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Rescue Physics SALT LAKE COUNTY S H E R I F F ’ S O F F I C E SEARCH RESCUE Force Units and Strength of Components Strength of Anchors Basic Statics The T-Method and Haul System Forces Vectors Highlines, Anchors, Direction Changes, Rope Loads and Slopes Friction This presentation can be downloaded at http://www.xmission.com/~tmoyer/testinghttp://www.xmission.com/~tmoyer/testing (© Tom Moyer except where noted) Many images in this presentation were generated with RescueRigger (rescuerigger.com)

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Strength of Components Tree: Bombproof? Webbing: 4,000 lb per strand - knot Carabiners: 23 kN = 5,200 lb Brake Bar Rack: 44 kN = 10,000 lb Rope: 29 kN = 6,500 lb new (~4,500 lb with knot) Pulleys: 36 kN = 8,100 lb Litter end-to-end: 18 kN = 4,100 lb

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Safety Factors and Forces Anchors should be able to hold rescue loads with “sufficient” safety factor –Rescue load = 1000 lb “Sufficient” safety factor –NFPA says 15:1 –Some people say 10:1 –Some people say 4:1 Know the forces, know the equipment What is the safety factor used in the design of this airplane?

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Force Units 1 Newton (=.22 lb = 3.6 oz) 1 kiloNewton (=1000 N = 225 lb)

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23 Dans: 23 kN = 5,200 lb 90% of a Hummer: 26 kN each = 5,800 lb 1 Carabiner equals 1.5 Subarus: 15 kN each = 3,400 lb

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Rescue Loads Which Situation has higher load?

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35° Rescue Loads Which Situation has higher load? 1000 lb load

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Tied: 2 x 4000 lb x 2/3 ≈ 5,300 lb Wrap 3 Pull 2: 4 x 4000 lb ≈ 16,000 lb No Knot: Rope strength (6,500 lb) Girth Hitch: 2 x 4,000 lb ≈ 8,000 lb Strength of Anchors

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Statics Rule #1: Every action has an equal and opposite reaction.

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Statics Rule #2: Draw a box around any piece of the system. Replace anything you cut with force vectors. Rule #3: If the system is static, the vectors have to add to zero.

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Statics Does this system... differ from this one? 10 lbs

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Statics The rope tension is the same in both systems 10 lbs

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The T-Method Any box you draw has to be balanced. 2 pounds in = 2 pounds out. 1 lb 2 lbs

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Start at the haul rope with 1 lb pull. Trace the rope through the system and find the tension at each point. 1 lb tension 3 lbs tension 2 lbs tension 1 lb tension 1 lb pull The T-Method

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Vectors have a magnitude and a direction. Vectors are added graphically. Arrow lengths represent the magnitude of the forces. Force arrows can be moved around as needed. Vectors a c a + b = c a b a + b = 0 static a b c a + b + c = 0 static b

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1 lb Vectors 1 lb a b Pythagorean theorem: c 2 = a 2 + b 2 c 2 = 1 + 1 c ≈ 1.4 c Useful Trigonometry: Sin θ = b / c Cos θ = a / c Tan θ = b / a θ

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90 deg Direction Change Forces 1,000 lb rescue load Which tree is supporting the largest force? 1,000 lb Pulley Forces: 1,000 lb 1,400 lb

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Internal Anchor Forces 1,000 lb rescue load cos(30º) = 500 lb / T T*cos(30º) = 500 lb T = 577 lb 1,000 lb Carabiner Forces: T 1,000 lb T 30º 60 deg

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35° Litter Team Forces sin(35º) = T / 7 kN T = 7 kN*sin(35º) T = 4.0 kN = 900 lb Litter Team Forces: 7 kN T T 35º

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120 deg Highline Forces 1 kN load cos(60º) = 500N / T T*cos(60º) = 500N T = 1 kN Pulley Forces: T 1 kN T 60º T T

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W (weight) L (length) S (sag) More Highline Forces T / (W/2) ≈ (L/2) / S T ≈ (W/2) * (L/2) /S T ≈ W * (L / 4S) T W T W W/2 ≈L/2 S T T T Pulley Forces: Similar Triangles:

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W (weight) L (length) S (sag) More Highline Forces T ≈ W * (L / 4S) Example: L = 200 ft S = 10 ft Multiplier = 200 / (4 * 10) = 5 If W = 200 lbs, then T = 5 x 200 lbs = 1000 lbs

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Active Highline Forces Highline Tension ≈ 50 lbs x (number of haulers) x MA As shown here, T ≈ 50 x 3 x 3 = 450 lbs Some teams talk about a “rule of 12” Haulers x MA must be less than 12. This is equivalent to a 600 lb working load limit.

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Which rope has more friction? © Steve Attaway

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Friction from a Belt © Steve Attaway

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Exponential Function of Friction and Contact Angle © Steve Attaway

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Useful Friction Approximations 180º on carabiner T 2 /T 1 = 2 90º on rock T 2 /T 1 = 2 Tension increases if hauling. Tension decreases if lowering. What is T 2 / T 1 for a 180º change on rock? For 360º?

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Friction Example T 1 = 600 lbs T 2 = T 1 e T 3 = T 2 e = /4 Force in rope © Steve Attaway

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Which rope has more friction? Rope 1 Rope 2 Rope 3 Rope 3 has the greatest change in angle Rope 1 has the smallest change in angle Rope 3 has the most friction © Steve Attaway

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2 cos ( ) θ 2 200 lbs 0° 100 lbs 200 lbs 90° 141 lbs 200 lbs 120° 200 lbs 200 lbs 45° 108 lbs 150° 200 lbs 386 lbs t = L L = load suspended from the anchors.

2 cos ( ) θ 2 200 lbs 0° 100 lbs 200 lbs 90° 141 lbs 200 lbs 120° 200 lbs 200 lbs 45° 108 lbs 150° 200 lbs 386 lbs t = L L = load suspended from the anchors.

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