Hydrofoil basics & craft configuration

Discussion in 'Boat Design' started by Dante, Aug 14, 2006.

  1. Dante
    Joined: Aug 2006
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    Location: Finland

    Dante New Member

    Hi all!

    I've been reading this forum few times, and since here seem to be lots of very knowledgeable people I strike my first post here! :)

    I am planning to build small hydrofoil watercraft for single person, and I actually already built one, but since it was made on the scratch, it didnt perform too well. As a matter a fact, it could not get foilborne without towing assistance.
    I was not aiming for any extraordinary speed, but more to get nice ride above the water with quite low speed using only low power outboard engine as a power source. My craft was approximately six feet long, both foils were arranged to shallow V configuration of 30 to 40 degrees. Rear foil chord was 6 inches and span approximately 60 inches. Above the rear foil was another horizontal takeof foil with similar proportions.
    Front foil chord was 6 inches and span was some 32 inches. Foil section for all the foils was flat bottomed with circular suction side, with maximum thickness around 0.7 inches. Buoyancy of the craft was achieved with styrofoam sheets, which probably had enormous drag. As an engine it had only 4 hp Suzuki outboard, which seemed to be totally insufficient. Initially I thought it could suffice, because there are human powered hydrofoils, and compared to that, constant 4 hp is VERY much..
    Anyhow, craft could net get foilborne unassisted, probably my biggest mistake was having so poorly constructe "hull". In the future I am about to give my craft a second chance, but this time I am planning to do (at least) some design work beforehand. And this is where this forum and people of it steps in. I have load of questions, and probably most of them are addressed also somewhere elsewhere in this forum, but since these are basics which can benefit also other people, I dare to ask them once again.

    BASIC QUESTIONS:
    1) How can I calculate lift and drag for different foils (section, span, chord) with varying angle of attack? In other words, how can lift and drag coefficients be determined? Are they given as tables in some books wherein foil profiles are given, or should I use some flow calculator such as XFOIL? Does this calculation change if I use T or V configuration for the foils?

    2) How can I calculate hull resistance in single, two and three hull cases with different running speeds? Again, is there some software I should use, or is there some reliable formulas around in Excel form etc? Do I have to take position of hull with regard to waterline in to account?

    3) Now that/if I have resistances of foils & struts and hull(s) as a function of speed, how can this total resistence be converted to engine power requirement, i.e. how I can determine what will be the minimum sufficient power output of the engine to get the craft foilborne? Can I somehow determine what is the thrust of the engine with given propeller at different water speeds, assuming that the engine is running with full power? Is there some rules of thumbs for thrust for outboards in different hp classes?

    QUESTIONS ABOUT CRAFT CONFIGURATION:
    4) For my application, single hull is probably too unstable laterally, so what are the pros and cons of two or three hull configuration compared to each other? How should hulls be shaped, more like kayak style or flat bottomed planing surfaces?

    5) I think to use canard configuration for the foils generally, but I am not sure whether I should use V or T configuration for the foils. Surface piercing V configuration would be more stable, but also more prone to ventilation, but how big drawback this actually is? What are other differences?

    6) Which profiles are recommended or commonly used in T and V configurations? I am planning to use asymmetric profile at main (rear) foil, and symmetric at front foil, probably NACA 63412 at rear, only because it is often referred and looks "good" :(

    7) Can craft with T configuration be controlled manually without electrical or mechanical devices, only by actively controlling angle of attack of the front foil, or is it too unstable?

    8) Can I somehow define what is maximum angle of attack before foil stalls (or what ever is actual hydrodynamic analogue to stall) at different speeds? This is particularly interesting when craft is initially gaining speed for foilborne operation mode.

    9) Why there is so different sized foils with similar type of crafts? For example Flyak (http://www.foilkayak.com/) has very small foil compared to Halifoil (http://www.me.dal.ca/~dp_04_5/hydrofoil-foils.htm), although I think they are operating with very similar speed, weight and power ranges. Which are the factors that explain the difference?

    10) If normal outboard engine propeller is ducted (for safety reasons), should it improve or decrease the efficiency? What should be clearance between the duct and the propeller in optimal case? What about duct length?

    This post came leg long, sorry for that. I know answers to my questions could fill some textbook, but I hope you guys try to give some input anyhow. Also, as I probably will manufacture foils out of fibre glass and steel, any information concerning that is also welcome.

    Best regards,
    Dante
     
  2. tspeer
    Joined: Feb 2002
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    Location: Port Gamble, Washington, USA

    tspeer Senior Member

    Head over to the International Hydrofoil Society and buy their AMV CD's (there are three of them, now). The first CD has a whole hydrofoil design handbook.

    This simple analysis may help you start to get a handle on basic performance and sizing.

    You need to define your design requirements - such as the gross weight, and the speeds you want for take off, cruise, and maximum speed. Then you have to size the foils to meet your requirements. For example,

    Let:
    ARwet = wetted aspect ratio
    b = span of foil (maximum distance tip-to-tip)
    bopt = optimum span for the design gross weight and speed
    c = average chord of foil
    Cdo = parasite drag coefficient
    CDs = strut drag coefficient
    D = drag
    density = water density
    e = Oswald's span efficiency factor (~1)
    L = lift
    P = thrust power required
    pi = 3.142...
    Sref = planform or reference area
    Ss = area of strut
    V = speed through the water
    Vdesign = design speed for optimizing the foil
    VmaxLD = speed to operate at maximum lift/drag ratio
    Vminp = speed for minimum power required
    W = gross weight

    A simplified drag equation for a fully submerged hydrofoil is:

    D = Cdo*density/2*V^2*Sref + L^2/(pi*e*b^2*density/2*V^2)

    Since Lift = Weight and the thrust horsepower required = Drag * Velocity, the power required is

    P = Cdo*density/2*V^3*Sref + W^2/(pi*e*b^2*density/2*V)

    Cdo*Sref is the parasite drag area, and you should include the area of the struts as well as the area of both foils and the effective area of anything else that ads to the parasite drag. The span is the maximum span of either foil.

    The span loading (W/b) plays a crucial role. You can increase the span to compensate for different weights by maintaining the same span loading.

    A hydrofoil is completely unlike a floating hull because as the speed approaches zero, the drag of the hull goes to zero, but the drag from supporting the entire weight with a hydrofoil goes to infinity. But the drag also goes up when the hydrofoil goes very fast. In between is a speed at which the drag is a minimum, VmaxLD, and a speed at which the power required is a minimum (Vminp).

    The speed for minimum power is:

    Vminp = sqrt[sqrt[ 4/(3*pi*e*Cdo*Sref) ]/density] * sqrt(W/b)

    And the speed for maximum L/D is:

    VmaxLD = sqrt[sqrt[ 4/(pi*e*Cdo*Sref) ]/density] * sqrt(W/b)

    So the speed for minimum power is 76% of the speed for maximum L/D. The higher the span loading, the higher the minimum power speed will be.

    At maximum L/D, the power due to lift and the power due to skin friction and other parasite drags is equal. Above that speed, the parasite drag starts to dominate, and below that speed the drag due to lift dominates.

    The key parameter you need to improve the L/D is the wetted aspect ratio:

    ARwet = b^2 / (total wetted area)
    ARwet ~= b^2 / [2*(Sref+Ss)]

    Wetted aspect ratio takes into account the struts and both foils. Experience with aircraft has shown that wetted aspect ratio is the best single indicator of L/D.

    You should also look at the lift coefficient range at which you are operating. If you are operating outside the "drag bucket" of a laminar flow foil section, the profile drag could be more than doubled. But you can also design sections that fit your range of lift coefficients between takeoff and maximum speed.

    For example, if you take the H105 hydrofoil section (http://www.nasg.com/afdb/show-airfoil-e.phtml?id=1187) and add the NACA a=1 camber line (see first figure, below), you can shift the low-drag range to higher lift coefficients with only a modest increase in the minimum drag (second figure)

    The lift coefficient at max L/D is 58% of the lift coefficient for minimum power. You probably want to have some margin around your operating points, and allow for non-uniform lift coefficient along the span, so you should be able to at least double the lift coefficient between max L/D and minimum power and still stay inside the low-lift range of the section. This helps to size the foil area and the amount of camber in the section.

    In the example above, the highest camber (adding the NACA a=1 camber line multiplied by 0.6) results in a low-drag range from Cl=0.4 to Cl=1.1, and would be a good match to take off at Cl=1.0 and obtain max L/D at Cl=0.5. This would be about as small a foil as you could stand.

    Since the span loading has such a strong effect on performance, it's worth asking, "What's the optimum span for maximum speed?"

    The parasite drag area can be divided up into a foil contribution and a strut contribution:

    Cdo*Sref = Cdo*b*c + CDs*S

    P = (Cdo*b*c + CDs*Ss)*density/2*V^3 + (W/b)^2/(pi*e*density/2*V)

    [dP/db = 0] @ b=bopt

    bopt = 2 * (W/density)^(2/3) * (Cdo*c * pi*e)^(-1/3) * Vdesign^(-4/3)

    Vdesign is the speed for which you are trying to optimize the span. The faster the design speed, the shorter the optimum span will be. A heavier boat needs more span.

    The power at the design speed with the optimum span is (if I've done my sums right):

    Pdesign = density/2 * CDs*Ss*Vdesign^3 + 3/2 * (Cdo*c)^2/3 * [density/(pi*e)]^1/3 * W^2/3 * Vdesign^(5/3)

    For multiple foils, what matters is the total span loading. So the longest foil will have the same optimal span as the single foil, and the area distributed between the foils by sharing the chord length.

    XFOIL can help with some of the two-dimensional section coefficients, like Cdo and CDs.

    For surface piercing foils, like V foils, the span and area change constantly with the flying height, so this has to be taken into account, too. How these foils are operated can have a huge impact on their performance. Flying high with more foil out of the water is not necessarily better.
     

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  3. tspeer
    Joined: Feb 2002
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    Location: Port Gamble, Washington, USA

    tspeer Senior Member

    Once you've determined the thrust horsepower needed, you divide by the propeller efficiency to get the power you need to deliver to the prop. Keep backing up the drive train, adding in the losses along the way, until you arrive at the power needed from the output of the motor.

    Calculating the drag of the hulls is tough. If you're using slender displacement hulls, Michlet is a good choice. It can also handle the interference between the hulls (but not the hydrofoils).

    A surface piercing foil forward and fully submerged foil aft is a good way to go for stability. The aft foil must be more lightly loaded than the forward foil.

    Most ducts are designed to increase thrust at low speed. Their drag may cut performance at high speed. The hydrodynamically optimum clearance between prop and duct is zero. The practical clearance is a little greater. The optimum prop blade shape and twist is also different for a ducted prop than one without a duct - it has more chord at the tip. You may want to buy an over-sized prop and cut the tips off to fit the duct.
     
  4. Dante
    Joined: Aug 2006
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    Location: Finland

    Dante New Member

    Thank you for your reply, Tom!

    I am planning to enter formulas you presented to Excel sheet, but prior to that, I would like to ask couple of clarifying (or then plain stupid) questions...

    First of all, units (inch, cm, feet, knot, mph, kph, etc) for all variables used in formulae would be useful.

    Then, in simplified drag equation below
    D = Cdo*density/2*V^2*Sref + L^2/(pi*e*b^2*density/2*V^2)
    I fail to see how profile drag coefficient is incorporated in to that equation (unless it is included in Cdo). I assume profile drag coeffiecient is proportional to lift coefficient, thus it cannot be hidden indirectly in L, and in general value for it can be found from NACA tables or probably by calculating with XFOIL. So, how come it is not used anywhere in that equation? Can this equation be broken down into similar form as "regular" lift (or drag) equation containing variables such as lift/drag coefficient (depending on angle of attack), density and speed?

    How I can establish value for Cdo, is it dependant for example of surface finish? Is there some rule-of-thumb values which I could use?

    What will be the differencfe whether I optimize span for maximum speed or some other lower cruise speed? I suppose in my application I can merely calculate optimum span for main (rear) foil, because it should bear most of the weight, while front foil is mainly used to adjust angel of attack of the rear foil. Correct?

    BR,
    Dante
     

  5. tspeer
    Joined: Feb 2002
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    Location: Port Gamble, Washington, USA

    tspeer Senior Member

    You're welcome!
    Any set of units, so long as they are consistent.
    English: ft, ft/sec, lb, slug/ft^3
    Metric: m, m/sec, N, kg/m^3
    The profile drag coefficient is Cdo.
    No, for a parabolic drag polar, the profile/parasite drag coefficient is a constant. That's a good approximation within the drag bucket of a modern section, but you have to use the section data to get the actual variation of profile drag with angle of attack.

    You could lump the variation of profile drag with angle of attack in with the induced drag, effectively changing the efficiency factor, e.

    Or you could explicitly write out the variation in profile drag with angle of attack or lift and differentiate that when you do the optimization. To a large degree, it becomes a bookkeeping exercise, and there's not a unique way it has to be done.

    And don't get too hung up over the "optimum". An optimum is only valid for the particular cost function you define. If you change the cost function, the optimum changes. And typically, the change in performance is not very great for variations in the vicinity of the optimum.

    The main value of estimating an optimum value is it points you in the right direction and it establishes the best you can do. If the best you can do won't meet the requirements, something's got to give. If the design you initially draw up is way different than the optimum, then maybe it's worth looking at resizing things.

    You can calculate it with XFOIL or go with test data. It will be dependent on surface finish. Most calculations and test data are predicated on a smooth surface. For rougher surfaces, you might use handbook methods to bump up the parasite drag coefficient.

    A fully submerged foil has a power vs velocity curve that looks like a Nike swoosh. The slower the speed you chose to optimize for, the longer and larger the foil will be and the lower the power required will be. But the top speed will also be lower. So it depends on what the mission requirements are for the craft. You can go really fast on tiny foils, but it will take a lot of power just to get up to the high takeoff speed.

    In theory, the drag is independent of how the lift is distributed in the direction of motion. So you can size the foils as though you had only one big foil. Then divide that foil's area and lift between the forward and aft foils.

    You can also optimize the spacing so the aft foil surfs the wave created by the forward foil. Konstantin Mateev covers that in his tutorial on the IHS site. Since he's Russian, he uses different symbols, but the basic relationships are the same.
     
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