Dynamics of the racing iceboat: 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

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

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

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

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

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

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

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.

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

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

friction loss caused by molecules of (water/water vapor) which are dragged along between the ice and the runner

energy consumed in moving fractured particles of ice away from the runner groove

Sunday, August 24, 2014