The sail force coefficients used by this calculator are based on Personal VPP, a velocity prediction program written by Mikko Brummer in 1992.
Sail areas
Sail areas are calculated from the basic rig measurements Luff, Leech and Foot. The foot height above deck FAD is needed for the calculation of the heeling moment and for sail endplate calculations. The righting moment is calculated from the bouyancy of the ama at waterline times the distance between centerlines of ama and main hull.
Wind is apparent, not true
All the wind values are apparent wind, not true wind. VPPs usually base their data on true wind values, but since boatspeed is unknown, and sails work on apparent wind, this calculator has to rely on apparent wind.
Sail Drive and Heel
The sail drive is the actual force that is thrusting the boat forward. Drive is in the direction of the motion of the boat - it differs from the direction of the centerline of the boat by the amount of leeway, since a sailboat is always more or less "slipping sideways". Apparent wind angle is measured to the centerline of the boat.
The heeling force (Sail Heel) is, like the name suggests, the force that is heeling the boat over. It is perpendicular to the centerline of the boat and the mast. The heeling force acts at the height of the center of effort, given in the additional data as percentage of the rig height.
Heel angle and heeling moment
This Calculator calculates the heeling moment about the mast foot (base I), and this heeling moment is not directly comparable to the righting moment (RMC). Without knowledge of the bouyancy of the main hull and ama, we cannot calculate the true heeling moment.
However, given the RMC, this calculator can estimate the heel angle at a given wind. For this purpose, the calculated heeling moment is increased by 35%. Since sail forces depend on the boat heel, we must usually "iterate" to to get the given (input) heel and the estimated heel to match. Run the Calculator once, change the given heel to match the estimated one, and re-run by pressing Update. When the two heel figures are the same, the results are presumed accurate.
Aft Mast Calculator and IMS sail forces
The coefficients used in this calculator are more complete than those
used by the IMS-rule in three respects:
- the drive available is a function of leeway - important in close hauled conditions
- sail forces are corrected for rig aspect ratio
- the genoa overlap factor is more realistic than the blanketing factor of IMS
Leeway
When trying to pinch a boat, the leeway increases rapidly, decreasing the apparent wind angle (as measured to the centerline of the boat). Sail drive is lost at a steeper rate. Aft Mast Calculator allows for leeway in a simplified manner, since there is no boat data from which to estrapolate data .
Aspect ratio
The rig aspect ratio affects the pointing ability of the boat. A taller rig produces more drive at a given wind angle and for the same sail area than a lower one. There is a catch with high aspect ratio - heeling moment goes up - this puts a practical limit to the tallness of the rigs we use on contemporary cruising trimarans. Low aspect ratio also performs better off wind, which is generally the nature of world cruising in the trade winds.
Depowering
As wind increases, depowering is needed in order to avoid excessive heel.
This Calculator's Auto depower simulates this, by flattening and feathering
the mainsail (jib power remains unchanged). Feathering also lowers the
sail center of effort, helping to keep heeling moment under control. "Keep
full power" is the default setting. Unlike for the number fields, the Update-button is used to validate a change in depower. Decrease the luff and leach lengths of the foresails to "depower" the them.
Depowering starts when apparent wind speeds exceeds 14 knots.
Additional data
Additional data shows some key parameters used in the calculation of sail forces. Leeway is a function of AWA, which is obviously a simplification - again, boat data is needed to compute real leeway. The sail drive to heeling moment ratio is an important parameter for sailboat performance. In light winds, we want to maximise drive, ignoring heeling moment, but as wind picks up, the drive to heeling moment ratio becomes more and more important.
The Reset-button clears calculated fields and sets any inputed values back to default values for an aft mast rigged, modern 36 foot trimaran.
NOTICE --
11/15/2002 - This Aft Mast Sail Plan Calculator for a Cutter/Ketch rigged cruising trimaran is a completely reprogrammed attempt to predict sailing data using SailPowerCalc as a beginning programming model.
This calculator is a very beta-version that has not been tested. There are buggy coefficients that have not been ironed out for all points of sail. Apply the results with caution.
So what have we come up with? Lets call it a marriage between a cutter and a ketch without the main mast, mainsail, booms or a second mast, a unique rig designed to go on a 36' Cross Cruising Trimaran hull, to be used as a shallow draft research vessel around the world in riverine waters and estuaries.
Initially I was looking to discard the inefficient mainsail, and replace it with a clean leading-edge jib-hanked, freefooted sail, which would be acting in a parallel, harmonious fashion with the jib or genoa, and with no mast spreader overlap so they might be sheeted in for optimum pointing. I first envisioned two masts joined at the top, replacing the shrouds, with a vertical stay for the leading edge of the main, rigged "Bermudian" fashion but loose footed. One primary object was to have a light mast "gin pole" arrangement that could be lowered easily to pass under overhead obstructions. I discarded this idea as there was no easy solution to having the long thin unstayed or jumpered masts strong enough to not vibrate or fail in compression, short of the expense of carbon fiber sticks.
I then saw the possibility of the aft mast stepped configuration.
This necessitated that the mast be stepped aft, just forward of the cockpit area and above the rear main beam, canted forward approximately 10 degrees. The leading headsail is equivalent to an ordinary masthead genoa. The inner staysail is equivalent to the ordinary jib and the third staysail is equivalent to the normal Bermudian mainsail and performing a similar function in a more efficient manner, as its leading edge is not fouled by a mast and its foot not misformed by a boom. The foot of the headsails will sweep just clear of the cabin top, thereby gaining an effective aerodynamic "endplate."
The wind slot between these three headsails has been made slightly wider than on a conventional cutter rig of similar LOA, approximately 4 feet, which increases the effectiveness of the jib and main staysails, and very importantly, the parallel nature of this slot produces a much more favorable interaction between these sails than the ever-variable, triangular slot between the traditional main & jib. Equally important, the draft pockets on these staysails are in harmony, lifting and driving ahead, as opposed to a Bermudian mainsail which drives downward on a reach.
Adding a mizzen sail inside the backstay between the backstay jacks fixed on the rear of the mast, which were installed to keep the winching effort well above the mastfoot pivot, turned the boat into a ketch without the addition of another mast and its associated rigging. This also presented the opportunity of flying another small rag, a mizzen tops'l between the mast and the mizzen stay. This increased the total available sail area on this single-masted rig.
The ketch rig divides the sail area up into more manageable size sails, and it produces a rig with a lower center of effort (less heeling moment) than a sloop of the same sail area.
Tweaking the adjustment of the ketch's mizzen and mizzen tops'l provides a finite adjustment to balance the helm of the boat. Literally the boat can be made to sail without a hand touching the wheel.
The CE's (centers of effort) of the sails with this rig maintains the boat's balance under a variety of sail combinations. The calculator above is configured for the use of a spinnaker for downwind work, but given the large forward sail area winged out, from a cruising standpoint, I don't see much need of it and the necessary touchy up-forward sail handling and equipment needed.
The three forestay sails will all have roller furling, Shorten sail initially by furling the inner jib staysail, and continue smartly under the genoa, main staysail and mizzen combination. With the wind really coming up, furl the genoa, and the main, unfurl the jib, with the mizzen to balance. Not only is the sail area reduced significantly, the height of the CE is lowered substantially and correspondingly the overturning forces; and the rig is still in balance! Storm conditions arriving, unfurl the main staysail, and furl the rest. And all this could be accomplished without ever turning the boat into the wind or leaving the cockpit if single handing as all the sheets and halyards operate from the same station and winch, immediately adjacent to the helm.
Consider a couple of other interesting comparisons.
a) For a conventional sloop to carry the same sail area as this rig, it would require a mast at least 7' to 10' taller. It's sail area would have to be even larger to match this rig's effective sail area, when the inefficiency of the sloop's mainsail is factored in. This larger sloop rig then contributes more overturning force, as well as more leeway force, as well as more bow burying force.
b) For identical sail areas, our "single-masted ketch" has an even lower height CE than the traditional two-masted ketch. Plus, the weight of this rig (and particularly the mast) is more favorable centered over the boat's motion center, contributing less to the vessel's pitching motion This is almost like gaining the benefits of a modern carbon mast (without having to buy one). And the mizzen is not operating in the shadow of it's own mast.
c) Gone is the heavy, low slung boom, as is the first aid required for bashed heads. Gybing is far less dangerous. And without sail tracks on a mast, jammed mainsail and mizzen slides are gone. All the sail handling and winching is done from the cockpit with ease.
And finally the most often asked question about this rig; how is a leaning mast kept up? Well, like any other mast, utilize creative, structural rigging. The only time any other sailboat's mast is standing straight up, is at rest, at the dock. Otherwise it is always leaning over under sail. There are even numerous vessels which, at rest, had their mast raked back at a greater angle than this design is raked forward.
As the many virtues of this mast-aft rig are evaluated, an emergency situation where all sail must be scavenged immediately with no time to point up into the wind is easily accomplished on any point of sail with this rig.
Some of those virtues in summary:
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1) A cruising rig that is more aerodynamically efficient, which should enable the same speed with less sail area, or more speed with the same sail area
2) A rig that delivers an aerodynamically clean leading edge for all the sails
3) A rig that allows the whole sail plan to be roller-furled away or deployed, if desired.
4) A rig that allows the furling of the sails without turning to weather.
5) A rig that divides up the total sail area into smaller manageable sizes.
6) A rig that maintains its balance center (CE) with different sail combinations.
7) A rig that produces less heeling moments.
8) A rig that can be operated without leaving the cockpit. One person could sail this fairly large rig from anchor up to anchor down. All the sails can be roller-furled, and the main staysail, mizzen staysail and mizzen tops'l all self-tack. The genoa and jib need to be tacked over past the forestays, and this can be accomplished as the boat comes about with roller furling in just seconds from the cockpit without ever going forward.
9) And lastly, a rig that has the leech of all the sails operating clear of the mast, spreaders and shrouds, allowing sheeting for optimal performance of each sail, and eliminating spreader wear areas on genoa, jib and mains'l.
In conclusion I believe the Aft Mast Cutter/Ketch rig to be an efficient evolution of the ketch concept.
Barefoot
FOR INFORMATION ONLY, ALL RIGHTS RETAINED
20021122