Hull speed calculation

[stevey_frac]

Had a question about hull speed:

This video shows steam launch Arlette going a claimed 13 knots:

http://www.youtube.com/watch?v=OwLuG9ExwV8

However, by my calculation, the hull speed of that boat should be about 7 knots (1.34 * sqrt(30)). I thought it was essentially impossible without advanced designs to exceed hull speed? And this craft is going nearly twice hull speed! Am I doing my math wrong? Or is hull speed something that can be overcome with more power, Jeremy Clarkson style?

--Steve

[DetroiTug]

That calculation applies to a true "displacement" hull with counter stern. The Arlette, appears to be a planing or semi-planing hull, note the flat vertical transom.

The advantages of a displacement hull is they are typically more seaworthy and they require less horsepower to make hull speed. A displacement hull under way builds a bow wave and stern wave and rides between the two. I was reading a while back on this very subject, and according to that, if a loaded displacement hull is towed faster than it's calculated hull speed it will completely submerge. The bow wave becomes so high that it eventually eclipses the bow and the hull takes on water and under it goes.

-Ron

[Edward]

Dear Steve ,

Most people manage to overestimate their boats' top speed but the formula V=Root L x 1.3 is generally accurate ; but only generally accurate , it is not an absolutely inflexible inviolate rule .
Arlette is definitely very fast and instead of using a factor of 1.3 a somewhat higher one should be used.

This is for two main reasons :
Firstly she has a very good hull shape . She is based on a Thorneycroft design ( Cygnet : http://www.steamboattrust.org.uk/cygnet.htm ) and in addition her owner/designer/builder spent several months with numerous model hulls on various towing trials before finalizing the design.
Secondly she is very light for her length , 1 ton . This was achieved by paring almost everything down to the minimum : her hull is 1/2" strip plank cedar , the deck is only 1/4" thick and although the seats look as if they are about 3/4" mahogany they have had the undersides routed out to give a much lighter weight.

So yes , more power can raise the factor but not if it comes with its usual commensurate increase in weight . It is the higher power to weight ratio that matters . I believe her antique engine produces slightly more than 11hp .

Her speed on Windermere was measured with GPS but I don't know if Windermeres' altitude of 111 ' above sea level was taken into account. Also note that her speed in the video is one way only and I'm not sure for how long she maintained it .


Best regards Edward

[Lopez Mike]

I agree with Edward that the 1.3 constant mustn't be taken as ironclad. It is, however, a very useful starting point for most middle of the road designs. A ton for a 30' boat is a remarkable feat of design and construction.

The question that has no easy answer is, "What is your boat's waterline length?" Is it measured at rest? At speed? What speed?" Mine 24' hull has an at rest waterline length of perhaps 19-20 feet. At 6.3 kts (GPS in no current conditions) the water flows along the hull all the way to the stern! 24' now. The stern wave at that point rises to deck height and the hull is tilted several degrees to the rear. Shortly thereafter the pressure drops and sanity returns.

I see that in the 13 kt. run there was only one person on board. On my own little boat I notice the effect of a couple of extra bodies above 4 to 5 kts. Also, fire tube boilers are nice for short spurts of speed. Stored energy and all that.

The stories of sinking boats from being towed too fast are true in that they have sunk a few but not from digging the bow in. The exception would be some demented action such as attaching the tow rope on a sailboat half way up the mast. Mostly they were from towing at ridiculous speeds in heavy conditions. Broaching and swamping. My own experience of driving my 36' sailboat (about a 29' water line) at far beyond 'hull speed' has been that looking aft is not recommended. The stern wave is alarming!

In the case of Arlette, the fine beam to length ratio, a relatively flat run aft, the sharp break at the transom and light weight make the turn in the drag v.s. speed curve much less dramatic. There are some great graphs in Oceanography and Seamanship (Von Dorn) that illustrate this well.

Mike

[dhic001]

I would have thought that a boat being towed under would be more likely due to flooding from aft. I remember John Hannah commenting that Mark Balemi towed him up the Firth of Thames in Greenbank, towing with Mark's modern planing launch. Greenbank at that time would steam at about 8.5 knots, at which point the stern way would be just below the belting at the back of the counter. Under tow, at about 9.5 knots the stern wave climbed onto the counter and started advancing towards the aft coaming. John felt that any faster would have resulted in it coming inside the boat from astern.

As an aside, we towed Zeltic up the coast last year at about 8 knots. The bow wave was the most substantial I've ever seen on Zeltic, but even at that speed she was quite happy. Wish I could get her to go that fast under her own power though.

Daniel

[fredrosse]

As stated above, hull form is very relevant. For example, just after the WWII there were surplus 26 ft lifeboat hulls available at give-away prices. These were full form displacement hulls, with a maximum hull speed = 1.3 x SQRT (LWL), or about 6.5 knots. At 1 or 2 tons displacement, only a few horsepower (2 - 5 HP) would drive these boats at hull speed. Many of these had a lever arrangement so the 10 passengers could force the levers back and fourth, turning the propeller, that was adequate for lifeboat service.

Many people bought these lifeboat hulls, and put automotive engines into them. With nearly 100 horsepower they could only get 1 or 2 knots faster, the excess power just created big waves, but the boats went no faster. Many were completely surprised (and disappointed) as much less technical information available to armature boat builders back then.

As far as fast/low powered boats go, the present realm of planing daysailers fits into this class, displacement hulls with a vertical transom, with little or no "rocker" at the stern. The sails (with a stiff wind) might produce 10 - 15 horsepower, and these little sailboats (16-20 feet LOA) can often make 15+ knots, far above the displacement hull equation calculated maximum speed. That is because of their appropriate hull form, and light displacement.

[artemis]

... As far as fast/low powered boats go, the present realm of planing daysailers fits into this class, displacement hulls with a vertical transom, with little or no "rocker" at the stern. The sails (with a stiff wind) might produce 10 - 15 horsepower, and these little sailboats (16-20 feet LOA) can often make 15+ knots, far above the displacement hull equation calculated maximum speed. That is because of their appropriate hull form, and light displacement.

And a very important part of planing SAILBOAT hulls is the fact that the hull is designed to achieve her best speed when the hull is inclined from vertical. Reduced wetted area, etc.

David Gerr (author of many boat design books and director of the Westlawn Institute) has developed a 'hull speed' calculator that is more accurate than the 1.34*sqrt L (he has verified it against lots of models etc). It uses the displacement length ratio to change the 1.34 factor.

The formula is: V = 1.24*L^1.433 / D^0.311
where V is kts, L is feet, D is displacement in pounds and ^ is "raised to the xxx power".
So long, light boats can reach a higher 'hull' speed.

[gondolier88]

Some boats rise out of the water and sink by the stern when towed, usually counter sterned boats. Fine entry angle boats with a transom tend to cut water better and make the best towing boats, also, the longer a boat is the better it tows. Any boat with a rockered keel is almost impossible to tow under. As has been mentioned, where the tow is attached also makes a big difference, about mid-stem height is ideal, but requires an unsightly fitting, although many trailable boats have an eye for a shackle at about that height anyway.

Arlette is truly magnificent to watch at speed, and is a marvel of ingenious design- it not only works, but is beautiful too.

Greg

[stevey_frac]

... As far as fast/low powered boats go, the present realm of planing daysailers fits into this class, displacement hulls with a vertical transom, with little or no "rocker" at the stern. The sails (with a stiff wind) might produce 10 - 15 horsepower, and these little sailboats (16-20 feet LOA) can often make 15+ knots, far above the displacement hull equation calculated maximum speed. That is because of their appropriate hull form, and light displacement.

And a very important part of planing SAILBOAT hulls is the fact that the hull is designed to achieve her best speed when the hull is inclined from vertical. Reduced wetted area, etc.

David Gerr (author of many boat design books and director of the Westlawn Institute) has developed a 'hull speed' calculator that is more accurate than the 1.34*sqrt L (he has verified it against lots of models etc). It uses the displacement length ratio to change the 1.34 factor.

The formula is: V = 1.24*L^1.433 / D^0.311
where V is kts, L is feet, D is displacement in pounds and ^ is "raised to the xxx power".
So long, light boats can reach a higher 'hull' speed.

Thanks for that.. Have to bookmark this post.

Based on this formula, the boat I wish to build should have a hull speed of 8 knots, just shy of 15 km/hr. That's not too shabby! That's assuming I can keep her under 7000 lbs though.

Perhaps I can make the hull a bit thinner, and glass is... Have to ask the designer!

--Steve

[Lopez Mike]

Mucho thanks to Ron for that Gerr formula. Also it will get penciled up on the wall here.

The business about performance v.s. heel angle has gone through many modifications over time and applies to some hulls but not others. Several factors have gotten all tangled up over the years.

As you know, sailboat hulls come in an extreme variety of shapes. It was noted quite early on that in light airs on a reach or a run, some hulls went faster when heeled over a small bit. It took many years before on the water experience made it into print. It turns out that the best speed off the wind coincides with a neutral helm. The boat, in fact, can be sailed by heeling it with the tiller left unattended in many cases. This is well known in with the Laser dingy, an easily planed hull.

As soon as the boat is hard on the wind, though, I know of no exception to the rule that a level boat will sail right through a boat heeling. In the case of the laser, five degrees of heel up wind will get you beat.

These are lightweight boats in which the boat can be heeled from second to second by crew shifting position.

With heavier traditional hulls, the situation is not so clear. There is very conflicting anecdotal evidence for both sailing as flat as possible and at some small heel angle. The situation is complicated by what one means by faster; speed on a knot meter or speed made to a windward goal. In a heavier boat the best speed to a windward point is never the best speed though the water. And the best speed to windward is gained at the cost of the wind pressure on the sails heeling the boat.

The number of variables is astounding and few naval architects claim to have a very good handle on it. The new numerical simulations are getting close to a solution but even the most rabid proponents of computer simulations will admit to more than one constant being pulled out of one of their orifices, so to speak.

For our humble boats, I wouldn't get too excited about going faster than the average without some significant sacrifice. Light weight, beam to length ratio, accommodations, fuel consumption or who knows what?

As I noted earlier, I have no idea what number to enter into these formulas for my waterline length.

As a humorous note, one of the most successful sail design and building groups in America's Cup history called itself WBG Group. After a few years passed, they confessed that it stood for We Be Guessing.