ANALYSIS

The analysis conducted began with the forces required to hold up a 200 lb. mass with a factor of safety of 10 and was then followed through the device in order to find the minimum forces which all parts must be able to sustain. This led to the camming angle that was calculated based on equations that were derived from a much more basic scenario than what will be experienced by the device. These same equations are also used for spring loaded camming devices so the values produced considering a factor of safety on the input coefficient of friction should be acceptable. See appendix A for exact derivations.

Scope of testing and Evaluation:

The scope of testing and evaluation will involve taking the device into a controlled environment where a rope will be ascended using a prusik knot along with the device while the climber is being backed up on another rope or by a third ascending method. The rope will then by inspected after a number of ascents for any visual damage to the rope threads. After this the device will be loaded into the tensile testing machine in order to find the maximum loading at which the device catastrophically fails.

Analysis:

The analysis for the device is described here; each calculation has been given its own description as follows.

1. The first calculations made were a starting point for force the device would be under, the basic loading is taken to be a 200 lb. mass. Here the loading is simply given a factor of safety to account for potential dynamic loadings which are prone to happen to climbing gear. The loadings used for calculations were chosen using standard ratings for climbing gear.

2. The second calculations were a look back at the initial calculations to see how large of an acceleration the body would be under given a five-foot vertical fall from above the device. This showed an acceptable rate of max deceleration given this scenario.

3. Here the physical forces of stopping the rope with friction alone are calculated and steel is used as a material for parts which will be under heavy physical loadings such as the cam and back plate.

4. Calculation 4 mathematically describes the shape of the cam, which must use friction to engage with the rope and cam directionally. Polar coordinates are used due to the nature of the equations.

5. This calculation further describes the exact shape of the engaging half of the cam, which must be of an exact profile based on the equation found for the general profile in A4. This equation will be directly imported or modified to another coordinate system and then imported to solid-works in order to build this part.

6. The forces that are to be placed on the cam to stop the rope will be transferred onto a connecting pin, which is attached to the back plate. The shear force that will be placed on the connecting pin is calculated here.

7. Calculation seven deals with the additional forces of a spring holding the cam in an initial position on the rope. This will cause a frictional force when moving the device up the rope, which will be an additional force to the gravitational force on the device when finding the maximum force to raise the device on a rope.

8. Calculation 8 looks at the spring force and the minimum force it can apply to the cam for the maximum raising force to remain under 5 lb.

9. Calculation nine deals with the forces that the attaching carabiner will put on the back plate under maximum loading conditions.

10. Calculation 10 finds the maximum forces on the pin in order to select a material that can withstand the forces generated under maximum loading given the worst-case scenario for device loading.

11. These calculations go over a material selection and look at the maximum loading before failure given the material selected.

12. Continuation of calculation 11.

Design Issues:

There were several design issues which were encountered, such a primary method of construction used for similar devices being steel which has been worked into unique shapes which act as a single piece for the entire housing for the device. The calculations for such shapes as well as the manufacture would prove challenging so a much more basic design was used in the design calculations which involved more straightforward forces. The second issue in calculations is a lack of publication on the coefficient of static friction for nylon on steel, so for calculations a kinetic coefficient of friction was used.

Calculated Parameters:

Maximum device loading: 2370 under frictional loading only

Polar equation in mm for cam profile: 8.863e^(Pi*0.2)

Best Practices:

While there is no standard for a factor of safety in climbing gear design and manufacture there are standard loadings used to rate devices at their failure loadings, these typically range from 15-22 KN. For this device a rating of 3500 lb. of force was chosen which equates to 15.6 KN. The camming angle was modified to account for some loss of friction due to wet condition or rope treatments. The back plate thickness was a standard thickness of a similar device and of a similar material that will be used. The hole for the carabiner was also of a similar diameter of a device which falls under this category. The factor of safety for climbing devices is built into a standard for the amount of force such devices should fail under, for pieces of climbing protection this loading can be as low as 2 KN while for carabiners it can be as high as 65 KN depending on the material and usage. For belay devices there is no true standard but the devices are approximately rated to 15 KN.