I also think that a 1:100 Titanic that is over 8' long taking almost half a minute to pass by would not be representing the prototype as she would appear at 23 knots. The difference is more apparent as the scales get smaller and smaller. Perhaps the best advice would be to operate the model at a speed in which the wave shape looks right. Choosing to operate your model in a scale like manner goes a long way as well. Dave 



Here's more ammo.
The real ship is the US Coast Guard 110' Island Class cutter. Wikipedia says 29.5 knots max speed. Now, I don't know what speed the boat in the first photo is going, but I would estimate 20 knots. The model is from Imex and is modeled in 1:48 scale, so it should be 27.5" long. The second photo is from our model clubs' fun run this past July. According to the formulas, a pure scale 20 knots should be 0.4 knots (0.7 feet/sec) and the square root version 2.9 knots (4.9 feet/sec). I didn't measure the speed of the model, I'm only looking at the bow wave. They both come up to the chine. The video shows the model driving around the lake at a slightly slower speed. Unfortunatly, there is no fixed reference to determine speed. But does is it appear to be going faster than 1 boat length in 3 seconds? Dave





Gentlemen this discusion of formulars and scale speed is very nice. Having said that it comes down to trottle control and apparent speed. Many jam the trottle wide open and say ''wee look at it go'' which works for a PT boat but a tug or a liner looks close to scale at much less power( unless you underpower it of course). It's all APPARENT SPEED and you don't need a calculator to find that. Just look at the boat and adjust the throttle accordingly. That is unless you plan to check it by radar.
Scale weight? Build the boat,set it in the water,ballast down to proper waterline= scale weight 



Well, no model will ever look totally 'correct' to the real ship. The water will break differently and wakes will be different. That is because despite all our math prowess, we still haven't figured out how to scale the water down. Maybe the supercollider can pull it off, or turn the earth into a black hole. We still haven't got consensus on that yet...
I agree with Charlie, if you can make the bow wave look like it's breaking at the right spot for top speed, you are good enough. Mathmatically, I have no idea if that makes person X right or person Y. 
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