Paddle-In Hydrofoil (PIH) Surfboard

PIH Surfboard Ruminations

For a related discussion about "paddle-in" hydrofoil surfboard development, click this link to a thread at Swaylock's Surfboard Design Forum:

http://www2.swaylocks.com/forums/shortboard-hydrofoil-video

Check out these articles by Terry Hendricks (Ph.D.) too:

http://www.rodndtube.com/surf/info/Hydrodynamics.shtml

Scissor-Tailed Flycatcher

This is a quick sketch of my Scissor-Tailed Flycatcher inspired foil concept for a hydrofoil surfboard.  The Scissor-Tailed Flycatcher is common on the rural Texas coast.  

Scissor-Tailed Flycatcher

The sketch was quick, and the Spitfire wing had similarities to the Flycatcher wing.  I think the spitfire wing would be highly responsive for slower/smaller to medium speed/size waves.  I think front foil shape will need to vary with peformance (desired responsiveness) and wave type/speed (mellow shallow angle wave faces versus steep dredgers).

Bird wing shapes differ -- flycatcher versus falcon -- according to needed performance.  Birds can individually alter wing shape too (pulling wing tips in).  I think streamlining (wings swept back) can be used to reduce sensitivity and improve speed.

Apparently the Scissor-Tailed Flycatcher is very agile and maneuverable.

Scissor-Tailed Flycatcher Performance:

"They are agile in the air, spreading their long tails wide to make abrupt turns and stalls.

The tail proves useful as they expertly catch insects on the wing with sharp midair twists and turns.

The Scissor-tailed Flycatcher flies in straight lines with fast wingbeats, its tail folded. It also often hovers with its tail spread or makes abrupt turns in midair."

Surfboard for Hydrofoil Experimentation:

Version 1.0:  Cardboard Mock-Up of Twin Foil PIH, 06/30/2013  (revised design needed):

Below is a conceptual, full size cardboard mock-up (yardstick underneath) of what I was seriously considering at the middle of last week, 6/26/2013.  This weekend I decided it needs significant re-design.  Total foil surface areas are calculated to lift 84 kg at 2.5 sq. in./kg, total area adjusted for angled foil surfaces.

The front wingtips for this design would be angled significantly downward at the black lines marked on the foil -- tips not angled in picture.  Wingspan of the front foil is 21" with tips not angled downard.  The horizontal section is the low velocity secion.  In theory, the down-angled tips are the progressive velocity portion for higher speeds.  But I am certain the rear stabilizer foil would hydroplane at higher velocities.  (Maybe a hydrofoil-hydroplane hybrid would be something worth exploring).

According to Brett Curtis (in Oz), you need somewhere between 2.5 - 3.1 sq. in./kg at ~ 3 mph (5 kph) for lift.  Quarter this for each doubling of speed.  However, you need the larger surface when you take off to initiate lift at low velocity.  As velocity climbs, you need less surface area.  This is why we want progressive velocity foils that reduce surface area and remain stable as speed increases.

As Brett mentioned elsewhere, the quadrupling effect comes from a standard lift equation.  Swied proved it in one of his posts:

http://www.swaylocks.com/node/1025391?page=2

http://www.grc.nasa.gov/WWW/K-12/WindTunnel/Activities/lift_formula.html

Swied quote: 
It follows right along with the lift equation that I posted above.
Here is the equation again:
         L = (1/2) d v^2 s CL  
The density of water, the surface area of the foil, and the Coefficient of lift remain constant, so the equation can be simplified as...
          L = a * v^2
where L = lift force, a = constant, and v = velocity
Say you are going 3 mph, then L = a * 9.  If you double your speed to 6 mph, then L = a * 36.  There you have it: 36/9 = 4.  Doubling your speed quadruples lift.
_____

Elliptical vs. Angular Tips, 07/04/2013:

I am thinking a front foil with down-angled, elliptical tips (below) is closer to what I want (symmetrical).  Elliptical tips have much cleaner lines than parabolic tips. They give me some streamlining, and more area to work with than triangular or trapezoidal tips.  And I can still have a rectangular, low-velocity horizontal foil section between the down-angled tips.

This is a graphic I made with ellipses and a rectangle using Microsoft PowerPoint.  I was just playing with the shapes and dimensions until I got something that looked right -- no specific design objective.  If I scaled this particular foil (wing) up, it would be 6" x 27" (15.24 x 68.58 cm) with a "flat lift area" of 143 sq. in.  But with down-angled tips, it would have an "effective lift area" of 122 sq. in.  Using only PowerPoint, I can print a full-size and precise template. (BTW I do not  mean to imply PowerPoint is an ideal graphics design program.  I have it readily available, so I found a way to use it.)

The following are foils with elliptical tips and elliptical foils.  All foils pictured have the same surface area but differing chord lengths (leading edge to trailing edge), 07/06/2013.

Foils with Elliptical Tips

Elliptical Foils

Angular vs. Gravitational Acceleration:

Just a quick comment without elaborate discussion:

What I like most about 45 degree down-angled foils is that vertical and horizontal lift vectors are equal (have the same magnitude).  They also can be surface-piercing, asymmetric foils with symmetrical outlines.

The greatest lift force is perpendicular to the bottom surface of the asymmetric foil.

With 45 degree lean angles (or greater), centrifugal/centripetal acceleration may be a more important consideration than gravitational acceleration.

Earth's gravitational acceleration is 32 ft/second per second.  Times 3 = 96.  So if my calculations are correct, a turn with a fixed radius of 10 feet at 21 mph will produce a centrifugal/centripetal acceleration of 96 feet/second per second.  Apparent rider/board weight will be 3 times greater than stationary (gravitational) weight.