Higher
VECTORS
SUBJECTS STUDIED AT SCHOOL
Maths
DANIEL FRIEDRICH
Senior lecturer, University of Edinburgh
FURTHER EDUCATION:
MSc and PhD in Applied Mathematics
CAREER JOURNEY SO FAR
Three years as a postdoc at the University of Edinburgh developing simulation software
Eight years as a lecturer in engineering mathematics at the University of Edinburgh
Chemistry
Physics
FUTURE ASPIRATIONS
Mathematical models are becoming more and more important for the solution of societal challenges. It is my ambition to develop innovative teaching and research which motivates my students and bridges the gap between applications and advanced mathematics.
Q&A WITH DANIEL
What does your company/organisation do?
The University of Edinburgh has two main roles:

Teach the next generation of graduates so that they can make a positive difference locally and globally.

Research and develop innovative solution for today’s and tomorrow’s challenges.
What types of activities do you do in your job?
My work as a lecturer in the School of Engineering is almost equally split between teaching undergraduate and postgraduate students and research in mathematical methods to decarbonise energy systems.
What does a typical day at work look like for you?
My work as a lecturer in the School of Engineering is almost equally split between teaching undergraduate and postgraduate students and research in mathematical methods to decarbonise energy systems.
What are your favourite things about your job?
Both the teaching as well as the research parts of my job can be frustrating but also very satisfying. It is great when the students grasp a difficult concept or when we are solving a tricky research question.
HOW DANIEL USES VECTORS AT WORK
I teach vector calculus to engineering students because it is needed for many engineering applications such as to calculate the length of tortuous routes or the mass of arbitrary shaped objects.
I use vectors in my research to find optimal routes to connect wind farms to the electricity grid and to calculate the power output of the wind farm for different wind speeds and directions.
ACTIVITIES
Problem 1  Power output of a wind turbine
The power output of a wind turbine depends on the speed and direction of the wind relative to the wind turbine. Usually the wind turbine is pointed in the same direction as the wind.
Unfortunately, the wind turbine has a fault: it can't follow the wind direction and is stuck in direction t = (4, 3). Calculate the speed and angle of the wind relative to the wind turbine for a wind velocity of
w = (3.4).
Problem 2  Non horizontal wind
A similar reduction in output power would occur if the wind is not blowing horizontally.
The wind turbine has now been fixed and can follow the wind again but only in the xy plane. However, now the wind is blowing up the slope the wind turbine has been built on. Calculate the speed and angle of the wind relative to the wind turbine for a wind velocity of
w = (3, 4, 1)