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Rescue Physics
SALT LAKE COUNTYS 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
• FrictionThis presentation can be downloaded at
http://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 Units1 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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StaticsRule #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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StaticsDoes this system...
differ from this one?
10 lbs
10 lbs 10 lbs
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Statics
The rope tension is the same in both systems
10 lbs 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
1 lb
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
tens
ion
1 lb
tens
ion
3 lb
s ten
sion
2 lb
s ten
sion
1 lb
tens
ion
1 lb
pul
l
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
ac
a + b = c
a b
a + b = 0static
a
b
c
a + b + c = 0static
b
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1 lb
Vectors
1 lb
a
b
Pythagorean theorem:c2 = a2 + b2
c2 = 1 + 1c ≈ 1.4
c
Useful Trigonometry:Sin θ = b / cCos θ = a / cTan 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
1,00
0 lb
Pulley Forces:
1,000 lb
1,00
0 lb1,400 lb
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Internal Anchor Forces
1,000 lbrescue load
cos(30º) = 500 lb / TT*cos(30º) = 500 lbT = 577 lb
1,00
0 lb
Carabiner Forces:
T
1,00
0 lb
T
30º
60 deg
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35°
Litter Team Forces
sin(35º) = T / 7 kNT = 7 kN*sin(35º)T = 4.0 kN = 900 lb
Litter Team Forces:
7 kN
T
7 kN
T
35º
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120 deg
Highline Forces
1 kN load
cos(60º) = 500N / TT*cos(60º) = 500NT = 1 kN
Pulley Forces:
T
1 kN
T
1 kN
60º
T
T
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W (weight)
L (length)
S (sag)
More Highline Forces
T / (W/2) ≈ (L/2) / ST ≈ (W/2) * (L/2) /ST ≈ W * (L / 4S)
T
W
T
W
W/2 ≈L/2 ST
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 ftS = 10 ftMultiplier = 200 / (4 * 10) = 5
If W = 200 lbs, thenT = 5 x 200 lbs = 1000 lbs
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Active Highline Forces
Highline Tension ≈ 50 lbs x (number of haulers) x MAAs 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
020406080
100120140160
0 1 2 3 4 5
Friction times Contact Angle
Ten
tion
Rat
io
© Steve Attaway
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Useful Friction Approximations
180º on carabinerT2/T1 = 2
90º on rockT2/T1 = 2
Tension increases if hauling. Tension decreases if lowering.
What is T2/T1 for a 180º change on rock? For 360º?
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Friction Example
T1 = 600 lbs
T2 = T1 eµβ
T3 = T2 eµβ
β = π/4
β = π/4
0
500
1000
1500
T1 T2 T3 T4
friction =.25friction =.35friction =.45
Forc
e in
rop e
© 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 smallestchange in angle
Rope 3 has the most friction
© Steve Attaway