Modelling Seminar

# Organizers

 Dr. Martin Bracke 48-573 bracke[at]mathematik.uni-kl.de Prof. Dr. René Pinnau 48-577 pinnau[at]mathematik.uni-kl.de

# Registration and dates

 regular dates: Tue, 13:45-15:15 in 48-210 start date: 18.04.2017

For the registration please subscribe via URM until 13.04.2017 (https://urm.mathematik.uni-kl.de).

The seminar starts in the first week of the lecture period. During the first session the projects will be presented and assigned to the students.

# Project 1: A liter of light – Cheap light for slum regions

How does the optimal "bottle light" look like? Based on the idea by the Brazilian mechanic Alfredo Moser, a social enterprise under the My Shelter Foundation was launched in the Philippines by Illa Diaz in spring 2011: A transparent plastic bottle (1.5 – 2 liters) is filled with water plus some bleach (to prevent algae growth) and then fitted into a hole in the roof of a typical windowless slum hovel.

During daytime this design performs like a light bulb and delivers light equivalent to 40-60 watt to the interior – just by refraction of sunlight! It simply works, the solar lights are easily constructed at virtually no cost and the aim of the My Shelter Foundation is to illuminate 1 million homes by the end of 2017.

Can we model the light bottle to verify the amount of light reaching the interior of a hovel? Is it really 40-60 watt, how deep to we have to mount the bottle into the roof and which role does the shape of the bottle play? Is it even possible to compute an ideal shape for the bottle?

RemarkThis task was originally posed as a modelling project at the "Mathematik-Modellierungswoche 2017" in Tramin (Italy) by Christof Wiedemair.

# Project 2: Winner of the Tour de France - made by non-circular chainwheels?

Under the brand name of Biopace the Japanese company Shimano sold oval shaped chainwheels for consumer bikes already in the 1980s. The idea was to make better use of the non-even driver's force application during pedaling. But the concept was not really accepted by the market and hence, Shimano stopped the production in 1993. Other companies, namely O.Symetric and Rotor, picked up the idea: In 2012 the two quickest athletes at the Tour de France used non-circular chainwheels and in 2016, Tour de France champion Chris Froome was equipped with chainwheels made by O.Symetric.

Both companies promise significant advantages over round chainwheels – and sporting success seems to prove them right. But are the differences really so enormous? Wouldn't Chris Froome have won the tour with round chainwheels? And would it be possible to adapt the shape even better to the individual requirements and capabilities?

Remark: This task was originally posed as a modelling project at the "Mathematik-Modellierungswoche 2017" in Tramin (Italy) by Matthias Ratering.

# Project 3: Human body motion capture

In the research group wearHEALTH, we want to capture human body kinematics in-field. For this body-worn
inertial measurement units (IMUs) show great potential. One major requirement to wearable
systems is an easy handling. Our goal is to develop an algorithm for a robust and accurate motion
tracking which only needs a minimal number of sensors. In this seminar we would like to develop an
appropriate model to encounter for the missing sensor information. Furthermore we need to
investigate the tradeoff between a reduced number of sensors and the accuracy of the reconstructed
motion. In our laboratory we are able to validate our ideas through real experiments, e.g. based on a
simple example like the squat motion.

# Project 4: Acoustic volume measurement - The farmer's trick

In industrial facilities it is often necessary to measure the filling level of closed containers like silos.
Currently a solution is to prepare the containers with radar sensors inside the container. This solution is
very costly and can’t be done for each container.
However, long experience allows farmers to estimate the filling level of their grain silos by throwing a
stone against its side and listening to the acoustic response.
In designing an automated system based on this principle, the following questions arise:

• What would be an appropriate model to describe the acoustic response? Which parameters are
important?
• Can we determine the filling level from the acoustic response?
• How should the measurement system be designed?

In this seminar we would like to investigate the possibility of determining the filling level based on acoustic
measurements from outside, motivated by the "farmer’s trick".

# Project 5: Optimization of paper planes

Suggested by two seminar participants.