# Time to Capture a Moving Target Travelling along a Circular Trajectory
## 4 Discussion  
In the case of selecting a target moving along a circular trajectory with a computer mouse, if the moving speed of the target was constant, the time to select a target was inversely proportional to the width of the target and changed in proportional to the distance between the target and the starting point, as in the traditional Fitts' law. These results were similar to the results in the experiment of clicking a target moving in a straight line using a joystick [15]. It suggests that although the target is moving, if it is moving at the same speed, the target selection time is well explained by the traditional Fitts' law.  
However, there was a research question of how to represent the time for selecting targets moving at different speeds with a single model. [PERSON] (1991) set the speed of a moving target as a variable, and included this variable in the modified Fitts' Law. If this model is applied to the case of selecting a target moving along a circular trajectory, increasing the target speed has the effect of reducing the target width. Consequently, the model that best fits the collected data should be determined when the value of K is positive. Also, increasing the speed of a moving target should increase the time it takes to click the target.  
However, the result of this experiment showed that the optimal K value was negative, and as the speed increased, the time to click the target decreased. This result was inconsistent with the assumptions of the [PERSON] model. [PERSON]'s (1991) model described that when clicking on a moving target, clicking on a fast-moving target was more difficult than clicking on a stationary target or slow-moving targets. He might not take in account the subjects' tendency to speed up the movement of the mouse in order to click on the moving target. Comparing the target selection error data and the target selection time data simultaneously, when the speed of the moving target more increases, the number of click errors increases and the click time tends to be decreased. That is, it can be said that the subjects increased the mouse movement speed while sacrificing the accuracy of clicking the target.  
On the other hand, when \(K\) value of proposed model was very high, the movement speed of the target had no effect on the target selection time. That is, in this case, the [PERSON] model proposed in this paper approaches to the traditional Fitts' model. The degree of [PERSON] model fits was 0.9029, even in the case where the speed of the moving target did not affect the target selection time. Even though the target movement speed was not included in the model, it is a very high value that the coefficient of determination is more than 0.9. This result might be due to confounding factors. [PERSON] et al. [16] argued that the high \(R^{2}\) between the difficulty index (ID) and the mean travel time (MT) is due to the strong confounding between the travel distance (\(A\)) and the difficulty index (ID). Anyway, in this study, a more suitable model was found by considering the speed of the moving target as an additional variable. The fit of the model was higher than when the target speed was not considered (\(R^{2}\) = 0.9137). However, unexpectedly, the optimal \(K\) value that gave the best model fit was negative.  
A negative optimal \(K\) value may not mean that when subjects click a target, they use an effective target width that is wider than the actual target width. This can be caused by the human reaction tendency to quickly click on the target, which is affected by the speed of the moving target. In the future, more sophisticated models should be developed to include the tendency of humans to react to moving targets.