**Simple Pulley Forces Tension and eTCL demo example calculator, numerical analysis ** This page is under development. Comments are welcome, but please load any comments in the comments section at the bottom of the page. Please include your wiki MONIKER in your comment with the same courtesy that I will give you. Its very hard to reply reasonably without some background of the correspondent. Thanks,[gold] ---- <> ***Preface*** ***Introduction*** [gold] Here are some TCL calculations for the Simple Pulley Forces and Tension. The impetus for these calculations was checking the loads, rope tension forces, and developing safety flags on a simple pulley system for industry. Most of the testcases involve replicas or models, using assumptions and rules of thumb. The output units can be changed in the internal calculator formulas as TCL code. Any convenient and consistent output units might be used like millimeters, inches, feet, or dollars to donuts. ---- *** Simple Pulley Tension*** The TCL calculator uses metric units as best understood. But to readers outside the USA and using the more rational metric system, the original problem sets in older college textbook(s) and even the current USA manufacturing standards on nylon rope use English units as pounds and feet. The calculations cover an angle from zero to 90 degrees on a simple pulley system and nylon rope. As a peg point, any bending of the nylon rope over a pulley, house beam, or tree branch reduces the strength of the rope to some extent. As a rule of thumb, the bending of a rope can reduce the rope load strength to as much as 25 percent of rated maximum load. The customary half inch nylon rope has a breakage limit of 5000 pounds for unbent rope and the normal safety ratio is 5:1. for industry only Meaning the theoretical safe load limit on the nylon rope is , 1000 pounds force, 454 kilograms (f/g)., or 4.5E3 newtons. The normal safety ratio is 5:1 for industry, but the entertainment industry or stage has much more strict standards with a 10:1 safety ratio. .From the manufacturer rope standards, a load of 1000 pounds is approaching the safe working load (SWL) or maximum working load of simple pulley systems using half inch nylon rope, either as a dead weight or considering the angle force multiplication factor. The simple pulley hung on top of pole (crane) , house beam, or tree branch is at center of three forces as the top point or apex of a right triangle. The mass is strung on a vertical rope directly under the simple pulley. The calculator uses the height of the pulley above ground or floor and the horizontal distance to the puller to calculate Angle2 and the force vectors in a plane. The rope tension is usually measured or referenced to the rope tie above the pulley. Sum of forces acting on pulley point derives as Rope tension force = sqrt (2*cos(Angle2)*F2**2 + 2*F1**2). Angle1 is the look angle between height (|) and horizontal (_) , opposite altitude leg. The second Force F2 is acting through Angle2, which gives the cos(Angle2) factor in the equation for sum of forces. Angle2 is at pulley, between height (|) and hypotenuse (\). Further, Angle2 is called the stress angle opposite horizontal leg. In the program. the allowed range of Angle2 equals zero to ninety, 0-90 degs. While the TCL calculator screens use metric units, the problem set up is similar for the force vectors and relative mass-force units as pounds. For English pounds, enter pounds in mass slot and relative vectors in feet and the approximate tension in pounds should appear in check answer window. Most pulleys and nylon ropes come with recommended safe loads from the manufacturer. The calculator problem set up assumes the same strength rope is used for all tie points. But it is clear that a reinforced tie or metal chain attachment above and retaining the pulley would be more secure in most situations. Wire rope clips, metal clamps, chain hoist hooks, and double saddle clamps are used to secure heavy loads as more secure than rope knots. Needless to say, the horizontal distance from the load to the puller has a safety aspect also. A person standing under a suspended heavy load or within the drop or fall distance is not safe. Probably, any horizontal distance for an involved human puller or involved workers should be greater than the 1.5 times height of the package lift distance or pulley height. The operational safety radius for non-involved persons and marking the safety zone with orange cones is generally 2 times the pulley height, as a rule of thumb. ---- ***Load Warning Flags in Program*** A safety warning flag or program error condition is suitable in the TCL calculator if any entered mass or set of problem angles goes over the safe load limit for the nylon rope. The warning flags for loads are " WARNING, mass entry exceeds safe limit" and " WARNING, estimated load exceeds safe limit". Also, any calculated Angle2 outside the 0-90 degree range is flagged as an error. The warning flags for excessive mass entries and calculated loads are catastrophic errors and the calculated load warning flags are given priority in the program over other possible errors. The warning flags are set separately in the program, so single or multiple warning flags are possible. Still checking program with hand calc. Report will include null flags, as issues for program development. If an error is fired as text in the check answer slot and locks from the expected number (variable type) in the TCL program, three paths are possible as either 1) set check slot back to zero to continue, 2) clear, or 3) restart. As an alternate procedure, resetting the check entry slot back to zero (0), will allow user to continue lowering load until safe limit is found. Current safety regulations for industry use establish a separate operational or working safety zone for involved personnel in the hoist operation and a second safety zone for the non-involved personnel and general public. The radius of danger or boundary for the operational working zone for involved personnel is set at 1.5X altitude. During the lift operation, the involved personnel should keep a distance of at least 1.5X altitude from the center of the hoist operation and the overhead load. The radius of danger or boundary safety zone for non-involved personnel, general public, and orange cones is set at 2X altitude. As a concept, the operational working zone for involved personnel is similar to a donot or concentric hollow core between the radius of the working boundary and the non-involved boundary. These working and safety zones are included in the report. The normal safe working load (SWL) is 5:1 for industry, but the entertainment industry or stage has much more strict standards with a 10:1 safety ratio, safe working load. This calculator was designed for industry;do not use this calculator for the entertainment or stage industry. Many countries, regions, and industries have different or updated standards for the SWL ratios and dimensions of the worker safety zones, so check your country, local authority, and company regs for the current updates. However, all the available textbook vector problems do not consider safety zones and a possible (if range) error condition would fire every time on the gui screen. ---- ***Push Button Operation*** For the push buttons, the recommended procedure is push a testcase and fill frame, change first three entries etc, push solve, and then push report. Report allows copy and paste from console. For testcases in a computer session, the TCL calculator increments a new testcase number internally, eg. TC(1), TC(2)., TC(3), TC(4) etc. The testcase number is internal to the calculator and will not be printed until the report button is pushed for the current result numbers. The current result numbers will be cleared on the next solve button. #####)))))))) Contribu ---- ***Testcases Section*** **** Testcase 1 **** ---- **** Testcase 2 **** --- **** Testcase 3 **** ---- **** Testcase 4a **** ---- ---- ***Screenshots Section*** ****figure 1.**** [Babylonian Combined Market Rates png page 1] ---- ***References:*** * Mathematical Treasure ---- ***Pseudocode & Equations Section*** ====== Western trapezoid formulas and trapezoidal prism volume following includes algebraic expressions, terms, and notation not used on tablets ====== ---- **Appendix Code** ***appendix TCL programs and scripts *** ====== ====== ---- ---- [gold] This page is copyrighted under the TCL/TK license terms, [http://tcl.tk/software/tcltk/license.html%|%this license]. **Comments Section** <> Please place any comments here, Thanks. ---- <> Numerical Analysis | Toys | Calculator | Mathematics| Example| Toys and Games | Games | Application | GUI