Beginning in the early 1970s my colleagues and I at Deere developed a variety of mathematical models and simulations to investigate power hop, a type of dynamic instability that can occur in tractors operating with moderate to high draft loads in the field. Although these models could predict the phenomenon, the results were so complicated and volumunous that we were unable to grasp a general understanding. Then in April of 1989 we had a breakthrough and decided to reformulate the problem as a dynamic stability investigation. I had purchased a copy of Mathematica in late 1988 and was intrigued with its capabilities, so we decided to build this new formuation as a series of Mathematica Notebooks. Within 2 weeks we were getting new results and displays that were easy to comprehend. These were expanded and utilized extensively over then next few years. Later we often remarked that we would not have been able to develop these results so quickly without Mathematica. Dr. Bernard Romig of the Deere & Company Technology Center did most of the Notebook development.

Numerious field tests and test track tests confirmed the Mathematica models, and showed that adjustments of fore-aft location of the tractor center of gravity and the stiffnesses of the tires were necessary to control power hop. In particular, it was necessary to reduce tire stiffnesses by operating at significantly lower inflation pressures. As a result, tire manufacturers extended their load-inflation pressure tables to the required lower pressure ranges early in 1992, and these are now being used worldwide. In addition to controlling power hop, use of these lower inflation pressures has been shown to significantly increase tractor productivity and fuel economy, reduce soil compaction, improve ride quality, and reduce tire wear.

All of this research is summarized in the 2008 Distinguished Lecture published by the American Society of Agricultural and Biological Engineers.

We think this was one of the earliest industrial applications of Mathematica. It played a key role in supporting research that led to fundamental changes in how to configure and adjust tractors used by farmers worldwide.