Hydrofoils
3. Lift

 

a) Principle

Lift is the force which enables the hydrofoil to get out of the water. It should be as big as possible.

The fluid flows on both sides of the foil along streamlines which separate at the leading edge and meet again at the trailling edge. Let us consider two extremely close particules located on the same streamline. One of them runs along the upper surface and the other along the under surface. According to a basic principle of physics, both particules meet at the trailling edge. Let us now examine different configurations.

  • The symmetrical profile is parallel to the direction of the flow

    • Both particules have the same speed. The wing creates no lift.

  • The symmetrical profile is placed with a small incidence

    • The particule which runs on the upper surface has a longer way to go. Consequently, it has to go faster in order to meet the other particule at the trailling edge.

    Bernoulli's theorem reads: P+½*r*V2 = constant

    Accordingly, this overspeed results in a depression. Moreover, the particule running on the under surface goes slower and we therefore have an overpressure under the foil. However, one should note that the depression on the upper surface is always greater than the over pressure on the under surface as illustrated by the figure below:

    With an asymmetrical profile, tilting the foil is not necessary to create lift.

    Pressure distribution for a 11° incidence angle calculated with the XFoil software

  • The symmetrical profile is placed with a big incidence angle

    • When the incidence becomes too big, the streamline on the upper surface can no longer stick to the profile: one speaks of burbling. In the mean time, a recirculation zone is created because of the fluid's vicosity. In this zone, the flow becomes turbulent and eddies appear. This is called burbling.

    Conclusion: the lift coefficient increases with the incidence angle and then drops suddenly because of the burbling phenomenon.

    b) Dimensioning

    We decided to make two types of foil:
  • a symetrical one, of the NACA0015 type, which creates lift as soon as its incidence is different from zero.


    • Coordinates of the NACA0015 profile
     
  • an asymetrical one, of the EPPLER817 type, often used when designing foils. It creates a greater lift for a given incidence.


    • Coordinates of the EPPLER817 profile
    Ballasting of the foils
    For our experiments, we had to make our profiles heavier. Indeed, they are mainly made of polystyrene which is much lighter than water. As we did not wanted the foils to float (it would have turned our model over), we inserted metallic bars in them. The foils were then heavier than water, and they could also play the role of a keel.


    Vidéo 1.65 Mo

    Calculation of the ballast
    The purpose of this ballast was to make the foils a little heavier than water. In other words, the weight of the foil had to be a little more important than its buoyancy. The latter is equal to the weight of volume of water removed.As we knowthe coordinates of the profiles and their width, we can calculate the volume of each foil and, therefore, the buoyancy they undergo along the vertical axis:

    As we also know the density of polystyrene (37 g/m3), we can calculate the weight of each foil:

    The difference between those two weights gives the weight which has to be added:

    The results are presented in the following array:
     

    Foil Vfoil (en 10-4 m3) Mlest (en g)
    NACA0015
    9.38
    900
    EPPLER817
    7.44
    716

    Remark: the Eppler817 foil was so thin (less than one inch) that we could only insert one bar (of 670 grams). However, the aluminium fixations bars weighing 50 grams, the total weight of the foil was just enough to make it sink.

    Estimation de l'incidence :
    At this stage, it is possible to estimate the minimum incidence necessary for the hydrofoil to take off. For that, we will make a power balance that make themselves felt on our scaling model when the hull is out of water. We have obtained, first without taking into account ???..., the following results:
     

    Forces (en N) : NACA0015 EPPLER817
    Buoyancy of the foil:
    +9.20
    +7.29
    Weight of the foil:
    -0.34
    -0.24
    Weight of the ballast:
    -8.83
    -6.57
    Weight of the hull:
    -1.80
    -1.80
    Weight of the fixation bars:
    -0.48
    -0.48
    z-resultant:
    -2.25
    -1.80

    After these calculations, we have an idea of the lift needed to thwart this resultant and enable the hull to come out of the water. This lift can be expressed in the following way:

    Note : those graphes have been made thanks to the following references: Aérodynamique Expérimentale by P. Rebuffet for the NACA0015 and the site of the Nihon university for the EPPLER817.

    Cz  values can be directly be on these graphs :
     
    Incidence
    NACA0015
    		  Incidence
    EPPLER817
     5°
     Cz=0.5 donc
    Flift=+1.18 N
     0.5°
    Cz=0.52
    Flift=+1.22 N
    10°
    Cz=0.9 so
    Flift=+2.35 N
    3.5°
    Cz=0.86
    Flift=+2.02 N

    Using those graphs we can Ainsi, we are able to provide the incidence of the profile for which the hydrofoil will take off :

    c) Experiments

    How to mesure lift?
    In order to mesure lift, we had to fix our model to the canal so that it would not drift away with the current. The choice of the fixation was not easy because it was supposed to prevent the model from drifting without preventing it from moving vertically (this degree of freedom had to stay free so that we could see our model raise above the water). We decided to hold our model with threads fixed on each side of the foil, as presented on the diagram below.

    However, because of the current, the foil had tendency to go back to a position without constrains, ie. without incidence. This prevented to hydrofoil from going up and, therefore, we this solution did not suit us.

    In order to thwart this couple which brought the foils in a position wihtout incidence,we used a second fixation which we attached on the front of the hull. When pulling the thread backwards, we create a couple which cancels out the undesired couple.

    However, we were careful not create any vertical forces. Therefore, we made sure the strings remained horizontal so that the forces we created artificially did not interfere with the lift the foil would create.
    We could then mesure the lift in the following way. We fixed the flow rate, the water height and the incidence so that the model would rize. We waited for the hydrofoil to stabilize itself. We then added weights in the hull until the hydrofoil reached its initial position (without current). At this point, the total added weight just compensated the lift created by the foil which we could therefore calculate.


    Vidéo 4.08 Mo

     

    d) Results

    After some calculations, we obtained the following graphs. The coordinates of all the points are also available.

    Evolution of Cz function of the incidence of the NACA 0015 profile

    Comment:
    The results are OK. Indeed, the general aspect of the graph is correct since lift increases with incidence.

    Remarks:
    - each experimental point is in fact the moyenne of several measurements made for different flow rates.
    - the flow rate range was too narrow to make a lot of measurements.
    - we observed an hysteresis phenomenon during this experiment, we meant we could not have very precise values.

    Evolution of Cz function of the incidence of the EPPLER 817 profile

    Comment:
    For the Eppler profile, our results are also satisfying. The Cz coefficient increases with incidence and its values are higher than those of the NACA profile (at a given incidence). Moreover, the hydrofoil takes off for an incidence i close to the one we calculated in the dimensioning part.