## Air acoustics: acoustic correction (1928 – 1929)

The speed of sound is 340 meters per second at 20 degrees Celsius. The then common military aircraft velocity was between 30 and 110 meters per second. Therefore, the direction in which an aircraft is observed with a listening device is not the direction where it is at that moment.

Van Soest developed a corrector that uses a cylindrical plane table board. A plane table board in use with listening devices is a projection surface on which a route (or flight line) of an aircraft is projected. This is called the flight curve. Based on some observation points, the actual location of an aircraft can be indicated by extrapolation of the flight curve. Van Soest worked out the track equation for the cylindrical plane table board. The plane table board showed along the circle edge of the cylinder the map angle and along the vertical axis the elevation from 0° to 90°. The horizon corresponds to the ground circle of the cylinder, the zenith with the entire top circle.

When depicting a horizontal aircraft flight path, the points on the horizon are at elevation 0 and the passing point closest to the listening device is at the highest elevation. Aircraft flight curves for various elevations are shown on the planchet, this curvature set is based on the formula: tg (e) / tg (e_{p}) = cos (a*a_{p}) where e is the elevation of the target, e_{p} the elevation pass point, a is the chart angle of the target and a_{p} is the map angle of the passing point.

The plane table board is divided into two parts, one for altitudes between 1000 and 2500 meters and the other for altitudes above 2500 meter. In the case of the factory version of the listening device, the acoustical correction device was a rotatable cylinder placed inside a glass cylinder. The listener observes the direction of an aeroplane and puts an ink dot on the glass cylinder at the push of a button. He does this three times in succession. The plane table board cylinder is then rotated by the plane table board reader so that the three observation points (dots on the glass cylinder) fit as well as possible on one of the flight curves. The real position of the aircraft must then be further on the same curve.

The question is how far? Van Soest asked for help by the Leiden astronomer Prof. dr. Willem de Sitter. De Sitter developed together with his assistant mr Gaykema a theory that offered a solution.

The result was a table with extrapolation factors based on the speed of the aircraft, an estimated fixed processing time by the reader, and a factor that was dependent on the altitude of the aircraft. The latter factor is indicated in the plane table board by a letter in the fields that run straight through the flight curves (see correction cylinder figure). If the last observation by the listener falls in the box with for instance E, the E-line of the table is used.

If the last observation is in the area of the example letter E and the estimated flight speed is 60 meters per second, then the correction factor is 5. The setting of this factor is done using a cylindrical curved transparent plate on which a bundle of concentric circles with serial numbers (= correction factors) is shown. This plate was located between the glass cylinder and the cylindrical plane table board and could be moved horizontally and vertically. The reader then places the last observation on the fifth circle while the middle point of the set of concentric circles is aligned with the observed light curve. The middle point then determines the predicted map angle and the elevation which can be read from the mechanically connected rulers.

The puncturing of the ink dots on the glass cylinder of the corrector was later replaced by the continuous writing of the tracking process of the target by the listener with the help of a pen or pencil. The listener had to make small circular movements around the observed target. In this manner, the sound contact was not lost and the target was continuously followed. As a result, a spiral was written on the plane table board. The reader could then set a suitable curve on the plane table board faster.