What is the formula for calculating the center of balance?

The formula for calculating the center of balance is indeed (w1 x d1) + (w2 x d2) / gross weight because it takes into account both the weights and their respective distances from a reference point. In this formula, w1 and w2 represent the weights of the objects being balanced, while d1 and d2 denote their distances from the reference point or pivot. The result of this calculation gives the moment created by each weight, which is essential in determining the overall center of balance of a system.

By dividing the total of these moments by the gross weight, you are effectively finding the weighted average distance from the pivot, thereby determining the center of balance accurately. This calculation is foundational in ensuring stability and safety in various applications, such as in vehicle loading and in military operations where balance is crucial for maneuverability and effectiveness.

The other options do not provide the correct method for calculating the center of balance because they either omit critical factors or do not use the proper relationships needed to accurately assess balance.