Evaluation Of The Gravitational Constant Using A Conventionial Instrumentation In Biomechanics Research

  • P. Luhtanen
  • H. Mononen
  • A. Salo
  • M. Salonen
  • J. Viitasalo
Keywords: gravitational constant, free fall condition, camera

Abstract

The purpose was to validate the evaluation method of the gravitational constant in free fall conditions using camera recorder unit at frame frequency of 100 Hz with full frames and APAS analysis system with selected smoothing techniques. A 2-D reference frame in the plane of movement was used to calibrate the distance scaling. A reflecting ball was dropped from a height of 1.70 m a dark gray textile as the background. The optical axis of the camera was perpendicularly into the centre of the dropping line which was 17.75 m from the camera. The drops were filmed with and without shutter of the camera. The recordings were digitised in the automatic and manual mode for each full frame starting from 10 frames before releasing. The gravitational constant was calculated using a cubic spline smoothing technique with the values of 1.0 and 0.3. The measurements were repeated in the sets of five drops. An example of the plotted g values in a sample is shown in Figure 1. [figure] Figure 1. A plot of the gravitational constant in a trial respect to the time. Selected characteristics were observed from the curves as follows: 1. extreme value of the g; 2. deviation (-dg and +dg) from the correct value of the g; 3. delay from the release to the value of g ( tl ); 4. delay from the release to the value of (g-dg) ( t2 ); 5. average of the g within the deviation of the -dg and +dg (for t3 ); 6. duration of the g within the deviation of the-dg and +dg .from g ( t3). ANOVA was applied to the selected characteristics in the g curve in respect to the digitising method, utilisation of the shutter and smoothing method. The best average estimation and minimum deviation of g were reached with automatic digitisation, with shutter and 1.0 cubic spline smoothing technique. However, in this case the delay to reach the correct g was the longest and time for the average g was the shortest as compared to all other used analysis combinations. The extreme g values differed from the correct value from 5.2 % to 11.8 %. The worst average value of the g within the deviation of the -dg and +dg from g (for t3 ) differed from the expected 5.4 %. It can be concluded that the instantaneous acceleration is very sensitive to the method of recording. digitising and smoothing techniques.
Section
Equipment / Instrumentation