I think though that the weight of the rig should be considered in this equation. On the harryproa, the rig to leeward will decrease righting moment.
Not sure what we typically have on the lake where I sail, or on the coast to the ocean, or how you judge "unstable" or "stable" air, in this context. But if it is a windy day, where you are more likely to capsize in the first place, my assumption is that the air is unstable, which would give a lower hellmans exponent, so less of and advantage to the harryproa?
I made a simple Excel sheet to investigate.
My assumptions were a 1000kg proa where 100kg is in the beams/trampoline, and 100kg in the rig/sails, which would fly a hull at 10 degrees. You can see the rest of my assumptions in the pictures below.
I found out that if we don't consider wind gradients, the weight of the rig is the dominant factor here. So if all else equal, the boat with the rig to leeward (harryproa) will have less righting moment margins. Because the heeling moment (with a constant wind), is the same in both cases, if you think about it.
But then I added some math to include wind gradients, and then the results aligns well with your words. Because then the height of the rig impacts the sail forces due to the wind gradients, and the boat with the rig to leeward produces less heeling moment at high angles of heel. But it depends a lot on the wind gradients (hellmans exponent) of the location.
I'm sure you have done similar calculations, but I'm sharing my results here for others.
This is results without wind gradients (Hellman = 0):
This is results with some wind gradient (Hellman = 0.2):
This is results with an even higher wind gradient (Hellman = 0.4):
So in this case, the harryproa would be less likely to capsize, imo, despite having less stability while just starting to fly a hull. So that is interesting.
I have very little experience reading the wind and judging the wind gradients, but a guy I'm sailing with claims he has observed that the wind some days is completely calm on the surface, while there is still a decent wind some meters up, indicating a high gradient (and hellman exponent), I assume.
This is the table from Wikipedia.
| location | α |
|---|---|
| Unstable air above open water surface: | 0.06 |
| Neutral air above open water surface: | 0.10 |
| Unstable air above flat open coast: | 0.11 |
| Neutral air above flat open coast: | 0.16 |
| Stable air above open water surface: | 0.27 |
| Unstable air above human inhabited areas: | 0.27 |
| Neutral air above human inhabited areas: | 0.34 |
| Stable air above flat open coast: | 0.40 |
| Stable air above human inhabited areas: | 0.60 |
But then you could just increase the beam of the harryproa, I guess, since there is no rig load on the beams, so the beams could be both longer and lighter.
Doug, good point about the windage of the WW hull flying. The hull will expose the same area on both the cat and the harryproa, if we continue to consider as many things as possible equal. That area might add more heeling moment than the blocked sail though. But on the cat it will block less of the sail, so better for the harryproa.
Björn
On Thu, Jun 7, 2018 at 12:30 PM, Chris Purkiss chrispurkiss@bigpond.com [harryproa] <harryproa@yahoogroups..com.au> wrote:
The heeling moment on a cat increases until the windward hull is out of,the water then it starts to decrease after that. A harry proa is the same as soon the windward hull is clear of the water then heeling moment starts to reduce. All the calls are done assuming the windward hull is just clear of the water.
Chris PurkissM. 0428755749
On 7 Jun 2018, at 7:37 pm, Björn bjornmail@gmail.com [harryproa] <harryproa@yahoogroups..com.au> wrote:Rick, you wrote (in another thread):" An interesting feature of the harryproa configuration with regard to heeling is that the heeling moment reduces as the boat heels. A cat with the mast in the middle or on both hulls has initial increase in heeling moment when one of the hull lifts. "Why does the heeling moment reduce on the harryproa, but increase on the cat?On Fri, Jun 1, 2018 at 1:30 AM, Rick Willoughby rickwill@bigpond.net.au [harryproa] <harryproa@yahoogroups.com.au> wrote:My first flat panel hull V14 taught me a lot about section shape. My V11 hulls were the fastest up to that point and they had round sections. The V14 were constant flare flat panel. For the same weight the design data indicated 3% higher drag. However the lowest drag length was about 15% shorter than the round section and that results in a weight saving. In operation the V14 hull was definitely faster, and by a significant margin.With regard to the 24 hour record, that boat was a V11 version 7.2m long with a round section. The record was set in 2008 but broken by a surfski in 2015.The fellow who set the record in 2008 has built one of my V16 hulls with the aim of retaking the record. The V16 hull is the first version to use the variable flare generated by the 32 parameter shape function using GODZILLA (Michlet). The new hull is shorter, lighter and faster at target power level of 110W.The link has a video showing the plug built to make the female mould:This link has a video of the boat with Greg operating at 110W giving some commentary on speed and other aspects of tuning the boat:As it turned out he did not go to LA as he could not muster the support needed for the attempt there. He did try on the Calgary dam but weather and the short course affected his average speed. I do not know if he plans to have another go this summer. The 2008 record was set on Whitefish Lake in Montana.On 1 Jun 2018, at 3:44 am, mcrawf@nuomo.com [harryproa] <harryproa@yahoogroups.com.au> wrote:I'm predisposed to agree with Rick Willoughby on the flat bottoms for two reasons: a) The flat bottoms work better with intelligent infusion than a half-circle (meaning: I will eventually be able to afford to build the boat), and b) One of Rick's designs for a human-powered pedal boat held the 24-hour distance world record at one point.
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