Homework #4               Glaciology, GEOL 4888,  Spring 2019 Humphrey

1. We did a regelation experiment in class.  We used a 24 gauge copper wire.  We loaded a 2.2kg weight on each side of the wire, and hung it over a piece of ice that had a diameter of 7cm.  The wire regelated about 2cm in 1.25 hour. In your notes you will find an expression for regelation velocity.  On the basis of your equation: how does the calculated velocity compare to the observed?

Couple of hints: to do this correctly you need to take into account the curvature of the wire as it is dragged through the ice, but it turns out that the forces can be fairly well approximated by assuming the copper is a rigid straight bar and horizontal. Therefore the driving stress is just the total weight (force in Newtons) divided by the wire area, assuming it is a horizontal, not curved, wire. Also note that you will need the thermal conductivity of copper (in Joule/(m s C). [don’t forget to multiply the mass by gravity to get the force]

[If you like math problems: it is possible to calculate the shape of the curve of the wire. As far as I know, nobody has ever published this shape!]

2. Consider a glacier in coastal Alaska that is 10 km long, 200m deep and 1km wide. The mass balance curve shows the average net accumulation in the accumulation region is 0.5m per year. The ELA is about 4 km up from the snout. What is the approximate balance velocity at the ELA?