Buoyancy and floatation measurement

I am trying to develop a scale to measure the comparative ability of various surfboards to support the weight various sized people. I believe the theory behind my questions is well trodden in the field of naval architecture, thus I am posting this question in this forum. I want to develop a simple comparison scale for use by prospective surfboard buyers that will allow them to determine precisely the extent to which a particular surfboard will support their weight in water when compared to another surfboard.

For example surfboard X has a “FloatFactor” of 10 and surfboard Y has a “FloatFactor” of 11. Thus the prospective purchaser could quickly conclude that surfboard Y will float their body weight 10% better (and therefore be easier to paddle). By 10% better, I guess I mean it would sink 10% less distance when their weight is applied to it. I admit I am not sure how to quantify "better". I am guessing that the amount by which the surfboard will sink into the water when the person stands on it is the measure of how well it will float a person.

The variable of volume distribution may also be a factor. For example if a larger % of the surfboard’s volume is located in the areas that support the body weight (ie under where the feet are placed) perhaps the surfboard will “float” better? Even if this is the case I may have to ignore this aspect as it would make things too difficult to measure.

At first guess I would say that a scale graduated in kg would be appropriate. The kg rating being the weight that when added to a surfboard would make the "surfboard + person" unit neutrally buoyant. Then I thought maybe I am overcomplicating this, perhaps if prospective customers just knew the volume and weight of the surfboard, this would be enough information. then again, maybe displacement is the measurement that would convey the characteristic I am grasping at?

However, I am now starting to think it may not be that simple (but it may be).

I am starting to think that to make the scale linear and meaningful that maybe the scale would have to be unique to each body weight and/or vessel displacement. For example, the amount that a 120kg person would sink the Queen Mary II when they step on board when compared to the effect of a 60kg passenger would be negligible. However the difference in effect on a surfboard would be enormous. The variables of body weight and vessel size may affect the construction of my FloatFactor scale, I am just not sure how. As I write this I am starting to think that "displacement” is the term that is critical to the concept.

Can a meaningful, linear scale for floatation comparison purposes be established if the only three known variables are surfboard weight, surfboard volume and water density?

Here are some other thoughts I have had that may or may not be valid. Feel free to correct me. Surfboard A has less volume than surfboard B. However surfboard A is less dense than surfboard B. Thus surfboard A and surfboard B may both exhibit exactly the same capacity to support a person's weight in the water. If so, both surfboards would sink an equal distance when the same person stands on them. Also would the displacement of the 2 surfboards be equal in this case? Do I have all this correct? Would this equality of sinking distance be true for all body weights? Perhaps distribution of volume comes into play? The concept seemed simple at first, but it may be more complex than I first imagined. Any comments appreciated.
Thanks

 

What you are talking about is pounds per inch of immersion. I suppose you could use the reverse, how many pounds it takes to immerse the board one inch. The fewer pounds per inch the less buoyant, or less able to support weight.

Example. a board that sinks 1 inch per 100 lbs is more buoyant than a board that will sink one inch when loaded with fifty pounds.

This is a commonly used parameter in shipbuilding.

 

Try something like this.

Board weight = B (kg)
Board Volume = V (m3)
Surfer Mass = M (kg)

Take SG = 1.025

then Buoyant Force (in kg for arguements sake) = 1.025 * V - B

Then graph that as a percentage of Body Mass for different body masses.

You will end up with a linear curve that decreases with increasing body mass. ie the lower the number the less it is likely to support you. If you think about it carefully, you should be able to apply reasoning to the numbers.


The immersion idea mentioned above wouldn't be very effective in my view since the majority of the time, the boards are underwater anyways, and tpi is reliant upon waterplane area.

Hope this helps.

raw.

 

Thanks, I will investigate both approaches.

Ike, would pounds per inch of immersion be a linear curve when pounds are graphed against immersion distance for a given vessel? How would you calculate it from the known variables?

Raw, you are correct in saying that many surfboards are actually under water when the surfer sits on them (or stands on it if he/she has good balance) while stationary. But I would guess some are not submerged. It is diificult to tell, as mostly the stern will be submerged and the bow above water. Whether the board is effectively (on average?) above or below the water line is hard to determine. I would gues most surfboards would be either just submerged (0-2ft) or showing a very small amount of freeboard (1 inch maximum). I guess this means planing effect is a factor. I also guess this introduces another factor , the effect of depth of submergence on bouyant force. I knew this was more complicated than I first thought. I will do some graphs as suggested and see if I can make some headway. I'll be back.

 

The problem as I see it, isn't how best to quantify your results, but how to measure the boards accurately and simply in the 1st place.
Given that most boards are manufactured using the same type of foam blanks, and the weight of the FRP skins on most would be similar, (except I guess in the case of a very heavily built board) then all you nee to do is establish the volume of each board.
A board with a volume of say 50 litres might require a mass of say 75 kg to submerge it. A 75 litre volume might require 100 kg to submerge it. Establishing the flotation of a board in the 1st instance should be fairly straight forward. Take a board or foam/FRP block of a known volume and keep adding weight to it until it just starts to sink. You can then use that info to calculate the mass to submerge of any other board.
As I said, how you then go about measuring the volume of other boards then becomes the only difficulty...

 

Easily done by immersing the board in a water tank then measuring the change in water level.......

 

Yes - of course, but I'm assuming that enu is trying to quantify boards from various boardmakers. Something he can put up in a surf shop to say that board X will support a 100kg person whereas board Y will only support a 75kg person.
If he's only talking about quantifying boards that he's made himself then that is the way to do it

 

Enu, the thicker the board the more bouyant it will be, this is usually the 3rd figure on a board, i.e. 6'3" X 19" X 2 1/4" and if it is a short board then it the rider should sit with the water at waist level i.e. the board submerged about 3 inches. This is why any custom board manufacturer always checks the weight of the client and the height of the person.

You could work out the volume of a few boards using the measurements to calculate it as a rectangle and then sit on them to see which one floats your weight properly so you can work a ratio of box vs weight supported and increase from there, it will not be exact but close enough. Do remember though that how much a board supports is only relevant to sitting on it or paddling out not surfing on it which is determined by the shape, rails and bottom curve.

 

Thanks again. Measuring the volume precisely is the other aspect to the problem to which I am also applying my energies. However it is a problem I believe I can solve. Measuring through some sort of displacement method is the way I intend on proceeding with this. Volume and weight measurements of finished boards will be made to get high accuracy. It is probably possible to measure the volume of blanks milled from a CNC machine using the software, however I don’t think I will go this way. Note that I believe that 2 boards of the same length X width X thickness dimensions may have significantly different volumes. It will be interesting to compare the actual measured volumes to a simple comparison volume (based on height x width x thickness) to see how much boards of overall equal dimensions vary in volume. I know they can vary in weight significantly.

It is the mathematics of the buoyancy problem which eludes me. I am just not sure if a “mass required to achieve neutral buoyancy” measure is the most meaningful scale to use to determine how much easier it will be for a person to paddle one board over another. My first instinct was that this would be the measure to use, but I am not sure how linear this scale would be as various board volume and body weight combinations interact. I am thinking there may some exponential or other non linear aspect to the “Float Factor” curve as body weights, board volumes and board weights vary and interplay with each other.

For example (I theorize), as board volume decreases perhaps the effect of body weight becomes more significant to energy required to paddle it at a planing speed. Conversely as body weight decreases, perhaps the effect of board volume becomes less significant. As per my previous example, a person’s body weight has an insignificant effect on the hydrodynamic hull drag of the Queen Mary II when they step aboard. However on a 5’8” long surfboard, small variations in body weight will make a huge difference to how much energy will be required to make the board plane when paddling.

Here is a further example of the maths problem I think is hiding within this whole concept. Perhaps a 40kg kid would have to transfer 10% more energy to the water to paddle a 5’8” at 8 knots than to paddle a 12’2” board at the same speed (shape of course will matter, but I will have to ignore this effect). Whereas an 80kg man may have to transfer 80% more energy to paddle the 5’8” than the 12’2”, and a 120kg man 120% more.

I just don’t have the naval architecture mathematics knowledge to be certain how the variables work together to affect paddling energy required. It may well be as simple as using a measure of “mass required to achieve neutral buoyancy”, but before I proceed I want to get the maths right.

I am also not sure if volume distribution comes into play. I know shape does play a role, but I will have to ignore this effect. All things being equal, a flatter board will require less energy required to paddle at a planing speed than a board with more rocker (curve in the board when viewed in side elevation). I will simplify shape from the equation but not sure if volume distribution is significant, although I am guessing I will also remove this variable. Addition of these variables would make it all too complex, as the application of body weight is dynamic and quantifying volume distribution would be difficult.

Perhaps the best measure would be “joules per kg of body weight required to paddle at planing speed”. This may be an exponential curve when using body weight as the X axis. This is after all effectively what I am trying to quantify.

 

I don't know much about boat design, in fact nothing and that's not much.

But fitness and marketing I do.

I assume you are going to custom build surfboards to clients weight.

In sports you generally find that participants of each sport are generally the same build. ie marathon runners are by nature thin and lean, while rugby players are very heavy and neither would be successfull in each other's sport. Training only helps your natural body type.

Be carefull you don't spend too much money developing a concept that nobody wants.

Feel the water before jumping in or wiped out.

Marketing

Good idea, but probably not what you are thinking about, making custom surfboards not for heavy people but for people already in the sport.

One of our local sports footwear people sell sports shoes, obviously, but they analysing their client's feet on a computerised sensing pad.

Thus they are able to sell you the right shoe for your foot.

Or do they? I personally think it is probably a gimic. They have been in business for a while with several branches so the concept must work.

Can you do the same thing with surfboards? Put your clients on a board with sensors in a floatation tank as humans are not symetrical you can design a board to suit the weight distribution of your clients.

As for design, I don't think all the geek figures in the world are going to solve your problem. Geeks can only give you figures because someone with a brain has done the testing to provide them with the information.

Unfortunately I feel the answer to your problem if you really want to do it is by testing.

Get a surfer, some weight belts from a sports supplier and test different sized boards with the surfer wearing different weights.

As someone has already pointed out dynamics as well as flotation has to be taken into account.

Besta luck.

 

Thanks again. I'm not actually looking at building boards to suit a peson's weight. I want to provide a tool for consumers in the from of information. At the moment when a person looks at 3 surfboards, they can only estimate their volume, weight and ability to float a mass. Of course more experienced surfers can be fairly accurate with this estimate, but it is difficult to split similar boards.

 

Enu, that is the reason that if you want a board designed for you / your weight you go to a professional. As a surfer of about 20 years now and having shaped many boards myself I have been through the trial and error of board selection. So to sum things up there are a few factors you have to take into consideration

Waves are not a contstant, each wave is different and each day is different, if you were designing for a wave pool then perhaps you could use a exact science to quantify the different boards weights to exactly the clients requiements, but there in lies the other consideration, a beginner surfer will not notice the difference in board flotation to a degree that the differrence between one 5'8" board and another whereas a better surfer will know exactly what he requires and will be able to advise the shaper accordingly.

A example of what I mean is most good surfers will have more than one board with different length according to the surf conditions, this means that the boards float and paddle differently. You need to be able to paddle faster for bigger surf and the wave moves faster.

Essentially what I am trying to say is that the flotation difference of three boards of the same length width and thickness is not that relevent, whereas the length width and thickness compared to the surfers weight and surf conditions is.

 

Thanks antonfourie, your point is well taken. However as an example, I own 2 6'4" long surfboards that are within a quarter of an inch of each other in width and max thickness dimensions, and they float (and thus paddle) totally differently. One is a high performance lightweight board and the other is a fish style board. They have very different planshape outlines and thickness distributions. I would say their volume would be markedly different, how different one would never know, thus the birth of my concept.
With respect I would also say that experienced surfers are sensitive to small changes in volume. Apart from the issue of whether my idea is valid, the physics and maths of the problem interests me. Thanks for you input.