ladder foils

[haybayian]

Hello boat designers,
I have built a 40' boat and a sportscar from scratch and I am now interested in hydrofoils. My hope is to build a 15' two seater powered from a 1500 cc Mazda engine and a small aircraft propeller. I am at the beginners end of the learning spectrum and apologize in advance for the naivety of my questions.

I would like to start by asking a question about foil types. The ladder type in particular. Would a craft equiped with 3 or four ladder foils be self stabilizing the way V types triangular surface piercing ones are? Is there any advantage in building a craft with ladder foils rather than V foils?


Thanks.

Haybayian

[marshmat]

Hi haybayian,

Ladder foils date back a long way..... A.G. Bell used this design on his prototypes back in the 1910s; his HD-4 set a 70 mph record in 1919 that stood for something like 10 years. So yes, they are viable. But I think he had six or eight foils on each of four struts, and a pair of aircraft engines. And the thing looked just plain weird by any standards.

In any event, the HD-4 and numerous other ladder-foil craft have been successful, and perusing Bell's work via Google will no doubt give you some inspiration as to how it might be done at a smaller scale.

[haybayian]

Thanks Matt for your tips. Yes AG Bell and Baldwin's work are a good introduction to ladder foils.

Haybayian

[haybayian]

Thanks Matt for your tips. Yes AG Bell and Baldwin's work albeit ancient are a good introduction to ladder foils.

Haybayian

[tspeer]

...Would a craft equiped with 3 or four ladder foils be self stabilizing the way V types triangular surface piercing ones are? Is there any advantage in building a craft with ladder foils rather than V foils?

Yes, you can make a craft with ladder foils that is self-stabilizing. It isn't necessary for all the foils to be ladder foils to achieve this. You can use ladder foils forward and fully submerged foil(s) aft. The aft foils must be more lightly loaded (carry less weight per unit area) than the forward foils.

The rungs on a ladder foil should be tilted (or the entire foil unit tilted) so that the end of one rung is still in the water when the end of the next rung starts to leave it. This will result in a continuous variation in area, and is a technique invented by A. G. Bell. Otherwise, the craft will hunt, bouncing from one rung to another as n rungs are not enough , but n+1 rungs are too much.

You can find a simple estimate here (http://www.tspeer.com/Hydrofoils/generic.pdf) of a V foil compared to a ladder foil. You'll also find some data there from Bell's HD-4, illustrating that it is possible to achieve near-constant drag over a reasonable speed range.

Bell's and Baldwin's reports on the HD-4 are very informative. They can be found in the Beinn Bhreagh Recorder (http://bell.uccb.ns.ca/agbi_docs_frm.asp), Vol 23, starting on page 21a for Bell's report, and page 60 for Baldwin's detailed technical report.

http://bell.uccb.ns.ca/Images/B/vol23/B2375.GIF
http://bell.uccb.ns.ca/Images/B/vol23/B2376.GIF

The HD-4 was a very advanced concept. It was a trimaran whose hull had a monocoque construction reinforced with high-modulus unidirectional fibers.

One could do a whole lot worse than to build a modern-day reproduction of the HD-4.

[haybayian]

Thank you very much Tom for your remarkable answer. Your explanation makes ladder foils more understandable to me. I will follow your suggestions and read more about AG Bell's hydrofoil:idea: .

Haybayian.

[tspeer]

When I started looking at ladder foils with a panel code, I discovered that the conventional wisdom about ladder foils was mostly wrong. Many people think that the induced drag of a ladder foil is low or even eliminated because of the end-plate effect of the struts, and that the drag of all the junctions is high.

In fact, the opposite is true. Induced drag due to lift comes from the fact that the foil is deflecting a body of water with a finite width. It's not just leakage around the tip. Most people tend to make ladder foils with comparatively short span, which leads to high induced drag. In addition, the rungs are not loaded evenly. Interference between the rungs causes the upper rungs to be loaded more than the lower rungs. This does two things - the lift is more concentrated than one would think, leading to more drag, and the lift is concentrated at the surface where the induced drag is much higher due to free-surface effects.

Junction drag, on the other hand, is really not much of a problem. Junction drag is proportional to the physical thickness squared, and when the thickness ratio is on the order of 12% or less, that's not much. Plus, the rungs on a ladder foil tend to be small in chord and thickness due to the support provided by the struts, reducing the physical thickness further. Junction drag is also proportional to velocity squared. When there are a lot of junctions in the water, the velocity is low and the junction drag is low. At high speed, most of the junctions are out of the water and produce no hydrodynamic drag. By contrast, induced drag is inversely proportional to velocity squared, so it makes up the lion's share of the drag at low speed. So even though there are a lot of junctions in a ladder foil, they tend to contribute a comparatively small proportion of the overall drag.

Ladder foils do have some nice features. If a rung ventilates, you only lose the lift for that rung, instead of having the whole foil let go. And they can be structurally stiff because of the reinforcement of the struts. One of the downsides is they're butt ugly.

You should endeavor to make the foils as wide as possible, subject to the practical constraints of structural strength and stiffness. And, of course, the depth at which you want to fly, compared to the area of the foils. Bell's HD-4 was basically planing on the bottom 1 or 2 rungs when it was at top speed.

I think if I were doing a modern variant of the HD-4, I'd consider ladder foils for the main foil, but use an inverted T foil at the stern. The reason is for stable pitch-heave coupling, you need the forward foils to be more sensitive in heave and the rear foil(s) to be more sensitive in pitch. That way, when the craft rises, it tends to pitch down, reducing the lift; and when it pitches up, causing it to fly up, the forward foil comes out of the water and pitches the craft back down. So a surface piercing foil forward and a fully submerged foil aft, with the aft foil more lightly loaded than the forward foil, is a good way to achieve this.

And I'd make the incidence of the stern foil controllable so it could be used to adjust the pitch trim in flight. Pitch trim has a big influence on the performance of surface-piercing foils, especially V foils, because it controls the flying height and how much foil is immersed.

[tspeer]

Here's a shot of the HD-4 at speed in rough water:
http://bell.uccb.ns.ca/Images/B/vol23/B2358.GIF
And some drag and power data. Power, of course, is drag times velocity, so the power required goes up even when the drag is constant.
http://bell.uccb.ns.ca/Images/B/vol23/B2380.GIF
http://bell.uccb.ns.ca/Images/B/vol23/B2384.GIF
Imagine what he could have done if the Navy had given him better motors!

[haybayian]

Thank you again Tom for all this . You are quite generous with your time. I will save these messages and use what you are saying as a point of reference in my design.
The following remark: " Ladder foils do have some nice features. If a rung ventilates, you only lose the lift for that rung, instead of having the whole foil let go. And they can be structurally stiff because of the reinforcement of the struts. ". .......is what intrigues me about ladder foils.

Haybayian