Hagedoorn considered using the 242 square foot Notre Dame Para-foil of aspect ratio of two as his aerofoil. He did not design or build a hapa that was stable at speed. He computed the triangle of velocities (true windspeed, apparent windspeed and water speed) for notional kite/hapa combinations with lift/drag ratios of kite and hapa of five to one each, on a towline slope of three in ten. He also computed the air speeds and water speeds for a notional range of kite/hapa combinations with lift/drag ratios from two to ten for both elements, with pull over mass on the towline of from one to twelve, all at a towline slope of three in ten.

But the practice is radically different from Hagedoorn’s mathematical models! Kites parafoils and hanggliders have progressed greatly since his 1960’s designed Notre Dame Para-foil. However kites and hapas with lift/drag ratios of five to one, let alone ten to one, have not been realized. Also the towline slope posited of three in ten is yet to be proved and may not be constant.

Let us consider existing hapas (The marks are my own).

Mark 1 0.833 square foot projected area Aspect ratio 8.5 to 1

Mark 2 1.3 square foot projected area Aspect ratio 4.46 to 1

Mark 3 1 square foot projected area Aspect ration 5.7 to 1

Fabric 18 square foot projected area Aspect ratio 0.42 to 1

Fabric 3.67 square foot projected area Aspect ratio 0.27 to 1

The Mark 1,2 and 3 hapas seem to have drag angles varying with speed from 25° to 35° , i.e. lift/drag ratios from two to 1.4. The Mark 3 hapa worked well at October 2016 Speedweek. I do not know the lift/drag ratios of inflatable kites, but as kitesurfers are not very close-winded, even when using efficient boards and skegs, I suspect they are low.

In order to lift the weight of a person one must have sufficient vertical projected kite area and sufficient apparent wind. An enormous kite is dangerous. The vertical projected kite area is reduced by the semicircular shape and the far from vertical slope of the kite lines of kitesurfer kites. Thus all kitepowered man lifting has succeeded only at relatively high water speed. Until now! Happily Mark 1,2 and 3 hapas cope well at such speeds, but unhappily they confine ultimate sailing to the Young, the Athletic, the Strong and the Light in Weight.

What is left for us Oldies? I am not concerned with how close-winded I may fly, but only with flying! So I am only concerned with lift, not drag. I plan to deploy my 18 square foot fabric hapa initially in drogue mode, which would produce a drag co-efficient of 1.2 (see Ian Hannay's Natural Aerodynamics, AYRS 117 page 41). For the aerofoil I would use a Skyhook 111A hangglider of 216 square foot wing area, aspect ratio 2.63 to 1, which flies at an airspeed between 15 to 25 MPH (22 to 37 feet per second).

The advantage of a hangglider over kites is that the flier has control over the angle of attack in a hangglider via the A frame control bar, provided the Aquaviator’s arms are long enough and he has the strength to push forward hard enough. This ability to produce “superlift” i.e. lift above the sustainable figure, for a short time before the flow collapses, is necessary for the craft to take off. See AYRS 117 page 39.

Abbott and Doenhoff tell us that a lift co-efficient of unity is the best that one can normally expect at an acceptable lift/drag ratio. So with the Skyhook 111A hangglider we get:-

Lift = 0.5 * Cl * Air density * wing area * velocity^2

The minimum airspeed is 22 ft/sec so, with a Cl of 1.0, we get:-

Lift = 0.5 * 1 * 0.0024 * 216 * 22^2 = 125 lbs

But the all-up weight is 250lbs so, we need to operate at a Cl of 2 so that :-

Lift = 250 lbs = 0.5 * 2 * 0.0024 * 216 * 22^2

hence the need for superlift by pushing forward the A-frame control handle erecting a large angle of attack and producing a lift co-efficient of 2.0. A “B” bar would be better, enabling the Aquaviator to pull it back to his stomach while still enabling him to push the bar further out.

The drogue must produce sufficient resistance to resist the aerofoil from merely blowing downwind and losing its apparent wind of 22 ft/sec. The hangglider will have a lift/drag ratio of less than its advertised five to one ratio due to its enhanced angle of attack on takeoff, so let us say three to one. So the required drag is 250 lbs ÷ 3 = 83lbs.

The 18 sq ft drogue has a drag co-efficient of 1.2 (AYRS 117 page 41), so :-

Drag = 83lbs = 0.5 * 1.2 * 1.956 * 18 * Vw^2, or Vw = SQRT( 83 / (0.5 * 1.2 * 1.956 * 18)) = 2 ft/sec i.e 1.3 MPH

This 2ft/sec water speed downwind must be added to the aerofoil’s air speed of 22 ft/sec, making a required true windspeed on 24 ft/see i.e. 16 MPH.

Before the “superlift” collapses the drogue must be deployed into hapa mode while the hangglider reduces its angle of attack as it picks up speed and becomes less downwinded. The lift/drag ratio of the 18sqft fabric hapa is poor, that is one to one, drag angle 45° but as I am only concerned with flying and not with travelling close-winded or achieving fast ground speed, all that is required from the hapa is sufficient resistance to stop too much leeway. Thus I will maintain sufficient apparent wind to fly.

The hangglider would fly close to the sea surface so ground effect would reduce the induced drag. This is the main component of drag in a low aspect ratio aerofoil with a lift co-efficient as high as two due to the wingtip eddies i.e. vortex lift which is so marked in delta wing aircraft. Ground effect also increases the amount of lift generated. The quantity of ground effect depends on the height of the wing tips divided by the length of the wingspan. The lower the wingtip height and the lower the aspect ratio the more the benefit of the ground effect is felt.

The wing span is 24 feet and I compute the wingtip height at one foot [

*with the sail at maximum angle of attack - Admin*]. This gives a 70% reduction in induced drag. (see K. Sherwin “Manpowered Flight” page 53). I have not included this welcome bonus in my figures, but not because of any lack of faith in the benefits of ground effect.

If in the process of the above project I invent the slowest, lowest, most inefficient manned aircraft ever, so much the better!

What could possibly go wrong!

Roger Glencross

October 2016

Appendix 1

Weight breakdown

Pilot 150

Hangglider (dry) 45

Campari Catamaran as undercarriage 55

All-up weight 250lbs

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*Mathematical equations edited for clarity by Admin*]