# Scaling for a Model: Velocity Gradient

Discussion in 'Sailboats' started by ancient kayaker, Sep 6, 2010.

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### ancient kayakeraka Terry Haines

An accurate model sailboat tends to have more sail area than it can handle. I am trying to develop a formula or procedure for determining by how much the sail area should be reduced.

The effect of the scaling factor is simple enough, as the sail's heeling moment varies as the 3rd power of the scaling factor whereas the hull's righting moment varies as the 4th power, which is why the smaller boat gets too much area, of course. There are various means available to overcome this, including lowering the CoG by fair means or foul, including a deeper (non-scale) keel or fin.

For a true scale model, changing the keel leads to it having to be removable so the true scale fin can be substituted for show purposes; although some folk will not go to such lengths. Any non-scale changes above the waterline, of course, would be highly undesirable.

However, eventually one is faced with the need for reducing sail area in all but light winds, especially if the scaling factor is large and the full-sized boat is designed for racing so it has a lot of sail to begin with.

To do that right I need to know the reduction of wind speed at the height of the model's sails. For a typical model around 1m or so, I suspect the wind is reduced by as much as 50%. I can find various formulas and data but none for down to within a foot or so of the surface, which is what I need.

Anyone have hard data for this?

Once I have some data to work with, I can explore various acceptable (i.e., to scale) alternatives such as reefing or using heavy weather sails, while still adhering to scale.

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I don't have any hard data but you might find some on Lester Gilberts site: http://onemetre.net/index.htm I'm fairly sure he has made a study of the wind speed gradient close to the surface. Lester is a nice guy-don't hesitate to contact him.
I know that most development class rc models that allow any number multiple rigs have at least 5 rigs. I know the sail area varies as the square of length,displ. as the cube of length etc..
I'm curious-what is the model for/about?
I've built numerous non-scale models for experimental purposes and I produced rc models for a while-glad to help if I can.....

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### PARYacht Designer/Builder

The laws of mechanical similitude suck, don't they. There's no good way around the dramatic reduction in stability (16x), which explains a lot of pond yacht shapes.

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### ancient kayakeraka Terry Haines

Thanks Doug. I have seen that web page before but unfortunately I could not open the spreadsheet. I found I already had a copy of it on my hard disk; typically I don't know half of what I have there! However, the graphs in the web page suggest wind speed reductions for a model of about 50%, depending on size and surface conditions.

Good point Paul, but I haven't given up!

At this point I figure for a 1:12 model I have to deal with a heeling moment that's x12, however if the wind's down by say 50% then the wind pressure is down to 1/4 and I only have to deal with a x3 scale heeling moment. With that assumption I need a linear sail reduction of 3rd root of 3, or about 1/1.44, which would give me a sail area reduction of about 50%. I don't know if that is equivalent to a typical reefing level as I haven't found data on reefed sail areas yet.

1:12 would bring a 12m yacht down to a model around 1.5m, which is a bit large for conveninence, and what I really would like to try is an old fashioned AC type J-boat; however the scaling factor to bring that down to a reasonable sized model would be ridiculous. Not that I mind ridiculous, but even I have my limits!

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### tspeerSenior Member

A power law is often used to model the variation in the mean wind speed with height. But I think it would become increasingly inaccurate close to the surface. At the scale of a model boat, I would expect it to be operating in the laminar sublayer of the turbulent wind gradient. So a linear mean wind gradient is probably going to be closer to the mark.

No matter what statistical model you use, the wind is going to be highly variable. I suggest you simply measure it yourself and see. I believe 10m is a fairly standard height for reporting wind speeds. You can take your own ratios between 10m (or as high as you can reach if you want to adopt that height), the masthead height of the boat and deck level.

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### daiquiriEngineering and Design

I agree with this.

AK, maybe you could also contact Fredschmidt (http://www.boatdesign.net/forums/profile/fredschmidt.html), he is into sailboat RC modeling and appears to have a pretty meticulous approach to that art. Maybe he has some data to share with you.
Cheers!

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If you are willing to do some research, you can start with the AMYA web site. Or google up some of the several popular classes. These include IOM (international one meter) EC12, Marblehead, etc. Many of these classes are well organized and they have some sensible rules. For example they have "A rigs", "B rigs", and "c rigs". Each of the rigs have different areas,heights, and so on. The reason for the separate rig types is, as you can imagine, different wind velocities on the race course.

I believe that you could asses these rig variations and come up with some pretty good approximations of what you can use. As far as I know there is no neat formula, chart, or nomograph that has accomodation for various scales. Once again it is a matter of using what has worked in the past, just like the big boats

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### fredschmidtNaval Architect

I sent some data for AK. I never really paid attention to the problem raised by AK since I only have one year of study in RC and dedicated to the two classes of RC racing, IOM and RG 65. I gave him the link: http://onemetre.net/Design/Gradient/Gradient.htm

About "An accurate model sailboat tends to have more sail area than it can handle" I do not have much experience to analyses, and in principle I had one doubt if the hull CoG and ballast ratio etc. correspond with original.

In principle I believe that if the model is exactly correspondent to real boat this statement would unfounded.

Naturally the wind velocities need also be scaled. So, if we have great real winds in a RC the sail area need be accordingly in scale similar that the real boat would use .

The SA/D²/³ for a IOM is ~ 24 that correspond to a light racer. Reliance has ~ 48 and this signifies that Reliance is a overpowered boat and consequently the CG and ballast needs to be adequate and the model need have all in scale with much more reason.

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### Perm StressSenior Member

"An accurate model sailboat tends to have more sail area than it can handle. I am trying to develop a formula or procedure for determining by how much the sail area should be reduced.

The effect of the scaling factor is simple enough, as the sail's heeling moment varies as the 3rd power of the scaling factor whereas the hull's righting moment varies as the 4th power, which is why the smaller boat gets too much area, of course. There are various means available to overcome this, including lowering the CoG by fair means or foul, including a deeper (non-scale) keel or fin.
..."

Much simpler approach would be to sail in lighter winds.

Also avoid ponds or small lakes surrounded even at half a mile distance by trees, buildings, etc..

Best of all is a sea or BIG lake beach without high cliffs behind to mix the air at large scale.

Some pond or lake surrounded by flat ground from all sides for kilometers in all directions would be good; however, land is more rough as water, and during daytime often warmer as the air, causing much more turbulence -both mechanical and due to heating of moving air from below.

Quite good conditions could be found at sea beach (provided there are no high cliffs immediately behind it) with warm winds blowing towards the shore over cool water; if there is some protection from the open-water waves like reef close by or shoal slightly offshore with deeper water immediately at the beach, conditions will be as perfect and steady as they could be in the real world.

In any case, if sail center of area is below ~0.3-0.5m (1-1.5ft) above water surface, wind will be extremely variable and scale model behavior erratic. This is because of nature of all turbulent (above ~6knot) winds -from 0 to ~0.4m height wind speed increase dramatically in all published graphs. But it have to be remembered that all the graphs are smoothed and averaged. In the real world it simply mean highly unstable conditions this close to the surface.

All the matter is much more complicated as ^3 or ^4 scaling of forces and moments. There are certain physical limits to minimum size of the scale model to copy behavior of full size boat, without regard to scale as such.

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### ancient kayakeraka Terry Haines

Thanks for the inputs: this thread has attracted more attention than I expected. A sailing model has to deal with existing conditions, like the full-size boat.

Ideally it would sail in a modest and shallow lake of adequate area with low banks in the middle of a desert or prairie, which is hardly common. Under those conditions, the ideal wind speed at its level would be reduced by the square root of the sailing factor, allowing all other dimensions to be reduced in proportion.

I didn't know much about the IOM - a good factory-built one seems to cost a great deal more than any of my full-size boats! The A/B/C rigs of the IOM are interesting; getting data on racing 12m boats is not as easy as it is for the older J-boats which are much featured in literature, but even for the J-boats only the maximum rig area is usually provided. But clearly scaling the heavy-weather rig would be the way to go for a practical true-scale model.

Much the same practical issues arise in other modelling endeavours. A model railroad looks more realistic if time is scaled by the square root of the sailing factor for practical reasons, and a scale model plane typically flies faster than scale speed although the speed scaling does not follow the square root law one might expect and is significantly effected by the type of plane.

This has been an interesting journey: thanks again to all for your inputs.

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### Earl BoebertSenior Member

Well, I have a fair amount of experience in doing this:

http://www.usvmyg.org/YankeeIII/YankeeIII.htm

Basically, getting a scale boat to "look right" requires a combination of art and science. To reduce the J boat Yankee to 3 feet, the great model yachtsman John Black did the following:

1. Reduced the scale sail plan by .9 (.81 area)

2. Increased the aspect ratio of the main to fool the eye into thinking the rig is taller than it is.

3. dropped the keel by 1 3/4 inches.

When I adapted his design for R/C, I added the extra gimmick of making the fin thicker, which provides room for the extra ballast made possible by modern materials, and enables that ballast to be placed properly without doing (too much) violence to the profile. An exchange between myself and another builder on this topic can be found at: