takoteur

Evaluation of the elevation of a kite is often a major consideration to the kiter and to the kaper. There are two dimensions that it is possible to know more or less accurately: the length of line and the elevation angle. The elevation angle is measured with a compound of protractor and plumb line which is also named an astrolabe. The length of line is better estimated when there are regular marks on the line, for example every 50m. The base is the ground distance TN between anchoring and the vertical line KN from the kite. The elevation angle is named KTN or beta.		A home made astrolabe
HYPOTHENUSE CALCULATION Once length of line and angle are known, a simple trigonometric calculation will give an estimate of the elevation and of the kite base. The hypothenuse is TK in the triangle TNK. A simple formula: Elevation = length of line x sin (elevation angle) KN = KT x sin KTN Calculation for 100m line length and elevation angle 65° gives 90.6m as calculated elevation.
		THE LINE IS CURVED Some kiters are guessing that this is too much approximate because the line is curved. In fact it is difficult to know exactly the true curve of the line. I have observed that there are two angles which could be measured with the astrolabe and give a better clue of the curve of the line. These are the line angle "alpha" at the anchoring place and the line angle "gamma"at the bridle. With these angles I have been able to define new calculation methods which provide more close results. Another consideration should be the elongation of the line under tension which is ranging from 1% to 5% depending on the line and the stress.
LUCANE 72 METHOD This method was published in Le Lucane magazine n° 72 of the Cerf-Volant Club de France in June 1995. Its principle is that the true elevation KN of the curved line TSK is between the line considered as straight TM (elevation MW) and the line considered as two segments TJ and JC (elevation CV). The formula is that the elevation is the average between the two extreme elevations. The result is not too bad. The comparison with other methods shows that shifting a little the average would give a more accurate result. This method shows that the two extreme elevations are in fact not much different. Calculation as for the hypothenuse and alpha = 55° gives a calculated elevation of 88,9m
THE SEGMENTS METHOD This method is considering the line as two segments which are defined from the line angles at the anchor and at the bridle. As seen on the drawing, the calculated elevation is always lower than the true elevation. However the accuracy is fair when the line is moderately curved. Calculation as previous example , 100m length line, kite elevation angle beta = 65°, line angle at anchor alpha = 55° and line angle at bridle gamma = 70° gives a calculated kite elevation of 89,9 m.
THE ARC METHOD This method is also based on the angles of the line at the anchor and at the bridle. now the line is considered as a circle which is tangent to the line at the anchor and at the bridle. It seems that it is the draw which is the closer to the true curve of the line. As with the same examples than other methods, the calculated elevation is 90,2 m. It is interesting to remark that apart the hypothenuse method which is also the maximum elevation with a line absolutely straight, the calculated elevation of the arc method is the highest value in this example. If the Lucane method was set as the average of the hypothenuse and the segment method, as maximum and minimum elevation, result would be 90.25m
		CONCLUSION Depending on the curve of the line some methods gives better accurate results than the others. The elongation of the line shall also be considered with line such as polyamide under major stresses.$ In fact it is found from these different formulas that the accuracy of most of them is depending first on the knowledge of the line length and the accuracy of the measures of line angles. This is more than sufficient for kiters and kapers daily routines There is a loadalble calculation file where it is easy to compute it and following methods: takoteur.xls There is another geometric method based on kite elevation angle measured at two places which distance is known. It doesn't give more accurate results. Only if geotagging or photogrammetry of images is done, an accurate elevation is necessary. In this case, an altimeter combined with the camera is the only way to get accurate results if properly used and calibrated