How to measure product of inertia?Product of inertia can be measured directly by using a vertical two plane spin balance machine (POI series). Spin balance machines spin the payload about a desired axis and detect any unbalances generated. This is by far the most accurate method of determining product of inertia. But some payloads cannot be spun (some satellites for example), or cannot be spun about all axes (missiles for example). For these payloads, product of inertia can be calculated from moment of inertia measurements (which do not require spinning). Three moment of inertia measurements per plane are required, at widely spaced angles (ideally 0, 45, and 90 degrees). Some moment of inertia measurements can be used in several orthogonal planes, so a total of only 6 measurements is required to get product of inertia in 3 planes. Product of inertia is directly related to these moment of inertia measurements.
How accurate is this method?Calculating product of inertia based on moment of inertia measurements is not as accurate a method as directly measuring product of inertia by spinning the payload. Accuracy of this method depends on several factors, including:
- Accuracy of the moment of inertia measurement instrument used
- Angles used between measurements
- Payload characteristics (payloads with large products of inertia will be easier to measure)