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Elevator - Force and Power

Required force and power to lift an elevator

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Work done by Lifting the Elevator

The work done by lifting an elevator from one level to an other can be expressed as

W = m ag (h1 - h0)                     (1)

where

W = work done (J, ft lbf)

m = mass of elevator and passengers (kg, lbm)

ag = acceleration of gravity (9.81 m/s2, 32.17 ft/s2)

h1 = final elevation (m, ft)

h0 = initial elevation (m, ft)

The generic equation for work done by a force can be expressed as

W = Fc s                      (2)

where

W = work done by force (J, ft lbf)

Fc  = force acting on the elevator at constant speed (N, lbf)

s = distance moved by elevator (m, ft)

Forces acting on the Elevator

Since works done in (1) and (2) are equal - the equations can be combined to 

Fc s = m ag (h1 - h0)              (3)

Force at constant Speed

Since the difference in elevation and the distance moved by the force are equal - (3) can be modified to express the force required to move the elevator at constant speed to

Fc = m ag                      (4)

Force at start/stop

When the elevator starts or stops - the acceleration or deceleration force in addition to the constant speed force can be expressed as

Fa = m (v1 - v0) / ta                   (5)

where

Fa = acceleration force (N, lbf)

v1 = final velocity (m/s, ft/s)

v0 = initial velocity (m/s, ft/s)

ta = start or stop (acceleration) time (s)

Power required to move the Elevator

The power required to move the elevator can be calculated as

P = W / t   

  =   m ag (h1 - h0) / t               (6)

where 

P = power (W, ft lbf)

t = time to move the elevator between levels (s)

Example - Force and Power to Lift an Elevator

An elevator with mass 2000 kg including passengers are moved from level 0 m to level 15 m. The force required to move the elevator at constant speed can be calculated as

Fc = (2000 kg) (9.81 m/s2)

   = 19820 N

The power required to move the elevator between the levels in 20 s can be calculated as

P = (2000 kg) (9.81 m/s2) ((15 m) - (0 m)) / (20 s)

   = 14865 W

   = 14.9 kW

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