What happens when a hydrofoil boat pitches forward?
Wardi said:
RVELL,
I am interested to know how actual loadings change on both main foil and canard when a forward pitching moment is applied.
I am assuming that as the forward pitching moment is applied, the canard initially takes a small load, but as it is depressed, the main foil has less incidence and takes less load, this in turn places extra load on the canard and the process continues until an equilibrium is achieved. What loading would be on the canard at this point?
Wardy, You have asked a good, thoughtful question. The answer is rather lengthy.
Perhaps we should start with some definitions. “Load or loading” I would define for our purposes as the amount of weight a foil supports. This is expressed in pounds, kilos, etc. The load of a given foil can also be expressed as percent of the total weight of the hydrofoil boat. This is designed into the boat. For example, if you design the Center of Gravity to be behind the front foil 90% of the distance between the foils, the front foil will carry 10% of the load and the rear 90%. Of course, center of gravity can shift, as every Moth sailor knows, but for the purposes of explaining how the boat corrects for pitch, let’s assume the sailor is snoozing at the helm and the small changes due to geometry are to be overlooked.
“Wing loading” is the lift (or weight) per unit of area. This is expressed in pounds per foot^2, pounds per inch^2, kilos per meter^2, etc. It is the ratio of lift over area
Lift is the amount of upward force a foil creates when traveling through the water. A state of equilibrium is reached when the hydrofoil is neither climbing nor diving. Then lift will equal load.
To answer your question: let’s assume an example, to make the math simple, starting with 100 units. We will assume:
Boat weight, total = 100 pounds
Front foil load (lift) = 10% or 10 pounds
Rear foil load (lift) = 90% or 90 pounds
The point Tom Speer has made (correct me, Tom, if I misinterpret you) is that the areas of the front and rear foils should not be 10% and 90% respectively. The wing loading of the front foil should be higher than that of the rear foil. So the front foil might be, say, 5% and the rear foil 95% of the total area. This would give the front foil a wing loading of roughly double that of the rear.
Refer to my graph posted 2/17/04 “Percent Change in Lift vs. Wing Loading”. Assume you design the rear foil to be loaded at .25 lbs / in^2. The front foil would then carry a wing load of .50 Lbs in^2 – or in this example, twice the wing load.
So if you experience a disturbance from equilibrium, say a pitch forward, what will be the dynamics?
First, the load shift is more or less temporary. Something caused the pitch forward, but the boat’s Center of Gravity is designed into the boat and remains relatively unchanged. The CG is behind the front foil 90% of the distance between the foils, so the load on the foils remains 10% / 90%.
What happens to the lift? Assume a pitch forward of 1 degree – the same amount I used in my graph. If you had equal wing loading the lift would be reduced by the same percentage for both the front and rear foils. The result would be a rapid dive followed by a crash.
If the foils had unequal wing loading as in our example, the graph shows the front foil would lose 50 % of its lift and the rear foil would lose 100 % of its lift.
It is at this point that I disagree with previous assertions that this is a stable state. I believe you are still diving because both foils have lost lift, but your rate of dive is not increasing, and you are not diving as badly as if you had equal wing loading. Probably in a canard configured airplane the unequal change in lift would lead to an eventual pitch up. The airspeed will increase and lift will change non-proportionally and this may result in a pitch correction. However, in a hydrofoil we do not have the luxury of altitude excursions.
We need something that generates a strong pitch up, and we need it fast. One or two or three inches of altitude (heave) are all we have in which to recover.
This is why we need a front foil that rapidly increases its lift as it increases its submergence. Examples of this type are front foils with a surface following wand that changes the angle of incidence or actuates a flap. Another example is the ladder foil or the “V” foil. They both increase their area as they increase their submergence.
Your idea of a surface following planing foil has merit as well, however the whole discussion of relative wing loading then becomes irrelevant. When you put a large foil up front to dance on the water you will be depending on only the lift generated by the underside of the foil. About 2/3 of the lift of a submerged hydrofoil is produced by the relative vacuum created on the topside of the foil. Therefore the lift of a planing foil will be reduced to about 1/3 of the lift of a same-sized submerged hydrofoil. In other words, a “planning” foil needs to be about 3 times as large as a submerged foil.
I advocate using a supercavitating type foil for this purpose. It is designed to generate lift from the bottom surface and not from the top, so you do not experience the surge in lift experienced when the “normal” foil submerges deep enough to collapse the topside air bubble created while planning.
This is a long answer to a short question, but I do not know how to make a brief answer that is comprehensible on its own. The brief answer is, following a disturbance that causes a forward pitch the load does not change. In our example, it remains roughly 10% / 90%. The lift changes, and not for the better.
Ray Vellinga