From the manual:
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Illustrations included in this section are for a general visual understanding of the FIRST STRONGHOLD ARENA, and dimensions included in the manual are nominal. Please refer to the official drawings for exact dimensions, tolerances, and construction details.
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Obvious disclaimer, so take what's below from the manual with a greater or lesser degree of skepticism:
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The BATTER is a series of seven (7) ramps with two (2) dividers that create the base of the TOWER. Ramps are 6-8 deg. inclines. The ramps directly in front of the low GOALS are 2 ft. wide and 4 ft. deep.
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A RUNG is a bar mounted on a TOWER face that is 1 ft. 9 in. wide and constructed of 1-1/2” Steel DOM Tubing. Each TOWER has three (3) RUNGS, one on each face of the TOWER, designed to support SCALING robots. The top of the rung is 6 ft. 4in. from the FIELD carpet. The RUNGS protrude 5-1/4 in. from the face of the TOWER.
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So, the manual states that the top of the ring is 76" above the carpet, and the top of the batter is higher than the carpet. Used as a logical check, it would seem that your calculations may be off a little. Also, it's important to note exactly where you are measuring to - the top, middle, or bottom of the rung.