Village Well Sweep (Zhuravel) Lever Lab

Torque balance · counterweight · draw-cycle effort

Pole 0° · holding · Village yard

Lever status

Pole angle- Effort F- Rope tension- Mech. advantage- Net torque- Load benefit- Moment of inertia- Energy- Optimum counterweight-

-Effort N

-Mech. adv.

-Counterweight kg

-Bucket kg

DID YOU KNOW?

Keys

1-8 presets Space pause R release the pole G run the draw cycle C camera F fullscreen Z/Y undo/redo +/- counterweight ←/→ pivot ? this help

Drag the bucket up or down to tilt the pole. Drag the stone up or down to change the counterweight. Drag to orbit, wheel or pinch to zoom.

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WebGL 2 is needed. The controls and numbers on the right still work.

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well, sweep pole and baked textures

Lever and bucket

Bucket mass (empty)

Counterweight

Pivot position

Pole length

Well depth

Draw pace (stroke time)

Load (water in the bucket)

Damping

Bucket mouth (fill speed)

Camera and light

Torque balance about the pin

Blue = bucket side, orange = counterweight side, grey = pole. Net = bucket + pole - counterweight.

Draw-cycle effort

Operator force at the bucket end (+ lifts, - pulls down) over one cycle: lower, fill, raise, pour. Dashed = static peak.

Peak effort vs counterweight

The V-shaped curve bottoms out at the optimum counterweight, where lowering and lifting take equal effort.

Swing: angle and energy

Cycle results

Structure and fill

Sweep vs hauling by hand vs windlass

Challenges

The science

1. Torque balance

About the pivot pin, with the pole at angle θ above horizontal (bucket side down positive), arms L_c = f L and L_b = (1 - f) L, pole centre offset d = L/2 - L_c:

tau_net = g cos(theta) (m_b L_b + m_p d - m_c L_c)
F = tau_net / (L_b cos(theta)) = g (m_b L_b + m_p d - m_c L_c) / L_b

2. Mechanical advantage and the best counterweight

VR = L_b / L_c    m_c* = ((m_e + m_w/2) L_b + m_p d) / L_c
at m_c*:  F = -/+ m_w g / 2   (equal effort down and up)
load benefit B = (m_e + m_w) g / F_peak

3. Rotational dynamics

I theta'' = tau_net + tau_op - c theta'
I = m_b L_b^2 + m_c L_c^2 + m_p L^2/12 + m_p d^2     (velocity Verlet, dt = 1/240 s)
rope tension T = m_b (g + a_y),  a_y = vertical acceleration of the bucket

4. Energy and work

E = 1/2 I omega^2 - g sin(theta) (m_b L_b + m_p d - m_c L_c)     (constant without damping)
W_op = integral F v dt = m_w g depth   (a sweep cuts the force, not the work)

5. Filling the bucket

dy/dt = Cd r sqrt(2 g (H - y)),  r = A_mouth / A_bucket
t_fill = sqrt(2/g) / (Cd r) (sqrt(H) - sqrt(H - y_f)),  y_f = 0.95 H

6. Structure (cantilever)

sigma = M r / I_a, M = m_b g L_b, I_a = pi r^4 / 4
delta = F L_b^3 / (3 E I_a),  f = (1/2 pi) sqrt(k / m_b),  tau_pin = R / (pi d_pin^2 / 4)

Simplifications

One degree of freedom (the pole angle). The bucket is a point mass at the pole tip in the dynamics, the rope is inextensible and drawn nearly vertical, the pole is rigid in the dynamics and its flex is a static readout, no groundwater (see the sibling lab for that), no wind. Wood properties (E 10 GPa, strength 40 MPa) and the orifice coefficient C_d = 0.6 are typical textbook values: verify before relying on them. The stone and bucket numbers are model choices.

Educational model with rigid-pole dynamics and static structure readouts; not an engineering design for a real well. The Overload preset only drops the bucket side over empty ground, never over a person. "Zhuravel" is the transliterated name of a traditional well sweep (called a shadoof elsewhere).

Independent checks