# The Physics of ribbon curling

One of the greatest scientific mysteries of the 21st Century has been solved, I joke of course. This piece of science news is in my mind a wonderful display of how you don’t always need a commercial (or even a logical) reason to study something. Anyone who is particularly keep on gift wrapping may know that when a sharp blade is run down the side of a ribbon it curls up, and, whilst it may shock you up to this point there has been very little scientific understanding of the process. Well a team in America decided that it was time for all of that to change, developing a robust model to put this to bed once and for all!

Draping thin pieces of PVC film over a blade, they were able to, using a weight chart the differences in the curls depending on different variables. The width of the curls were measured, as was the winding speed (the speed the ribbon glides over the blade) and found some interesting results (really quite interesting given the subject is ribbon curling):

• There is a period of time it takes the ribbon to relax after it is pulled across the blade, which yields irreversible curs (almost feels cruel);
• The curl effect is due to the outer side of the ribbon, the side touching the blade, being stretched whilst the inner side is not, causing deformation;
• The sharper the blade the tighter the curls; and
• The greater the tension on the ribbon the tighter the curls.

The experiment can be seen here:

However this is not all. The added twist, pun intended, is that as you keep adding load the curl goes past the half way point on the ribbon (thinking perpendicular to the direction of motion) the distortion starts to be dampened, as more than half of the ribbon now has the deformation making the curls less sharp.

Whilst this is  all good news for us, the only downside is optimal tension is of course dependent on the structure of the ribbon itself. This does mean that in order to wrap gifts with the optimal curls you are going to need to familiarize yourself with the mathematical models first. To do this, you should see the study here.

P.S Thank you for your patience with my slow posting – it’s been pretty busy. My next large post will be this weekend, and will cover the geological machinery of the Earth, linking the carbon cycle, the water cycle, the rock cycle and plate tectonics.

## 6 responses to “The Physics of ribbon curling”

1. Nice, I always liked to make them curl over my finger nail. Also looking forward to post about Earth!!

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• Thank you for visiting and your continued support! I will try to make it a good one

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