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VOACAP will provide the take off angle, right down the the minute of the day.
Run VOACAP, determine when you plan to make comms, then look at the radiation angle chart. Then determine the FOT for each planned window and the take off angle for the time of the window and plug them into the antenna modeling portion of VOACAP. You will have to play around with the lengths, heights, etc, in the software, but it will get real close. Build your antenna as close to the specs that the software modeled.
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