What was Masada's Roman ramp steep angle?
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Alex points out in comments that a machine may be transported in sections, and this was apparently the intent here. A 19th century article in the Cyclopædia of Biblical, Theological, and Ecclesiastical Literature, Volume 12 By John McClintock, James Strong, concerning this construction has this to say (emphasis mine):
The second path on the west ascends from a narrow sloping bank of white marl which is about 1000 feet high and which Josephus calls the White Promontory upon this rises the great ramp about 300 feet high which the Romans piled up against the rock during the siege, a work so laborious that it seems almost incredible that human efforts could have accomplished it in so short a time. At the top of the ramp is the masonry wall which the besiegers built as a foundation for their engines before discovering the great tragedy that had been enacted within the fortress where the garrison had fallen by one another's swords
So the seige machinery was to be constructed at the top of the ramp, not pulled up the ramp itself.
Note: If you are still interested in some more recent information concerning this siege, a more recent publication which has some good discussion is Making History: Josephus And Historical Method edited by Zuleika Rodgers. (This lists several sources of other articles discussing the ramp, most of which are modern publications so aren't falling into the viewable category on Google books.) This article does provide some good dimensions for a different ramp, one built by Caesar, which was 23.5 meters high, 97 meters in length and 50 meters wide. You might use this as a comparison for your calculations.
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