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In lead climbing using a dynamic rope, the fall factor (''f'') is the ratio of the height (''h'') a climber falls before the climber's rope begins to stretch and the rope length (''L'') available to absorb the energy of the fall. : == Impact force == The impact force is defined as the maximum tension in the rope when a climber falls. Using the common rope model of an undamped harmonic oscillator (HO) the impact force ''Fmax'' in the rope is given by: : where ''mg'' is the climber's weight, ''h'' is the fall height and ''k'' is the spring constant of the rope. Using the elastic modulus ''E'' = ''k L/q'' which is a material constant, the impact force depends only on the fall factor ''f'', i.e. on the ratio ''h/L'', the cross section ''q'' of the rope, and the climber’s weight. The more rope is available, the softer the rope becomes which is just compensating the higher fall energy. The maximum force on the climber is ''Fmax'' reduced by the climber’s weight ''mg''. The above formula can be easily obtained by the law of conservation of energy at the time of maximum tension resp. maximum elongation ''xmax'' of the rope: : Using the HO model to obtain the impact force of real climbing ropes as a function of fall height ''h'' and climber's weight ''mg'', one must know the experimental value for ''E'' of a given rope. However, rope manufacturers give only the rope’s impact force ''F0'' and its static and dynamic elongations that are measured under standard UIAA fall conditions: A fall height ''h0'' of 2 x 2.3 m with an available rope length ''L0'' = 2.6m leads to a fall factor ''f0'' = ''h0/L0'' = 1.77 and a fall velocity ''v0'' = (''2gh0'')1/2 = 9.5 m/s at the end of falling the distance ''h0''. The mass ''m0'' used in the fall is 80 kg. Using these values to eliminate the unknown quantity ''E'' leads to an expression of the impact force as a function of arbitrary fall heights ''h'' and arbitrary fall factors ''f'' of the form:〔Ulrich Leuthäusser (2010):(【引用サイトリンク】title=Viscoelastic theory of climbing ropes )Retrieved December 2, 2010〕 : This simple undamped harmonic oscillator model of a rope, however, cannot explain real ropes. First, it is evident that real ropes hardly oscillate after a fall. After one period the rope has settled and stopped oscillating. The HO also cannot explain correctly the experimental values of a climbing rope such as its static and dynamic elongation and the correct relations to its impact force. This can be corrected only by considering friction in the rope. On the basis of a Viscoelastic Standard Linear Solid model one gets more complicated expressions for impact force and static and dynamic elongations.〔 Friction in the rope leads to energy dissipation and thus to a reduction of the impact force compared to the undamped harmonic oscillator model. It also leads to an additional elongation of the rope. The diagram shows how the impact forces of real climbing ropes under standard UIAA fall conditions relate to their measured dynamic elongations. It also shows that the HO model cannot explain these dependencies of real climbing ropes. When the rope is clipped into several carabiners between the climber and the belayer, an additional type of friction occurs, the so-called dry friction between the rope and particularly the last clipped carabiner. Dry friction leads to an effective rope length smaller than the available length ''L'' and thus increases the impact force.〔Ulrich Leuthäusser (2011):(【引用サイトリンク】title=Physics of climbing ropes: impact forces, fall factors and rope drag )Retrieved January 15, 2011〕 Dry friction is also responsible for the rope drag a climber has to overcome in order to move forward. It can be expressed by an effective mass of the rope that the climber has to pull which is always larger than the rope mass itself. It depends exponentially on the sum of the angles of the direction changes the climber has made.〔 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Fall factor」の詳細全文を読む スポンサード リンク
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