Planning hull speed?

I've been trying to find an explanation of the limiting factors for the top speed of a planning hull of a given length. Since we're not talking about being stuck in a wave through- what say keeps a minitransat 6.5 proto from going as fast as a volvo70? If I provide enough sail power lat. and long. stability and steering control, and a keel foil the boat won't trip over; why won't the little one go any faster? I can't find any specific explanation in my books.

Thanks

JohnO

 

I will try to give an intuitive answer so that I might stand to be corrected later. Froude's Law indicates that at sub-planing speeds hull velocity is directly proportional to the square root of waterline length.

Froude's Law

Froude's Law also states that a displacement hulled boat will go no faster than the wave length created by the hull as it moves through the water. This wave length is equal to 1.34 x LWL. In other words, a boat with a 25-foot waterline length will go no faster than 6.7 knots. Most boats can be overpowered or may sail down the back of a wave and temporarily exceed this calculated maximum, but they cannot maintain that speed unless they have a low displacement/length ratio when they plane.
The prediction of hull speed before planing is most simply the square root of hull waterline length in feet x 1.34.

Depending on hull shape and power available from the sails, some boats easily exceed "maximum theoretical hull speed" . Obviously this will happen at a lower speed for a 20 footer than a 60 footer. Then the hull is riding up on it's own bow wave, therefore planing. Then to achieve double the theoretical hull speed in each case may entail a relatively small further increase in power, say 20% for arguments sake. The 60 footer is still going at about 1.7 times the speed of the 20 footer. For the 20 footer to catch up to the longer boat is going to require a very large increase in power as drag forces, particularly wavemaking turbulence of the hull and appendages, and drag forces produced by the rig then increase rapidly, and are difficult to overcome.
Remember the 20 footer needs to achieve about 3.5 times it's theoretical hull speed now to catch the planing 60 footer. (travelling at double it's hull speed).
Then instability issues become a major factor for the 20 footer trying to go at 3.5 times it's sub-planing hull speed.
Having said that 49ers and Aussie skiffs will do just that and more!

 

You've answered your own question. That's exactly what you have to do. I find it helps if you sometimes imagine things at extremes: So strip the mast, keel, rigging and excess interior weight away and fit a jet engine to it. It's now obvious that there is still some speed potential in the hull!

So all you have to do (in competition with every young and old designer in France) is to find a way of increasing the power (more sail, more righting moment, less weight) and reducing the drag (less WS, thinner foils, less displacement, etc) while staying within the class rules. Bingo!

Ironically, the optimum solution of these trade offs seems to come at differing size points, the windsurfer being a classic example. Unfortunately I think their concept would prove even more uncomfortable than a mini for sailing the Atlantic. (Although on the other hand, I am having problems imagining anything more unpleasant than sailing a mini.)

Once you break away from class rules, you are able to explore other solutions, and splitting the hull into two and dumping the lead ballast does great things for increasing your righting moment (sail carrying ability) and losing weight.

I have to go now; there is someone at the door. Oh no! run everyone..... it's the missionaries from the Fundamentalist Sect of the Foilers are THE Solution Everything Church.

 

Yes,
trimarans and windsurfers are close to 50 knots, I beleive, and they are much smaller (shorter) than a V60/70.
It's all about power/weight.

V70 vs Open 650?
Larger monohulls have more stability (power) than smaller ones, I guess.
You also have more wind higher up

 

Thanks for the replies.

I should have narrowed my question more concisely to planning ocean going mono hulls in planning mode. What sparked my qustion is this: There seems to be a point at which adding more power to for example a mini 6.5 going downwind, planning, true wind 30 knots and building, boat speed 20 knots-at some point adding one more knot of breeze just makes the boat uncontrolable. For Vo70 The sort of 'terminal velocity' seems to be around 40knots. Is there formula for rough aproximation of this terminal velocity/point of diminishing returns?

From what I have read there seems to be a point where even when planning there is a rapid(non linear?)increase in resistance; and I guess the bigger boat 'sees' the water as thinner than the littler one?

 

Diminishing returns

No, there is no rough formula. As stated by others, the 'terminal velocity' is not related to hull resistance. For planing hulls travelling above hull speed, the resistance curve is reasonably linear. The primary limiting factor is available righting moment. More specifically it is the righting moment/drag ratio that is important. This ratio does not scale directly with size. For planing hulls, friction is the predominant resistance factor, which scales proportional to the square of the waterline length. For similar boats, the available righting moment is proportional to the displacement, which scales according to the cube of the waterline length. From this, it should be obvious that the righting moment/drag ratio improves as size increases, hence bigger boats are generally faster than smaller ones.

Note that all high performance dinghys capable of reaching sppeds equal to or higher than larger keelboats all use devices which either (or both) increase available righting moment (wings, trapezes etc) or reduce drag (foils, planing hulls).

Mal.

 

Yep,got it now thanks. Have to brush up on relativity and similtude-an identical hull form doubled in size has 16 times more stability! so even if the smaller boat had way better disp S/A ratio the stability advantage of the bigger is tremendous and so on....

 

Mal gives a good description but there is also another factor. Waves.

To a bigger boat the waves are proportionally smaller. THe little boat struggles in that when the wind is string enough to go really fast the waves are too big. The top speed of a 49er in faster is the water is smoother than if it is rougher for the same wind strength.

Nobody

 

Does the width of the boat have any significance in its top speed before it needs to plane to reach a higher speed.
Is there any way of working out how much extra force is required to go from top hullspeed to planning.
When a boat planes does its stern dip into the water creating a trough which increases the effective hull length which in turn increases max attainable speed.

Lots of questions need answering fast as we are making our hull as we speak for our school rc boat race.

On a side line do flares at the bow of the boat help dissipate bow waves from swamping the deck as i had noticed on some of the v70s that they appear to have quite a large flare. This is particularly relevant at our scale as the waves are proportionally bigger.
At the moment our hull design is very narrow as i thought that narrower would be faster i think off the top of my head that the ratio is about 5. some of the competitors last year mocked us for having such a narrow hull but this year our hull is even narrower. Do you reckon it would be even possible for a 2kg boat which has a waterline length of 70cm to even plane. We are expecting in a 5m/s wind to get about 7-8N of lift from the sail. Will this be enough to make it plane?

Thanks Alex.
NBHS RC Design Team

 

At the weights and lengths I think you are talkling about the boat won't plane. Therefore you want to get the least drag in displacement mode. For this a narrow hull will be good however you will loose righting moment.....


Nobody

 

planing

Alex, NB is right. RC models have been described by some as planing but it almost always is wrong. Time and time again especially where unlimied keel depth is legal narrow(9/1 beam to length or narrower) boats win.

 

Why are the competition all building boats which are clinically obese.

 

refresh: RC rule?

Alex, refresh me on the rule: is ballast, keel depth or sail area controlled; if so what are the limits?
In RC boats where keel depth is unlimited or nearly so narrow has almost always been faster. I can't think of a single "open" RC development class where wide has worked. In the IOM class(semi-development) where keel depth is restricted and ballast limited I believe a relatively wide boat did well for a while.

 

the max length is 700mm and the min weight is 2kg
the max keel depth from top of deck to bottom of bulb is 300mm. I have included a diagram of the hull we are currently working on. Any comments on this would be usefull we are also planning to add some flares to the front which we think will help it ride over the waves as that is often a major concern with rc models.

Also the keel weight cannot exceed 55% of the total weight