Quantitative Evaluation of Effect of Gravity on Small-Scale Modeling

In many cases, small-scale modeling requires the scaling up of the gravitational acceleration. Yet this requirement sets a technical problem, and unless the use of a centrifuge is available, it is not fulfilled. Consequently there is a distortion in the extrapolated results of the small-scale model, which lacks scaling of gravity. So far, the extent of the effect of gravity scaling on the extrapolated results has been speculated. A quantitative way to evaluate this effect is suggested here. An expression for the distortion in the extrapolation of a measured model variable is developed, based on similitude requirements. This expression depends on the geometrical scaling factor, and on the ratio of a variable measured model value to the value of its gravitational component. It shows that for geometrical scaling factors of 10 and 50, the distortion is less than 10% when the gravitational component of the variable is less than 1% and ∼0.2%, respectively.