Abstract
The Majority of precise photographic measurements in use today are stereophotogrammetry. Owing to remarkable developments of theories and instruments in this fields, very precise measurements and wide use are possible by means of stereophotogrammery. A single photograph also can be applied under some limited conditions.
Owing to various unfavourable circumstances in engineering investigations, we are sometimes forced to take a photograph of a moving object at a single station. It is, accordingly, necessary to study the posibility and limitation of use of the single photograph. Concerning application of the single photograph to investigate the motion of a boby, theoretical considerations for methods and errors are dealt with in this paper.
As the spatial motialon of a point can be described by the motion of the projected points onto the two projected planes, for example, the image plane (ZX-plane) and the plane (XY-plane) normal to it. The major problem is, in this case, to determine the motion projected onto the XY-plane. Then under the assumption that a object moves on a stra jght line, the motion of the object projected onto the XY-plane is able to be described by the followings:
Equation of the straight line: Y= aX +b (a and b : const.)
Motion on the straight line: s (T) =c1T+c2T2+… (c1, c2, …: const.), in which s is a distance along the straight line and T time.
Even if the photograph were oriented, the motion of the object, as well as the position of the object, could not be perfectly determined by the images on the photograph. However, if some of the factors which describe the motion of the body are known, the remaining factors may be determined by use of the single photograph. For example, when the coordinates of a point on the straight line along which the object move or one of the coefficients c1, c2, … are known, other necessary factors specifying the motion are determined from the coordinates of the several images on the photograph taken at different times.
In the above cases, the unknown coefficient a which refers to the direction of the straight line are obtained from the directions m of the rays which reach the correspooding images from the object. In this method of evaluation of the motion, we should pay attention to that the error in a comes up to ten times as great as that in m when the images used are close to one another on the photograph. The way to decreases the error in a is to use the images which are considerably apart from one another.
