DaySailer.org Forum

I had a wild ride on short squall yestday -- caught me alone under full sail. I turned and ran with the board up. I did about 1.5 miles in about 10 minutes, so I was going around 9mph. I looked up the hull speed formula (1.34 x sqrt WL length) and came up with about 5 knots (around 6mph), so planing added about 3 mph to the theoretical max.

Questions: (1) Why does displacement not figure into the max. hull speed formula? I have similar WL and sail area to a neighboring Catalina 18, but I'm sure my 600-lb dinghy moves faster than the half-ton balasted c18. (2) Is there a theoretical top speed for the DS II (or any planing hull) after it gets on top of its bow wave?

--Talbot

My understanding of hull speed is that it is more of a rule of thumb calculation and there are many factors which allow a displacement (non-planing) hull to exceed that speed. It may have been fairly accurate back in the days of heavy displacement sailing ships, but not so much for today's modern designs (although I believe tugboats still follow the rule pretty closely). There are dozens of non-planing hull forms that easily exceed theoretical hull speed (catamarans, kayaks, rowing shells, semi-displacement racers to name a few).

2 of the calculations that are used to calculate speed on the myriad of today's hull shapes are the Hull Fineness Ratio (HFR - ratio of the hull's maximum beam to the length) and the Prismatic Coefficient (ratio used to evaluate the distribution of a hull's wetted area). Both of these approximate displacement and can be used with other algorithms to model a more realistic speed number, but there are so many complicating factors (wave height, wind speed, cross current, etc...) that I'm not sure any of them could be fully validated in the real world.

I'm not sure I'd want to find out the theoretical top speed for a DS without a crash helmet. I think it's one of those things that given the perfect conditions with no waves you could get going stupid fast like a windsurfer.

I don't know how fast I was going but I had a really good couple of mile run last summer. We were riding some pretty good size waves diagonally on a beam/broad reach. It really felt like windsurfing! Then we got passed by a windsurfer so I guess we weren't going as fast as I thought. I can't say that it felt safe but it sure was fun!

How fast can a DSII go?

About as fast as a DS 1.

(sorry, couldn't resist. )

Let me give a couple of serious answers to your questions:

talbot wrote:Questions: (1) Why does displacement not figure into the max. hull speed formula? I have similar WL and sail area to a neighboring Catalina 18, but I'm sure my 600-lb dinghy moves faster than the half-ton ballasted c18.

Water waves of different length travel at different speeds (that's different from the way sound works, by the way, or light waves, for that matter).

Because of that effect, the point you reach "hull speed" is when the bow wave will have its trough at the stern and you are sailing "uphill" constantly. (Remember, the speed of this wave depends only on it's length). For most hulls (and yes, that's most and not all) this behavior of the bow wave means that the drag increases dramatically as you get closer to that speed. At some point near the "hull speed" the driving force from your sails (or engine) can't keep up and that's your top speed.

If your hull is light (and flat) it doesn't take too much power to put it on a plane. For the DS, sailing in the right circumstances will allow sail power to get the boat over the "hump" in the drag curve, after which the total drag is less again (but will then increase with speed).

Some hulls have no humps (some of the fast skiffs). Some hulls have insurmountable humps (oil tankers). Some boats can be pushed on a plane with an engine but might not plane under sail (I believe the McGregor would be an example).

talbot wrote:(2) Is there a theoretical top speed for the DS II (or any planing hull) after it gets on top of its bow wave?

Yes - but it's specific to the boat. Your top speed is reached when the (maximal) drive from your sails matches the drag at that speed. Boats with higher sail carrying ability for the same weight (skiffs, trapeze boats, windsurfer) would go faster. Unlike the speed of the bow wave for a given length, there's no easy formula.

For what it's worth, I found a formula called Crouch's Planing Speed that gives an estimate of around 8 kn for a 600 lb boat carrying 150 lb. Crouch's formula does not worry about length, because it assumes that a planing hull has already climbed on top of its bow wave. There is also a Gerr formula for semi-dispacement hulls that also appears to come in at around 8 kn. A little hard for me to interpret, because Gerr was expressed in horsepower required for certain speeds. I used the minimal ratings on the charts. See www.psychosnail.com

Anyway, my calculation of 10mph in yesterday's squall was hardly maximum, but still pretty zippy.

The reason horse powers show up is that the limit is reached when driving matches resistance. Estimating resistance depends on details of the hull shape etc. plus total displacement, but "planing dinghy" might be generic enough to get you into the ballpark if you can estimate the weight. A DS would be heavier than 750lbs when sailed, esp. if you count motors and other non-racing gear.

After that, to estimate the maximal possible drive, you need not the sail area, but the maximally available righting force (hiking or trapeze whatever the case may be for the boat). For the DS, that's crew weight times distance from the centerline to their belly buttons (approx). Then you go into the tables that relate heeling force to driving force coefficients and pick the best case for the kind of rig a DS has.

Since you know what heeling force you and your crew can maximally hold by your combined weight while hiking, you multiply that by the ratio between driving to heeling coefficient. That gives you the maximal driving force. This should be largely independent of the wind. If the wind's too strong, you have to dump power. It does depend much more on the point of sail, because the ratios between heeling and driving forces are so dependent on this.

This estimate would work for a reach (where the crew hikes to keep the boat flat). Downwind, where you don't hike, there are other limits to how much driving force you can handle (stability). Once you know or estimate that limit, you can convert it into "hose powers" to plug it into Gerr's equation.