Boring Bar Max Overhang for a Deflection Limit
The inverse of the boring-bar-deflection tile: the longest a bar can stick out before its tip deflection reaches the allowable, L_max = (3 E I x deflection / F)^(1/3) with I = pi d^4/64. A 0.75 in steel bar under 100 lb held to 15 mil can reach 6.0 in (L/d 8); a stiffer carbide bar (90e6) reaches 8.6 in. It also flags the L/d against the chatter limit - if the deflection-limited overhang is past ~4:1 steel / 6-8:1 carbide, chatter governs and the real max is shorter. Answers 'how far can I stick out' instead of the deflection at one length. Static solid-round model. The tool and setup govern.
Formula and source
I = pi d^4/64; L_max = (3 E I delta_allow / F)^(1/3); L/d ratio for chatter risk. (E = 30e6 psi steel, ~90e6 carbide)
The cantilever tip-deflection model delta = F L^3/(3 E I) with I = pi d^4/64 solved for the overhang, a standard mechanics-of-materials result applied to tool overhang, by name.
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