ice

• properties
• compression strength
• 300 psi to 1800 psi
• coef. of friction
• .0050 to .015 -- pounds of drag per pound of load
• with snow cover it is much higher
• density
• types
• hard black ice
• 8 deg F to 20 deg F
• 20 deg F to 33 deg F
• 34 deg F to 36 deg F
• snow ice
• 8 deg F to 20 deg F
• 20 deg F to 32 deg F
• 33 deg F to 38 deg F
• 
  
• shell ice
• slush ice
• snow cover
• light fluff - less than .2 inches
• light density snow less than .5 inches
• light density snow - .5 inches to 2.0 inches
• moderate density snow - .5 inches to 1.5 inches
• hoar frost or rime ice

model of friction on ice with runner

runner tip ice contact

• assume for this discussion that the ice is hard, smooth, and black at 28 degree F
• an extremely sharp "v" shaped tip
• face angle is between 105 degrees and 85 degrees
• sharpened and smoothly sanded up to 600+ grit sandpaper
• runner is held in chock or pillow blocks so that under normal sailing conditions it is perpendicular to the ice
• the crown along the profile allow a smooth entry into the ice while the tip is sliding forward
• with a sharp tip like this the pressure on the ice is always sufficient to dig into the ice
• in the digging process the extreme tip of the runner tears apart the chemical bonds of the crystalline structure in the ice
• little chucks of torn out ice get trapped under the face of the runner
• a groove is formed in the ice at the face of the runner
• some chucks are ground into a smooth dust and melt under the runner face
• larger chucks are moved out of the groove as spoil outside of the groove
• depth of the groove increases with
• weight of (boat, skipper, induced wing lift)
• shorter runner
• smaller face angle
• sharper runner tip

simplistic theory of friction between two different materials

• consult a table that lists the known coefficient of friction between the two materials
• for example copper on steel
• static coefficient - 
• dynamic coefficient

marble packing model of friction (theoretical)

• hypothetical composite surface
• base of the surface
• perfectly flat steel plate 1.5 miles square
• steel plate is very thick and does not flex
• small steel marbles
• marbles are machines perfectly round
• diameter of a marble is .001 inches
• layer 1 construction
• one row of steel balls lined up perfectly straight across the back edge of the flat steel plate
• number of balls in row: 1000 * 12 * 5280 * 1.5 = 95,040,000 balls
• the next row of balls is offset by .0005 inches and placed tight against the preceding row
• the process is repeated row by row until the whole layer of the base is filled with balls
• the top surface of the layer is totally flat
• a magical welding process welds each ball to its neighbors at their point of contact
• layer 2 construction
• the same process as layer one except each row of balls lays in the groove created by layer 1
• a magical welding process is used to weld the balls in layer 2 to each other
• the same magical welding process welds layer 2 balls to layer 1 balls
• layers 3 through layer 1000
• same process as layer 2
• lubrication of balls
• a mysterious process applies a very slippery viscous material to the surface of all balls
• the lubricated surface maintains under the sliding load of a steel runner
• hexagonal close packing
• the above layout of marbles is called hexagonal close packing
• each marble in a layer touches 6 adjacent marbles in the same layer
• each marble in a layer touches 3 marbles in the above layer and 3 marbles in the below layer
• in total each marble touches 12 other marbles
• Close packing of equal spheres on Wikipedia
• depth of 1000 layers is approx .74 inches
• 
  
• experiment A:
• a steel plate of 36 inches long by 3/8" wide rides on the top surface of the marbles
• the steel plate is lightly loaded with weight
• plate is pulled in a forward direction at 40 mph
• experiment A: results
• plate will slide smoothly over the marble surface as it contacts the slippery material on a certain number of surface marbles
• as the plate contacts the marbles they will bend slightly but not deform
• in this bending process there is some energy lost which is called hysteresis loss
• the hysteresis loss is a direct function of the weight on the runner and is caused by the heat generated in the flexing process
• a second loss is encountered which is skin friction
• skin friction can be thought of as the capillary attraction between the slippery fluid on the marble and the steel plate as it dragged forward
• skin friction is strictly a function of the area of the plate with the weight on the plate having no impact
• in this case the area is: 36 in. x .375 in. = 13.5 square in.
• experiment B:
• now assume the weight on the steel plate is slowly increased
• experiment B: results
• at some point the weight on the marbles will great enough that the glue joint between the marbles will fracture and some marbles will be dislodged
• when the joint is broken, energy is lost, with this friction called fracture loss
• after the fracture loss, there are dislodged marbles which must moved out of the path of the runner - this loss is called transport loss
• runner friction is a sum of:
• hysteresis loss
• friction loss caused when an object rides over the surface of hard ice without digging into the ice
• the flex in the ice crystals generates heat which translates into energy loss
• think of a friction less bearing on a large steel wheeled vehicles that is pulled along over a thick steel plate
• here the steel wheel does not dig into the steel plate, but there is still friction from the plate have to flex ever so slightly as the wheel moves above
• skin friction loss
• friction loss caused by molecules of (water/water vapor) which are dragged along between the ice and the runner
• fracture loss
• friction loss caused by the fracture of the chemical bonds between ice crystals
• transport loss
• energy consumed in moving fractured particles of ice away from the runner groove

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optimize parameters

call to solution algorithms to optimize on various parameters

• runner_tip_radius (grid)
• weight (parm1) [fibbo]
• side_slop (parm2) [fibbo]
• lap_time
• upwind_vmg [fibbo] (35 deg to 85 deg)
• zero force [fibbo] (1.25*wind to 3.5*wind)
• downwind_vmg [fibbo] (95 deg to 165 deg
• zero force [fibbo] (1.25*wind to 4.5*wind)

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Tech Articles

• Tuning Guide - Ron Sherry - Composite Concepts
• You Tube Video - Ron Sherry talks DN iceboating
• The physics of sailing - John Kimball
• High performance sailing - Frank Bethwaite
• Float your boat - Mark Denny
• Downwind faster than the wind
• Downwind faster than the wind - Video
• Directly upwind and downwind faster than wind - Video
• Putting numbers on Iceboat Performance - Bob Dill
• Performance characteristics of Iceboats by Peter McCrary: Sailing Scuttlebutt in 1974
• Ken Smith - Collective wisdom of DN iceboat.
• http://en.wikipedia.org/wiki/Forces_on_sails
• WB-Sails: Effect of side bend on the mast

Tech Web Sites

• Engineering Toolbox
• Physics Info
• Rapid Tables

Photo Albums

• Wisconsin Iceboating

Clubs

• Four Lakes: Iceboat.org
• Green Lake:Green Lake Ice Yacht Club
• Minnesota:  Minnesota Ice Sailing Association
• 
  
• Oskosh
• Maine
• Conn
• Gull Lake
• Toledo
• Northern Michigan

Classes

• DN: dnamerica.org
• Renegade
• Side by Side
• Skeeter
• Stern Steer

Forums

• DN America Forums
• Minnesota Iceboating Forum

Miscellaneous
Poem: Iceboat Fever - Archie Call

Introduction to mathematical model

• aerodynamic wing forces
• lift from the wing
• drag from the wing
• induced drag from wing
• factors that influence aero wing forces
• apparent wind angle
• area of the wing
• aspect ratio of wing
• camber of the wing
• bending of the mast
• mast thickness
• batten thickness and shape
• wing rake
• wing side slop
• boom angle to boat centerline
• tip shape wing top
• gap between boom and fuselage
•  aerodynamic drag of boat components
• fuselage, plank, springboard, skipper, runners, rigging
• factors that influence aero drag of components
• frontal area of component that sees the apparent wind
• streamlining of component
• runner friction
• forward sliding friction
• lateral resistance friction
• excess resistance caused by
• torque mismatch
• steering runner actions initiated by skipper
• ice surface not strong enough for given side pressure
• factors that influence runner friction
• weight of boat and skipper
• lift from wing
• coef. of friction of ice
• snow cover
• runner length
• runner width
• facet angle
• tip sharpness
• smoothness of runner tip
• straightness of the runner tip grind
• lack of hollows in runner tip grind
• runner camber
• lead in front profile
• lead out rear profile
• thermal conductivity of runner
• air temperature
• roughness of ice
• looseness in steering system
• wobble in chocks or pillow blocks
• tightness of runners in chocks
• misalignment of runners
• runner plank crown
• stiffness of runner plank
• constraints in the model
• hiking limit
• maximum lift that the boat can tolerate
• when this limit is exceeded the boat will hike up about the front runner and the leeward runner
• factors influencing hiking limit
• height of wing
• plank length
• fuselage length
• springboard length
• attachment position of plank to fuselage
• side slop
• rake
• sail hoist
• runner side force limit
•  maximum lateral side force that the runners can tolerate
• when this limit is exceeded the runner(s) will side sideways at right angles to line of boat travel 
• factors influencing runner side force limit
• weight on rear runners
• weight on front runner
• runner facet angle
• runner tip sharpness
• hardness of ice

model variables

variables used in the mathematical model

• boat
• boatVel  //boat speed (MPH)
• boatAng  //angle of boat to true wind (DEG) ie. beam reach = 90.
• wind
• windVel   //wind speed (mph)
• massDensityAir  //density (.0023 pounds/cf)
• appWindAng  //apparent wind angle (degrees)
• appWindVel  //apparend wind speed (mph)
• ice
• race course
• wing
• runners
• platform
• skipper
• parasitic aero drag
• weight
• performance measures
• specialty analysis

Golden rectangle search

solve for one variable

• golden rectangle search
• fastest search algorithm to find the minimum of unimodal function
• assume the function is:  y = f(x)
• tau = (1. + sqrt(5.))/2 ; golden rectangle constant of 1.61803
• lower bound = x1
• higher bound = x4
• minimum lies between x1 and x4
• one interation
• set x3 = (x4 - x1) * tau 
• set x2 = x1 + (x4 - x3)
• evaluate y1 = f(x1), y2 = f(x2), y3 = f(x3), y4 = f(x4)
• eliminate x1 if
• y3 gt y2
• eliminate x4 if
• y2 gt y3
• each iteration reduces the interval to 61.8 % of its original interval
• reduction factor after n intervals
• 1 = 61.8 %
• 5 = 9.0 %
• 10 = .81 %
• 15 = .073 %
• 20 = .006 %
• 25 = .00059 %
• 30 = .000053 %
• 15 intervals is OK for most solutions
• 10 intervals is sufficient for rough solutions
• 20 intervals is plausible for precise solutions
• number of function calls = (number of intervals + 3)
• nested golden rectangle search
• nesting of the search is needed to solve multiple things at once
• for example: solve for
• weight between 450 pounds and 600 pounds
• mast side slop between 5 degrees and 20 degrees
• lap time for the optimum VMG courses (upwind and downwind)
• boat angle between 10 degrees and 80 degrees upwind
• boat angle between 100 degrees and 170 degrees downwind
• boat speed between (.5 * TrueWindSpeed) and (5 * TrueWindSpeed)
• total function calls = (10 + 3){weight} * (10 * 3){slop} * 2{Upwind-Downwind} * (12 + 3){VMG} * (15 *3){SPEED}
• total function calls = 76,050 for above solution  

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runner length thought experiment

Thought Experiments:

• a thought experiment involves thinking about a hypothetical situation which has a tangential relationship to iceboating
• by thinking about the situation you gain valuable insight into a technical matter
• for example:  we are trying to analyze why sharp longer runners have better lateral resistance than sharp shorter runners
• constants for both long and short runners
• hard black ice at 30 deg F
• 90 degree face angle
• runners are stoned to very smooth straight edge with a 600 grit
• 500 pounds of weight on special sled (runners plus sled)
• two runners on the sled mounted in friction less pillow blocks
• runners are separated by 20 inches on the sled
• a wizard is pulling the slid forward at 50 MPH
• think about Runner A:
• traits
• runner that is 40" long
• very little crown
• 90 deg facet
• stoned to a very sharp tip
• smooth hard black ice with temp of 30 deg F
• weight on the runners = 550 pounds
• the runner digs a groove into the hard black ice
• the depth of this groove is a function of the runner length and the hardness of the ice
• friction force of runner acting in opposite direction to boat travel is about (.01 * weight) on the runners, or 5.5 pounds
• the .01 is called coef. friction of steel on ice
• friction force at right angles to the runners is about (.75 * weight), or about 412 pounds of lateral resistance
• this force is much higher than forward resistance because the tip of the runner is tearing up the ice along the whole runner edge as it is pulled sideways
• in this tearing up process the tip is slicing into the bonds of the ice crystals and separating the chemical bonds
• most of the tearing up process is going on at the extreme tip of the runner
• once a little bit of ice is torn up at the extreme tip it is easily pushed up the face of the groove in the ice
• the 412 pounds of side bite amounts to 10.3 pounds per inch of runner length (i.e. 412/40 = 10.3)
• now think about Runner B:
• traits
• everything is the same as Runner A:, except the length is only 20" long
• the coef. of lateral resistance is going to be similar to the longer runner
• the runner tip is digging in twice as deep because there is twice as much weight per inch on the runner tip
• each inch of the shorter runner must dig up twice as much ice as each inch of the longer runner
• if we assume the side bite of the shorter runner is 412 pounds then the side bite per inch of runner length = 412/20 = 20.6 pounds
• as it gouges out a portion of the ice the whole ice structure higher up is weakened 

runner goals

Goals of the runner

• forward sliding friction
• want minimum forward sliding resistance on the ice
• lateral resistance
• desire sufficient lateral resistance to prevent slipping sideways out of runner groove on the ice
• turning ability
• ability of runner(s) to easily turn out of groove during tacking, rounding, or normal steering maneuvers by the skipper

design parameters of the runner

• face angle (approx. 90 deg)
• tip sharpness (expressed as a very small radius of the very tip)
• runner length
• runner crown
• thickness of the runner
• height of runner (dist. up to the lowest portion of any stiffening element)
• thermal conductivity
• hardness of the metal
• grain in the metal

minimum forward sliding resistance

• low thermal conductivity
• minimum hardness
• minimum tip sharpness
• maximum face angle
• quality of sharpening and stoning at the tip (no hollows, or burrs)
• long runner length
• minimum crown in runner
• if snow cover
• want minimum thickness
• may want shorter runner length
• appropriate temperature wax on sides of runner

maximum lateral resistance

• maximum tip sharpness
• minimum face angle
• long runner length
• minimum crown in runner

turning ability

• minimum runner length
• maximum runner crown

counter acting goals

• sliding resistance, lateral resistance, and turning ability all counter act each other in the appropriate design parameters
• lateral resistance
• goal: only have sufficient resistance to cover most points of sailing -- but not to excess
• if you try to cover 100% of all sailing situations then your forward sliding resistance will be too high in general
• for example a hollow ground runner would do the trick on lateral resistance, but it would increase forward sliding resistance to intolerable levels
• the skipper can adjust their sailing strategy and tuning to somewhat deal with with low lateral resistance
• pinch up the middle of the course
• take wide hitch at leeward mark
• add side slop to mast
• too little lateral resistance and you will side slip
• too much lateral resistance will increase sliding resistance
• turning ability
• goal: only have sufficient crown to provide adequate turning ability
• too little crown creates excess drag while turning
• too much crown reduces lateral resistance and increases sliding resistance
• forward sliding friction
• goal: given that you have covered lateral resistance and turning ability, then go all out to minimize sliding resistance with what is left

Lift vs. Drag

Forces

Forward forces

• lift from the wing

Rearward forces

• form drag from the wing
• skin drag from the wing
• induced drag from the wing
• runner friction due to regular weight of boat
• added runner friction due to wing lift
• parasitic aero drag due to boat compents

Performance measures

• Boat speed
• boat angle
• VMG
• jump start speed
• optimum upwind boat angle
• upwind time
• downwind time
• tacking loss
• downwind hitch gain
• percent time while at hiking limit
• intermediate lap times
• starting lap time
• finish lap time

Outline1

column 1	column 2	column 3	column 3
components	velocity made good	apparent wind	wind
apparent wind	iceboat vs. sailboat	racing rules	acceleration
static vs. dynamic	runners	aero drag	ice
hiking	points of sailing	forces	snow
	wing lift
side slip	stern steer
solution techniques	grid search	binary search	fibbonacci search
	parallel tangents (PARTAN)
components	platform	wing	runners
skipper	steering	rigging	fuselage
plank	springboard	mast	boom
sail	blocks	sheet line	fore stay
side stay	framing stay	diamond stay	hound
MasterOutline
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Iceboat vs. sailboat

differences

• sailboat in displacement mode
• must move the water aside leading to a speed limit that follows the square root of the water line length
• sailboat in skimming mode
• catamarans, c-scows, racing dingies
• sailboat with foils (ie. Americas Cup 2014)

Static vs. Dynamic

Static analysis

• wind speed and direction is constant
• boat is operating at constant velocity
• all forces on boat are at steady state
• race course is of unlimited length
• tacking is instantaneous
• mark rounding is instantaneous
• boat is not hiking
• ice conditions are constant
• boat heading is unchanged
• boom angle is constant
• fairly easy to compute
• not realistic, nor representative in real world racing

Dynamic analysis

• wind speed can vary in intensity and direction
• boat can be accelerating or decelerating
• race course is size limited
• real world tacking is dynamic and complex
• what are practical alternatives to deal with hiking
• how to avoid runner slip
• how much time is lost by not sailing a hitch at downwind mark in heavy air

Apparent wind

The apparent wind is the resultant wind that the iceboat experiences as a result of the real wind coupled with the wind generated by the speed of the boat itself.

Thought experiment A:

• there is no real wind
• a wizard pushes the boat due north at 10 MPH
• the apparent wind is 10 MPH coming directly from due north

Thought experiment B:

• there is a 10 MPH real wind coming from true north
• a wizard pushes the boat due east at 10 MPH
• the apparent wind is now comprised of two components
• real wind of 10 MPH from the north
• boat generated wind of 10 MPH coming from the east
• the resultant apparent wind is a vector directed over the port side of the boat at 45 degrees
• the magnitude of the apparent wind is the sqrt(10*10 + 10*10), or the sqrt(200), which equals 14.14 MPH

Thought experiment C:

• the real wind of speed W is coming from the north
• the boat is angled at T degrees to the real wind and is traveling at speed B
• the apparent wind has speed V
• the apparent wind has an angle of A to the boat

• from trigonometry
• V = sqrt((B+W*cos(T))**2 + (W*sin(T))**2)
• A = atan(W*sin(T)/(B+W*cos(T))

Significance of apparent wind:

• the iceboat generally travels at speeds that are in excess of 3 times the real wind
• the multiple of real wind speed generates high apparent wind speeds which in turn generates a large amount of lift in the wing
• the apparent wind angle is quite small which allow the iceboat to point much higher than a typical sailboat

Points Of Sailing

• start
• upwind leg
• downwind leg
• port tack
• starboard tack
• windward mark rounding
• leeward mark rounding
• finish
• sailing the diamonds
• pinching up the middle
• sailing your own race

Platform

Horizontal base of the iceboat providing the basic structure of the boat.

1. flexes on the plank and springboard to ride smoothly over the ice
2. is the righting moment to counteract hiking produced by wing lift
3. overall size and weight determine how much vertical wing area is practical

 Major components of the platform

• fuselage - strongest and stiffest component that carries the whole load
• plank - supports the rear runners and flexes dynamically on the ice
• springboard - extends the platform and also flexes
• skipper - sailor, whose weight of skipper is an integral factor 

components

column 1	column 2	column 3	column 3
platform	fuselage	plank	springboard
chocks	runners	wing	blocks
boom	runners	skipper	sail
mast	sheet line	side stays	fore stay
framing stay	rigging	foot pedals	tiller
winch	jam cleat	halyard	hound
mast diamond	bob stay
Menu
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Runner Chocks

runner chocks

Chart of Performance

chart