Normal Tension for a Suspended Steel Tape
The pull that makes taping-corrections unnecessary. Stretch the tape harder and it lengthens; let it hang and its own weight shortens the span. At exactly one pull those cancel and the tape reads true with no arithmetic. Setting the two corrections equal and substituting the span weight W = w L removes the length from both sides and leaves P^2 (P - P0) = A E W^2 / 24 -- whose square root is the textbook P = 0.204 W sqrt(A E) / sqrt(P - P0), because 0.204 is just 1 over the square root of 24. A 100 ft tape weighing 0.02 lb/ft, 0.006 sq in in section, standardized at 10 lb, wants 34.4 lb; pull the usual 20 lb instead and the span reads 0.036 ft LONG. Also shows the residual at whatever pull you actually used. Normal tension can exceed a practical or rated pull, and a fully supported tape has no sag to cancel.
Formula and source
set the tension correction equal and opposite to the sag correction, (P - P0) L / (A E) = w^2 L^3 / (24 P^2); substituting the span weight W = w L eliminates L and gives P^2 (P - P0) = A E W^2 / 24, solved by bisection. Square-rooting the same relation gives the textbook implicit form P = 0.204 W sqrt(A E) / sqrt(P - P0), where 0.204 = 1/sqrt(24).
Normal tension as defined in the standard surveying references (Ghilani/Wolf, Elementary Surveying), by name. The component corrections are the same tension and sag expressions the taping-corrections tile uses, so the two tiles cannot drift.
Audience
This tile is built for trades and the adjacent professions in the Field, Backcountry, and SAR group. The interactive calculator runs entirely in your browser. No account, no fee, no advertising, no tracking.
Related tools
Posture
Rough Logic answers the math question the working professional asks on the job. The site is a calm, fast, ad-free, account-free, ever-free reference. It does not interpret code. It does not replace the licensed professional. It does not store your inputs. The Authority Having Jurisdiction governs all installations and inspections.