Calcuation to estimate planning speed

Does anyone know what is the equation determining when a hull will come up on plane as in light center board sail boats, and perhaps fast catamarans?

My books have equations that do not make any sense. It seems to me that you have to have an expression that includes speed, "lifting" surface area, and weight, and perhaps something related to the incline of the hull surface. Does the aspect ratio of the surface come into this at all? As in a mono-hull vs. a cat hull?

This should be similar design condition for both powered and sail craft, and even sponson equipped float planes and water skiers. But I can not find the correct expression and what I have derived seems to leave too many important variables out of the calculation to have any meaning.

Thanks.

 

The hull planes if you have the power to push it well beyond its hull speed and it has a surface to plane on. The transition from displacement to plane can be hardly noticeable or result in quite severe attitude changes depending on shape and distribution of weight.

Michlet is not really useful for analysing drag in planing mode but it will give you a good indication of the speed where wave drag really starts to kick in, rises sharply (for typical hulls) and then levels out or even drops away. The levelling out point is around where you are planing. I have attached an example of an 8ft long flat bottomed dinghy. The two curves are for different displacement.

The equation for "hull speed" is given as kts = 1.34 * (WL length (ft))^0.5. So a typical beamy 16ft WL boat would be experiencing significant wave drag at 5.4kts and starting to rise at the bow. Depending on shape and weight distribution you would expect it to be fully planing by 10kts. If it does not have good planing surfaces or good weight distribution then it might plough on beyond 10kts making ever bigger waves and requiring considerable power.

For the 8ft dinghy the hull speed is nominally 3.7kts and you can see the wave drag is really kicked in at this speed. The drag curve settles down around 6kts and that is the speed where you would expect this little hull to be on the plane.

I have not seen transition analysis. In a transition region neither the displacement analysis nor the planing analysis apply. You can use these to get the conditions before planing and once on the plane but it is not necessarily a smooth transition between the modes of operation.

Rick W.

 

That is interesting Rick. What is the reason for the very noticably dip in drag, sort of just before the boat can plane. Is it a wave formation that starts to "push" the boat onto the plane?

 

The chart contains data directly from Michlet. I have not looked at the wave patterns to see how they might interact to give the result shown. I would also question their absolute accuracy because Michlet does not adjust for changes in trim. They will be accurate at low speed and should have the correct shape in the transition.

I have watched interactions of waves on some of my hulls and it is possible to find a sweet spot where things are a bit easy when pedalling. The wave and hull interactions can be observed with catamaran hulls.

I know Leo Lazauskas has made a lot of observations and can no doubt tie the maths involved to the observations but I just use the tool - I don't understand its ins and outs. A bit like my current car. It is now 8 years old and I have opened the hood 4 times. I can still drive it though.

There is a neat, but memory hungry, little animation on Leo's site that shows wave cancellation on a tetrahull SWATH:
http://www.cyberiad.net/waketet.htm
Waves are complex and I remain ever thankful that Leo produced Michlet. It satisfies my engineering bent to quantify. I do photograph waves but normally just to compare with Michlet not to understand their physics.

Rick W.

 

Sorry Rick, I've got to pull you up there. 'Hull speed' and minimum planing speed are not related. A hull can plane before hull speed is reached if designed properly.

David Gerr has devised a more 'refined' hull speed where the 1.34 coefficient is replaced by some function of the displacement:length ratio (ie long light boats have a higher hull speed).

Speed to get on the plane is determined by creating enough lift. Lift is determined by wetted surface area (a moving target), speed, aspect ratio, inclination angle (ie V angle), angle of attack (trim) and fluid density. I think the Savitsky method (paper is availble on this site somewhere) should cover it.
Sorry for the short answer, I'm in a bit if a rush.

 

yes, I have since reviewed the Savitsky document, it is a complex issue I guess. I understand what happens, but all of the estimating methods I have seen does not seem to consider hull shape for planing. Clearly some hull shapes are better than others. ISTM that in addition to surface area, weight, angle of attack, and speed, you need a lift coefficient that would be dependent on the hull shape. And the induced drag of the lift you generate would have to be included along with the reduced skin friction drag.

My thought was how do you figure out when a light sail boat would start planing. Where the CG is seems to also affect whether you get up "on plane". And then how can you estimate the maximum speed you will reach once on plane with a given size sail.

Suppose one designed a planing catamaran, and would it be faster than a foil equipped cat? I think determining the drag on a foil equipped hull should be strait forward, and my thought was are the wetted area, induced and parasitic drag of the foils lower than the drag on a planing hull. I suspect it is not, the foils really only have an advantage trying to make good speed in rough water (which is when there is a lot of wind). But on smooth water it would be questionable if there is any advantage.

What do you think?

 

I believed that the Arrow design catamaran, I think from Lindsey Fletcher, we made them out of ply in the 60's was a planing catamaran. They certainly were very fast, and the flat bottom was leaving a clean transom at speed.

 

Hi Petros,

I'm talking from distant memory here, so may be wrong, but as I recall the Savitsky method uses a beam wise Froude number - ie Froude number based on beam, not length. It also, IIRC, uses the aspect ratio of the planing surface. So I think these probably implicitly account for the hull shape. Don't forget of course, that this is not lift and drag in the sense of an aerofoil - there is no low pressure suction side, just a stagnation point with high pressure 'pushing' the hull up. So you don't need to consider the curvature of the hull like the curvature of a foil section. I think maximum planing speed is more limited by stabilty (longitudinal and transverse) and control than drag, just look how fast powerboats go. Cats don't generally make good planing hulls because the hulls and long and slender - exactly what you don't want.

 

I know about the idea that cats can not plane, there are actually some pretty old threads on this forum about that, but it is false. Float equipped light airplanes are catamaran-like hulls and they have to plan or they will not get off the water. Some of these aircraft are pretty low power as well, there are many ultralights with 40 to 60 hp that have float options. If the floats did not plane they would never reach take-off speed.

Though either you have to have a large drag producing step, (a retractable step perhaps?) or some sort or foil, you will have a difficult time producing a lot of dynamic lift on cat hulls. That why I wanted to know if there was a strait forward way of calculating it to see if a simple planing hull would be better for a fast cat than foils.

 

Planing cats/multihulls/monohulls

Parliers 60 footer works, in fact,I think he held the 24 hr record for a short time. Originally, he planned to use some sort of variable geometry to reduce the drag of the step in nonplaning conditions-I don't think he used it-at least it didn't work too well against ORMA 60's in light + conditions.
At any rate ,as you already know I'm sure, the biggest problem with planing hull design is what happens in non planing conditions. I've come up with a potential solution for multihulls-check out the "Ultimate 18'Trimaran" thread under
the "multihulls" thread. There are pictures referenced near the end of the thread of a small conceptual model illustrating the concept.My system expands on Parliers idea: it utilizes a rotating hull to allow the tri to sail on a high Length/beam ratio(18-20/1) displacement hull up to X speed then rotate the hull and what was the deck of the displacement hull is now the bottom of a stepped planing hull. Simpler than it sounds and provides a way to "shift gears" while taking advantage of both hull types thru their appropriate speed ranges. As Parliers boat did mine uses two small hydrofoils for pitch stability.
Ultimate 18' Tri ? - Boat Design Forums
Address:http://www.boatdesign.net/forums/showthread.php?t=17644
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As to what will plane when check out Pierre Gutelles's book "Design of Sailing Yachts". He has a section on planing hull sailboats.
But ,in my opinion, the best source possible for accurate information on weight,area, angle of attack for light sailboats is to measure and watch windsurfers sailing-you can learn an immense amount very quickly.

 

Froude Number > 2.3

Don't challenge me on any of this.

I run a crude spreadsheet that I think of as a VPP for dummies. For example, it uses Gerr's speed:length ratio to predict hull speed. This allows me to see (at 4 decimal places) the speed increase expected from making the boat 1 pound lighter. Cool !

But somewhere down the sheet is a note that the Froude Number, Fn, must be greater than 2.3 for a planing hull. Then the spreadsheet calculates the minimum planing speed for the weight of my boat:

Minimum Planing Speed - Knots (Fn=2.3):

2.3 x ((32.2 x (all up displacement in pounds)^0.333)^0.5)/1.6889


For example, my 18' keelboat at 2,323.2 pounds (including crew) may plane at 13.902 knots.

The formula has no input for the shape of the hull. It just calculates the speed required to lift 2300 pounds. It also does not indicate how difficult it will be to get my hull to 13.9 knots. However, in my ignorance, I believe it may be somewhat representative. If the boat was surfing down a wave at 13.9 knots, it may very well be planing.

Is it not true that any hull can plane given enough speed or horsepower?

 

That formula takes nothing into account for the angle of attack and the surface geometry? Both of these have a large impact of the lift generated, I do not see how this is possibly accurate. Does it presumes a "typical" hull geometry and angle of attack? How else can it work?

The angle of attack determines the amount of acceleration of the water, which determines the lift. Consider the basic force equation F=Ma. Force (or lift) is directly related to the amount of mass (in this case the mass flow rate, or speed of the hull over the water) multiplied by the acceleration of the mass (which is directly related to the angle of attack of the planing surface relative to the water flow direction). how can you reduce planing speed down to where there is no angle of attack and have it accurate?

 

Hell, I don't even know what a Froude number is . . .

But if the boat had one and it was 2.3 or greater, it may plane at 13.902 knots (if the angle of attack and the hull geometry were right).

 

"I know about the idea that cats can not plane, there are actually some pretty old threads on this forum about that, but it is false. Float equipped light airplanes are catamaran-like hulls and they have to plan or they will not get off the water. Some of these aircraft are pretty low power as well, there are many ultralights with 40 to 60 hp that have float options. If the floats did not plane they would never reach take-off speed."

Are you sure, and is the comparison a perfect one?

Imagine say a displacement hull like a rowing shell, or a pair of deep-hull racing surf skis (sit on top kayaks). Fit it with 40 to 60hp and some aerodynamic lift. Surely it would go fast enough to achieve "planing" speed even without planing, because the power is very high for such a small craft and the wavemaking and skin drags are so low. After all, a racing surf ski in the surf drops down the face of a wave which is moving at (IIRC) 17-20+ knots, and that's just on gravity power. A racing kayak does 9 knots over the mile IIRC and that's with the power on only one person....add another 50hp and surely the speed would increase quite nicely??????

The early creators of seaplanes have great difficulty in "unsticking" until canoe and yacht designers like Linton Hope etc did their hull designs. But isn't it to be expected that a shape designed to work with lift from wings and 40-60hp is very different from a shape that will perform better with no aero lift and much less power, and therefore comparisons between the two could be fraught with danger? After all, the top hulls in the 50hp outboard racing class are very different from the top hulls in the A Class cats.

You can create a planing cat - I've sailed a stepped hull one. It was a complete dog of a thing in every way and despite certainly planing, it was slower in all conditions than a conventional cat because the planing shape was so much higher in other forms of drag. The world's best A Class cats and top-class F18s show little or no sign of true planing behaviour.

 

Petros, on the same hull - if it is a planing hull, a small outboard for instance has a much slower minimum planing speed than the same hull with a large motor on. I think the problem is that there are so many different hull types and shapes, each with a different characteristic that it is difficult to put a specific rule up. Even something simple like weight distribution in a boat makes a big difference in the power required to get it to plane. Of course brute force can get anything to plane but is not always practical.

The hull's designed for sailers are very different from planing power boat hulls. Having a motorized sailer is a compromise to which one is the priority, sail or power - it seems the planing hull shape is compromized the most since a planing hull won't sail so well, while a sailing hull can still be motor driven.