1. Objectives: To use angle knowledge to solve problems that the Coastguard face To apply trigonometry to work out loads and tensions To solve problems with friction Mechanics lesson SaRmechanics.lgfl.net

2. Search and Rescue – sar.lgfl.net© 2016 London Grid for Learningsar.lgfl.net Job Requirements Maths required: Angle facts Trigonometry Exponential calculations Using radian measure Converting units Equipment required: Protractor Ruler Pencil Pen Rubber Calculator

3. Search and Rescue – sar.lgfl.net© 2016 London Grid for Learningsar.lgfl.net Videos Introduction to Coastguard rescue teams What Maths is involved in rescue systems? Bridle rope arrangement Rope friction - tensionless hitch 1

4. Search and Rescue – sar.lgfl.net© 2016 London Grid for Learningsar.lgfl.net Bridle ropes Watch this video: Bridle rope arrangementBridle rope arrangement 1000kg This angle affects the load on these lengths of rope

5. Search and Rescue – sar.lgfl.net© 2016 London Grid for Learningsar.lgfl.net Bridle ropes You can use trigonometry to find the loads. 1000kg If you measure the angle at the connection, you can work out the angles where the rope is connected to the load as you have an isosceles triangle. 30 o 75 o

6. Search and Rescue – sar.lgfl.net© 2016 London Grid for Learningsar.lgfl.net Bridle ropes You can use trigonometry to find the loads. 1000kg 75 o The 1000kg weight is distributed between the two ropes. You can use trigonometry or a conversion table to find the tension put on each rope. 500kg

7. Search and Rescue – sar.lgfl.net© 2016 London Grid for Learningsar.lgfl.net Bridle ropes You can use trigonometry to find the loads. 1000kg 75 o To find the tension on the hypotenuse, we use trigonometry: Hyp = Adj / cos(θ) = 500 / cos(15) = 518kg 500kg 15 o Hyp Adj

8. Search and Rescue – sar.lgfl.net© 2016 London Grid for Learningsar.lgfl.net Bridle ropes You can use trigonometry to find the loads. 1000kg 75 o By finding out the angle, we can work out the tension on each rope. Or, if we know the tension limit, we could work out the minimum angle. 518kg 30 o 75 o

9. Search and Rescue – sar.lgfl.net© 2016 London Grid for Learningsar.lgfl.net Table of factors (no trigonometry) Sling angle You can use the factors in this table to divide your load and find the tension on the ropes.

10. Search and Rescue – sar.lgfl.net© 2016 London Grid for Learningsar.lgfl.net Tensionless hitch Watch this video: Rope friction - tensionless hitch 1Rope friction - tensionless hitch 1 A tensionless hitch harnesses the power of friction around an object to create a very strong holdfast. You can use the Capstan equation to calculate the hold tension (T hold ) required for any load tension (T load ) using the friction coefficient ( μ ) and the total angle of turns around the object ( θ - measured in radians). T load = T hold e μθ

11. Search and Rescue – sar.lgfl.net© 2016 London Grid for Learningsar.lgfl.net Capstan equation table T load = T hold e μθ T: tensione: eμ: coefficient of friction θ: total angle made by rope (radians)2π radians = 1 full turn No of turns Coefficient of friction μ 0.10.20.30.40.50.60.7 11.93.56.612234381 23.5124315253518816661 36.64328618811239281612437503 412152188123228286751354002643702631 5235351239228675166356241535529353553321281

12. Search and Rescue – sar.lgfl.net© 2016 London Grid for Learningsar.lgfl.net Rope strength 1kg = 9.81N = 0.00981kN 1kN ≈ 102kg Rope Diameter Minimum Breaking Strength Safe Load (Safety Factor 12)Weight (in)(mm)(lbf)(kN)(lbf)(kN)(lbm/ft)(kg/m) 3/1658803.9173.30.3260.0090.013 1/4614866.611240.5510.0160.023 5/168229510.21910.8510.0250.036 3/810324014.42701.20.0360.053 7/1611432019.23601.60.0480.071 1/212567025.24732.10.0630.094 9/16147200326002.670.080.119 5/816891039.67433.30.0990.147 3/4181278056.810704.760.1430.213