About us

As a group of master students at the Norwegian University of Science and Technology in Trondheim, Norway, we are happy to publicly deliver this website. Consisting of three mathematicians and two engineers—all Norwegians—working with the mathematical modeling of custom-built alpine skis have been serious fun!

We hope you will find the online information and results valuable. Below is written more detailed about the course we followed and our team process.

Best regards,

Bjørn Harald Snersrud,
Fredrik Hildrum,
Herman Galteland,
Jon Vegard Venås and
Magnus Norum.

This booklet presents details of the outcome of a teamwork project for students in the course «TMA4850 - Experts in Teamwork - Mathematics in Applications» at the Norwegian University of Science and Technology (NTNU) during the Spring 2014 semester. The course agenda is to set up a larger group project with practical applications, where students from various disciplines come together and contribute with their academic skills. Moreover, a special focus is given to how groups operate and function, and facilitation during the teamwork stimulates continuous evaluation and implementation of concepts with regards to group effectivity.

With a quite ambitious project given the time constraints and previous knowledge, there have been several challenges during the course. But we feel the results are considerable higher than what was realistically expected initially.

We want to thank our supervisor Trond Kvamsdal both for outlining a project description on modeling flex curves in alpine skis, developed by ski producer Endre Hals, and support during the course. Also, a special thanks goes to Endre Hals for inviting us to his production facility, providing data during the modeling and giving us a pair of skis for testing purposes. In addition, we received great help from both Arne Morten Kvarving from SINTEF and Ph. D fellow Kjetil André Johannessen with regards to generating useful data structures for the ski model.

Our team has worked under the governing village theme "Mathematics in Applications", and as a foundational philosophy the so-called MAC-model has been used. Introduced to us by the village supervisor Trond Kvamsdal, the Mathematics, Applications and Computer science model highlights the effective interactions between different scientific groups. Powerful modern teams within the areas of applied mathematics need to cooperate with people from the specific physical application, and implementations of numerical procedures benefit highly from expertize from the computer science world.

With "mathematical modeling of flex curves in customized alpine skis using isogeometric analysis" as the project title, the necessity of both mathematical- and applicational skills is clear. Since Bjørn Harald's expertize lies in industrial mechanics, it was quite natural that he studied some of the underlying structural mechanics and designed the CAD ski model. Moreover, as Magnus have knowledge on material properties and practical experience as a carpenter, he focused in particular on testing the materials in the ski core.

When it came to the necessary mathematical basis, both Jon Vegard and Fredrik had previously worked together with the finite element method. With this foundation, the topic of isogeometric analysis stood out as exciting and interesting. Since neither of them had knowledge on this subject, the task was quite ambitious. During the project it became evident, due to Jon Vegard's extensive contribution and gained knowledge from a specific course, that he operated the main mathematical analysis, both theoretically and numerically. Also, Jon Vegard will continue with a master study on this topic, and thus saw this project as very useful practical preparation.

Herman is a master student in mathematics, with specialization in abstract algebra and cryptography. It was not easy to obtain a project description that could fit his skills with the other members' capabilities. But when the idea of generating a web presentation displaying details of the project, Herman decided that he could contribute on this development. Since Fredrik had some past familiarity and personal enthusiasm with making websites, they cooperated the process throughout the semester.

As the isogeometric analysis approach establishes direct interaction between CAD and the finite element method, Bjørn Harald and Jon Vegard interacted repeatedly to obtain a useful model. Also, on the structural mechanics side, both Magnus and Bjørn Harald worked side by side on theory and applications.

All in all, the academic composition fitted the project description quite well. Some additional competence in computer science may have resulted in a more advanced implementation of the numerics, and that the link between CAD software and the finite element codes could have been easier to establish. Though not of crucial importance, the group, however, also recognizes that presentational skills, such as a creating website, is useful for public recognition of the project, and thus the work of Herman and Fredrik suited the team well.