Propelled String Dynamics

The string shooter was first demonstrated by Bruce Yeany, who showcased its ability to form a stable, self-supporting loop. His demonstration caught the attention of the scientific community and led to a series of research papers that further explored the shape and dynamics of the shooter. The device itself can be used to illustrate various physical concepts and demonstrate techniques in computational science and engineering.

The shooter consists of a continuous loop of string propelled at high speed by two motor-driven wheels. As the string is shot forward, it forms a stationary, self- supporting loop that maintains its shape without any external support. What is surprising is how the string behaves when in motion. We expect the string to be limp but when in motion, it acts more like a springy wire. When tapped, waves can be seen on both the upper and the lower part of the string moving away. The same happens when the string is moved from side to side. It is said that a string cannot be pushed, but this device does exactly that. The string is pushed forward by the wheels, it has inertia, and it keeps moving forward until the loop is pulled back by the rotating wheels.

This report investigates the physical forces that allow the string to maintain its shape and stability. Key factors include the interplay between inertia, tension, and drag forces. By analyzing the loop’s shape and the forces at work, we aim to uncover the mechanics that make the string to behave in such an unexpected way.

Here we describe how to use the Matlab codes.

Visualization 

To use this script, you need to input values for the angle of projection (theta0_values), the angle of return (thetab_values), the horizontal distance of the loop (D), the mass of the string (M), the total length of the string (L), and the vertical offset of the string loop (b). All these quantities must be measured carefully using appropriate apparatus. Once the script is run, it will plot the upper and lower branches of the string loop. These two branches might not meet exactly at a point due to an initial guess for the drag coefficient (f). In that case, manually adjust the value of f until the two branches align properly. The value of f that results in the best fit should be noted down for later comparison with the result from the optimization step.

Optimization

The Optimization script uses least squares fitting to find the best-fit parameters for the string shooter model. First, import your experimental data from CSV files into MATLAB and assign the data to the variables XUpper, YUpper for the upper branch and XLower, YLower for the lower branch. Set these as x1 = XUpper; y1 = YUpper; and x2 = XLower; y2 = YLower; in the script. Running the code will generate a plot comparing your experimental data with the fitted model and will display the optimized parameters, including the drag coefficient f.