S&S 34 Hull Speed

from Tim Dallas, Superstar:

Many crew, when out for the first time on SuperStar, have asked me what the theoretical hull speed of the boat is.  This seemingly innocent question normally arises when sailing down wind under spinnaker and we hit 8 knots.  This results in various responses from the regular crew, the foredeck babble hysterically and retreat into the folds of the headsail piled on the foredeck, the sheet trimmers dive for cover to avoid the mainsheet in what they believe will be an inevitable crash gybe and the helm usually grins grimly (if possible) whilst wondering how the hell we are going to get the kite down without bringing the rig with it!

Of course once the leeward mark is rounded, without much more than the need for a little additional laundry, the question is still unanswered.  So I've been doing a little research:

Many people who claim to be in the know about maximum hull speed use variations on the equation;

Max speed (knots) = 1.341 x SQRT(LWL in feet)

But this formula yields 6.6 knots for the S&S34, which clearly isn't right as SuperStar easily exceeds 7 knots in a moderate breeze when reaching.

Other authors have stated that both the bow and stern of a vessel create waves, when the these waves build to the extent that their wave length coincides with the water line length of the vessel the hull will, effectively, fall between the waves.

Hence this limits the maximum speed of the vessel, unless it has the power to climb over the bow wave, i.e. PLANE.

Now, this theory appears to me to be flawed because SuperStar has seen 8.7 knots with the kite up and we weren't planning!

Incidentally I Googled 'Yacht Hull Speed Calculations' and got 202,000 hits!  I only checked about 20 of them and only one actually disputed the formula quoted above.

Addit from Simon:

There are reasons why we can exceed the "theoretical" hull speed above.  The main one is that when going hard downwind the stern tucks down and the waterline extends right to the transom.  This brings waterline length up to 28.6ft and the "theoretical" hull speed as calculated above up to 7.2 knots.  The S&S 34 waterline length is also designed to increase when heeled.

The other factor is that the "hull speed" is not totally fixed.  It is defined as the point at which hull resistance increases dramatically due to the wavelength of the bow wave becoming the same as the waterline length as shown above.

An important calculated dimension in this regard is the so-called Froude number which is the boat velocity in metres per second divided by the square root of the waterline length (in m) times the acceleration of gravity (in m/s, = 9.8).  When this equals 0.40 the bow wavelength exactly matches the waterline length.  As the Froude number increases above 0.40 the hull resistance increases dramatically and despite extra wind, sail area etc the boat won't go much faster. If you do the calculations you will find that for the S&S 34 DWL at a Froude number of 0.4 this equates to the 6.6 knots quoted above.

Notice I said "not much faster" - extra power will result in some extra speed, but proportionately not nearly as much as when the Froude number is less than 0.4.  The maximum speed is therefore not totally fixed as the limit is a little elastic.  In  practice, for our type of hull it is said to be difficult to exceed a Froude number of about 0.45 (allowing for the increased waterline length factor and all other factors above).  If you do the calculations, you will see that this gives a maximum speed of about 7.5 knots.

If the hull can climb up on it's bow wave, this reduces resistance, as the hull stars to semi-plane, and once again increased power results in increased speed.  This occurs at a Froude number of about 0.5.  However, heavy displacement type hulls such as the S&S 34 can't get over the "hump" in resistance at 0.40-0.50 except under special circumstances, such as surfing waves in the ocean. 

As our boats are relatively light compared to some other displacement hulls, have a lot of overhang (ie can increase waterline length more downwind than many other designs), it may be that we can under some circumstances do a bit better than 0.45. After all, our boats were designed as racers by the greatest designer of the 20th century!  However, I think that it is generally hard to exceed about 7.5 knots, requiring plenty of wind and sail power, and to do this by more than a knot or so would require us to start semi-planing, ie surfing on waves.  The more we can surf, and the more power we have in the sails, the faster we can go in exceeding the theoretical limits above.  The fastest I have heard of in an S&S 34 was 17 knots - that wasn't on the river and it definitely wasn't us!