# Planing upwind

Discussion in 'Sailboats' started by BigB, Aug 25, 2009.

1. Joined: Aug 2009
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### BigBNew Member

Friends,

I'm brand new to this forum and this is my first posting.

I'm hoping that somebody can explain to me the physics that allow a boat like BMW Oracle or Alinghi to sail upwind at double the true wind speed for a prolonged period of time. I've sort of been curious about this phenomenon for some time but my interest was sparked again this week when BMW Oracle released a photo of the vessel sailing upwind at 20 kts. in about 10 kts. of true wind.

I understand how planing monohulls like dinghies and sportboats can exceed the wind speed for a periods of time when broad reaching. But I've never understood the science of how it happens upwind.

I imagine a bell curve (or polar) comes into play. In other words, an upwind multihull like BMW Oracle cannot immediately exceed the wind speed upon first trimming its sails. And at the other end of the bell curve must be another limit, i.e., a boat cannot go, say, six times faster than the true wind.

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An ice boat can go 5+ times wind speed.... Its basically a matter of power to carry sail and drag-I've run across some good explanations and when I find them I'll post.
Frank Bethwaite* has a formula that predicts when a monohull is likely to plane upwind:
SCP=Sail Carrying Power= RM in ft.lbs divided by [the distance between the Center of Effort and the Center of Lateral Resistance in ft.]
The formula is: SCP divided by Total weight in lbs.
If the answer is 30% or higher the boat will plane upwind.

This is very good-for understanding sailing faster than the wind:
http://www.animations.physics.unsw.edu.au/jw/sailing.html

* "High Performance Sailing"-the formula was designed to analyze skiffs -which in Australia are planing monohulls from 12 to 18'.

3. ### Paul BPrevious Member

The boats mentioned are not monohulls, nor do they plane.

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### Manie BSenior Member

what is this RM

thanks

5. Joined: May 2009
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===============
RM= Righting Moment
For Bethwaites purpose the RM= [the distance between the CG of the crew and the boat CL in feet] multiplied by the crew weight in pounds.

6. ### Paul BPrevious Member

Manie, he doesn't get it.

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### FanieFanie

BigB, as I have it, those planing boats are not all rounders, they are designed to perform optimal in a certain direction to wind and that's it. Those guys must be very wealthy to be able to build those boats.

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### tspeerSenior Member

One problem with a boat like the BOR90 is defining just what the wind is! When the mast is over 50m high, the wind is quite different at the head than it is at the foot. Wind speeds are conventionally reported at a height of 10m, so the craft may be sailing in more than the 10 kt reported. But that doesn't change the fact that the performance is remarkable.

Sailing performance is all about the lift/drag ratio of everything above the water and the lift/drag ratio of everything below the water. The fundamental sailing performance equations are:

Vb = Vt * sin(beta - gamma) / sin(beta)
beta = arctan(aero_drag/aero_lift) + arctan(hydro_drag/hydro_lift)

Vb = boat speed
Vt = wind speed
gamma = point of sail (0 = head to wind)
beta = apparent wind angle, measured between the apparent wind and the course through the water
aero_drag = aerodynamic force component parallel to the apparent wind
aero_lift = aerodynamic force component perpendicular to the apparent wind
hydro_drag = hydrodynamic force component parallel to the course through the water
hydro_lift = hydrodynamic force component perpendicular to the course through the water

From these equations you can see what's required to achieve any level of performance. Say the boat is going upwind at 45 deg to the true wind (gamma = 45 deg). In order for the boat speed to be approximately twice the wind speed, beta must be less than 15 degrees. This could be achieved if both the aerodynamics and hydrodynamics had lift/drag ratios of 8:1.

But 45 deg would not necessarily be the angle for best Vmg. If the lift/drag ratios (and thus beta) are kept constant - not too bad an approximation for a really high-performance sailing craft - it's better to foot for more speed to increase Vmg. The optimum upwind Vmg angle for constant beta is 45 deg + beta/2. A constant-beta craft going upwind at a boatspeed twice wind speed would have an apparent wind angle of 17 deg and get its best Vmg at 53.5 deg to the true wind. It would need to have lift/drag ratios of 6.7 or greater. The L/D of the hulls and foils might be less than this if the L/D of the rig and topsides was enough greater that beta was still 17 deg.

The sin(beta) term in the denominator means there is no upper limit to sailing performance, if you can make the drags low enough. Surprisingly, the lower the drag, the more important additional drag reduction becomes. If the lift/drag ratio is 4, reducing the drag by 1 unit is equivalent to adding 4 units of lift (with no additional drag!), but if the lift drag ratio is 6, then reducing the drag by 1 unit is equivalent to adding 6 units of lift.

Given that even Standard class sailplanes achieve lift/drag ratios over 40:1, the limits to sailing performance are more practical than they are aerodynamic or hydrodynamic. The drag due to lift is inversely proportional to the square of the span, so this drives the design to very tall rig heights and deep foils. This means there's a big overturning moment between the aerodynamic force and the hydrodynamic force, so the righting moment of the boat becomes the limiting factor. And the way to get the most righting moment with the least weight (drag, again) is to go with a big multihull.

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### FanieFanie

Tom, your reply's are technical and professional as always. I wish you'd post more ! I can't give you any more points, I think Jeff has it in for me.

How did your experiment and testing go ? If you did post it somewhere I missed it...

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### tspeerSenior Member

Thanks!

Not to take this thread off topic, but since you ask, it's going slowly. And expensively. Went to Canada for the Cow Bay regatta (met Richard Woods - hi, Richard!), and had a fabulous time. But on the way home the engine was blowing all its oil into the bilge. I put in 3 quarts in 2 days. The suspect is loss of compression in a cylinder leading to blow-by that pressurizes the crankcase. Now I'm probably looking at an overhaul, if not a new engine. Ouch! But I've also had other things taking up my spare time. I hope to get back to it more intensively next year.

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### FanieFanie

he he... need a pump to pump the oil from the bilge into the engine kinda like an open oil plan. Sorry it didn't work out. I also have too many other things interfering. I have an interest, will be on the lookout. Good luck.

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