Location: AUSTRALIA I will try to give an intuitive answer so that I might stand to be corrected later. 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. The prediction of hull speed before planing is most simply the square root of hull waterline length in feet x 1.34.
Remember the 20 footer needs to achieve about 3.5 times it's theoretical hull speed now to catch the planing 60 footer. Then instability issues become a major factor for the 20 footer trying to go at 3.5 times it's sub-planing hull speed.
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.
Ironically, the optimum solution of these trade offs seems to come at differing size points, the windsurfer being a classic example. 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 should have narrowed my question more concisely to planning ocean going mono hulls in planning mode. 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? 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). Location: Scotland 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.
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. Location: Australia At the weights and lengths I think you are talkling about the boat won't plane.
Location: Scotland Why are the competition all building boats which are clinically obese. In RC boats where keel depth is unlimited or nearly so narrow has almost always been faster.
When making potentially dangerous or financial decisions, always employ and consult appropriate professionals. Froude's Law indicates that at sub-planing speeds hull velocity is directly proportional to the square root of waterline length. Unfortunately I think their concept would prove even more uncomfortable than a mini for sailing the Atlantic. Have to brush up on relativity and similtude-an identical hull form doubled in size has 16 times more stability!
THe little boat struggles in that when the wind is string enough to go really fast the waves are too big.
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.

The top speed of a 49er in faster is the water is smoother than if it is rougher for the same wind strength. Do you reckon it would be even possible for a 2kg boat which has a waterline length of 70cm to even plane.
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. 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. 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? 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. 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. 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.