From the Official Site of the Duke Eco-Marathon Team
Last year we were unable to perform much analysis on our motor selection or pay close attention to driving strategy. By performing intensive motor testing this year and developing a MATLAB model of our vehicle dynamics, we hope to fully understand the efficiency spectrum of our motors and derive an optimized driving strategy.
When developing a MATLAB model for the car we started with deriving an equation of motion for our vehicle. The forces considered in our model include, vehicle weight, aerodynamic drag, rolling friction, inertial forces, as well as input motor torque. A simple force balance allowed us to derive the equation of motion shown above.
After developing an equation of motion for our car, we set out to determine experimental values for the parameters involved in our equation. These parameters include vehicle weight, coefficient of rolling friction, aerodynamic drag coefficient, as well as frontal area.We were easily able to weigh our 2013 vehicle to determine weight. When determining an experimental value for the coefficient of rolling friction however, we set up an experimental procedure in which we rolled the car down a ramp and measured how far it was able to free roll. By combining our experimental procedure with a simple energy balance we were able to calculate experimental values for our vehicle coefficient of friction. We performed the same tests with both our outboard and in-hub motor in order to be able to compare energy losses associated with each motor type. When determining experimental values for our frontal area and coefficient of drag we looked to existing competitor data. Since we plan to optimize both frontal area and drag coefficient for our 2014 car we looked at the PAC-Car (http://www.paccar.ethz.ch/) to settle on benchmark values for our initial model.
After determining our critical vehicle parameters we plugged them into our equation of motion and created a time marching algorithm. This allowed us to keep track of the position, velocity, acceleration, as well as energy usage of our vehicle while testing out several different motor torque inputs or driving strategies.
In order to actually develop efficiency values for our vehicle however, we needed to find a way to model our motor efficiency at a variety of power inputs. We are currently working on creating experimental motor efficiency values for our motors through the use of the test rig shown above.
By using the test rig to measure input current and voltage, as well as the output torque and speed we will be able to fully characterize our motor efficiency over a wide spectrum of torque and speed values. We will input these efficiencies into our MATLAB model and iterate through driving strategies to find the one that gives us the highest predicted overall vehicle efficiency. Currently we plan on testing our outboard motor as well as and in-hub motor, which was purchased from E-BikeKit. Both motors are brushless DC motors. The E-BikeKit motor provides optimal space saving because it does not require a chain (this makes it great for converting road bicycles to electric bicycles, which is what it is designed to do) but we hope to determine if it provides us with a better overall vehicle efficiency than our outboard motor. More information about E-BikeKit and the variety of electric bicycle motors that they design and manufacture can be found at www.ebikekit.com. We will keep you posted with the results of our testing!
original article posted November 25, 2013.