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• You might also take a look at a second calculator based on experiments by UR5EAZ at the end of this website Stacking Formula acc. DL6WU • W = wave length [m] • c = Speed of light in vacuum (299,792,458 m/s) • f = Frequency[Hz] • D = Stacking Distance [m] • B = 3 dB Beam Width = Half Power Beam Width (HPBW) From what boom length on is it valid? The 6WU stacking formula is said to give valid results from a boom length of 2wL on. Why so? Because DL6WU measured on 1296 MHz Yagis and the shortest one he published just had 10 elements. As time goes by the radio amateur community takes this number as given and there we have it! However, when investigating stacking Yagis below 2wL with 4nec2 or EZNEC we find that • Yagis Eplane: the formula gives a very close approximation from about 0.7 wL of boom length • Yagis Hplane: the formula tends to produce too close spacing by approx. 0.1 wL for Yagis less than 2 wL of boom length
What gain to expect? Increase in gain due to stacking to double number of Yagis in either plane with distances according this formula results in measured max. extra gain of 2.9 dB (cable and transformation losses excluded). Here Peter V. Viezbicke and DL6WU give same number. Their measurement charts look similar too. Here is an original chart, drawn by the hand of the very Günter Hoch himself Source: by courtesy of DL6WU • xaxis is stacking distance D/λ what means distance quoted in wave length; yaxis is resulting gain in dB • The chart line marked '+' is his NEC simulation, the one marked 'o' the measurement results • The vertical line named Dopt is the stacking distance his formula delivers • Φ is the Yagis 3 dB Beam Width. Discussion As there are quite differning designs with varying side and rear lobe levels the DL6WU formula can not serve all right to full extend and all occasions. As nothing but the main beams 3 dB width is ingoing nothing else counts here. Nevertheless Dopt rightly suggests optimum distance as a compromise between extra gain and increase of side lobes i.e. noise level for very most of designs. When optimising a stack to the max the DL6WU formula can not always deliver on the last quantum. Here we use NEC and TANT in combination to find best match for whatever goal we have put up. For best reception sufficiently low Antenna Temperature of the stack or mostly best G/T are recommended. The weighing between both much depends on the local noise level. For hardest punch of our TX signal slight over stacking i.e using up to 10 ... 15% larger stacking distances then the 6WU formula suggests may be a good choice. Literature Those who want to learn more about stacking and its optimation may find further details here. The issues of the Dubus magazine can all be ordered as single issues, it does not take the annual abonnement for this My Articles on Stacking in DubusMagazines Stacking beyond DL6WU  Part 1 Basics like phase shift in the YagiUda Antenna, pattern qualification for various stacking goals, background on DL6WU formula and analogy to Wave Optics. Pictured explainations on Effective Apertur Area in context to stacking and more Dubus 4/2013 & Dubus Technik XIII Stacking beyond DL6WU  Part 2 Diamond Stacking compared to DL6WU by normalised effective aperture areas (with Slobodan Bukvic, YU7XL), an introduction to phase shifted stacking schemes, Phased Arrays, Stagger Stacking in pairs and larger groups with explicite notes on how to feed such systems Dubus 1/2014 & Dubus Technik XIII Stacking beyond DL6WU  Part 3 Antenna G/T wise advantages of vertical 4 or 6 Yagi stacks on UHF against common Hframe arrangements for extraterrestrial communication Dubus 3/2014 On the Internet online TANT Appendix How to build a 4 Yagi array in NEC in compliance with the VE7BQH G/T Table (with VE7BQH) plus a detailed view on all parameters in the G/T Table For download as PDF at EA6VQ's www.DXMAPS.com 9/2011 What to use? 3 dB Half Power Beam Width taken from simulation or real pattern plots? In case you have a test range and suitable equipment to measure your pattern to an accuracy better 1 degree you might consider using measured 3 dB angle values instead of simulated values. While semi professional real world pattern plotting (1, 2) show a good coincidence between simulated pattern and measured pattern it might be better to verify the real Yagi including all challenges for building like boom correction issues, presence of parts, pole, mast clamp, strut ... . Which apparently leads to a more realistic stacking distance in case you cam measure 3 dB points very accurate. (1) http://www.nitehawk.com/sm5bsz/oland/index.htm (2) http://dg7ybn.de/technical/Radiation_Pattern_Measurements.htm#Real_World_Plot_2x_GTV_2_14w See the other stacking distance calculator further down. Which is based on a formula given by Vladimir, UR5EAZ that adds to the Dl6WU formula. In this you may enter either simulated or measured Eplanes 3 dB HPBW. How to link from your website to the "app" The "app" as a link will appear where you have placed it on your site. Clicking it will make your website contact my webserver and open the "app" just similar to doing that from this site. But please keep in mind that Javascript must be activated on the client side for this. Every client i.e. internet user is self responsible for appropriate browser security settings and up to date anti virus checks etc. on his/her PC. No guarantee is given, whatsoever, use these lines at your own risk UR5EAZ Stacking Distance Calculator for YagiUda Antennas You might consider using Eplane 3dB HBPW angle measured on real Yagi in this calculator. Length is electrically effective length of the Yagi in meters Whats behind this calculator? Hplane angle is derived from electrical length L and Eplane angle as follows: Hplane angle = Eplane angle * (1 + 0.25 * λ / L) as per UR5EAZ From there on the computation follows the well known DL6WU formula as shown above. This formula is derived and contributed by Vladimir, UR5EAZ. Tnx! Click to open as " app " in a small browser window How to link from your website to this "app" The "app" as a link will appear where you have placed it on your site. Clicking it will make your website contact my webserver and open the "app" just similar to doing that from this site. But please keep in mind that Javascript must be activated on the client side for this. Every client i.e. internet user is self responsible for appropriate browser security settings and up to date anti virus checks etc. on his/her PC. No guarantee is given, whatsoever, use these lines at your own risk 73, Hartmut, DG7YBN 