Human Powered Airboat

Discussion in 'Boat Design' started by alan craig, Dec 4, 2014.

  1. philSweet
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    philSweet Senior Member

    <<math error>> see post 20 and 21 for correction

    I'm struggling with this idea. Lets start with your .4m hydro prop optimized for an HPV application. Then we look at an equivalent air prop and it looks like it has a diameter of 12.6 meters if the induced velocity,Tc, and eta_i is to remain the same. Now we constrain the diameter to 3 meters. The Tc is increased by a factor of 18.


    eta1_i = 2 / [ 1 + sqrt(1+Tc)]
    eta2_i = 2 / [ 1 + sqrt(1+Tc*18)]

    at the limit Tc = 0, the ratio eta2/eta1 =1
    as Tc increases the ratio drops.

    At Tc = .2 , eta1 = .954, eta2 = .636, and the ratio is .667

    If you add power (and optimize the design keeping the diameters constant),
    then the thrust increases (as P^2/3) and Tc increases. If the power increases by 2.83, the thrust will double, Tc will double, and the efficiencies will now look like

    At Tc = .4, eta1 = .916, eta2 = .518, and the ratio is .565.

    Thus increasing power in the face of any increasing drag law will make the sub-optimal prop even more sub-optimal.
     
    Last edited: Dec 8, 2014
  2. markdrela
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    markdrela Senior Member

    It probably won't. If you're concerned only with cruise (not acceleration), then the optimum prop geometry is very nearly the same for any power input.

    As I stated in my second post, the main issue with prop/pilot matching is the rpm variation with power. So if the pilot sees an excessive variation of pedal rpm with power, the theoretically best fix for that is variable gearing, not variable pitch. But the dependence is rpm ~ Power^0.333 which is quite weak, so variable gearing would buy very little.

    There is however another consideration:
    On a dynamic-lift vehicle (airplane or hydrofoil), rpm scales as Weight^(1/2), so it is desirable to have gearing to accommodate a wide range of pilot weights. On the Daedalus HPA we had variable pitch as a substitute for variable gearing, because the latter was not mechanically practical. On the Decavitator HPH we also had fixed gearing for simplicity, and dock-adjustable prop pitch. Dock-adjustable pitch is very easy to implement BTW, so as a design choice it's a no-brainer.
     
  3. daiquiri
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    daiquiri Engineering and Design

    The equation for ideal efficiency will tell you a few important basic things about props, but will not tell you the whole story because it doesn't describe the subtle imperfections of the real world - like blade stall, transition bubbles, radial flow, air compressibility effects and water cavitation - just few examples.

    Take the first equation you wrote:
    Eta_id = 2 / [ 1 + sqrt(1+Ct)]​
    where:
    Ct = Thrust / [0.5 rho V^2 (pi/4 D^2)]​
    and V is the axial inflow to the prop.

    Let's translate the term Ct into the more commonly used term Kt, so that we can use the Wageningen or other available empirical data. The relationship between the two is:
    Ct = pi/8 Kt/J^2​
    so the first eq. becomes:
    Eta_id = 2 / [ 1 + sqrt(1+8/pi Kt/J^2)]​
    The real efficiency is defined as
    Eta_re = J/2pi Kt/Kq​
    and the realistic values of Kt and Kq are obtained from the model tests of from the CFD.

    Now if you plot the two curves (the real one based on a Wageningen 2-blade prop), this is what happens:
    Eta_ideal vs Eta_real.gif
    Kt and Kq curves are approximated by straight lines for simplicity, but without losing the important aspects of a real-prop characteristics.
    As you can see, there are some significant differences, the most important being the fact that the real Eta has a peak followed by a zero. The zero of the real Eta happens for the same value of J (advance ratio) where Eta_ideal has a maximum theoretical value of 1.0
    0.0 against 1.0 - that's an aspect one cannot ignore, and it is one of several which you can note.

    So, without getting into discussion of why is it happening from the aerodynamic point of view (it would require a whole book, not a forum page), it is clear that you cannot rely on the analysis of the ideal efficiency to understand how will the props behave in the cases discussed so far. You have to analyse the actual propeller's behavior, feeding the numbers to a physically realistic model of the prop. In few words, you are seeing the difference between ideal and real worlds at work here. :)

    Cheers!
     
  4. markdrela
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    markdrela Senior Member

    I think you're making this more complicated than necessary.
    Most of the discussion has been about matching the prop to the boat for a wide range of input power at cruise. Let's assume we design the prop correctly, so that at the design cruise speed, design rpm, design thrust, etc., the prop will be close to its peak efficiency. This design point will also have some value of J_design = V_design / (n_design * D).

    Now, if we assume that boat drag ~ V^2, then the prop in cruise will operate at this same J = J_design value for any input power, and therefore it will also be close to its max efficiency for any input power, either smaller or larger than the design value. The fact that the prop's efficiency falls off for smaller or larger J values is not relevant, because the prop will not be operating there in cruise.
     
    Last edited: Dec 7, 2014
  5. markdrela
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    markdrela Senior Member

    This argument assumes that the speed is constant as you increase power. But in reality the speed will of course increase with increased power. Assuming boat drag ~ V^2, the speed increase will be such that Tc stays constant, J stays constant, and hence eta_ideal and eta will also stay nearly constant.
     
    Last edited: Dec 7, 2014
  6. philSweet
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    philSweet Senior Member

    ARRG. I missed it. Thanks for the fix. Although I said that I was increasing speed, I did not do so in the calcs.

    So the Tc remains constant, and the suboptimal prop remains about the same in terms of efficiency ratio. And there would be little change to the prop design if diameter was kept the same.
     
  7. daiquiri
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    daiquiri Engineering and Design

    I agree with what you say, just please let me remind you that in this particular case (see the boat in the OP) we have diameter limits on both props, which particularly penalize the air prop for this application.

    By saying this I assume that one is looking for a leisure-cruise human-powered catamaran (max continuous power input of approx. 150 W), pushing the boat at approx. 5-6 kts.
    In this case, a 0.3-0.4 m water prop can be designed with a considerably higher efficiency than the air prop shown in the pics. That's all I was arguing right from the beginning.

    Increase the power input and speed of the boat, and the 3-m air prop gets back into the game again.

    This, at least, is the result I get from the tools I have at disposal (prop charts for water props and a software I developed by myself for air props, plus the Javaprop). It could as well be that you folks at MIT have more advanced tools which allow you to make an air prop which matches the performance of the water prop in these conditions. I couldn't find that match, getting approx. 65% air-prop efficiency vs. approx. 75% efficiency of a water prop.

    Cheers
     
  8. Village_Idiot
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    Village_Idiot Senior Member

    So, maybe slightly off-topic, but has anyone tried or examined the effects of a shrouded (ducted) prop for a HPV? Shrouds are known for improving low-speed thrust, which seems to be the main objective of the HPV in a leisurely cruise mode.

    Secondly, I wonder if there is as much design science put into aero prop blades as there is in hydro prop blades. For example, with a hydro prop, one can add cupping to the blades to increase effective thrust per given pitch (although you lose considerable reverse thrust with heavy cupping). If one designed cupping into an aero prop, perhaps you could get away with a lower pitch for the same amount of thrust, and perhaps slightly lower kW needed for a given speed.

    Third, do overall aerodynamics play a significant role in an air-prop-powered vessel? Likely not with a HPV, but let's consider a motorized airboat that can exceed 50 knots (now we are definitely getting off-topic!). It seems that attention to detail at the intake side (as well as the exhaust side) can enhance flow to and through the prop, and provide greater thrust per given input. I feel like there is a lot of wasted air/energy coming off the tips of the props laterally instead of longitudinally (hence the shroud suggestion in my first point above).

    Lastly, I have noticed while running airboats (and tunnel/outboard prop boats) in very shallow waters (less than 0.15m), the boats pick up quite a bit of speed. This is due, of course, to the hull of the boat being lifted out of the non-compressible fluid and thus decreasing drag (I call it the water-ski effect), as well as better "trapping" of the water that flows through the prop (in the case of the outboard). When you return to deep water, performance/speed decreases drastically. Obviously, I can only notice this effect while on plane with the motorized boats, but I wonder if similar effects can be achieved in HPVs, especially those designed for higher performance with trained athletes at the helm. It would be interesting to compare performance numbers of the HPV traversing, say, 100m with 10m depth, and 100m with 0.1m depth. Probably not useable in competition, but may be handy when going for the record books.
     
  9. markdrela
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    markdrela Senior Member

    5-6 kts for 150W implies a fairly draggy boat IMO. Regardless...

    What really matters here is the density-weighted area ratio,

    (rho_water * CDA_hull) / (rho_prop * A_prop)

    since in cruise this is in fact equal to the thrust coefficient Tc, and hence gives the ideal efficiency. This is true for any power level... either plodding along at 50W, or sprinting at 1000W.

    So...
    With an air prop size limit of about 3m, and no size limit on the water prop, what really matters in the air vs. water prop decision is not the power level -- what matters is how clean is the boat. The smaller the boat's CDA, the smaller the efficiency gap between the air and water props. Decavitator had close to the smallest CDA possible for a cat. That's clearly not the case for the boat in the video.

    Adding air drag does not change this, BTW. This merely changes the effective density-weighted drag area to

    rho_water*CDA_hull + rho_air*CDA_air

    and everything else stays the same.
     
  10. markdrela
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    markdrela Senior Member

    A duct works by increasing the mass flow through the prop, and thus has the same effect as increasing prop diameter. But the duct also adds its own drag which eats into this benefit. And if the duct is not shaped correctly, especially its leading edge, it can easily hurt more than it helps.


    Yes. But air props typically have smaller disk loadings (smaller Tc), so fancy design features like skew and rake can't and don't add much performance, but they do add structural problems. So air prop blades tend to be mostly straight.

    This is due to a decrease in wavemaking drag in shallow water. In the limiting case where you're "hydroplaning" on a thin film of water, the wavemaking drag is zero.
     
  11. philSweet
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    philSweet Senior Member

    I'm still struggling. I think this deserves a bit more than a one liner.

    In the displacement case, resistance and wave drag increase as shoaling occurs. In the planing case, it is complicated, with wetted area, trim, and bottom pressures all changing. Away from the skimming/hydroplaning limit case, I believe you could have a shoaling situation with an increase in wave drag that is also accompanied by a lower trim angle or less wetted area and an overall drag reduction.

    A boat that is planing in shallow water creates larger perturbation velocities near the surface than the same boat in deep water does. But it does so at a smaller trim angle, hence the drag reduction. If the bottom is flat, wouldn't the wave height be the exact same for the shallow and deep water cases.

    1. Could a particular hull have an operating point where the wave drag increases, but overall drag decreases, as the bottom shoals?

    2. Is there an operating point (speed, depth) where an optimal hull (same loa, boa, weight) would have greater wave drag, but lower overall drag than the optimal hull for the deep water case.
     
  12. Leo Lazauskas
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    Leo Lazauskas Senior Member

    When the boat is travelling at greater than the critical depth-based Froude
    number. Below that critical Fn, wave drag is greater than the deep water case.
     

  13. kach22i
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    kach22i Architect

    Even without pedaling that prop will act like a sail, weather you want it to or not.

    Refer to the windmobiles of dr. Amick:
    http://ecomodder.com/forum/showthread.php/windmobiles-mr-amick-20412.html
    [​IMG]


    For reference on other human powered craft, check out this human powered hovercraft:


    http://www.steamboatwilly.org/
    [​IMG]


    http://steamboatwilly.org/human_powered_hovercraft/history.html
     
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