Scale models and double hulls

[boataid]

Ok so Ive got a couple things to toss out there. For starters I designed a Catamaran Hulled Stand Up paddle Board in a surfboard design program called akushaper. At full scale it gave me a volume of roughly 230 litres. This seemed satisfactory as I designed the model to be from the waterline down (or that which woud represent displaced volume). My desire was to have a board sub 50# plus a 250# paddler and up to 100#'s of gear. According to my calculations the 230 litres would equal a displacement load of 500#'s. So heres my problem. I wanted to build a 1/3 scale model to confirm load capabilities. The full scale board is 15 feet. Like I said the hulls equalled 230 litres of volume. Anyways i reduced the model to 1/3 its size. I had expected it to be about 75 litres of volume but lo and behold it was like 8 litres. Not only that but I assumed the 1/3 scale model would support 1/3 of 500#, that being 166#'s but the scale model clearly wont do that. So I built the model and loaded it. Dry the model weighs 6.6#'s. It was able to float 22.5#'s plus its own weight for a total of 29.1#'s. Clearly my belief that I could reduce everything by 1/3 was incorrect. So heres my question: If I have a 1/3 scale model that supports 29#'s, what will the full size board support? Does that make sense?

Question #2. It was stated in another thread that a double/multi hull adds 11% more drag than a monohull. How why is this? If both weigh the same wont they displace the same exact amount of water and thereby drag?
If You have answers, especially to question #1 I would be very grateful. Thank you.

[Guest625101138]

The volume is the cube power of the scaling factor. For a scale factor of 3 the volume will change 3X3X3 = 27.

For a given weight and power level there will be a particular monohull shape that will give the lowest drag. If you compare the monohull to a catamaran having lowest drag for the same weight and power it will be around 11% slower.

There are two reasons for this. The most significant is that two hulls will have greater wetted surface than one hull for the same total displacement. This is because displacement is a cube function of scale and area is a square function of scale. So the volume of each of the catamaran hulls will be half but the area is greater than half so more drag due to viscous effects on the surface. The other factor is wave drag. The shorter hulls of the catamaran have a lower hull speed than the monohull so the onset of significant wave drag is at a lower speed for the catamaran.

If there is a length constraint on the boat then the catamaran could have lower drag. I expect that for the load and power you are considering something less than 14ft would favour the catamaran. If the allowable length is longer than 14ft then it would favour the monohull. The lowest drag monohull would be about 28ft long. The lowest drag cat would be maybe 20ft long.

The Rocat shown here:
http://www.rocat.co.uk/
will give you an idea of something close to the lowest drag hulls for a catamaran for the sort of load and power you describe. It is around 11% slower than the lowest drag monohull for similar load and power:
http://www.chesapeakerowing.com/HudsonSingle.htm

Interestingly the Rocat designer was not aware of this fundamental difference. Some buyers were disappointed when they were completely outclassed while racing monohulls. 11% is a big difference in boat speed while the 40% extra power to bridge the gap is huge.

Rick W

[boataid]

Wow thank you. Just to clarify the scaling factor...... so would the 22.5#'s of load be scaled like this: 22.5# x 3= 67.5# x 3 = 202.5# x 3 = 607.5#, thereby meaning the 1/3 scaled hulls would be capable of supporting a load of 607.5# at full scale?

[Guest625101138]

Yes. If your scale model hulls support 22.5lb and they are scaled up 3 times they will support 607.5lb at the full scale.

Rick W

[Ad Hoc]

boataid

That is incorrect

22.5x3, x3, x3 = 607.5, is not the same as 22.5 x (scale factor) ^3.
Since 22.5^3 = 11390.625!
You are misinterpreting (or confusing) simple "multiplication" with "indices".

So, if your volume is 230L and you want this at 1/3rd scale

That becomes (scale)^to the power of 3, hence, (1/3)^3 = your constant = 0.037

Therefore 230 x 0.037 = 8.5L

As for cat v mono.

It all depends upon the Froude number (speed) and form factors of the boats and how far apart the hulls are too. Since in the Fn range 0.8~1.3 for example of L/D ratios of 6~7+ cats are approx 50% better than a mono. It is all horses for courses, and no blanket statements. Every application has its place.

Boat design is not....oh, oh oh..i see XXX on one boat, must be good for me. Unless your boat is exactly the same, one cannot make such generalised statements.