Sweep and Cavitation

Discussion in 'Sailboats' started by sigurd, May 22, 2006.

  1. sigurd
    Joined: Jun 2004
    Posts: 827
    Likes: 8, Points: 18, Legacy Rep: 65
    Location: norway

    sigurd Pompuous Pangolin

    I feel uncertain about the way that the effect of sweep on cavitation is explained. First of all, what is the span? In a plane the span is from wingtip to wingtip right? In my mind it seems most relevant to refer to chord as being parallell to flow, and span to be perpendicular to flow (free stream velocity).
    For the rest of this post abide by these two definitions, but please correct me if I am wrong though.
    So in my mind, what happens if you rake a blade, is that you increase chord and decrease span.
    Obviously, one effect is that the AR is lower, leading to larger induced drag.
    Reynolds number has also gone up a tad I guess, to what significance?
    And since the thickness is still the same, you have infact created a different foil section, one that has a lower % thickness. My take on cavitation is that water is trying to follow the surface of the section, but the section thickness decreases so fast that the water has too high inertia to fill it in (same as when you plane, there is a trough behind you). That's why a raked (either way) board works: it is a slower change in thickness, thus less velocity for the water is required.
    So why, by golly can't you get the same effect by just making a longer chord with lower % thickness in the first place? (and not rake it)
     
  2. markdrela
    Joined: Jun 2004
    Posts: 307
    Likes: 30, Points: 28, Legacy Rep: 324
    Location: MIT Aero & Astro

    markdrela Senior Member

    The "thinner streamwise airfoil" argument for explaining the behavior a swept wing is faulty -- it assumes that each streamline remains in the 2D plane parallel to the freestream flow. But in reality it makes sideways excursions as it goes over the wing. So the pressures on the swept wing are not the same as the pressures on an unswept wing with the same streamwise airfoil.

    The rigorous way to determine the flow on a high-AR swept wing is to look at slices perpendicular to the spanwise axis, not slices parallel to the freestream flow. So sweeping the wing does not change its effective airfoil shapes. Sweeping merely reduces the effective freestream velocity that the wing's airfoils see by a factor of cos(sweep).

    An example:
    Let's say you have two same high aspect ratio wings, operating at two different conditions but at the same total lift:
    1) Sweep = 0 deg, V = 40.0 kts, lift = L
    2) Sweep = 45 deg, V = 56.6 kts, lift = L (note: 40/cos(45) = 56.6 )

    You can say the following things:

    a) The surface pressure distributions on both wings will be the same, therefore...
    the margin from cavitation for both wings will be the same.

    b) The induced drag will be the same, since Di = L^2 / ( pi * q * projected_span^2 )
    and q * projected_span^2 is the same.

    c) The airfoil flow viewed in the plane perpendicular to the spanwise axis will be the same, even in the boundary layers, so the margin from separation and stall will be about the same.

    d) The swept wing will have a friction drag roughly 2x larger, since that depends mainly on q * wetted_area, and q is 2x larger for the swept wing.

    All these things assume that the aspect ratio is sufficiently large so that the flow near the root and tips is a small part of the overall wing flow. The flow near the root and tips is fully 3D, and infinite-swept-wing theory doesn't apply there.

    Sweep delays cavitation to larger speeds, so it looks attractive for something like a speed-record foiler sailboat. But it's not clear if its structurally feasible to make the AR high enough to take advantage of the concept. Also some local cavitation at the root and/or tip may be unavoidable, dunno.
     
  3. sigurd
    Joined: Jun 2004
    Posts: 827
    Likes: 8, Points: 18, Legacy Rep: 65
    Location: norway

    sigurd Pompuous Pangolin

    "The "thinner streamwise airfoil" argument for explaining the behavior a swept wing is faulty -- it assumes that each streamline remains in the 2D plane parallel to the freestream flow. But in reality it makes sideways excursions as it goes over the wing. So the pressures on the swept wing are not the same as the pressures on an unswept wing with the same streamwise airfoil."

    I assumed that the spanwise movement was largely irrelevant yes. Can someone show me smoke over a swept wing or something? How much does it "kink" sideways?

    "The rigorous way to determine the flow on a high-AR swept wing is to look at slices perpendicular to the spanwise axis, not slices parallel to the freestream flow. So sweeping the wing does not change its effective airfoil shapes. Sweeping merely reduces the effective freestream velocity that the wing's airfoils see by a factor of cos(sweep)."

    Does the fluid really suddenly go perpendicular to the leading edge? Why? what if it is a piece of paper or something?
    So span is actually measured along the leading edge, and chord perpendicular to it? I take this drawing to mean that span is unrelated to the length of the leading edge: http://www.grc.nasa.gov/WWW/K-12/airplane/induced.html
    But I will try to understand what you mean with the terms regardless. Sorry if I seem pedantic, it is not my intention, but there are apparent contradictions in my knowledge of the most basic terms. For instance that NASA site seems to be riddled with contradictions. It would be neat to know the exact definitions of how to measure the angles and lengths in the 3d world.

    "b) The induced drag will be the same, since Di = L^2 / ( pi * q * projected_span^2 )
    and q * projected_span^2 is the same."

    What is projected span? What is q?
     
  4. markdrela
    Joined: Jun 2004
    Posts: 307
    Likes: 30, Points: 28, Legacy Rep: 324
    Location: MIT Aero & Astro

    markdrela Senior Member

    Attached PDF drawing shows what's going on.
     

    Attached Files:

  5. markdrela
    Joined: Jun 2004
    Posts: 307
    Likes: 30, Points: 28, Legacy Rep: 324
    Location: MIT Aero & Astro

    markdrela Senior Member

    projected span = span as viewed from the front = unswept_span * cos(sweep)
    q = freestream dynamic pressure = 0.5 * rho * V_infinity^2
     

  6. sigurd
    Joined: Jun 2004
    Posts: 827
    Likes: 8, Points: 18, Legacy Rep: 65
    Location: norway

    sigurd Pompuous Pangolin

    Thanks for the illustrations and explanations. I still don't understand most of it but I'll try to nibble at some of the loose ends to see if the murkyness disappears :)
    It looks like the flow over the swept wing goes a bit spanwise (span = distance between root LE and tip LE?) and then back, to emerge from the TE straight behind where it entered the LE.

    Would a low aspect, highly tapered, unswept foil enjoy a similar delay in cavitation inception as an untapered swept foil of the same area, projected span and leading edge inclination?
     
Forum posts represent the experience, opinion, and view of individual users. Boat Design Net does not necessarily endorse nor share the view of each individual post.
When making potentially dangerous or financial decisions, always employ and consult appropriate professionals. Your circumstances or experience may be different.